Economics and mathematical methods, 2017, v.53: Abstracts

Summary

Vol. 53, No. 1

Makarov V.L., Bakhtizin A.R., Sushko E.D., Ageeva A.F. (Moscow) ARTIFICIAL SOCIETY AND REAL DEMOGRAPHIC PROCESSES
Economics and mathematical methods, 2017, 53 (1), 3-18.
      Valerii L. Makarov — Director, Central Economics and Mathematics Institute, Russian Academy of Sciences, academician of the Russian Academy of Sciences, makarov@cemi.rssi.ru
      Albert R. Bakhtizin — Doctor of Economics, Deputy Director, Central Economics and Mathematics Institute, Russian Academy of Sciences, albert.bakhtizin@gmail.com
      Elena D. Sushko — PhD in Economics, Leading Researcher, Central Economics and Mathematics Institute, Russian Academy of Sciences, sushko_e@mail.ru
      Alina F. Ageeva — PhD in Architecture, Lead Engineer, Central Economics and Mathematics Institute, Russian Academy of Sciences, ageevaalina@yandex.ru

Abstract. The paper describes the use of agent-based approach to population movement modeling. It provides an overview of the most characteristic demographic agent-based model (ABM), developed in the past decade. The EU demographic model for simulating mortality, fertility and migration processes based on the behavior of individual agents in the artificial society is produced. Thus, the creation of new agents (birth of the children) in the model is a result of the individual choice of female agents of reproductive age, and this choice depends on their values and culture. The population of agents in this regard is not uniform – some agents follow the modern reproductive strategies (low fertility rates), and some – the traditional (high fertility rates). The migration of agents is based on the difference in the level of income in different countries. The results of experiments carried out using the model are analyzed and provided.
Keywords: agent-based modelling, demography, types of population reproduction, migration, forecasting the population size and structure in the region.
JEL Classification: J11, F22, C63, C88.
The research has been supported by the Russian Science Foundation (Project No. 14-18-01968).

      REFERENCES (with English translation or transliteration)
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Makarov V.L., Bakhtizin A.R. (2013). Social simulation is a new computer breakthrough. Agent-based models. Moscow: Ekonomika Publ. (in Russian).
Makarov V.L., Bakhtizin A.R., Sushko E.D. (2015). Simulating the Reproductive Behavior of a Region’s Population with an Agent-Based Model. Economy of Region 3, 312–322 (in Russian).
Makarov V.L., Bakhtizin A.R., Sushko E.D., Vasenin V.A., Borisov V.A., Roganov V.A. (2016). Supercomputer Technologies in Social Sciences: Agent-Oriented Demographic Models. Herald of the Russian Academy of Sciences 5, 412–421 (in Russian).
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Received 03.08.2016

Balashova S.A. (Moscow)ASSESSMENT THE IMPACT OF INNOVATIVE CAPACITY QUALITY ON THE INNOVATION ACTIVITY OF THE OECD COUNTRIES
Economics and mathematical methods, 2017, 53 (1), 21-35.
Svetlana A. Balashova — Ph.D., Associate Professor, Department of Mathematical Modelling in Economics, Faculty of Economics, RUDN University, Moscow, Russia; balashova_sa@pfur.ru

Abstract. This paper presents an empirical examination of the relationship between the quantitative characteristics of national innovative capacity and the key indicator of innovation activity – patent activity. The theoretical basis of this study is Paul Romer's model of the new knowledge production and the concept of national innovative capacity by Michael Porter and Scott Stern. Empirical assessment is carried out using econometric tools for panel data. It is shown that the estimates of the model parameters have changed significantly over the past 15 years: the total stock of knowledge held by the country cannot be considered the major driver of innovation activity nowadays. The total level of capital (physical and human) deposited in the knowledge sector of the economy is the key point. The quality characteristics of national innovative capacity such as the level of intellectual property protection, business involvement in the production of new knowledge, the integration of science and education have a significant impact also.
Keywords: innovation potential, intellectual property rights, patenting activity, R&D, fixed effects model, panel data, feasible GLS.
JEL Classification: C23,C51, O31,O34, O38.
Research reported in this paper was supported by The Russian Foundation for Basic Research (Grant No. 15-06-05146).

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Izsak K., Markianidou P., Radosevic, S. (2013). Lessons from a Decade of Innovation Policy: What Can Be Learnt from the INNO Policy TrendChart and The Innovation Union. Final report. EU. Available at: http:// ec.europa.eu/ (accessed: August 2016).
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Mingaleva Zh.A. (2009). On the Usage of International Patent Statistics Databases for Analysis of Innovation Activities Results. Perm University Herald. ECONOMY 2, 65–71 (in Russian).
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Received 12.04.2016

Danielyan V.A. (Moscow) SOCIO-ECONOMIC DETERMINANTS OF RETIREMENT AGE: LITERATURE REVIEW
Economics and mathematical methods, 2017, 53 (1), 36-56.
Vladimir A. Danielyan — Researcher at Laboratory of Mathematical Economics at the Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russia; v.danielyan@gmail.com

Abstract. The paper reviews publications on retirement considering socio-economic determinants of retirement age. We explore, describe, compare findings of both theoretical, empirical works to reveal some stylized facts of older persons retirement behavior as well as presented in the publications’ explanations of those facts. We summarize results that concern effects of technical, organizational change, unemployment rate, medical insurance, service sector availability, cultural characteristics on retirement behavior of older workers. Next we try to compare influence of some considered factors on Russian workforce with that influence in the other countries, using obtained information in review as a background.
Keywords: retirement age determinants, labor force participation of older workers, life expectancy, technical changes, cultural characteristics.
JEL Classification: J26, J14.
The research was funded by “Rossijskij gumanitarnyj nauchnyj fond” fund, project No. 14-02-00234? “Metodologiya proektirovaniya institucionalnyh reform”.

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Received 28.04.2016

Smolyak S.A. (Moscow) THE IMPACT OF RELIABILITY ON THE VALUE OF MACHINERY AND EQUIPMENT
Economics and mathematical methods, 2017, 53 (1), 57-74.
Serguei A. Smolyak – Doctor of Science (Economics), Chief scientific researcher, Central Economics and Mathematics Institute (CEMI), Russian Academy of Sciences, Moscow; smolyak1@yandex.ru

Abstract. We propose a model for the valuation of machinery and equipment items which accounts for the possibility of their failures. Dealing with the consequences of such failures requires either the scrapping of equipment, or having the equipment to undergo repairs, following which the condition of it improves in a random way. The value of a machine is determined by reference to its highest and best use. Such a method presupposes, at any time, making an optimal choice as between the options for utilizing the machine for its intended purpose, its repair or disposal. The model also takes into account the fact that some technical and economic performance characteristics of the machine deteriorate with its age, and that some operating costs (such as property tax and insurance costs) are, in turn, dependent on the underlying value of the machine. To achieve solutions in this context, we apply a non-conventional version of the discounted cash flow analysis which only requires relying on the information related to the valuation date. Forecasting changes in market conditions over the coming lifetime of the machine is not required. Thus, we present the results of modelling that allow identifying the impact of durability, failure rate and maintainability on the value of machinery and equipment items of a different age.
Keywords: machine, equipment, valuation, highest and best use, depreciation, effective age, repair, random benefits, discounting.
JEL Classification: C44, C61, D46, D81.

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Kovalev A.P. (2010). Evaluation of the Active Part of Fixed Assets. Moscow: Finstatinform (in Russian).
Kovalev A.P., Kushel' A.A., Korolev I.V., Faddeyev P.V. (2006). The Fundamentals of Machinery and Equipment Valuation. Moscow: Finansy i statistika (in Russian).
Marshall Valuation Service, 2011 (2011). Marshall and Swift Publication Company. 915 Wilshire Blvd., 8th Floor, Los Angeles, CA 90017.
Mikerin G.I., Smolyak S.A. (2010). Efficiency Assessment jf Investment Projects and Property Valuation: Opportunities for Convergence. Moscow: CEMI RAS (in Russian).
Nazarov O., Rutgaiser V. (2011). Machinery and Equipment Valuation. Moscow: Kvinto-Konsalting (in Russian).
Oklahoma Business Personal Property Valuation Schedules (2010). Ad Valorem Division, Oklahoma Tax Commission. Available at: http://www.tax.ok.gov/advform/2013BPPValuationSchedule.pdf (accessed: February 2016).
Rykov V.V., Balakrishnan N., Nikulin M.S. (eds.) (2010). Mathematical and Statistical Models and Methods in Reliability. N.Y.: Springer.
Scarsini M., Shaked M. (2000). On Value of an Item Subject to General Repair or Maintenance, with General Repair. European Journal of Operational Research 122, 625–637.
Smolyak S.A. (2008). Problems and Paradoxes of Machinery and Equipment Valuation. Moscow: RIO MAOK (in Russian).
Smolyak S.A. (2013). Assessment of Depreciation of Buildings: Tiemann‘s Model and Its Generalizations (part 1). Property Relations in the Russian Federation 12(147), 6–20 (in Russian).
Smolyak S.A. (2014?). The Dependence of the Market Values of Machinery and Equipment Items on their Age: Problems and Mathematical Models. Audit and Financial Analysis 5, 138–150 (in Russian).
Smolyak S.A. (2014b). Valuation of Machinery and Equipment Taking their Operating Conditions into Account. Property relations in the Russian Federation 8(155), 70–82 (in Russian).
Smolyak S.A. (2014c). Overhaul Policy Optimization and Equipment Appraisals Concerning its Reliability. Journal of the New Economic Association 2(22), 122–131 (in Russian).
Smolyak S.A. (2014d). Assessment of Depreciation of Buildings: Tiemann‘s Model and Its Generalizations (part 2). Property Relations in the Russian Federation 1(148), 25–35 (in Russian).
State of Nevada. Department of Taxation. 2009–2010 Personal Property Manual (2008). Available at: http:// www.carson.org/Modules/ShowDocument.aspx?documentid=19386 (accessed: February 2016)
Tiemann M. (1970). Reformvorschlage zum Ertrags- und Sachwertverfahren. In: “Allgemeine Vermessungsnachrichten”. S. 523–530.
Vilensky P.L., Livshits V.N., Smolyak S.A. (2015). Investment Project Assessment: Theory and Practice. Moscow: Poli Print Servis (in Russian).
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Guide Machinery and Equipment Appraiser (2015). Correction Factors and Characteristics of the Market of Machinery and Equipment. Correction Factors and Characteristics of the Market of Machinery and Equipment. Nizhny Novgorod: Volga Center Methodical and Information Support of Valuation (in Russian).

Received 01.12.2015

Kurmanova Yu.M. (Moscow) MODELING OF INVESTOR’S BEHAVIOR ON COMBINED MARKET: FROM SPECIFIC TO GENERAL
Economics and mathematical methods, 2017, 53 (1), 75-93.
Yulia M. Kurmanova – Post-graduate student, economist, Federal research institution “Informatics and Management”, RAS; Institute of System Analysis, Moscow; fo-daxa07@mail.ru

Abstract. The article is devoted to a very important problem – increase of effectiveness of investment strategy. Directly considered the optimization problem of investor’s behavior on combined market representing as total real and financial markets. The author analyses different types of scenario – from specific to general, and offers a classification of problems depending on investment direction. The author also proposes methods for addressing the problem in the conditions of stationary and non-stationary macro-economic environment. Developed the new specific formulation of problem and presented the decision algorithm depending on macro-economic environment. The paper introduces the problem-solving recommendations for general problem description. New elements are introduced, for example, the decision making using maximization criteria of the two values, defined as selection criterion – the indicator of the effect, which are calculated depending on type of investments for the accounting period; aligned the level of risk in considered segments of combined market for guaranteeing the correct selection. Proposed are the methods for problem solving for stationary and unstable macroeconomic environment concerning risks and uncertainty. Provided the new special problem and algorithm for its decision in a special type of economic environment. Author proposes an algorithm for general problem solving.
Keywords: combined market, stationary economic, non-stationary economy, investment strategy, investment, investor’s behavior, optimization, efficiency criterion.
JEL Classification: C02, G02, G11, G17.

REFERENCES (with English translation or transliteration)
Ajzin K.I., Livchits V.N. (2006). The Risk and Return of Securities on the Stock Markets on Stationary and Non-Stationary Economy. Audit and Financial Analysis 4, 195 –199 (in Russian).
Bernstein W. (2004). The Intelligent Asset Allocator. How to Build Your Portfolio to Maximize Returns and Minimize Risk. Moscow: Lori (in Russian).
Bernstein W. (2014). The Investor’s Manifesto: Preparing for Prosperity, Armageddon, and Everything in Between. Moscow: Al'pina Pablisher / Al'pina Biznes Buks (in Russian).
Fama E.F. (1970). Efficient Capital Markets: A Review of Theory and Empirical Work. Journal of Finance 25(2), 383–417.
Gvishiani D.M., Emel'yanov S.V. (1978). Multi-Criteria Decision-Making Tasks. Moscow: Mashinostroenie (in Russian).
Izvestiya (2015). The Competition of Forecaster Has Won Analysts from MorganStanley. Izvestiya 30 ??????? (in Russian).
Kossov V.V., Livchits V.N., Shaxnazarov A.G. (2000). Methodical Recommendations on Evaluation of Investment Projects Efficiency. The Ministry of economy of the Russian Federation, the Ministry of Finance of the Russian Federation, the State Committee for construction, architectural and housing policy; the leaders of the group of authors. Moscow: E'konomika (in Russian).
Kurmanova S.M., Kurmanova Ju.M. (2012). Optimization of Investor's Behavior on the Mixed Market. Economic Analysis: Theory and Practice 22(277), 16–22 (in Russian).
Levit B.Y., Livchits V.N. (1972). Nonlinear Network Transport Problems. Moscow: Transport, 1–144 (in Russian).
Livchits V.N. (1971). The Choice of Optimal Solutions in Technical-Economic Calculations. Moscow: E'konomika (in Russian).
Livchits V.N. (1984). The Optimization in Long-Term Planning and Design. Moscow: E'konomika (in Russian).
Livchits V.N. (2013). System Analysis of Market Reforms in the Non-Stationary Economy of Russia: 1992–2013. Moscow: LENAND (in Russian).
Livchits V.N., Livchits S.V. (2010). System Analysis of Non-Stationary Economy of Russia (1992–2009): Market Reforms, Crisis, Investment Policy. Moscow: Poli Print Servis (in Russian).
Lur'e A.L. (1973). Economic Analysis of the Planning Models of a Socialist Economy. Moscow: Nauka (in Russian).
Mertens A.V. (1997). Investments: Lectures on Modern Financial Theory. XVI. Kiev: Kievskoe investicionnoe agentstvo (in Russian).
Pervozvanskij A.A., Pervozvanskaya T.N. (1994). Financial Market: Calculation and Risk. Moscow: Infra-M (in Russian).
Peters E'. (2000). Chaos and Order in the Capital Markets. A New View of Cycles, Prices, and Market Volatility. Moscow: Mir (in Russian).
Prokhorov Yu.V. (1988). Mathematical Encyclopedic Dictionary. Moscow: Sovetskaya e'nciklopediya (in Russian).
Smolyak S.A. (2002). Assessment of Efficiency of Investment Projects in Conditions of Risk and Uncertainty (Theory Expected Effect) Moscow: Nauka (in Russian).
Smolyak S.A. (2006). Discounting Cash Flows in the Evaluation of Efficiency of Investment Projects and Value of the Property. Moscow: Nauka (in Russian).
Tarasenko F.P. (1963). Introduction to Information Theory. Tomsk: Tomskij universitet (in Russian).
Trubitsin A.V. (2013). Rational Economic Behavior: Models and Prospects. Moscow: RAS Institute of Economy (in Russian).
Vilenskij P.L., Livchits V.N. (2010). The Investment Analysis. Textbook for Students of MBA Program, Students Majoring in "Strategic Management" and "Finance". Moscow: Gosudarstvennyj universitet – Vysshaya shkola e'konomiki, Vysshaya shkola menedzhmenta, Biznes E'lajnment (in Russian).
Vilenskij P.L., Livchits V.N., Smolyak S.A. (2015). Evaluation of Investment Projects Efficiency: Theory and Practice. Moscow: PoliPrintServis (in Russian).
Yudina I. (2004). Investor Behavior: Rational Versus Irrational. In the collection of scientific works "Information Economics and Management Dynamics of Complex Systems." Issue IV. E.Yu. Ivanova, R.M. Nizhegorodceva (eds.). Moscow, Barnaul: Biznes-Yunitek (in Russian).
Zubov M. (2016). Ruslan Grinberg is the Most Accurate Forecaster : "The Government Does Not Want to Invest Money in Projects That They Are Not Stolen. But the Risks of Inaction is Even Greater». Moskovskij komsomolec 26 February, 4 (in Russian).

Received 28.03.2016 ?.

Golshtein Ye.G., Malkov U.H., Sokolov N.A. (Moscow) EFFICIENCY OF AN APPROXIMATE ALGORITHM TO SOLVE FINITE THREE-PERSON GAMES (A COMPUTATIONAL EXPERIENCE)
Economics and mathematical methods, 2017, 53 (1), 94-107.
      Yevguenii G. Golshtein – Doctor of Science (Physics & Mathematics), Professor, Head of Laboratory, Central Economics and Mathematics Institute (CEMI), Russian Academy of Sciences, Moscow; golshtn@cemi.rssi.ru
      Ustav H. Malkov – Candidate of Science (Physics & Mathematics), Leading scientific researcher, Central Economics and Mathematics Institute (CEMI), Russian Academy of Sciences, Moscow
      Nikolai A. Sokolov – Candidate of Science (Physics & Mathematics), Senior scientific researcher, Central Economics and Mathematics Institute (CEMI), Russian Academy of Sciences, Moscow; sokolov@cemi.rssi.ru

Abstract. The authors provide a short description of an approximate algorithm proposed by Ye.G. Golshtein to solve finite non-cooperative three-person games in mixed strategies. The search for a solution to such a game is reduced to the minimization of the so-called Nash function having a large number of local minima. By enumerating the original pure strategies the method finds an exact solution of the game whenever a complementarity condition holds. Otherwise, if the complementarity condition is slightly violated, a reasonable approximation to the set of Nash equilibrium points is generated. A series of numerical tests have been conducted to reveal both the algorithm's advantages and its minor points. With the growth of interdependence coefficient of tables that determine winnings of the players, the efficiency of the algoriths decreases.
Keywords: non-cooperative games, Nash equilibrium, finite games, pure and mixed strategies, an approximate algorithm, numerical tests, linear programming.
JEL Classification: C02, C72.

      REFERENCES (with English translation or transliteration)
Golshtein Ye.G. (2014). An Approximate Method for Solving Finite Three-Person Games. Economics and Mathematical Methods 50(1), 110-116.
Golshtein E.G., Malkov U.Kh., Sokolov N.A. (2013). A Numerical Method for Solving Bimatrix Games. Economics and Mathematical Methods 49(4), 94-104.

Received 30.03.2016

Votyakov A.A. (Moscow) ON OPTIMAL BODY EMBEDDING IN RHOMBIC DODECAHEDRON
Economics and mathematical methods, 2017, 53 (1), 108-113.
Anatolii A. Votyakov — PhD in Physics and Math., Senior Researcher, Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russia; avotyakov@mail.ru

Abstract. To properly assess the value of a natural crystal, it is necessary to know what products can be made from. In the language of mathematics, geometric body having the form of a crystal, it is necessary to put a body having a shape of a product . Attachment diamond rhombic dodecahedron — this is a classic problem of production technology jewelry algorithms solutions which are investigated in this paper. Embedding problem is reduced to a linear programming problem. The estimation of the complexity of algorithms. It is proved that the complexity of the algorithms in the attachment body crystals belonging to the class of rhombic dodecahedron is decided for 14 comparisons questions.
Keywords: natural crystals, diamond, rhombic dodecahedron, investment in the rhombic dodecahedron, consistency conditions, comparison, estimation of complexity.
JEL Classification: C610.

REFERENCES (with English translation or transliteration)
Babat L.G., Freedman A.A. (2015). Parallel Embedding of Polyhedrons and Efficient Use of Natural Diamonds. Economics and Mathematical Methods 51, 3, 54–63.
Votyakov A.A. (2015). On Optimal Body Embedding in Octahedron. Economics and Mathematical Methods 51, 3, 115–123.

Received 21.03.2016

Malyshev V.L. (Moscow) THE NEED TO CHANGE A MECHANISM OF INDUSTRIAL ACTIVITIES
Economics and mathematical methods, 2017, 53 (1), 114-127.
Valerii L. Malyshev – Doctor of Science (Economics), Leading scientific researcher, Central Economics and Mathematics Institute (CEMI), Russian Academy of Sciences, Moscow

Abstract. The paper considers the possibility of sovereignizing the Russian economy in the situation of sanctions by industrialized countries. The author submits that the basis for the possible independence of the functioning of the economy should be the improvement of productive activities, which will allow not only for substituting imports, but creating the condition for DOS leads the Russian economy in the present world economic order to a status of "technological power". Reform the Russian economy in order to achieve this goal, according to the author, one should start with the nuclei of economy – the process of reproduction. The transition to the proposed resources reproduction mode, unifying the operation of producer and consumer, with each product information symmetry inter-sectoral inter-firm cooperation will enable the Russian economy to operate as the economy ex ante and a single economic space.
Keywords: reproduction resources production, micro, macro, enterprise maximizing behavior inter-industry inter-firm relations, inter-sectoral inter-firm cooperation, information asymmetry, information symmetry, productive consumption, consumer manufacturing, organic composition of production resources (capital).
JEL Classification: D.

REFERENCES (with English translation or transliteration)
Arrow K. (2004). Collective Choice and Individual Values. Moscow: Publishing House of the HSE.
Blaug M. (1992). The Methodology of Economics or How Economists Explain. Cambridge University Press. ?oscow: NP “Zhurnal "Voprosy e'konomiki"” (in Russian).
Buchanan J., Tullock G. (1997). Calculation of Consent. In: "Nobel Laureates in economics". Moscow: Alpha Taurus.
Coase R. (1993). The Firm, the Market and the Law: the Case of LTD. Moscow: Catallaxy.
Dictionary on economy (2004). SPb.: Economic School.
Eucken U. (1995). The Basic Principles of Economic Policy. Moscow: Progress.
Glazyev S.J. (2013). On the Aims, Problems and Measures of Development and Integration. Russian Academy of Sciences. Scientific Council on integrated issues of Eurasian Economic Integration, competitiveness and sustainable development. 29.01.2013.
Hodgson J. (2003). Economic Theory and Institutions. Moscow: Delo.
Kantorovich L.V. (1960). Economic Calculation of the Best Use of Resources. Moscow: Publishing House of the Academy of Sciences of the USSR.
Malyshev V.L. (2013). From the Manufacturer of the Product. The Opportunity to "Jump" in the Development of the Russian Economy. Moscow: Ekonomika.
Malyshev V.L. (2016b). On the Institutional Capabilities of the Championship of Russia. Moscow: Ekonomika.
Marx K. (1980). The Economically Manuscripts 1857–1861 gg. (The original version of "Capital"). Part I. Moscow: Politizdat.
Marx K. (1975). Critique of the Political Economy of Capital. Vol. 1. Moscow: Politizdat.
Mau V. (2005). Economic Policy in 2004 Year: Model Search Consolidation Economic Growth. Voprosy ekonomiki 1, 4–27.
Method of Determining Wholesale Prices for Products of Industrial and Technical Purpose (1974). Moscow: GC Prices of the USSR.
Nelson R., Winter S. (2002). Evolutionary Theory of Economic Change. Moscow: Delo.
North D. (1997). Institutions, Institutional Change and Economic Performance. Moscow: Nachalo.
Prime Minister Putin (2008). Final Press Conference of President Putin Has Opened His New Prospects. Rossiyskaya Gazeta 15 February, 33(4590).
Russia in Figures (2000). M: Goskomstat of Russia.
Samuelson P., Nordhauz B. (2007). Economics. Moscow: Williams.
Schumpeter J. (1982). The Theory of Economic Development. Moscow: Progress.
Seligman B. (1968). The Main Currents of Modern Economic Thought. Moscow: Progress.
Veblen T. (2007). The Theory of Business Enterprise. Moscow: Delo.
Williamson O. (2001). Introduction. In: "The Nature of the Firm" O. Williamson, Winter J.G. (eds.). Moscow: Delo.

Received 11.01.2016.

Borodin D.V., Krasnoschekov L.V. (Moscow) THE MACROECONOMIC ASPECTS OF NON-SYSTEMATIC SPECULATIVE INVESTMENTS
Economics and mathematical methods, 2017, 53 (1), 128-143.
      Dmitry V. Borodin — Ph. D., Head of corporate finance, PJSC “Research and Production Corporation “United Wagon Company”; Assistant professor in Finance department, Bauman Moscow State Technical University, Moscow, Russia; dmitrii.v.borodin@gmail.com

      Leonid V. Krasnoschekov — Economist of Project “Helicopter Ka-62”, JSC “KAMOV”, postgraduate student at Moscow University of Finance and Law, Moscow, Russia; krasnoshyokov@gmail.com

Abstract. It is evident that speculative incentives to liquidity preferences decrease the economic growth rate. The growth of this incentive is motivated by the growth of non-systematic savings. This paper suggests a definition of non-systematic savings and non-classical saving distribution scheme. The economic mathematical method was developed to analyze the force of non-classical saving distribution scheme impact on the US stock market. To compare these two incentives we suggested two-phase two-factor model in which the first phase made it possible to identify the classical incentive and the second phase allowed to identify a non-classical incentive. The result achieved by means of applying this method allowed to identify the growing impact of non-systematic savings on the most important parameters of the US stock market. The period of starting of this impact was determined. The assumption about time of transition from the classical scheme of savings distribution to a non-classical was made on the strength of assessment time of impact non-systematic savings on the stock market. An alternative approach to the analysis of the impact of non-classical savings allocation scheme was applied to complete the achieved result. This approach is based on a well-known impact of some parameters of the stock market on statements of assets of the stockbrokers. The transition from one distribution savings scheme to another is reflected in the regression curves of aggregated statements of the stockbrokers’ assets on the stock market parameters. Two-phase two-factor model in which first phase let identify classical incentive and second phase allowed to identify non-classical incentive was written to reflect the change of regression model over time. The confidence interval for point of intersection in two-phase regression was determined. This confidence interval allowed to make alternative assessment of the time in which the regression curve of aggregated statements of the stockbrokers assets on the stock market parameters was transformed. An estimate received by means of applying of the first method is included in the confidence interval for a point of intersection in a two-phase regression proving the change in savings allocation scheme.
Keywords: savings distribution, national saving, investment, automated trading system.
JEL Classification: G23.

      REFERENCES (with English translation or transliteration)
Abel A., Bernanke B. (2008). Macroeconomics. Saint Petersburg: Piter (in Russian).
Bolshev L.N., Smirnov N.V. (1983). Tables of Mathematical Statistics. Moscow: Nauka (in Russian).
Goriainov V.B., Pavlov I.V., Teskin O.I., Tsvetkova G.M. (2002). Mathematical Statistics (in Russian).
Gusev A.A., Gorunovich S.?. (2006). Household Savings: Impact on the Stock Market. Saint Petersburg: Zolotoe Secheniye (in Russian).
Hinkley D.V. (1969). Inference about the Intersection in Two-Phase Regression. Biometrica 56(3), 495–504.
Hudson D.J. (1966). Fitting Segmented Curves Whose Join Points Have to Be Estimated. Journal American Statistical Association 61, 1097–1129.
Krasnoshchekov L.V. (2013). Automated Trading Systems: Definition, Structure and Properties. Scientific and technological youth journal. MGTU im. N.E. Baumana 11, November. Available at: http://onxhiytvnq.mjwxg5dvfzzhk.cmle.ru/2jmj7l5rSw0yVb-vlWAYkK-YBwk=ZmlsZS9vdXQvNjM2MDQ3 (accessed: August 2016, in Russian).
Krasnoshchekov L.V. (2014). Yield of Automated trading As Equivalent of Rate of Return on Money Assets. Scientific and technological youth journal. MGTU im. N.E. Baumana 10, October. Available at: http://onxhiytvnq.mjwxg5dvfzzhk.cmle.ru/doc/737222.html (accessed: August 2016, in Russian).
Muravyova V.S., Orlov A.I. (2007). Non-Parametric Assessment Intersection Point of the Two Regressions. Industrial Laboratory. Materials Diagnostics 73(11), 63–67 (in Russian).
Nusratullin I.V. (2011). Theoretical Aspects of Interruption of the Steady Development of the Economics from Viewpoint of Neoclassical Economics. Economic and Law Issues 10, 61–71 (in Russian).
Orlov A.I. (2007). Applied Statistics. Moscow: Ekzamen (in Russian).
Orlov A.I. (2012). Consistent Tests for Homogeneity of Two Independent Samples. Industrial Laboratory. Materials Diagnostics 11, 66–70 (in Russian).
Seber G.A.F. (1980). Linear Regression Analysis. Moscow: Mir (in Russian).
Zar J.H. (1984). Biostatistical Analysis. Englewood Cliffs: Prentice-Hall.
Zarubina V.S., Krishchenko A.P. (eds.). Moscow: Izd. MGTU im. N.E. Baumana — BMSTU Press (in Russian).

Received 13.03.2015

Vol. 53, No. 2

Pozamantir E.I. Hierarchical system of intersectoral balance models and the models of territorial production distribution. Part I. Enunciation of the task and a general approach to its decision
Economics and mathematical methods, 2017, 53 (2), 5-23.
Elmar I. Pozamantir - Doct. Sc. (Techn.), Professor, Chief Scientific Researcher, Federal Research Center "Informatics and Management" RAS, Institute of Systems Analysis (ISA) RAS, Moscow, Russia, e.pozamantir@yandex.ru

Abstract. Model of input-output balance (MIOB) is interconnected with model of territorial manufacturing locations, consumption and transportation of products in the following way. In MIOB total production and consumption volumes on the country are determined for each kind of product. Along with it, unit costs of transport services for its transportation are used, but it isn't taken into account that their value depends on territorial location of places of producing and consuming products being transported. Moreover, not only total volume of transport activities in this field depends on these locations, but distribution of that volume by territorially independent or partially interchangeable element of the transportation system as well. In its turn, it determines the necessity to develop those of them that prove to be "bottlenecks". Transport elements' development requires investment in territorially fixed elements of the transportation system and these investments must be consistent with the total volume of investment in transport determined in MIOB. A system of models is constructed, in which MIOB and model of choosing territorial manufacturing locations are interconnected. From MIOB to model of territorial manufacturing locations total for the country production and consumption volumes, as well as investment volumes are transferred, and in the location problem these total values are distributed on the country's territory so that total production and transportation costs were minimized. In the opposite direction values of average transportation distances determined by the chosen location are transferred, as well as a list of transport objects, capacity of which must be increased in order to realize the chosen location. It's shown that the problem of choosing manufacturing and consuming locations represents a problem of linear programming of extremely large dimensions; however it has a special block structure allowing organizing an effective computing process. The equations which connect between themselves the separate blocks are divided into parts, corresponding to each block through introducing additional variables and their values are improved iteratively on the base of using dual estimates of blocks limitations. Verification and calibration of the model are foreseen through making calculations according to the data of a reporting period and comparing the data received as the result of calculation and the reporting data. Keywords: output volume, territorial location, calculated transport network, network junctions and sections, volumes of dispatches and receipts in junction, multi-level block linear programming.
JEL Classification: C02, C31, C68, E17, L91, L92.

REFERENCES (with English translation or transliteration)
Aganbegyan A.G., Seliverstov V.E., Suslov V.I. (2007). Multiregional Systems: Economic-Mathematical Research [Book]. Novosibirsk: Siberian Scientific Publishing House (in Russian).
Birman I.Y., Mints L.E. (eds.) (1963). Mathematical Methods and Problems of Economic Activity Location [Book]. Moscow: Economizdat (in Russian).
Dietzenbacher E. (2013). Input-Output Analysis: The next 25 Years // Economic System Research Lenzen. 25, 4, 369-389.
Gontar N.V. (2013). Factors and Present Peculiarities of Industrial Complex Location in Russia [Book]. Moscow: Plekhanov REU (in Russian).
Granberg A.G., Seliverstov V.E., Suslov V.I. (1985). Optimization Interregional Interindustry Models [Book]. Novosibirsk: Nauka (in Russian).
Leontieff V.V. (1925). Balance of the USSR National Economy. Methodological Analysis of the Central Statistic Board. [Article]. Planned Economy. Moscow: Gosplan of the USSR, 12 (in Russian).
Makarov V.L., Bakhtizin A.R., Sulakshin S.S. (2007). Applying Computable Models in State Management [Book]. Moscow: Scientific Expert (in Russian).
Melentiev B.V. (2014). Regional Economic Policy [Book]. Novosibirsk: IEOIP SB RAS (in Russian).
Pozamantir E.I. (2014). Computable General Equilibrium of Economy and Transport [Book]. Moscow: Poly Print Service (in Russian).
Pozamantir E.I., Tischenko T.I. Macroeconomic Assessment of Infrastructure Development Efficiency (on Example of Transport Complex) [Article]. In: "Investment Efficiency Assessment", Livchits V.N. (ed.). Moscow: CEMI RAS, 97-108 (in Russian).
Shirov A.A. (2015). Multileveled Research and Long-term Strategy of Economy's Development [Book]. Moscow: MAX PRESS (in Russian).
Tobben J., Kronenberg T.H. (2015). Construction of Multi-Regional Input-Output Tables using the CHARM Method. Economic System Research 27, 4, 487-507.

Received 17.08.2016

Graborov S.V., Pitelin A.K. Majoritarian optimality of direct and indirect taxation on citizens
Economics and mathematical methods, 2017, 53 (2), 24-39.
      Sergei V. Graborov - Cand. Sc. (Economics), Senior scientific researcher, Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russia; migmary@gmail.com
      Аnatolii K. Pitelin - Cand. Sc. (Economics), Leading scientific researcher Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russia; pitel@cemi.rssi.ru.

Abstract. The article deals with the optimization of nonlinear multidimensional tax structure under the majority rule. The optimization under the majority rule means determining the composition of the citizens' majority and tax structure providing the minimum of tax payments for each team member. The vector optimization of the tax structure serves as a source model. Fixed rates of income and assets, as well as by their demand functions characterize all the citizens-taxpayers. Income and property taxes are paid under a nonlinear scale, and the consumption tax is based on a linear scale, with tax rates and tax bases thresholds being the optimizable values. In addition to the tax functions and individual criteria, the composition of the source model includes some limitations on the aggregate amount of tax payments, as well as on the valid values of tax rates. The original model is converted into the task of majority optimization. In order to accomplish this task, the group of simple common citizens, whose individual criteria will be taken into account, is determined. The values of threshold levels for the tax bases and corresponding tax rates to them, which are the best at the same time for all the members of the majority, are considered to be a decision of this task. It is shown that a steady majority group of citizens, in which nobody would benefit, if he goes out of it, may be formed of the taxpayers, whose income or property does not exceed the median sizes. And the best way for all members of this group is the progressive income and assets taxation. The need of introducing some additional conditions forming a coalition, which ensure taking a single decision on optimal tax rates by all members of the majority group is established. The conditions (under which the criteria of all members of this group are the same) are found and proven, and that guarantees taking a single decision on tax rates. The paper presents a majority of the optimal variant of common using progressive direct and differential indirect taxes for citizens. The order and the formulas for calculating the respective tax rates are presented.
Keywords: fiscal decisions, multi-objective optimization, majority rule, direct and indirect taxes.
JEL Classification: H2.
This work was carried with the financial support from the Russian humanitarian scientific foundation within the research project "Applied procedure for assessing the macroeconomic efficiency of fiscal decisions" (project 15-02-00284).

      REFERENCES (with English translation or transliteration)
Arrow K.J. (2004). Social Choice and Individual Values. Moscow: National Research University Higher School of Economics (in Russian). Atkinson A.B., Stiglitz J.E. (1995). Lectures on Public Economics. Moscow: Aspekt Press (in Russian).
Caucutt E.M., Imrohoroglu S., Kumar K. (2006). Does the Progressivity of Income Taxes Matter for Human Capital and Grouth? Journal of Public Economic Theory 8, 1, 95-118.
Chernik, D.G., Shmelev Yu.D. (2011). The Crisis and Taxes. Moscow: Ekonomika (in Russian).
Graborov S.V. (2013). Public Choice Procedures of a Linear Budget and Tax Structure. Economics and Mathematical Methods 49, 2, 71-86 (in Russian).
Graborov S.V. (2015). Majority Optimization of Taxes, Social Transfers, Prices and Wages. Economics and Mathematical Methods 51, 1, 80-96 (in Russian).
Hariton C., Piaser G. (2007). When Redistribution Leads to Regressive Taxation. Journal of Public Economic Theory 9, 4, 589-606.
Korovkin V.V. (2006). The Basices of Tax Theory. Moscow: Ekonomist (in Russian).
Meshcheryakova O.V. (1995). Tax Systems of Developed Countries in the World (Reference). Moscow: Fond "Pravovaya kul'tura" (in Russian).
Persson T., Tabellini G. (2000). Political Economics: Explaining Economic Policy. London: The MIT Press.
Pushkareva V.M. (2001). The History of Financial Thought and Policies of Taxes. Moscow: Finansy i statistika (in Russian).
Roemer J. (1999). The Democratic Political Economy of Progressive Income Taxation. Econometrica 67, 1, 1-19.
Stiglitz J.E. (1997). Economics of the Public Sector. Moscow: MGU, Infra-M (in Russian).
Tax Reforms. Theory and Practice (2015). Maiburova I.A., Ivanova Yu.B. (eds.) Moscow: Yuniti (in Russian).
Zak J.A. (2011). Adoption of Multicriteria Decisions. Moscow: Ekonomika (in Russian).
Zanadvorov V.S., Kolosnitsyna M.G. (2006). Economic Theory of Public Finance. Moscow: National Research University Higher School of Economics (in Russian).
Zakharov A.V. (2009). The Models of Political Competition: Review of Literature // Economics and Mathematical Methods 45, 1, 110-128 (in Russian).

Received 23.06.2016

Bazhenov O.V., Galenkova A.D., Kosova E.S., Safronov A.A., Sutormina M.A. Econometric estimation of factors' influence on the size of the financial sector
Economics and mathematical methods, 2017, 53 (2), 40-49.
      Oleg V. Bazhenov - Cand. Sc. (Econ.), Associate Professor of the Department of Accounting, Analysis and Audit FSAEI HPE "Ural Federal University named after the first President of Russia B.N. Yeltsin", Ekaterinburg, Russia; 6819@list.ru
      Aljona D. Galenkova - student, FSAEI HPE "Ural Federal University named after the first President of Russia B.N. Yeltsin", Ekat erinburg, Russia; agalenkova@mail.ru
      Ekaterina S.Kosova - student, FSAEI HPE "Ural Federal University named after the first President of Russia B.N. Yeltsin", Ekaterinburg, Russia; ekanuts@mail.ru.
      Anton A. Safronov - student, FSAEI HPE "Ural Federal University named after the first President of Russia B.N. Yeltsin", Ekaterinburg, Russia; antsaf96@yandex.ru.
      Marina A. Sutormina - student, FSAEI HPE "Ural Federal University named after the first President of Russia B.N. Yeltsin", Ekaterinburg, Russia; sutormina-m@mail.ru.

Abstract. Currently, among the researchers and experts there is no consensus about how are the size, structure of the financial sector and economic growth interconnected. Financial sector as an essential component of the national economy includes all the financial relationships between the various actors in the process of formation, distribution and use of financial resources. The main objectives of any economic policy are stability, economic growth, while sustainable development is closely connected with the financial sector's ability to successfully carry out their functions. Then, the main purpose of the financial system in the economy is to ensure long-term economic growth through effective financing of the economy. In their study, the authors analyze the effect of different rates of economic growth on the size of financial sector, based on regression analysis of panel cross-country annual data from 2000 to 2015 in the developed (USA, Canada, Germany, France) and developing countries (BRICS) with the help of a software package Stata. Based on the research conclusions of the tendency and the strength of influence of such factors as the economic growth of per capita consumption, the value of the discount rate, the rate ratio of issued bank loans and deposits, the share of investment in fixed assets in GDP and inflation on the size of the financial sector. The results may be used by scientists and economists forecasting the development of the national economy and individual financial and non-financial sectors of the economy. In addition, the authors of the study submitted and received on the basis of its findings may be of interest to financial institutions and economists who study the same or similar issues.
Keywords: finance, growth factors, regression analysis, per capita consumption, fixed investment, rate of inflation, national stock exchange, developing countries.
JEL Classification: С55, С58.

      REFERENCES (with English translation or transliteration)
Anzoategui D., Maria S., Martinez P., Rocha R.R. (2010). Bank Competition in the Middle East and Northern Africa Region. Review of Middle East Economics and Finance 6, 2, Article 2, 11-27.
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Fungasova Z., Solanko L., Weill L. (2010). Market Power in the Russian Banking Industry. Bank of Finland Discussion Papers No. 3, 1-27.
Lakstutiene A. (2008) Correlation of the Indicators of the Financial System and Gross Domestic Product in European Union Countries. Engineering Economics 3, 58, 7-13.
Lucas R.E.Jr. (1988). On the Mechanics of Economic Development. Journal of Monetary Economics 22, 1, 3-42.
Maznyak V.М. (2001). Bank Equity and Risk. Finansovye issledovanija 3. Available at: http://finis.rsue.ru/2001_N3/maznyk.htm (accessed: April 2016, in Russian).
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Ponomarenko S. (2004). Financial Sector and the Costs of Inflation in Countries with Transition Economies. М.: IEPP (in Russian). Robinson J. (1956). The Generalization of the General Theory. The Rate of Interest and other Essays. London: MacMillan, 86.
Ross S. (2016). How Does a High Discount Rate Affect the Economy? Available at: http://www.investopedia.com (accessed: April 2016). Schumpeter J.A. (1934). The Theory of Economic Development. (1912 translated by Opie R.) Cambridge: Harvard University Press, 137-148.
Shuaib I.M, Ndidi D.E. (2015). Capital Formation: Impact on the Economic Development of Nigeria 1960-2013. European Journal of Business, Economics and Accountancy 3, 23-24.
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Zhuang J., Gunatilake H., Niimi Y., Khan M.E., Jiang Y., Hasan R., Khor N., Lagman-Martin A.S., Bracey P., Huang B. (2009) Financial Sector Development, Economic Growth, and Poverty Reduction: A Literature Review. ADB Economics. Working Paper Series 173, 2-9.

Received 12.05.2016.

Afanasyev A.A. Crude oil and gas condensate forecasting in the computable simulation model for money circulation in the Russian economy
Economics and mathematical methods, 2017, 53 (2), 50-65.
Anton A. Afanasyev - Leading Research Associate, Central Economics and Mathematics Institute, Russian Academy of Sciences, Doct. Sc. (Economics), Professor, National Research University Higher School of Economics, Moscow, Russia; aanton@cemi.rssi.ru.

Abstract. The author proposes a modification of a computable simulation model for money circulation in the Russian economy developed in the Laboratory of social simulation CEMI together with academician V.L. Makarov and researcher A.A. Losev due to disaggregation of a block "Oil and gas industry" agent on the two modified model block - block "Exploration of oil and gas" and a block "Oil and gas production". In this article we will explore a model related to the exploration and production of oil and gas condensate leaving development of similar models for natural and associated gas for the next study. For modeling of crude oil and gas condensate production, we decide to divide all the 144 Russian oil fields and oil production centers into five groups according to the level of oil production in 2014. On the basis of the model's two sub-blocks of exploration and production of oil and gas condensate, designed to computable monetary economy of Russia, we forecast volumes of Russian oil and gas condensate production up to 2035 for five aggregated centers of oil production, the federal districts and Russia as a whole under the inertial scenario of economic development in 2014. Given values of internal oil prices, the rate of tax of oil extraction, price and rental rates for new fixed assets, other fixed costs in the production of oil, given at the 2014 level the calculations show a decrease in volumes of oil and gas condensate production in Russia by 5% for 2035.
Keywords: forecasting, crude oil and gas condensate production, Russian economy, computable simulation model for money circulation, oil fields, exploration, tax maneuver.
JEL Classification: C53, L71, Q35, Q41, Q47.
This study was supported by the Russian Foundation for Basic Research (project 17-06-00463 А) and Russian Foundation for Humanities (project 17-02-00457 А).

REFERENCES (with English translation or transliteration)
Afanasyev A.A. (2008). Economic-and-Mathematical Modeling and Forecasting of Natural Gas Production in the Tyumen Region. Gas industry 6, 19-25 (in Russian).
Afanasyev A.A. (2009a). Econometric Study of Production Functions of the Krasnoyarsk Krai Gas Industry. Economics and Mathematical Methods 45, 3, 3-11 (in Russian).
Afanasyev A.A. (2009b). Production Functions of the Tyumen Region Gas Industry and Subsidiaries of OJSC "Gazprom" in 1993-2007. Economics and Mathematical Methods 45, 2, 37-53 (in Russian).
Afanasyev A.A. (2012). Econometric Models of Natural Gas Forecasting. Oil & Gas Journal Russia 10, 65, 76-81 (in Russian).
Christiano L., Motto R., Rostagno M. (2010). Financial Factors in Economic Fluctuations. Working Paper 1192. Frankfurt-am-Main: European Central Bank.
Christoffel K., Coenen G., Warne F. (2008). The New Area-Wide Model of the Euro Area - a Micro-Founded Open-Economy Model for Forecasting and Policy Analysis. Working Paper 944. Frankfurt-am-Main: European Central Bank.
Chung H., Kiley M.T., Laforte J.-Ph. (2010). Documentation of the Estimated, Dynamic, Optimization-based (EDO) Model of the U.S. Economy: 2010 Version. Washington: Federal Reserve Board.
Edge R.M., Kiley M.T., Laforte J.-Ph. (2007). Documentation of the Research and Statistics Division's Estimated DSGE Model of the U.S. Economy: 2006 Version. Washington: Federal Reserve Board.
Erceg Ch.J., Guerrieri L., Gust Ch. (2006). SIGMA: A New Open Economy Model for Policy Analysis / International Finance Discussion Paper No. 835 (Revised). Washington: Board of Governors of the Federal Reserve System.
Fagan G., Henry J., Mestre R. (2005). An Area-Wide Model for the Euro Area. Economic Modeling 22, 39-59.
Fujiwara I., Hara N., Hirose Y., Teranishi Y. (2005). The Japanese Economic Model (JEM). Monetary and Economic Studies 23, 2, 61-142.
Gafarov N.A., Kalityuk S.A., Glagolev A.I., Moiseev A.V. (2011). The Global Gas Business, New Trends, Scenarios, Technology. Moscow: Gazprom expo (in Russian).
GEM: A New International Macroeconomic Model (2004). Washington: International Monetary Fund.
Harrison R., Nikolov K., Quinn M., Ramsay G., Scott A., Thomas R. (2005). The Bank of England Quarterly Model. London: Bank of England.
Klimenko A.V. Prediction of the Extractive Industries Taking into Account Natural Factors. In: "The Methods of Construction and Use of Macroeconomic and Sectoral Production Functions". Moscow: CEMI AS USSR, 152-174 (in Russian).
Laxton D., Isard P., Faruqee H., Prasad E., Turtelboom B. (1998). MULTIMOD Mark III: the Core Dynamic and Steady-State Models. Washington: International Monetary Fund.
Lees K. (2009). Introducing KITT: the Reserve Bank of New Zealand new DSGE Model for Forecasting and Policy Design. Reserve Bank of New Zealand Bulletin 72, June, 5-20.
Makarov V.L. (1999). Computable Model of the Russian Economy (RUSEC). Preprint number the WP / 99/069. Moscow: CEMI (in Russian).
Makarov V.L., Afanasiev A.A., Losev A.A. (2011). Computable Simulation Model for Money Circulation in the Russian Economy. Economics and Mathematical Methods 47, 1, 3-27 (in Russian).
Martos V.N. (1989). Guidelines for predicting recovery at the stage of field exploration. Moscow: VNIGNI (in Russian).
Murchison S., Rennison A. (2006). ToTEM: The Bank of Canada's New Quarterly Projection Model. Rapport technique No. 97. Ottawa: Banque du Canada.
Nasinnik Z.A. (1975). Forecasting cost of oil and associated gas. Moscow: Nedra (in Russian).
Nikonov N.I. (2006). Rational complex of exploration for oil and gas: a course of lectures. Ukhta: Ural State Technical University (in Russian).
Roger S., Vlcek J. (2012). Macrofinancial Modeling at Central Banks: Recent Developments and Future Directions. IMF Working Paper No. 2/21. Washington.
Varshavsky L.E (1976a). Genetic Modeling of Economic Development of the Oil and Gas Industry (on the Example of the Gas Industry of the USSR). Thesis for the degree of candidate of economic sciences on specialty 08.00.13. Moscow: CEMI AS USSR (in Russian).
Varshavsky L.E. (1976b). On Forecasting and Analytical Modeling of the Gas Industry. In: "Economy of the gas industry" 12, 16-24 (in Russian).
Varshavsky L.E. (1976c). The use of production functions in predicting performance gas development / In Economy of the gas industry - Vol. 5 Moscow: VNIIEGazprom, 1976b. - P. 21-28 (in Russian).

Received 22.11.2016

Denisov V.I. Motivational mechanisms and backgrounds of agricultural production growth in Russia
Economics and mathematical methods, 2017, 53 (2), 66-75.
Viktor I. Denisov - Chief Researcher, Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russia; lavtube@yandex.ru

Abstract. The old and new conditions of agricultural enterprises in Russia having impact on the final result of their activity where analyzed. The directions of development of the principles and practice of state aid to agricultural producers are recommended, as well as the most effective applications of means of support are shown. In addition to the old and present tradition of their allocation on-farm and clean production needs; it is proposed to guide them to financing the road construction, social development, labor markets and technologies. The results of the statistical analysis and probability calculations implies a high economic efficiency of support funds in this direction are listed. The strengthening of role of agricultural production in the overall development of the economy of the Russian Federation is displayed. The strengthening of the agricultural sector of Russian economy goes far beyond the purely sectoral aspects. The circle of solvable problems is extremely wide. The starting point here is the creation of conditions for uninterruptible saturation of the domestic agricultural market. The social order is to improve the supply of population with food, and reducing its retail prices. The consequence of achieving this goal will be the overcome of the dependence on imports, as well as the expansion of Russian export areas, the GDP growth, the weakening of the country's dependence of energy producing industries and the implementation of energy prices on the world market, reducing inflation. Solving these problems is a national priority of the accelerated economic development.
Keywords: AIC (agro-industrial complex) economy, state support of agricultural enterprises, economic-mathematical analysis and modeling, incentives for economic growth.
JEL Classification: Q50.
This work was supported by the Russian Foundation for Basic Research (project 16-06-00029).

REFERENCES (with English translation or transliteration)
Buzdalov I.N. (2005). Agricultural protectionism in the context of market reforms and globalization. Bulletin of the Russian Humanitarian Science Foundation 3, 32-38.
Buzdalov I.N. (2006). Condition and regulation problems of stability of agricultural industrial system. Bulletin of the Russian Humanitarian Science Foundation 3, 27-34.
Buzdalov I.N. (2008). Priorities for Rural Development. Bulletin of the Institute of Economics of Russian Academy of Sciences 3, 51-57.
Denisov V.I. (2004а). Agrarian reform: the necessary changes. Development Issues 4. 33-41.
Denisov V.I. (2004b). Motivational mechanisms of increased use of production and resource potential of agrarian and industrial complex. Society and economy 5-6, 43-51.
Denisov V.I. (2005). Prospects for strengthening investment activity in agrarian and industrial complex. Economic Science of Contemporary Russia 4, 76-88.
Denisov V.I. (2008). Prospects for strengthening investment activity in agrarian and industrial complex. International Journal of Agriculture 5, 52-63.
Denisov V.I. (2013). The objectives and criteria for assessing directions of state support of agricultural enterprises. Economic Science of Contemporary Russia 3, 65-72.
Nazarenko V.I. (2010). World agriculture and Russia. Ekaterinburg: Izdatel'stvo Ural'skoi gosudarstvennoi sel'skokhozyaistvennoi akademii.
Nazarenko V.I. (2014). Food security. Moscow: Pamyatniki istoricheskoi mysli.

Received 12.04.2016

Voronovisky M.M. On the herd behavior in the dynamic model of closed one commodity market with finite automata as participants
Economics and mathematical methods, 2017, 53 (2), 76-89.
Mark M. Voronovitsky - Ph.D (Mathematics), associated professor, associated professor, pensioner at the Market Economy Institute RAS, Moscow, Russia; v_mark50@hotmail.com

Abstract. We investigate the mechanisms of the herd behavior of participants in a closed model of one-commodity market. The herd behavior is a case of behavior when participants renounce from using all the own information and repeats the actions of majority of other participants of the collective. The investigation of a herd behavior of participants in real financial market is an important and a very complicated problem. A rather modest problem of investigation of the herd behavior in the agent is based on a model of a closed one-commodity market, which was formulated and investigated in our previous paper, is an object of this article. Two cases of choice by all agents of the same algorithm of definition of price was investigated in the previous paper. It was shown that in both cases trajectory of system after some time is a stationary set in which an average price at market oscillates close to its constant value. In this paper we show, that there is a possibility of the two other cases of herd behavior in the same model: one induces the growth of the average price at a market and the other - herd behavior induces decreasing the average price of market. It is obviously from this investigation that herd behavior can occur in the finite interval of time. The opportunity of herd behavior which has the interior state of market is a reason of its arising was discussed in the article.
Keywords: model, closed market, herd behavior, go to a bear, go to a bull/one commodity market, dynamics of prices, trajectory, stationary set, steady state, rational choice, finite automata.
JEL Classification: C51, D01.
This work was fulfilled in Market Economy Institute of Russian Academy of Sciences with support of Russian Foundation of Fundamental Researches (grant 14-06-00110).

REFERENCES (with English translation or transliteration)
Avery C., Zemsky P. (1998). Multidimensional Uncertainty and Herd Behavior in Financial Market. American Economic Review 88, 4, 724-748.
Banerjee A.V. (1992). A Simple Model of Herd Behavior. The Quarterly Journal of Economics CVII, August, 797-817.
Bichandany S., Sharma S. (2000). Herd Behavior in Financial Markets. A Review IMF Working paper, IMF Institute WP/00/48.
Bikhandany S., Hirsheifer D., Welch I. (1992). A Theory of Fads, Fashion, Custom, and Cultural Change as Information Cascades'. Journal of Political Economy 100, 5, 992-1026.
Makarov V.L. (2012). The Artificial Societies. Economics and Mathematical Methods 48, 3, 3-20 (in Russian).
Topol R. (1991). Bubbles and Volatility of Stock Prises; Effect of Mimenic Copnyagion. The Economic Journal 101, 176-809.
Tsetlin M.L. (1969). Automaton Theory and Modeling of Biological Systems. Moscow: Nauka (in Russian).
Voronovitsky M.M. (2016). The Dynamic Model of the Closed Market with One Commodity and Finite Automata as Participants. Economics and Mathematical Methods 52, 2, 57-72.
Voronovitsky M.M., Tsvetkov V.A. (2012). Models of Herd Behavior of Participanys of a Market. Moscow: Market Economy Institute of RAS (in Russian).

Received 21.06.2016

Yegorova N.Y. The use of heuristics procedures in the problems of multi-level governance
Economics and mathematical methods, 2017, 53 (2), 90-100.
Natalja Y. Yegorova - Doctor of Economics, professor, chief member of staff of Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russia; nyegorova@mail.ru

Abstract. In the article made a comparative economic and mathematical analysis with the release of the advantages of different algorithms for solving certain classes of problems of coordination of economic interests of subjects at different levels of hierarchical control systems. Methodology the article includes formal methods and algorithms using heuristic procedures and is based on the Pareto optimality concept, defining an agreed solution, as well as on the method of analysis of the correctness of the heuristics procedures, used in multicriteria problems, developed by O. Larichev. Different variants of the iterative search algorithm is a compromise solution, using heuristic procedures possible schemes closer to the ideal point of Pareto border area; assessed the correctness of heuristic procedures. The results of the article are to develop a modified iterative procedure for the coordination of economic interests in multi-level systems using the correct heuristic procedures.
Keywords: economic and mathematical tools, heuristics procedures, multi-level governance, the person making the decision, man-machine procedures, harmonization of administrative decisions.
JEL Classification: C02, C52, C65.
The article is prepared with the financial support of Russian fund of fundamental research (project number 16-06-00012) "Theoretical and methodological bases, models and methods of coordination in multilevel control systems".

REFERENCES (with English translation or transliteration)
Aganbegjan A.G., Bagrinovskij K.A., Granberg A.G. (1972). Modelling System of Public Economy Planning. Moscow: Mysl' (in Russian).
Antamoshkin O.A. (2009). Desision Making Support System on the Basis of Multu Attributive Methods. Vestnik Sibirskogo gosudarstvennogo aerokosmicheskogo universiteta imeni akademika M. F. Reshetneva (Vestnik SibGAU) 4, 69-71 (in Russian).
Bagrinovskij K.A. (1977). Basis of Planned Desisions Approval. Moscow: Nauka (in Russian).
Bushenkov V.A., Lotov A.V. (1982). Generic Attainability Sets Usage Constructions Methods. Moscow: VTs AN SSSR (in Russian).
Cnarnes A., Cooper W.W. (1961). Management Models and the Industrial Applications of Linear Programming. N.Y.: John Wiley & Sons.
Jengel' E.A. (2011). Models and Methods of Intellectual Support in the Process of Management Desosion Making. Vestnik Sibirskogo gosudarstvennogo aerokosmicheskogo universiteta imeni akademika M. F. Reshetneva (Vestnik SibGAU) 4, 106-112 (in Russian).
Larichev O.I. (1987). Objective Models and Subjective Desisions. Moscow: Nauka (in Russian).
Lopatnikov L.I. (2003). Economic - Mathmatical Dictionary of the Morden Mathmatical Science. Moscow: Delo (in Russian).
Lotov A.V. (1981). Analysis of Potentiol Possibilities of the Economical Systems. Eco-nomics and Mathematical Methods 17, 2, 261-267 (in Russian).
Makarov V.L., Bahtizin A.R., Sulakshin S.S. (2007). Computer Models Usage in Government Control. Moscow: Nauchnyi ekspert (in Russian).
Podinovskij V.V., Gavrilov V.M. (1975). Consistently Used Variables Optimization. Moscow: Sovetskoe Radio (in Russian).
Pomanskij L.B. (1983). Compliance of Economic Interect Approval. Economics and Mathematical Methods 19, 4, 598-607 (in Russian).
Salukwadze M.E. (1974). On the Existence of Solutions in Problems of Optimization under Vector-Valued Criteria. Journal of Optimization Theory and Applications 12, 203-217.
Simon H., Newell A. (1988). Heuristic Problem Soloing; the Next Advance in Operation Research. Operatic-research 6, 1, 1-10.
Trofimova L.A., Trofimov V.V. (2012). Management Desosion Making Methods. Saint Petersburg: SPbGUEF (in Russian).
Wierzbicki A.P. (1982). A Mathematical Basis for Satisficing Decision Making. Mathematical Modelling 3, 391-405.
Yegorova N.Y. (1987). Issues on Planed Desisions Approval with the Use of Computer Simulation System. Moscow: Nauka (in Russian).

Received 07.07.2016

Polovyan A.V., Vishnevskaya E.N. Regulating co-evolution of the economic and environmental population in the context of sustainable development
Economics and mathematical methods, 2017, 53 (2), 101-117.
      Aleksei V. Polovyan - Doctor of Economic Sciences, associate professor of management, Director, SI "Institute of Economic Research", Donetsk; polovyan@yandex.ru
      Elena N. Vishnevskaya - Candidate of Economic Sciences, associate professor of the economic theory and public administration, Donetsk National Technical University, Donetsk; vishn.elena@gmail.com

Abstract. New industrialization in the world and formation of new global industrial structure exacerbate the problem of sustainable development as environmentally friendly development of one countries is often reached due to pollution of others. And it eventually creates problems for everyone, the solution of which requires international regulation. To justify the ways of such regulation the mathematical model is constructed. The model describes the interaction of the two economic and ecological populations presented by sets of enterprises and population of the separate territories which differ in the dominating production technologies, patterns of behavior of economic agents and ecological consequences of their activities. Parameterization of the model made on the basis of indicators for the Germany (an example of ecologically clean territory) and Ukraine (an example of ecologically unfavorable territory). The experiments with the model allowed us to estimate the effectiveness of three different ways of regulating their coevolution with the aim of mitigating ecological problems: 1) punishment in the form of higher relative costs of the "dirty" behavior of economic agents in the ecologically unfavorable territories through the strengthening of environmental taxation, 2) rewards in the form of an increase of the relative benefits of the "clean" behavior of economic agents through a transfer to the territory of more efficient technologies for pollution's treatment, 3) the mixed impact, suggesting some combination of punishments and rewards. The simulation showed that the best results are obtained by the mixed impact when regulation starting with the rewards through the provision of access to new technologies, thus increasing the overall effectiveness of environmental management on a disadvantaged territory, and then gradually strengthening penalties, pushing economic agents to change their behavior patterns and to develop their own innovation system, capable of generating effective technological solutions to environmental problems.
Keywords: coevolution, ecological-economic population, system dynamics, agent-based modeling, economic regulation.
JEL Classification: C63, O33, Q56.

      REFERENCES (with English translation or transliteration)
Becker M. (2008). Handbook of Organizational Routines. M.C. Becker (ed.). Cheltenham: Edward Elgar Publishing.
Bergh J. van den, Hofkes M. (ed.) (2010). Theory and Implementation of Economic Models for Sustainable Development. Dordrecht, Boston, London: Kluwer Academic Publishers.
Bonabeau E. (2002). Agent-Based Modeling: Methods and Techniques for Simulating Human Systems. PNAS, 99(3), 7280-7287.
Bosetti V. (ed.) (2009). Modelling Sustainable Development: Transitions to a Sustainable Future. Bosetti V., Gerlagh R., Schleicher S. (eds.). Cheltenham: Edward Elgar Publishing.
Dementiev V. (2006). Trap of the Technological Dependence and Condition of Its Overcoming in Two-Sector Model of Economy. Economics and Mathematical Methods 42, 4, 17-32 (in Russian).
Dementiev V. (2009). Catching-up Development Through the Prism of the Theory of "Long-Wave" Technological Dynamics: the Aspect of "Opportunity Windows" under Crisis. Russian Economic Journal 1-2, 34-48 (in Russian).
Forrester J. (1970). World Dynamics. Portland, Oregon: Productivity Press.
Forrester J. (2007). System Dynamics - a Personal View of the First Fifty Years. System Dynamics Review 23(2-3), 345-358.
Gual M., Norgaard R. (2010). Bridging Ecological and Social Systems Coevolution: A Review and Proposal. Ecological Economics 69, 707-717.
Kallis G., Norgaard R.B. (2010). Coevolutionary Ecological Economics. Ecological Economics 69, 690-699.
Kuhndt M., Tessema F., Herrndorf M. (2008). Global Value Chain Governance for resource Efficiency Building Sustainable Consumption and Production Bridges Across the Global Sustainability Divides. Environmental Research, Engineering and Management 3, 45, 33-41.
Meadows D.H., Meadows D.L., Randers J. (1992). Beyond the Limits: Confronting Global Collapse, Envisioning a Sustainable Future. Post Mills, Vermont: Chelsea Green.
Nelson R., Winter S. (1982). An Evolutionary Theory of Economic Change. Harvard University Press.
Safarzynska K., Bergh J. van den (2010). Evolutionary Models in Economics: a Survey of Methods and Building Blocks. Journal of Evolutionary Economics 20, 3, 329-373.
Wiedmann T. (2009). A Review of Recent Multi-Region Input-Output Models Used for Consumption-Based Emission and Resource Accounting. Ecological Economics 69, 211-222.

Received 29.03.2016

Skarzhinskaya E.M., Tzurikov V.I. Collective action model. Part I: Equilibrium, justice, efficiency
Economics and mathematical methods, 2017, 53 (2), 118-133.
      Elena M. Skarzhinskaya - Doct. Sc. (Economics), Professor, Professor at Nekrasov Kostroma State University, Kostroma, Russia; yelena.skarzhinsky@gmail.com
      Vladimir I. Tzurikov - Cand. Sc. (Phys.&Math.), Doct. Sc. (Economics), Associated Professor, Professor, Kostroma State Agricultural Academy, Kostroma; tsurikov@inbox.ru

Abstract. The model proposed in the article proposes optimization decisions and describes a hybrid form of agents' economic organization. For an expected income, a strictly (upward) convex function is considered, depending upon the amount of investment (effort) put in by each agent. The model demonstrates how independent agents achieve a balanced but not an efficient outcome, free rider problem, as well as the dependence of aggregate income upon the principle of its distribution among agents and upon each agent's individual characteristics. A multitude of Pareto-effective states is created at the higher levels of investment. The possibility of increasing gain is indivisibly connected with coordinating agents' actions. We consider various methods of coordinating investments carried out by the agents. It is further shown that in the case where coordination is based on the agents' mutual trust, a preliminary agreement among agents as to the fair distribution of expected aggregate income (proportionate to the costs incurred) is required in order to achieve a Pareto-effective outcome. Coordination based on the potential of violence, or such that is achieved with the vindictive damages (sanctions), leads to transactional costs associated with information search and the process of penalization. We show that coordination allows increasing the aggregate gain relative to the equilibrium point levels; yet the presence of coordination costs or the absence of trust render the optimum gains unattainable.
Keywords: collective action(s), Nash equilibrium, Pareto efficiency, justice, specific investment, coordination, costs, optimum.
JEL Classification: C02, D23.

      REFERENCES (with English translation or transliteration)
Becker G.S. (2003). Human Behavior: Economical Approach. Selected Papers on Economic Theory. Moscow: National Research University Higher School of Economics (in Russian).
Crawford S.E.S., Ostrom E. (1995). A Grammar of Institutions. American Political Science Review 89, 3, 582-600.
Furubotn E.G., Richter R. (2005). Institutions and Economic Theory. The Contribution of the New Institutional Economics. Saint Petersburg: Izdatel'skii Dom SPbGU (in Russian).
Grossman S., Hart O. (1986). The Cost and Benefits of Ownership: A Theory of Vertical and Lateral Integration. Journal of Political Economy 94, 4, 691-719.
Hart O.D. (2001). Incomplete Contracts and Theory of the Firm / Williamson O.E. (ed.) (2001). The Nature of the Firm. Moscow: DELO, 206-236 (in Russian).
Hart O.D., Moore J. (1988). Incomplete Contracts and Renegotiation. Econometrics 56, 4, 755-785.
Kapelyushnikov R. (2010). The Multiplicity of Institutional Worlds: The Nobel Prize in Economic Sciences-2009: Working paper WP3/2010/02 (Part 1). Moscow: National Research University Higher School of Economics (in Russian).
Milgrom P, Roberts J. (2001). Economics, Organization and Management: Vol. 1-2. Saint Petersburg: Ekonomicheskaya shkola (in Russian). Olson M. (1995). The Logic of Collective Action. Public Goods and the Theory of Groups. Moscow: FEI (in Russian).
Ostrom E. (1998). A Behavioral Approach to the Rational Choice Theory of Collective Action. American Political Science Review 92, 1, 1-22.
Ostrom E. (2011). Governing the Commons: The Evolution of Institutions for Collective Action. Moscow: IRISEN. (in Russian).
Shastitko A. (2001). Incomplete Contracts: Problems of Definition and Modeling. Voprosy Economiki 6, 80-99 (in Russian).
Shastitko A. (2007). The Economic theory of Organizations: Textbook. Moscow: INFRA-M (in Russian).
Skarzhinskayai E.M., Tsurikov V.I. (2014). On the Efficacy of Collective Action. Russian Management Journal 12, 3, 87-106 (in Russian).
Skorobogatov A. (2007). Organizational Economics and Models Incomplete Contracts. Voprosy Ekonomiki 12, 71-95 (in Russian).
Tirole J. (2000). The Theory of Industrial Organization. Vol. 1. Saint Petersburg: Ekonomicheskaya shkola (in Russian).
Tsurikov V.I. (2010a). Model of Incomplete Contract and Redistribution of Rights to the Income Ex Post. Economics and Mathematical Methods 46, 1, 104-116 (in Russian).
Tsurikov V.I. (2010b). Incomplete Contracting, Including Transaction Costs and the Corruption Component. Parth 1. Economic Science of Contemporary Russia 3, 39-51 (in Russian).
Williamson O.E. (1996). The Economic Institutions of Capitalism: Firms, Markets, Relational Contracting. Saint Petersburg: Lenizdat (in Russian).

Received 12.04.2016

Podshivalova С.S., Podshivalov S.F. Temporal criterion of aggregating in a cluster transport task of cargo transportation
Economics and mathematical methods, 2017, 53 (2), 134-142.
      Christina S. Podshivalova - Penza State University of Architecture and Construction, Cand. Sci. (Tech.), Associate professor, Chair of Organization and Traffic Security, Penza, Russia; sharm-08@bk.ru
      Sergei F. Podshivalov - Penza State University of Architecture and Construction, Cand. Sci. (Tech.), Associate professor, Chair of Mechanics, Penza, Russia; podshivalov.s.f@mail.ru

Abstract. Heuristic approach for the solution of a transport task at a lot-based delivery of a homogeneous load in points of not-crossed clusters from several bases of service is considered. The mathematical formulation of a question is consolidated to a problem of linear programming. The algorithm of its decision consists of two stages and is based on ideas of aggregation and disaggregation of points in a cluster. At the first stage the optimization model is the problem of routing of the transportation from bases through each cluster. At the same time single run from each point is accepted equal to zero. Thanks to it the optimum ring or radial route is decided with the help of one algorithm. The problem of routing is solved by the method of dummy nodes and branches allowing to visit repeatedly tops of the transport graph. The minimum time of cargo run from base in a terminal point of unloading of a cluster on the weighed graph is used as a criterion of aggregation. It allows to consider an idle time in points of a transport network and the movement between them. At the second stage optimum distribution of weight of a load between bases and clusters in the received aggregated transport graph with the arches equal to the minimum time of cargo run is carried out. This approach has allowed to solve a transport problem taking into account features of delivery of small consignments.
Keywords: routing, cluster, transport problem, dummy node, linear programming, aggregation.
JEL Classification: С61.

      REFERENCES (with English translation or transliteration)
David F.R., Plante R.D., Wong R.T., Evans JR. (1991). Aggregation and Disaggregation Techniques and Methodology in Optimization // Operations Research. 39(4), 553-582.
Kostyuk Yu.L. (2013). Effective Implementation of Algorithm for Solving the Travelling Salesman Problem by Branch-and-Bound Method. Applied Discrete Mathematics 2(20), 78-90 (in Russian).
Kozhin A.P., Mezencev V.N. (1994). Mathematical Methods of Planning and Management of Freight Automobile Transportations. Moscow: Transport (in Russian).
Litl Dzh., Murti K., Suini D., Karel K. (1965). Algorithm for the Solution of a Task on the Direct-Sales Representative. Economics and Mathematical Methods 1, 1, 94-107 (in Russian).
Podshivalova K.S. (2007). Improving the Efficiency of Transportation of Groupage Cargo by Road Transport. Abstract diss. ... сand. тech. sciences. Volgograd (in Russian).
Taxa X.A. (2001). Introduction to Operations Research. Moscow: Vil'yams (in Russian).

Received 06.04.2015

Vol. 53, No. 3

Pozamantir E.I. Hierarchical system of intersectoral balance models and the models of terri-torial production distribution. Part 2. Structural, mathematical and calculation aspects of the model, the algorithm for the problem solving
Economics and mathematical methods, 2017, 53 (3), 3-17.
Elmar I. Pozamantir — Doct. Sc. (Techn.), Professor, Chief Scientific Researcher, Federal Research Center “Informatics and Management” RAS, Institute of Systems Analysis (ISA) RAS, Moscow, Russia, e.pozamantir@yandex.ru

Abstract. Model of input-output balance (MIOB, Makarov, 2007; Pozamantir, 2014) is connected with a model of territorial manufacturing locations, consumption and transportation of prod-ucts in the following way. In MIOB total production and consumption volumes on the country are determined for each kind of product. Along with it, unit costs of transport services are used, but it isn’t taken into account that their value depends on territorial location of the production and consumption places of particular products being transported. Moreover, not only total volume of transport activities in this field depends on these locations, but distribution of the volume by territory is a pendent or a partially interchangeable element of the transportation system as well. In its turn, it determines the necessity to develop those of them that prove to be “bottle-necks”. Transport elements’ development requires investment in territory-fixed elements of the transportation system and these investments must be consistent with the total volume of invest-ment in transport determined in MIOB. A system of models is constructed, in which MIOB and model of choosing territorial manufacturing locations are interconnected. Total (for the country) production and consumption volumes are transferred from MIOB to a model of territorial manufacturing locations, as well as the investment volumes. In the location task these total values are distributed over the country’s territory so that total production and transportation costs were minimized. The values of average transportation distances determined by the chosen location are transferred in the opposite direction, as well as a list of transport objects, which capacity must be increased in order to realize the chosen location. It’s shown that the problem of choosing manu-facturing and consuming locations is a task of linear programming of extremely large dimensions; however it has a special block structure allowing to organize an effective computing process. The equations connecting the separate blocks are divided into parts, corresponding to each block, by introducing additional variables, and their values are improved by iterations on the base of dual estimates of blocks limitations. Verification and calibration of the model is carried through calculations on the data of a reporting period and comparing the data received with the reporting data.
Keywords: output, territorial location, calculated transport network, network junctions and sections, volumes of dispatches and receipts in junction, multi-level block linear programming.
JEL Classification: C02, C31, C68, E17, L91, L92.

REFERENCES (with English translation or transliteration)
Golstein Ye.G., Udin D.B. (1969). Linear Programming Tasks of Transportation Type. Moscow: Nauka (in Russian).
Levit B.Yu., Livshits B.N. (1972). Non-Linear Network Transportation Tasks. Moscow: Transport (in Russian).
Makarov V.L., Bakhtizin A.R., Sulakshin S.S. (2007). Applying Computable Models in State Management [Book]. Moscow: Scientific Expert (in Russian).
Pozamantir E.I. (2014). Computable General Equilibrium of Economy and Transport [Book]. Moscow: Poly Print Service (in Russian).
Pozamantir E.I. (2017). Hierarchical System of Intersectoral Balance Models and the Models of Territorial Production Distribution. Part 1. Enunciation of the Task and a General Approach to Its Decision. Economics and Mathematical Methods, 53, 2 (in Russian).
Tsurkov V. (1981). Decompozition in the Big-Size Tasks. Moscow: Nauka (in Russian).

Received 17.08.2016

Yermakov V.V. Estimates of the impact of inter-budgetary government grants on regional development in the Russian Federation
Economics and mathematical methods, 2017, 53 (3), 18-37.
Vladimir V. Yermakov — Postgraduate student at the Department for Social Fi-nances, Financial University under the Government of the Russian Federation; legal advisor at the independent nonprofit organization St. Alexis Metropolitan of Moscow Central Clinical Hospital, Volunteer at the noncommercial organization “Miloserdie”; vld1970vld@gmail.com

Abstract. Basing on the knowledge of the developing system of the interbudgetary transfers from 1995 to 2013 and the academic prerequisites of their efficiency, we have collected and ana-lyzed the statistical data; substantiated choosing the criteria for evaluating the inequality of regions; selected a great number of necessary analytic indicators, characteristic of regional inequal-ity; suggested an econometric model; conducted testing of two research hypotheses: (1) grants-in-aid inter alia lead to equalizing regional fiscal capacities; (2) inter-budgetary transfers lead to reducing the trans-regional inequality according to socio-economic indicators. Our analysis shows that there is no scientific support to both hypotheses: inter-budgetary transfers do not statistically influence trans-regional inequality according to socio-economic indicators, and they do not lead to reducing significantly the inequality according to the actual fiscal capacity level. We propose that it might be caused not by inefficient expenditure, but by the missing correlation between the inter-budgetary transfer size and the regional socio-economic development level. The work results call for new scientific research with a view to substantiating a reconsideration of the budgetary policy and optimizing the financial mechanism.
Keywords: budget, intergovernmental transfers, inter-regional inequality, budgetary provision, socio-economic de-velopment.
JEL Classification: Е62, H7, R5.

REFERENCES (with English translation or transliteration)
Ahrend R. (2005). Speed of Reform, Initial Conditions, Political Orientation, or What? Explaining Russian Regions’ Economic Performance. Post-Communist Economies, 17, 3, 289—317.
Belotti F. (2013). XSMLE — a Command to Estimate Spatial Panel Models in Stata. Potsdam: German Stata Users Group Meeting.
Buccellato T. (2007). Convergence Across Russian Regions: A Spatial Econometrics Approach. Economics Working Paper No. 72. Available at: http://discovery.ucl.ac.uk/17480/1/17480.pdf (accessed: February 2016).
Capello M., Figueras A., Freille S., Moncarz P. (2013). The Role of Federal Transfers in Regional Convergence in Human Development Indicators in Argentina. Investigaciones Regionales, 27, 33—63.
Demidova O.A. (2013). Identification of Territorial Effects for the Main Macroeconomic Characteristics of the Russian Regions. Moscow: National Research University Higher School of Economics. Available at: http://regconf.hse.ru/uploads/2e017f2591a4579bdc0179454cb4cf9b69816b7f.pdf (accessed: December, 2015, in Russian).
Desai R.M., Freinkman L., Goldberg I. (2005). Fiscal Federalism in Rentier Regions: Evidence from Russia. Journal of Comparative Economics, 33, 814—834.
Drobyshevsky S., Lugovoj O., Astafeva E., Polevoj D., Kozlovskaja A., Trunin P., Lederman L. (2005). The Factors of Economic Growth in Regions of Russian Federations. Moscow: IEPP (in Russian).
Erdal F., Can E., Kocabas G. (2006). Convergence of Human Development Levels: A Casual Analysis. In: “Human and Economic Resources”. Izmir University of Economics and SUNY Cortland (24—25 May, 2006, Izmir), 207—212. Available at: http://eco.ieu.edu.tr/wp-content/proceedings/2006/0618.pdf (accessed: August 2015).
Freinkman L., Kholodilin K.A., Thiessen U. (2009). Incentive Effects of Fiscal Equalization: Has Russian Style Improved? DIW Berlin. German Institute for Economic Research, DIW Discussion Paper No. 912, 32. Available at: http://www.diw.de/sixcms/detail.php?id=diw_02.c.243894.de (accessed: September 2014).
Granberg A.G., Zajceva Ju.S. (2002). Production and Implication of Total Regional Product International Comparison. Part 2: “Corrections in Total Regional Product Concerning Different Money Buying Capacity in Territories”. Russian Economic Journal, 11—12, 48—70.
Guriev S., Vakulenko E. (2012). Convergence between Russian Regions. CEFIR / NES Working Paper series. Working Paper No. 180. Available at: https://www.hse.ru/pubs/share/direct/document/66963230 (accessed: April 2015).
Haughton J.H., Khandker S.R. (2009). Handbook on Poverty + Inequality. Washington: The World Bank. Available at: http://siteresources.worldbank.org/INTPA/Resources/429966-1259774805724/Poverty_Inequality_Handbook_Ch06.pdf (accessed: декабрь 2013 г.).
Ivanova V.I. (2014). Regional Convergence of Income: Spatial Analysis. Spatial Economics, 4, 100—119 (in Russian).
Kholodilin K., Siliverstovs B., Oshchepkov A. (2009). The Russian Regional Convergence Process: Where Does It Go? DIW Discussion Paper No. 861. Available at: https://www.hse.ru/pubs/share/direct/document/64658634 (accessed: July 2015).
Kolmakov I.B. (2007). Methods of the Optimal Distribution of the Transfers. Economics and mathematical methods, 43, 3, 102—120 (in Russian).
Kolomak E.A. (2010). Interregional Disparities in Russia: Economic and Social Aspects. Spatial Economics, 1, 26—35 (in Russian).
LeSage J.P., Pace R.K. (2009). Introduction to Spatial Econometrics. Statistics: Textbooks and Monographs. N.W.: Chapman and Hall/CRC Reference Press. Taylor & Francis Group, LLC.
Lugovoy О., Dashkeyev V., Mazayev I., Fomchenko D., Polyakov Е., Hecht A. (2007). Analysis of Economic Growth in Regions: Geographical and Institutional Aspect. Consortium for Economic Policy Research and Advice. Moscow: IET, 132. Agency CIP RSL (in Russian).
Marques I., Nazrullaeva E., Yakovlev A. (2013). Substituting Growth for Money: Intergovernmental Transfers and Electoral Support in the Russian Federation, 2001—2008 [Text] : Working paper WP1/2013/03. National Research University “Higher School of Economics”. Moscow: Publishing House of the Higher School of Economics. (Series WP1 “Institutional Problems of Russian Economy”) (in Russian).
Martinez-Vazquez J., Timofeev A. (2010). Intra-Regional Equalization and Growth in Russia. Comparative Economic Studies 56, 469—489.
Solanko L. (2002). Unequal Fortunes: a Note on Income Convergence across Russian Regions. Post-Communist Economies, 20, 3, 287—301.
Vakulenko E. (2014). Does Migration Lead to Regional Convergence in Russia? National Re-search University Higher School of Economics, Basic Research Program. Moscow: HSE Press. Working Papers. Series: Economics. WP BRP 53/EC/2014.
Zubarevich N.V. (2010). Regions of Russia: Inequality, Crisis, Modernization. Moscow: Independent Institute for Social Policy (in Russian).
Zverev D.V., Kolomak E.A. (2010). Sub-Federal Fiscal Policy in Russia: Interregional Differences and Relation. Series of «Scientific Reports: Independent Economic Analysis». No. 209. Moscow: Moscow Public Science Foundation; Siberian Center for Applied Economic Research (in Russian).

Received 23.09.2015

Pleschinskiy A.S. Analysis of the competition and cooperation in industries technological in-novation development
Economics and mathematical methods, 2017, 53 (3), 38-58.
Andrei S. Pleschinskiy — Doct. Sc. (Economic), Professor, Chief scientific re-searcher, Central Economics and Mathematical Institute RAS, Moscow, Russia; pleschin@cemi.rssi.ru

Abstract. The competition and cooperation when technological innovation developing is inves-tigated by means of proposed economic-mathematical model. The analysis is based on a two-level system of games. At the first, higher, level firms compete at the market, carrying out re-searches and development, independently or in cooperation, or rejecting the innovations. The production is based on traditional technology. After the players take these medium or long-term strategies they implement the tactical decisions of the second level of management. Firms com-pete by selecting volume of new technological production in case of completing the innovation, else in the absence of innovative development they use the old mode of production. For innova-tive and conservative strategies of two competing firms the terms of Nash equilibrium are formu-lated. Identified the minimum and maximum values of the development costs of the new tech-nology for each company that defines its strategies. These cost limits are determined by profit increase effects from them using the alternative strategies. They figure five areas in the positive values of innovative cost. In each area the players choose one profitable strategy. The efficiency of cooperation in the development of technological innovation on conditions of imperfect com-petition at the product market is proved. The results of competition and cooperation analysis in the development of reducing the cost of technological innovation are validated on numeric ex-amples of Cournot and Stackelberg duopolies.
Keywords: competition, cooperation, technological innovation, cost reduction, bimatrix game, Cournot duopoly, Stackelberg duopoly.
JEL Classification: C71, C72, D43, D52, L13.

REFERENCES (with English translation or transliteration)
Aghion P., Howitt P. (1999). Endogenous Growth Theory. Massachusetts: MIT Press.
Dementev V.E. (2008). New Production Markets: Leapfrogging Strategy Under Oligopoly Competition. Theory and Practice of Institutional Reforms in Russia 10, 5—10. Moscow: Central Economics and Mathematics Institute, Russian Academy of Sciences (in Russian).
Hay D., Morris D. (1999). Industrial Economics and Organization. Saint Petersburg: Ekonomicheskaya shkola (in Russian).
Nalebuff B., Brandenburger А. (2012). Co-Opetition. Moscow: Keis (in Russian).
Pavitt K. (1984): Sectoral Patterns of Technical Change: Towards a Taxonomy and a Theory. Research Policy 13, 343—373.
Pleschinskiy A.S., Jiltsova E.S. (2013b). Computable Model of Industry’s Modernization. Economics and Mathematical Methods 49, 3, 69—83 (in Russian).
Pleschinskiy A.S., Jiltsova E.S. (2013а). Analysis of the Results of Manufacture's Modernization in Conditions of Oligopoly Competition of Innovator and Its Pursuer. Economics and Mathematical Methods 49, 1, 88—105 (in Russian).
Porter M. (2007). Competitive strategy. Moscow: Al'pina Biznes Buks (in Russian).
Roketskiy N. (2015). Competition and Networks of Collaboration. Chapter of Ph. D. Dissertation at NYU. Available at: www.ucl.ac.uk (accessed: November 2016).
Tirole J. (2000). The theory of Industrial Organization. Saint Petersburg: Ekonomicheskaya shkola (in Russian).
Varshavsky L.E. (2009). Modeling Evolution of Markets of High Technology Products with Long Lifecycle: A Study of the Market of Civil Aircraft. Theory and Practice of Institutional Reforms in Russia 14, 49—64. Moscow: Central Economics and Mathematics Institute, Russian Academy of Sciences (in Russian).
Voronovitsky М.М. (2009). Investments Aimed at the Diminishing of Production Costs under Oligopoly Competence. Theory and Practice of Institutional Reforms in Russia 14, 31—48. Moscow: Central Economics and Mathematics Institute, Russian Academy of Sciences (in Russian).

Received 23.09.2016

Smolyak S.A. Regular oceangoing cargo ship speed optimization
Economics and mathematical methods, 2017, 53 (3), 59-77.
Sergei A. Smolyak — Doct. Sc. (Economics), Chiel scientific researcher, Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russia; smolyak1@yandex.ru

Abstract. We propose a model for choosing the most efficient speed of oceangoing freight ships carrying linear commercial voyages. The model takes into account the influence of age and speed of ship for different types of shipping costs. It is based on two principles: 1) the value of property does not exceed the sum of discounted benefits of its use for a small period of time and the value of the same property in the end of the period, and coincides with that sum at the most efficient use of the property. Therefore, the most efficient speed is such a speed at which the market value of ship is maximized; 2) if on the valuation date and in a period prior to the de-pendence on value of the objects of their characteristics (e.g. age) has been established it would be valid in a small period after valuation date. The paper also includes an analysis of other criteria to optimize the ship's speed which are offered in the literature.
Keywords: cargo ship, linear voyage, speed, age, voyage costs, operating costs, valuation, market value, deprecia-tion, optimization criteria.
JEL Classification: C51, D24, D46, L21.

REFERENCES (with English translation or transliteration)
Assessors’ Handbook Section 581 (2016). California State Board of Equalization. Equipment and Fixtures Index, Percent Good and Valuation Factors. Retrieved January 4. Available at: http://www.boe.ca.gov/proptaxes/pdf/ah58116.pdf (accessed: November 2016).
Buyanov A.I. (1938). Determination of the Optimal Service Life of Parts and Machines. Meckhanizatsiya i electrificatsiya selskogo hozyaystva 12, 16—20 (in Russian).
Cantorer S.E. (1963). Determining Optimal Device Life of Construction Equipment. Meckhanizatsiya stroitelstva, 7 (in Russian).
Chernomordyk G.I. (1948). Feasibility Study for Design Standards of new Railways. Moscow: Transzheldorizdat (in Russian).
Dai W.L., Fu X., Yip T.L., Hu H., Wang K. (2015). Emission Charge and Liner Shipping Network Configuration — an Economic Investigation of the Asia-Europe Route. Working Paper ITLS WP-15-23. Sidney: The University of Sidney.
Gibshman A.E. (1963). Determining Appropriate Service Life of Locomotives. Vestnik CNII MPS, 1 (in Russian).
Gibshman A.E. (1984). Determining of Economic Efficiency of Design Solutions in the Railway Transport. Moscow: Transport (in Russian).
Gkonis K.G., Psaraftis H.N. (2009). Some Key Variables Affecting Liner Shipping Costs. Working Paper. Athens: National Technical University of Athens. Gudehus H. (1963). Uber die optimale Geschwindigkeit von Handelsschiffen. Hansa 15, 23, 2387—2391.
Gudehus T. (2010a). Die kostenoptimale Geschwindigkeit von Frachtschiffen. Schiff & Hafen 62, 5, 12—16.
Gudehus T. (2010b). Gewinnoptimale Schiffsgeschwindigkeit und strategische Flottenplanung. Schiff & Hafen 62, 6, 12—17.
Hamburg Ship Evaluation Standard (2016). (The Long Term Asset Value, LTAV). (n.d.). Available at: http://www.vhss.de/index.php?id=12&L=1 (accessed: November 2016).
Harrison R., Figliozzi M. (2001). Impacts of Containership Size, Service Routes, and Demand of Texas Gulf ports. Austin, Texas: Center for Transportation Research, The University Texas at Austin.
Hiramoto F. (1977). Ship Maintenance and Repair Costs Versus Age. The Department of naval architecture and marine engineering. Anna Arbor: The University of Michigan. International Valuation Standards Council 2011 (2013). International Valuation Standards Committee. (G.I. Mikerin, I.L. Artemenkov (trans.)) Moscow: Rossiyskoe obshchestvo otsenshchikov (in Russian).
Kolegayev R.N. (1967). Determining the Optimal Durability of Technical Systems. Moscow: Sovetskoe radio (in Russian).
Kozin B.S., Kozlov I.T. (1964). The Choice of Schemes of Staged Development of Railway Lines. Moscow: Transzheldorizdat (in Russian).
Livchits V.N. (1971). The Choice of Optimal Solutions in the Feasibility Design Calculations. Moscow: Ekonomika (in Russian).
Livchits V.N., Smolyak S.A. (1973). Mathematical Modeling of the Processes of Depreciation of Fixed Assets. Trudy ICTP, 36, 136—165 (in Russian).
Lugovoy P., Tsypin L.G., Aukutsionek R.A. (1973). The Basis of Technical and Economic Design Calculations in the Railway Transport. Moscow: Transport (in Russian).
Lurye A.L. (1973). Economic Analysis of the Socialist Economy Planning Models. Moscow: Nauka (in Russian).
Maanum M.O., Seines H.P. (2015). Determinants of Vessel Speed in the VLCC Market — Theory vs. Practice. Bergen: Norges Handelshoyskole.
Masse P. (1971). Le choix des investissements. Criteres et methodes. Paris: Dunod.
Methodology (basic provisions) of Estimation of National Economic Efficiency of the New Equipment, Inventions and Innovations (1977). Moscow: Ekonomika (in Russian).
Mikerin G.I., Smolyak S.A. (2010). Efficiency Assessment of Investment Projects and Property Valuation: Opportunities for Convergence. Moscow: CEMI RAS (in Russian).
Mulder J., Dekker R. (2016). Optimization in Container Liner Shipping. Econometric Institute Report 2016-05. Rotterdam: Erasmus University.
Notteboom T.E. (2006). The Time Factor in Liner Shipping Services. Maritime Economics and Logistics 8, 1, 19—39.
Notteboom T.E. (2009). The Effect of high Fuel Costs on Liner Service Configuration in Container Shipping. Journal of Transport Geography 17, 325—337.
Palkin R.I. (1964). On the Economic Service Life of Construction Equipment. Stroitelniye i dorozhniye mashiny, 7 (in Russian).
Papadakis N.A., Perakis A.N. (1989). A Nonlinear Approach to the Multiorigin, Multidestination Fleet Deployment Problem. Naval Research Logistics 36, 515—528.
Peysakhzon B.E. (1952). Problems of Operation of Electric Railways. Moscow: Transzheldorizdat (in Russian).
Pocuca M. (2006). Methodology of Day-To-Day Ship Costs Assessment. PROMET — Traf-fic & Transportation 18, 5, 337—345.
Protodyakonov M.M. (1934). Research and Designing of Railways. Moscow: Transzheldorizdat (in Russian).
Ronen D. (1982). The Effect of Oil Price on the Optimal Speed of Ships. Journal of the Operational Research Society 33, 11, 1035—1040.
Smolyak S.A. (2008). Problems and Paradoxes in Machines and Equipmen Valuation. Moscow: RIO MAOK (in Russian).
Smolyak S.A. (2009). Ergo-Dynamics Models of Deprecistion of Machinery and Equipment. Economics and Mathematical Methods 45(4), 42—60 (in Russian).
Smolyak S.A. (2012a). Machinery and Equipment Depreciation Stochastic Model. Economics and Mathematical Methods 48, 1, 56—66 (in Russian).
Smolyak S.A. (2012b). Valuation of Equipment Undergoing an Overhaul. Economics and Mathematical Methods 48, 4, 66—79 (in Russian).
Smolyak S.A. (2013). Valuation of Machines and Equipment in Curable and Curable Depreciation. Economics and Mathematical Methods 49, 1, 54–72 (in Russian).
Smolyak S.A. (2014). Overhaul Policy Optimization and Equipment Appraisals Concerning Its Reliability. Journal of the New Economic Association 2, 102—131(in Russian).
Smolyak S.A., Filimonov V.V. (1975). Problems of Machinery and Equipment Reproduction Optimization. Trudy 6 zimney shkoly po matematicheskomu programmirovaniyu i smezhnym voprosam, 209—228 (in Russian).
Spravochnik otsenshchika mashin i oborudovaniya (2015). Nizhnii Novgorod: Privolzhskii tsentr metodicheskogo i informatsionnogo obespecheniya otsenki (in Russian).
Stopford M. (2009). Maritime Economics. London, New York: Routledge.
Stupin O.K., Limonov Z.L. (1973). Feasibility Study for Sea Cargo Ships. Leningrad: Sudostroyeniye.
Terborgh G. (1948). Dynamic Equipment Policy. New York: McGraw-Hill.
Vessel Operating Cost Savings at Terminal 46 (2014). Commercial Strategy Department, Port of Seattle.
Vilensky P.L., Livсhits V.N., Smolyak S.A. (2015). Investment Project Assessment: Theory and Practice. Moscow: Poli Print Servis (in Russian).
Zhou K. (2012). Optimization of Container Liner Speed and Deployment Based on New Environment and Bunkering Regulation. University Park: The Pennsylvania State University.

Received 12.07.2016

Shelemekh E.A. Calculation of exotic options in incomplete markets
Economics and mathematical methods, 2017, 53 (3), 78-92.
Elena A. Shelemekh — junior researcher, Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russia; letis@mail.ru

Abstract. We consider incomplete market with discreet time and without transaction costs, consisting of a risky and a risk-free assets. Return on risky asset is supposed to take on each step one of three values, so that increase, decrease and constancy of risky asset’s price are possible. There is exotic option in the market. In the article exotic option is a contract, for which payoff and moment of execution depend on some event, such as risky asset’s price reaches some given value. To calculate such an option in the incomplete market minimax approach was adopted. The approach reflects seller’s point of view and implies the following. Seller’s risk function is supposed to be exponential and to depend on the option’s initial price and on deficit of seller’s portfolio at the execution moment. Participants of the market do not know the distribution of risky asset’s price. The seller is prudent, i.e. the seller assumes that the distribution is the worst one (it maximazes seller’s expected risk) and seeks to minimize expected risk by portfolio management. For this problem we have derived a new recurrent equation describing evolution of minimax value for seller’s expected risk. A self-financing portfolio has been found, which minimizes maximum value of seller’s expected risk (optimal portfolio). It has been proved that a corresponding portfolio with consumption is a superhaging one with respect to any discrete measure and it’s capital does not exceed capital of any other superhaging portfolio. Thus it is impossible to improve obtained solution choosing another risk functions. By use of this resuts formulas for superhedging portfolios of binary and barrier options have been derived.
Keywords: exotic option, incomplete market, minimax approach, superhedging, binary option, barrier option.
JEL Classification: C73.
The research was supported by the Russian Science Foundation (Project № 16-06-00098 and № 16-06-00229).

REFERENCES (with English translation or transliteration)
Acciaio B., Beiglbock M., Penkner F., Schachermayer W. (2016). Model-Free Version of the Fundamental Theorem of Asset Pricing and the Super-Replication Theorem. Mathematical Finance 26, 2, 233–251.
Beiglbock M., Henry-Labordere P., Penkner F. (2013). Model-Independent Bounds for Option Prices — a Mass Transport Approach. Finance and Stochastics 17, 3, 477–501.
Billingsley P. (1977). Convergence of Probability Measures. Moscow: Nauka (in Russian).
Carr P., Nadtochiy S. (2011). Static Hedging under Time-Homogeneous Diffusions. SIAM Journal on Financial Mathematics 2, 1, 794–838.
Dyomin N.S., Andreeva U.V. (2011). Exotic Call Options with Limited Payments and Guaranteed Income in Black–Scholes Model. Control Sciences 1, 33–39.
Fahim A., Huang Y. (2016). Model-Independent Superhedging under Portfolio Constraints. Finance and Stochastics 20, 1, 51–81.
Follmer H., Schied A. (2008). Stochastic Finance. An Introduction in Discrete Time. Moscow: MTsNMO (in Russian).
Gushchin A.A. (2013). On the upper Hedging Price for Non-Negative Payoffs. Contemporary Problems of Mathematics and Mechanics VIII, Mathematics, 3, 60–72 (in Russian).
Hull J.C. (2009). Options, Futures and other Derivatives. Upper Saddle River: Pearson Prentice Hall.
Khametov V.M., Shelemekh E.A. (2015). Superhedging of American Options on an Incomplete Market with Discrete Time and Finite Horizon. Automatika i Telemekhanika 9, 125–149 (in Russian).
Kudryavtsev O.E., Levendorskii S.Z. (2009) Fast and Accurate Pricing of Barrier Options under Levy Processes. Finance and Stochastics. 13, 4, 531–562.
Petrosyan L.A. (1998). Game Theory. Moscow: Vysshaya shkola (in Russian).
Schachermayer W. (2012). Optimisation and Utility Functions. Documenta Mathematica. Extra Volume ISMP, 455–460.
Shiryaev A.N. (1998). Essentials of Stochastic Finance. Vol. 2. Theory. Moscow: Fazis (in Russian).
Shiryaev A.N. (2004). Probability. Moscow: MTsNMO (in Russian).

Received 14.12.2015

Belousov F.A. Model of civilization with two types of reproduction product (model of nomads and plowmen)
Economics and mathematical methods, 2017, 53 (3), 93-109.
Fedor A. Belousov — Scientific researcher CEMI RAS; Russia, Moscow, sky_tt@list.ru

Abstract. In this article a model of interaction of the two types of civilizations is considered. These two types of civilizations were conventionally called “nomads” and “plowmen”. Each type is charac-terized by its method of product reproduction, which is necessary for agents of both types. If plowmen reproduce product by using their skills, nomads reproduce nothing, instead they con-sume that resource which they find, including the resource they take away from plowmen and the other nomads. This product is also a resource; it is the main object of competi-tion between the agents. It is the main reason for aggression of one group of agents towards the others. In addition to the product that is reproduced by plowmen, there is also a wild resource that appears in the range in randomly defined places with a given intensity. According to the au-thor’s intention, the constructed model is a simplified model of the ancient world, in which each of the civilizations could be classified as one of the two considered types. Typical representatives of the civilization of plowmen are the civilizations of Mesopotamia, the front of Asia, Byzantine and Roman em-pires, etc. Classic nomadic civilization is represented by nomadic civilizations of the Great steppe. The model is implemented on the basis of the agent-based approach in the software pack-age AnyLogic. In this work a number of experiments have been conducted. In ex-periments the study has been made of how characteristics of coexistence of two types of the civi-lizations vary depending on the variation of considered parameters. Important parameters of the model, impact of which was studied, are the size of habitat and growth rate of the wild resource. Based on the obtained data, statistical and econometric analysis is conducted.
Keywords: artificial society, agent-based modeling, nomads, plowmen.
JEL Classification: C63.
The research was supported by the Russian Foundation for Basic Research (Project No. 16-36-00338).

REFERENCES (with English translation or transliteration)
Aivazian S.A. (2010). Methods of Econometrics. Moscow: Magistr, INFRA-M (in Russian).
Bazykin A.D. (1985). Mathematical Biophysics of Interacting Populations. Moscow: Nauka (in Russian).
Epstein J., Axtell R. (1996). Growing Artificial Societies: Social Science from the Bottom up. Washington Brookings Institution Press.
Heckbert S.M. (2013). An Agent-Based Model of the Ancient Maya Social-Ecological System. Journal of Artificial Societies and Social Simulation, 16, 4, 11. Available at: http://jasss.soc.surrey.ac.uk/16/4/11.html (accessed: January 2017).
Makarov V.L., Beklaryan L.A., Belousov F.A. (2014). Steady Regimens in Henning Model and its Modifications. Journal of Machine Learning and Data Analysis, 10, 1385—1395 (in Russian).
Toynbee A.J. (1934—1961). A Study of History. Moscow: Progress.
Wittek P., Rubio-Campillo X. (2012). Scalable Agent-Based Modeling with Cloud HPC Re-sources for Social Simulations. In: IEEE 4th International Conference on Cloud Computing Technology and Science (CloudCom) December 3—6. Taipei, Taiwan, 355—362.

Received 07.07.2016

TeplovaТ.V., Sokolova Т.V. The non-parametric data envelopment analysis method for port-folio design in the Russian bond market
Economics and mathematical methods, 2017, 53 (3), 110-128.
      Tamara V. Teplova — Doct. Sc. (Economics), Professor, National Research University Higher School of Economics, Head of Research and training laboratory of financial mar-kets analysis, Faculty of Economics; Professor, Department of Finance, Faculty of Eco-nomics; Russia, Moscow, tteplova@hse.ru
      Tatiana V. Sokolova — Cand. Sc. (Physics & Maths), National Research University Higher School of Economics, Analyst of Research and training laboratory of financial markets analysis, Faculty of Economics; Senior Lecturer, Department of Finance, Faculty of Economics; Russia, Moscow, sokol-t@yandex.ru

Abstract. In this paper for the first time on the base of the non-parametric Data Envelopment Analysis (DEA) method the authors build and test portfolios in the Russian bond market. Using DEA we perform integral evaluation and rank by optimality (efficiency) outstanding ruble cor-porate bonds from the perspective of a private investor. Our original algorithm for building an optimal bond portfolio includes two analytical procedures: firstly, we identify the determinants of the yield to maturity of ruble corporate bonds for a diversified sample of real sector companies from 2008 to 2015, and then we apply the DEA method for this sample in order to find the optimal set of bonds for the portfolio. At the final stage we test (for 2014—2015) an investment strategy based on picking for the portfolio the ruble corporate bonds that reached the efficiency frontier. In order to identify the determinants of ruble corporate bond yields we analyze a set of macroeconomic and firm-level (financial and non-fundamental) factors, characteristics of bond issues using econometric methods. For the first time in the Russian bond market, we consider not only current but also expected inflation and GDP growth, risk indicators (the volatility index RTS VIX as a proxy). We identify the optimal bond issues (the bond issues that reached the effi-ciency frontier) taking into account a set of different factors: yield to maturity, duration and li-quidity of bond issues, credit risk indicators of bond issuers. The results of a regression analysis confirm our hypothesis that yield to maturity is significantly influenced by revenue of a bond issuer, the repo eligible factor (inclusion of a bond issue in the Lombard list of the Bank of Rus-sia), the government’s share in the equity, the bond issuer’s debt burden indicators, the level of current and expected inflation. The efficiency (optimality) frontier mainly consists of bond issues of large companies with the government’s participation in the equity. Our hypothesis that invest-ing in the bond issues on the efficiency frontier can beat the bond benchmarks’ returns and “re-turn / volatility” ratios are partly confirmed, for the period of 2014 characterized by a decrease in prices of ruble bonds.
Keywords: ruble corporate bonds, active investment strategies, Data Envelopment Analysis.
JEL Classification: C51, C61, G11, G12.

      REFERENCES (with English translation or transliteration)
Aleskerov F.T., Belousova V.Yu., Petrushchenko V.V. (2015). Measuring Higher Education Institutions’ Efficiency: Data Envelopment Analysis and Stochastic Frontier Approach. Problemy Upravleniya, 5, 2—19 (in Russian).
Anderson R., Mansi S., Reeb D. (2003). Founding Family Ownership and the Agency Cost of Debt. Journal of Financial Economics, 68, 263—285.
Banker R.D., Charnes A., Cooper W.W. (1984). Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis. Management Science, 30(9), 1078—1092.
Bao J., Pan J., Wang J. (2011). The Illiquidity of Corporate Bonds. The Journal of Finance, LXVI(3), 911—946.
Boubakri N., Ghouma H. (2010). Managerial Opportunism, Cost of Debt Financing and Regulation Changes: Evidence from the Sarbanes–Oxley Act Adoption. Working Paper. HEC Montreal.
Bruslerie H. (2004). Active Bond Strategies: What Link between Forecasting Ability, Excess Return and Performance? Journal of Asset Management, 5(2), 105—119.
Charnes A., Cooper W.W., Rhodes E. (1978). Measuring the Efficiency of Decision-Making Units. European Journal of Operation Research, 2(6), 429—444.
Cici G., Gibson S. (2012). The Performance of Corporate Bond Mutual Funds: Evidence Based on Security-Level Holdings. Journal of Financial and Quantitative Analysis, 47, 159—178.
Cooper W., Seiford L., Tone K. (2007). Data Envelopment Analysis. A Comprehensive Text with Models, Applications, References and DEA-Solver Software. N.Y.: Springer.
Ferson W., Henry T.R., Kisgen D.J. (2006). Evaluating Government Bond Funds Using Stochastic Discount Factors. Review of Financial Studies, 19, 423—455.
Fethi M.D., Pasiouras F. (2010). Assessing Bank Efficiency and Performance with Operational Research and Artificial Intelligence Techniques: A Survey. European Journal of Operational Research, 204(2), 189—198.
Gutierrez R., Maxwell W., Xu D. (2008). Persistent Performance in Corporate Bond Mutual Funds. Working Paper. Eugene: University of Oregon.
Huij J., Derwall J. (2008). Hot Hands’ in Bond Funds. Journal of Banking and Finance, 32, 559–572.
Malhotra R., Malhotra D.K., Russel P.S. (2010). Using Data Envelopment Analysis to Rate Bonds. Journal of Business & Economic Studies, 16(1), 58—76.
Mansi S., Maxwell W., Miller D. (2011). Analyst Forecast Characteristics and the Cost of Debt. Review of Accounting Studies, 16, 116—142.
Robbins M.D., Simonsen W. (2002). Using Data Envelopment Analysis to Evaluate the Performance of Municipal Bond Issuers. State & Local Government Review, 34 (1), 20—28.
Silva F., Cortez M.C., Armada M.R. (2003). Conditioning Information and European Bond Fund Performance. European Financial Management, 9 (2), 201—230.
Teplova T.V., Sokolova T.V. (2011). Modeling the Cost of Corporate Debt in the Russian Market. Corporate Finance Management, 5, 198—220 (in Russian).
Wald J.K., Long M.S. (2007). The Effects of State Laws on Capital Structure. Journal of Financial Economics, 82, 297—319.
Zhou P., Ang B.W., Poh K.L. (2008). A Survey of Data Envelopment Analysis in Energy and Environmental Studies. European Journal of Operational Research, 189 (1), 1—18.

Received 12.04.2016

Vol. 53, No. 4

Braginsky O.B., Tatevosyan G.M., Sedova S.V. State development programs: ways to improve
Economics and mathematical methods, 2017, 53 (4), 3-12.
      Oleg B. Braginsky - Doct. Sc. (Economics), professor, head of the laboratory, Central Economics and Mathematics Institute, Russian Academy of Sciences; Russia, Moscow, braginsk@cemi.rssi.ru
      Georg M. Tatevosyan - Cand. Sc. (Economics), Leading Research Associate, Central Economics and Mathematics Institute, Russian Academy of Sciences; Russia, Moscow, tatevos@cemi.rssi.ru
      Svetlana V. Sedova - Cand. Sc. (Economics), Senior Researcher, CEMI RAS; Russia, Moscow, sedova@mail.ru

Abstract. The baseline conditions of the methodology for constructing sectoral and regional development government programs in Russia are examined in the article. A detailed analysis of the subject was given in the previous works of the authors. Critical assessment of the experience of the 1990-2000s is given. Relevant official documents are investigated. The authors propose an economic mechanism for the governmental programs' management. The latter includes program estimation system, specific pricing and financial provision system. Foreign experience in the governmental program management in the USA and in France has been studied. The article presents a modification of the previously developed model, which makes possible to identify and estimate the need for credit at different stages of program implementation. An example of design of a single program based on two governmental programs of the Russian chemical industry is demonstrated. The authors propose to make the program flexible, including not only large-scaled projects, but also the smaller ones, which, as a result of optimization, will be able to solve important problems of the industry development. Experimental calculations have been carried out.
Keywords: investment programs, investment projects, economic mechanism, economic indicators, pricing, financial provision.
JEL Classification: Е37, L52, C61, C88.
This article was prepared with the financial support of the Russian Foundation of Fundamental Research (project № 17-06-00198).

      REFERENCES (with English translation or transliteration)
Arkin V.I., Slastnikov A.D. (2014). Modeling for the Joint Mechanism of State Guarantees and Bank Credit Policy When Investing Risky Projects. Economics and Mathematical Methods, 50, 3, 105-118 (in Russian).
Blinkov B. (1932). Chemical Industry of the USSR. Economic Outline. Moscow, Leningrad: Gosudarstvennoye khimiko-tekhnicheskoye izdatel'stvo (in Russian).
Braginskiy O.B., Tatevosyan G.M., Sedova S.V., Pisareva O.M., Kunitsyna N.N. (2013). Methodology of Both Justification and Optimization of Investment Programs with Scarce Financial Resources (Case for the Russian Chemical Industry). Preprint WP/2013/303. Moscow: CEMI RAS (in Russian).
Code of Federal Regulations (1975). Contract Pricing. Washington. P. 283-287 (in Russian).
Federal Procurement Regulation (1975). Second ed. Part XV. Contracts Cost Principals and Procedures. Washington. P. 1501-1504.
Federal Trade Commission (1977). The United States Steel Industry and Its International Rivals: Trends and Factors Determining International Competitiveness. Staff Report of the Bureau of Economics to the U.S. Federal Trade Commission. November. Available at: https://www.ftc.gov/sites/default/files/documents/reports/u.s.steel-industry-and-its-international-rivals-trends-and-factors-determining international/197711steelindustry.pdf (accessed: September 2016).
Heshan K. Alfares Н.К., Adnan M., Jerallah Al-Amer, Shaikh Saifuddin. (2002). A mathematical programming model for optimum economic planning of the Saudi Arabia petrochemical industry. In: "The 6th Saudi Engineering Conference" (December, 14-16). Dhahran: KFUPM.
Kostromina G.G. (2010). Structural Problems of the Industrial Engineering Development in the Soviet Pre-War Economy. In: "The Victory's Economy. 1941-1946". Moscow: Institute of Economics, the Russian Academy of Sciences, 57-63 (in Russian).
Leonard B. (1981). U.S. Industrial Competitiveness: a Comparison of Steel, Electronics and Automobiles. Darby: Diane Publishing.
Lorenz E. H. (1990). Labor Supply and the Employment Strategies of French and British Shipbuilders (1890 to 1970). Working paper No. 132. January. South Bend: Kellogg Institute (at the University of Notre Dame).
Magomedov R.Sh. (2016a). On the Integrity of the Governmental Programs' Management System. In: "Theory and Practice of the Institutional Transformation in Russia" Erznkian B.A. (ed.). Issue 37. Moscow: CEMI RAS, 133-139 (in Russian).
Magomedov R.Sh. (2016b). The Role of the Troubled Asset Relief Program in Minimizing the Consequences of the Financial and Economic Crisis of 2008 in the US. Finance and Credit, 44 (716), 20-32 (in Russian).
Major System Acquisition Reform (1975). Statement by Sen. L. Chiles. Hearing before the Subcommittee on Federal Spending, Practices, Efficiency and Open Government of the Committee on Government Operations. U.S. Senate. 94th Congress. 1975. Part II. Washington.
Riemer W.H. (1969). Handbook of Government Contract Administration. Englewood Cliffs: Prentice-Hall.
Sedova S.V. (2017). About One Modification of the Model of the Investment Programs' Structure Formation Considering the Need for Credit. In: "Proceedings of the Eighteenth All-Russian Symposium "Strategic Planning and Enterprise Development"". Section 2. Moscow: CEMI RAS, 147-149.
Sedova S.V. (2015) Model of the Investment Programs' Structure Formation. Economics and Mathematical Methods, 51, 2, 89-102 (in Russian).
Tsarev V.V. (2004). Measuring the Economic Efficiency of Investments. St. Petersburg: Piter (in Russian).

Received 20.06.2017

Cherkashin A.K., Myadzelets A.V. Characterization of regional economic development in response to macroeconomic factors and conditions
Economics and mathematical methods, 2017, 53 (4), 13-25.
      Alexander K. Cherkashin - Doct. Sc. (Geography), Professor in Geoinformatics, Head of Laboratory of Theoretical Geography, V.B. Sochava Institute of Geography SB RAS; Russia, Irkutsk, cherk@mail.icc.ru
      Anastasia V. Myadzelets - Cand. Sc. (Geography), Senior research officer, Laboratory of Theoretical Geography, V.B. Sochava Institute of Geography SB RAS; Russia, Irkutsk, anastasia@irigs.irk.ru

Abstract. The opportunity of objective evaluation of invariant characteristics of socio-economic development of regional level territories is considered. The first integral functions of solutions of differential equations on macroeconomic parameters are used for the evaluation. Model equations are established from the Legendre tangential transformation formula of analytic functions under some natural limitations that take into account the persistence of the regional environment of economic activity. Economic environment parameters and connected integral characteristics reveal genetic peculiarities of a regional system. They are some latent economic indices taking into account the local infrastructure, production and management. The indices allow assessing and comparing territories on their potential of economic development. The model is realized for quantitative analysis of the connections of the domestic investments with industrial and agricultural production volume for the regions of Russian Federation for the period 1999-2012. Different types of general and regional invariants are determined as criteria of economic interaction efficiency using the model. Analysis of investment efficiency into the industry and agriculture and economic diagnostics of the regions are carried out based on calculated value of economic environmental transformations and their effect on the evaluation function.
Keywords: production factors and conditions, invariant characteristics, first integrals, tangential transformations, economic environment parameters, economic diagnostics, investment efficiency.
JEL Classification: С31, C51, С52.
The research was done with financial support from RFBR, project "Innovative development, territorial organization and life quality increase of population in Siberian and Arctic regions of Russia", No. 16-02-00570(a).

      REFERENCES (with English translation or transliteration)
Cherkashin A.K. (2005). Polysystem Modeling. Novosibirsk: Nauka (in Russian).
Kamke E. (1971). Handbook on Ordinary Differential Equations. Moscow: Nauka (in Russian).
Koltsov V.V. (2011). Invariants of the Russian Economy. In: "Collected Scientific Articles of International Scientific-Practical Internet-Conference Proceedings". Vol. 10. Odessa, Chernomorye. Available at: http://www.sworld.com.ua/index.php/ru/economy/economic-theory-and-history/2990-koltsov-bb (accessed: January 2017) (in Russian).
Pilyasov A.N. (2014). The Northern Futurology: the Next Two Decades. Arctic: Ecology and Economics, 4(16), 93-101 (in Russian).
Samuelson P. (2003). Foundations of Economic Analysis. Moscow: Economic School (in Russian).
Samuelson P. (2004). Social Indifference Curves. In: "Markers of Economic Thought". Vol. 4. "Economics of Well-Being and Social Choice". Moscow: Economic School, 135-164 (in Russian).
Samuelson P.A. (1964). Tax Deductibility of Economic Depreciation to Insure Invariant Valuations. Journal of Political Economy, 72, 6, 604-606.
Sato R., Ramachandran R.V. (2014). Symmetry and Economic Invariance. Tokyo: Springer.
Zaznobin V. (2010). Price-List Invariant in Credit and Finance System. New Europe, 906 (October, 10-16), 4-5.

Received 22.10.15

Afanasyev A.A. Forecasting of Gazprom gas production and its potential at under the foreign economic restrictions
Economics and mathematical methods, 2017, 53 (4), 26-35.
Anton A. Afanasyev - Doct. Sc. (Economics), Leading research associate, Central Economics and Mathematics Institute, Russian Academy of Sciences, Professor, National Research University Higher School of Economics; Russia, Moscow, aanton@cemi.rssi.ru

Abstract. This study is devoted to forecasting the Russian Gazprom natural gas production from the Tyumen region's fields and its production potential in the context of the Russian economic crises and foreign economic restrictions that has taken place since 2014, including a reduction in external and domestic demand for Russian natural gas as well as for gas of Gazprom. On the basis of gas production function estimated for 1985-2008 we make forecasts for 2017 of Gazprom gas production in Tyumen region (where the company is producing more than 90% of its gas) and estimate the under-utilized production potential of PJSC Gazprom in this region for 2014-2016. Basing on the additional econometric study of Gazprom gas production function (with labour) in the Tyumen Region we have empirically proved the growth of the coefficient of the company's neutral technical progress since 2014, one of the consequences of which, according to the author, was a continuous decline since 2014 the unit cost of natural gas production of the Gazprom subsidiary "Gazprom dobycha Nadym", which operates the largest Bovanenkovskoye oil and gas condensate field in the Yamal Peninsula which reserves are estimated to be 4.9 trill. cub. m of gas. It is concluded that in the Russian economic crisis that has been intensified since 2014 as well as the foreign economic and political restrictions that have been started in the same year, in the segment of gas production Russian Gazprom continues to be an effective natural monopoly with an increasing coefficient of neutral technical progress and minimal production costs, the marginal and average values of which coincide and do not depend on the volumes of gas produced.
Keywords: forecasting, natural gas production, Gazprom, Tyumen region, production potential, foreign economic restrictions, Gazprom efficiency, neutral technical progress, gas production costs.
JEL Classification: D42, E27, L71, Q47, R15.
This study was supported by the Russian Foundation for Basic Research (project 17-06-00463 А) and the Russian Foundation for Humanities (project 17-02-00457 А).

REFERENCES (with English translation or transliteration)
Afanas'ev A.A. (2008). Economic-and-Mathematical Modeling and Forecasting of Natural Gas Production in the Tyumen Region. Gas Industry, 6, 19-25 (in Russian).
Afanas'ev A.A. (2009a). Econometric Study of Production Functions of the Krasnoyarsk Krai Gas Industry. Economics and Mathematical Methods, 45, 3, 3-11 (in Russian).
Afanas'ev A.A. (2009b). Production Functions of the Tyumen Region Gas Industry and Subsidiaries of OJSC "Gazprom" in 1993-2007. Economics and Mathematical Methods, 45, 2, 37-53 (in Russian).
Afanas'ev A.A. (2012). Econometric Models of Natural Gas Forecasting. Oil & Gas Journal, Russia, 10, 65, 76-81 (in Russian).
Afanas'ev A.A. (2013). Money Turnover Model for a Gas-Rich Country. Dr. econ. sci. thesis. Moscow: CEMI RAS Publ. Available at: http://www.cemi.rssi.ru/staff/Thesis/index.php?ELEMENT_ID=7182 (accessed June 2017, in Russian).
Afanas'ev A.A. (2014a). Sustainable Strategic Goals of a Global Energy Company: Key for Gazprom's Future. Gas Industry, 704, 10-20 (in Russian).
Afanas'ev A.A. (2014b). Innovative Breakthrough under Global Crisis as the Source of Added Gazprom Revenues: Econometric Analysis. Gas Industry, 11, 15-19 (in Russian).
Gafarov N.A., Kalityuk S.A., Glagolev A.I., Moiseev A.V. (2011). The Global Gas Business, New Trends, Scenarios, Technology. Moscow: Gazprom Expo (in Russian).
Klimenko A.V. (1980). Prediction of the Extractive Industries Taking into Account Natural Factors. In: "The Methods of Construction and Use of Macroeconomic and Sectoral Production Functions". Moscow: CEMI AS USSR, 152-174 (in Russian).
Martos V.N. (1989). Guidelines for Predicting Recovery at the Stage of Field Exploration. Moscow: VNIGNI (in Russian). Nasinnik Z.A. (1975). Forecasting Cost of Oil and Associated Gas. Moscow: Nedra (in Russian).
Technical and Economic Indicators of Gas, Gas Condensate and Oil Production by Gazprom Group in 2014 (2015). Economic and Statistical Review. M.: Gazprom Expo Publ. (in Russian).
Technical and Economic Indicators of Gas, Gas Condensate and Oil Production by Gazprom Group in 2015 (2016). Economic and Statistical Review. M.: NIIgazekonomika Publ. (in Russian).
Technical and Economic Indicators of Gas, Gas Condensate and Oil Production by Gazprom Group in 2016 (2017). Economic and Statistical Review. M.: NIIgazekonomika Publ. (in Russian).
Varshavsky L.E. (1976a). Genetic Modeling of Economic Development of the Oil and Gas Industry (on the Example of the Gas Industry of the USSR). Thesis for the degree of Cand. Sc. (Economics) on specialty 08.00.13. Moscow: CEMI AS USSR Publ. (in Russian).
Varshavsky L.E. (1976b). On Forecasting and Analytical Modeling of the Gas Industry. In: "Economy of the gas industry" 12, 16-24 (in Russian).

Received 16.06.2017

Borodin K.G., Salnikov S.G. The development of cheese exports in Russia and EEU: problems, factors and estimation of the gravity model
Economics and mathematical methods, 2017, 53 (4), 36-53.
      Konstantin G. Borodin - Doct. Sc. (Econ.), All-Russian Institute of Agrarian Problems and Informatics after A.A. Nikonov; Russia, Moscow, borkg_cd@mail.ru. The author thanks prof. Ben Shephard for the useful advices.
      Sergey G. Salnikov - Cand. Sc. (Physics & Math.), All-Russian Institute of Agrarian Problems and Informatics after A.A. Nikonov; Russia, Moscow, salnsg@gmail.com

Abstract. The authors investigated the current state of cheese market in Russia and the Eurasian Economic Union (EEU). Developed two versions of the gravity model of cheese exports, the one evaluating the factors of the Russian exports developing, the second - of the EEU exports. The basis for assessment served the results obtained by the method of fixed effects PPML, the other methods were also used in the calculations. The other authors obtained the assessment of such factors as the "sanctions" and "EEU". Estimates made for sanctions shows a strong positive relationship with exports, i.e. the impact of sanctions in sum it was the impetus to the development of mutual trade in the EEU. The free niche formed in the Russian domestic market as a result of the embargo and sanctions, stimulated the growth of domestic demand, including demand for the products of the EEU countries. Estimates obtained for the factor "EEU" showed that it is not significant for Russia, since the Russian exports are directed primarily to the third countries' markets, especially in the period preceding the formation of the Union, while for the EEU in general, this factor is significant, due to the rest countries' of the Union orientation to the large Russian market.
Keywords: cheese market, exports, gravity model, EEU, sanctions.
JEL Classification: F14, F15, Q17.

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Analysis of the EU Dairy Sector (2014). EU Production and Exports to Russia (2011-2013). European Commission. 26 September. Available at: http://ec.europa.eu/agriculture/russian-import-ban/pdf/dairy-production_en.pdf (accessed: May 2017).
Analysis of the Situation in the Milk Market of the Member States of the Eurasian Economic Union for 2010-2014. (2015). Eurasian Economic Commission. Agricultural Policy Department. Available at: http://www.eurasiancommission.org/ru/act/prom_i_agroprom/dep_agroprom/monitoring/Documents/%D0%9C%D0%9E%D0%9B%D0%9E%D0%9A%D0%9E.pdf (accessed: April 2017) (in Russian).
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Bergstrand J.H. (1989). The Generalized Gravity Equation, Monopolistic Competition and the Factor proportions Theory in International Trade. Review of Economics and Statistics, 71, 1, 143-153.
Borodin K., Strokov A. (2015) Customs Union in the CIS. Journal of Economic Integration, 2, 368-393.
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Kazakhstan: The Market of Cheese. Food Industry of Ukraine. 21.06.2014 Available at: http://ukrprod.dp.ua/2014/06/21/kazaxstan-rynok-syra.html (accessed: December 2016) (in Russian).
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Kovaleva I.V., Suray N.М. (2015). Major Trends in Domestic Cheeses and Cheese Products Range Building. Izvestiya of Altai State University, 1, 2(86), 102-107 (in Russian).
Kuzina E.Y., Ostretsov V.N. (2016). State and prospects of cheese production in Russia. Dairy Farming Journal, 1(21), 115-123 (in Russian).
Musina О.N., Lisin P.A. (2015). World Leaders in Cheese Making for the Last 20 Years. Actual Problems of Milk Processing Technology.
Mayorova А.А. (ed.). Siberian Research Institute of Cheese Making. In: "Herald of Scientific Works", 15, 76-79. Barnaul: Azbuka (in Russian)
Pokrivcak J., Berkum S. van, Drgova L., Mraz M., Ciaian P. (2013). The Role of Non-tariff Measures in EU Dairy Trade with Russia. Post-Communist Economies, 25, 2, 175-189. Available at: http://dx.doi.org/10.1080/14631377.2013.787737 (accessed: May 2017).
Pöyhönen P. (1963). A Tentative Model for the Volume of Trade between Countries. Weltwirtschaftliches archive, 90, 93-99.
Rybolovleva Т. (2011) What Does Restrain the Development of Cheese Making in Russia. Foodmarkets.ru, Russian Food Portal. Available at: http://foodmarkets.ru/articles/topic/1190 (accessed: December 2016) (in Russian).
Santos S., Tenreyro S. (2006). The Log of Gravity. Review of Economics and Statistics, 88, 4, 641-658.
Solovyova О. (2016). Food Embargo for Artificial Cheese is Not a Decree. Independent newspaper. 10.08.2016. Available at: http://www.ng.ru/economics/2016-08-10/4_cheese.html (accessed: May 2017) (in Russian).
Tinbergen J. (1962). Shaping the World Economy. Suggestion for an International Economic Policy. N.-Y.: The Twentieth Century Fund.
Yarashevich V. (2014). Post-Communist Economic Integration: Belarus, Kazakhstan, and Russia. Journal of Economic Integration, 4, 582-623.

Received 14.12.2016

Lavrinov G.A, Khrustalev E.Yu., Khrustalev O.E. Tools for assessment and risk reduction in the formation of plans for rocket-space technology
Economics and mathematical methods, 2017, 53 (4), 54-61.
      Gennadii A. Lavrinov - Doct. Sc. (Economics), Professor, First vice-president, Russian Academy of Rocket and Artillery Sciences; Russia, Moscow, gelavrinov@yandex.ru
      Evgenii Yu. Khrustalev - Doct. Sc. (Economics), Professor, Head of the laboratory, CEMI RAS; Russia, Moscow, stalev@cemi.rssi.ru
      Oleg E. Khrustalev - Cand. Sc. (Economics), Senior scientific worker, CEMI RAS; Russia, Moscow, stalev777@yandex.ru

Abstract. Design and manufacture of high technology products with a long life cycle requires the formation of long-term scientific and technological plans and programs, which implementation is accompanied by a large number of uncertainties and various types of risks. One of the most important tasks that need to be addressed in preparing the development plans, are the methods and tools to identify and neutralize potential threats of disruption of planned activities due to the deviation of the plans' implementation from the original trajectory. The paper proposed economic and mathematical tools for accounting, management and compensating the risks inherent in the processes of creation and development of the modern rocket and space technology in the framework of innovative plans and programs of transcendental and empirical methods of development planning options. To build a short-term plan for the development of rocket-and-space technology the authors have developed multivariate control, allowing to move from one short-term option plan to another one, preserving balance without a loss of consistency.
Keywords: innovation project, economic and mathematical tools, multitask, programs and plans, risks and uncertainties, rocket-space technology.
JEL Classification: C65, D81, G32, O32.
The article was supported by the Russian Foundation for Basic Research (grant 16-06-00018: Mathematical and Logical-Linguistic Modeling of Organizational and Economic Mechanisms to Reduce and Compensate for Risk of Innovative Projects for Creating High-Tech Products with a Long Life Cycle (The Rocket-and-Space Technology Case)).

      REFERENCES (with English translation or transliteration)
Baranovskaya T.P., Vostroknutov A.E. (2008). Model Improvement and Assessment of Organizational Structures. Polythematic Network Electronic Scientific Journal of the Kuban State Agrarian University, 36, 61-76 (in Russian).
Batkovskij M.A., Merzlyakova A.P. (2011). Evaluation of Innovative Strategies for the Enterprise. Issues of Innovation Economics, 7, 10-17 (in Russian).
Bohnert A., Gatzert N., Jоrgense P.L. (2015). On the Management of Life Insurance Company Risk by Strategic Choice of Product Mix, Investment Strategy and Surplus Appropriation Schemes. Insurance: Mathematics and Economics, 60, January, 83-97.
Kachalov R.M. (2012). Management of Economic Risk: Theoretical Foundations and Applications. Moscow, Saint Petersburg: Nestor-History (in Russian).
Khrustalev E.Yu., Khrustalev Yu.E. (2006). Assessment of Economic Security High-Tech Industries. National Interests: Priorities and Security, 2, 46-52 (in Russian).
Khrustalev E.Yu., Slavyanov A.S., Sakharov I.E. (2013). Methods and Tools Selection of Mechanisms for Economic Protection of High-Tech Industries for Example Aerospace Industry. Economic Analysis: Theory and Practice, 30, 2-11 (in Russian).
Khrustalev E.Yu., Strelnikova I.A. (2011). Methods to Reduce Financial Risk while Creating High-Tech Products. Finance and Credit, 7, 13-21 (in Russian).
Khrustalev O.E. (2011). Methodical Bases of an Estimation of Economic Stability of Industrial Enterprises. Audit and Financial Analysis, 5, 180-185 (in Russian).
Larin S.N., Khrustalev O.E. (2009). Business Incubator as an Important Component of the Innovation Infrastructure of the Region: Analysis of Foreign and Russian Practice. Regional Economy: Theory and Practice, 17, 27-33 (in Russian).
Liu P., Zhang X., Liu W. (2011). A Risk Evaluation Method for the High-Tech Project Investment Based on Uncertain Linguistic Variables. Technological Forecasting and Social Change, 78, 40-50.
Lyubushin N.P. Babichev N.E., Kozlova L.V. Account of Risk Factor in the Analysis of the Creditworthiness of the Borrower. Economic Analysis: Theory and Practice, 10, 2-7 (in Russian).
Makarov Yu.N., Khrustalev E.Yu. (2010). Mechanisms of Restructuring the Science-intensive Industries (for Example Aerospace Industry). Economics and Mathematical Methods, 46, 3, 31-42 (in Russian).
Platon V., Frone S., Constantinescu A. (2014). Financial and Economic Risks to Public Projects. Procedia Economics and Finance, 8, 204-210.
Rudzka E.R., Khrustalev E.Yu., Tsyganov S.A. (2009). Methods of Accumulation of Scientific Knowledge for Innovative Development of the Russian Economy (Experience of the Russian Foundation for Basic Research). Problems of Forecasting, 3, 134-139 (in Russian).
Slavyanov A.S. (2013). Evaluation of the Effectiveness of Methods for the Economic Protection of Investments in Innovation Projects Space Activities. Controlling, 2, 35-47 (in Russian).
Varshavsky A.E. (2011). The Problematic of the Innovation: The Main Risks. Concepts, 1-2, 82-86 (in Russian).
Varshavsky A.E., Yarkin, A.P. (2009). The Comprehensive Program of Scientific and Technological Progress of the Country in the Long Term. Concepts, 1, 22-41 (in Russian).
Vilensky P.L., Livshits V.N., Smolyak, S.A. (2015). Evaluation of Investment Projects Efficiency: Theory and Practice. Textbook. Moscow: PolyPrint Service (in Russian).

Received 26.02.2017

Panova A.A. Contracts with academic administrators and the quality of hiring in the university
Economics and mathematical methods, 2017, 53 (4), 62-74.
Anna Alekseevna Panova - Research fellow Center for Institutional Studies National Research University - Higher School of Economics; Russia, Moscow, apanova@hse.ru

Abstract. In this paper we study the influence of academic and administrative contracts on the quality of hiring in the case when the choice of an academic position is a strategic one for a professor. Successful functioning of a university requires effective hiring. Since the talent of candidates at academic market is often unobservable for the university executive, the hiring is delegated to those who are better informed. Usually the most informed agents are heads of departments. In some universities such administrative positions are permanent, while in the other universities there is a regular rotation. Moreover in higher education both short term academic contracts and tenure contracts are present. Using a game theoretical model we study the emergence of moral hazard in hiring under different contract systems. We show that professors with low level of academic talent do not want to risk their career in case of a short academic term contract. Use of a short term administrative contract in this case negatively affects their stimulus for hiring more talented candidates; hence, the development of university is hindered. It is shown that both tenure contract and long term administrative contact without a right of termination permit to mitigate this problem and result in hiring of more talented candidates. The constructed model provides a possible explanation for rotation of heads of department in some universities and for existence of practically permanent heads of department in other universities.
Keywords: tenure, academic contracts, university, job security.
JEL Classification: I23, J41, J54, L29.
The article was prepared within the framework of the Basic Research Program at the National Research University Higher School of Economics (HSE) and supported within the framework of a subsidy by the Russian Academic Excellence Project '5-100'.

REFERENCES (with English translation or transliteration)
Boyko L. (2009). An Examination of Academic Department Chairs in Canadian Universities: tes. Toronto: University of Toronto.
Boyko L., Jones G.A. (2010). The Roles and Responsibilities of Middle Management (Chairs and Deans) in Canadian Universities. In: "The Changing Dynamics of Higher Education Middle Management". Vol. 33. P. 83-102. Dordrecht: Springer Netherlands.
Carmichael H.L. (1988). Incentives in Academics: Why Is there Tenure? The Journal of Political Economy, 96, 3, 453-472.
Carroll J.B. (1991). Career Paths of Department Chairs: A National Perspective. Research in Higher Education, 32, 6, 669-688.
Dnes A., Garoupa N. (2005). Academic Tenure, Post tenure Effort, and Contractual Damages. Economic Inquiry, 43, 4, 831-839.
Finkelstein M., Iglesias K., Panova A., Yudkevich M. (2015). Future Prospects for Young Faculty Across the Academic World. In: "Young Faculty in the Twenty-First Century: International Perspectives", 321-350.
Goedegebuure L., Boer H. de (1996). Governance and Decision-Making in Higher Education. Tertiary Education and Management, 2, 2, 160-169.
Kahn C., Huberman G. (1988). Two-Sided Uncertainty and "Up-or-Out" Contracts. Journal of Labor Economics, 6, 4, 423-444.
McPherson M. S., Schapiro M. O. (1999). Tenure Issues in Higher Education. The Journal of Economic Perspectives, 13, 1, 85-98.
McPherson M. S., Winston G. C. (1983). The Economics of Academic Tenure: A Relational Perspective. Journal of Economic Behavior & Organization, 4, 2-3, 163-184.
O'Flaherty B., Siow A. (1991). Promotion Lotteries. Journal of Law, Economics, & Organization, 7, 2, 401-409.
Panova A., Yudkevich М. (2011). Tenure System in Universities: Models and Explanations. Educational Studies Moscow, 1, 44-72 (in Russian).
Panova A.A. (2015). Administrative Staff in Modern Universities: International Experience Analysis. Journal University Management: Practice and Analysis, 6, 129-138 (in Russian).
Vasin S., Reznik D., Sazykina O. (2003). The head of the department: features of a collective portrait. Sociological Studies (Socis), 6, 106-108 (in Russian).

Received 23.07.2015

Ibragimova N.M. Modeling household income and expenditure multipliers in the SAM model: estimations for Uzbekistan
Economics and mathematical methods, 2017, 53 (4), 75-88.
Naylya M. Ibragimova - Senior Researcher, Institute of Forecasting and Macroeconomic Research under the Cabinet of Ministers at the Republic of Uzbekistan; Tashkent, Uzbekistan, Nelibragimova@gmail.com

Abstract. Key objective of the government intervention into the economy is to ensure dynamic growth of GDP and employment, as well as macroeconomic stability. However, in order to meet the requirements of inclusive development, current policy challenges of macroeconomic stability should be based on the advanced approaches to macroeconomic policies using findings from relevant macroeconomic models considering long-term development sustainability and social development issues. This article discusses results of construction and application of the consolidated social accounting matrix (SAM) for the estimation of total multiplier effects in the economy. The article describes the process of compiling SAM in the framework of the national accounts methodology, provides detailed technique of the SAM matrix transformation into the multipliers system, which enable thorough examination of the relationship between economic and social development (production system and institutional sectors) basing on multipliers decomposition and predict the impact of exogenous factors on the specific household quintiles' income and consumption expenditure. The processes of multiplicative economic effects formation and distribution for three aggregate sectors are shown on the example of Uzbekistan economy.
Keywords: social accounting matrix, SAM model, multiplicative effects, income quintiles, decomposition, Uzbekistan.
JEL Classification: C82, E01, E61, O1.

REFERENCES (with English translation or transliteration)
Abdykulova G.M., Klotsvog F.N., Khairulov D.S., Khusnutdinov R.A. (1999). New Approach to the Study of Financial Flows and Cost Proportions in the Economy. Problems of Forecasting, 4, 19-26 (In Russian).
Achjar N., Hewings J.D., Sonis M. (2005). The Decomposition of Goods and Services in a Block Structural Path Analysis in the Indonesian Economy. Studies in Regional Science, 35, 257-280.
Belousov A.R., Abramova E.A. (1999). Experimental Development of Integrated Financial Flows Matrices. Statistical Issues, 7, 11-24 (In Russian).
Bottiroli C.M., Targetti L.R. (1988). The Distribution of Personal Income at the Sectoral Level in Italy: A SAM Model. Journal of Policy Modeling, 10 (3), 453-468.
Jami H.M. (2006). A SAM Based Multiplier Model to Track Growth-Poverty-Inequality Nexus in Bangladesh. Berlin: Fachhochschule Fur Technik und Wirtschaft (FHTW).
Kiringai J., Wanjala B., Thurlow J., Waiyaki N., Mutunga C., Njenga M., Nafula N., Mutua J. (2007). A 2003 Social Accounting Matrix for Kenya: Methodological note. Kenya Institute for Public Policy Research and Analysis (KIPPRA) and International Food Policy Research Institute (IFPRI). Methodological Note.
Mikheeva N.N. (1998) Macroeconomic Analysis Based on Regional Accounts. Vladivostok: Dal'nauka (In Russian).
Mikheeva N.N. (2011). Social Accounting Matrix: Research Directions and Limitations of Use. ECO Journal (Novosibirsk), 6, 103-118 (In Russian).
Parpiev Z., Yusupov K. (2011). Testing Household Economies of Scale in Uzbekistan. Eurasian Journal of Business and Economics, 4 (7), 25-51.
Pyatt G., Thorbecke E. (1976). Planning Techniques for a Better Future. Geneva: ILO.
Pyatt G., Round J. (1979). Accounting and Fixed Price Multipliers in a Social Accounting Matrix Framework. Economic Journal, 89, 356, 850-873.
Robinson S. (1988). Multisectoral Models of Developing Countries: A Survey. In: "Handbook of development Economics" H. Chenery, T.N. Srinivasan (eds.). Amsterdam: North Holland.
Round J.I. (2003). Constructing SAMs for Development Policy Analysis: Lessons Learned and Challenges Ahead. Economic System Research, 15, 2, 161-84.
Saari M.Yu., Dietzenbacher E., Los B. (2014). Income Distribution Across Ethnic Groups in Malaysia: Results from a New Social Accounting Matrix. Asian Economic Journal, 28 (3), 259-278.
Shantong L., Ying G., Jianwu H. (2004). SAM-Based Multiplier Analysis for China's Economy. Paper prepared for the XIIINFORUM World Conference.
Stork Z., Vavra M., Zavacka J. (2009). Hubert: A DSGE Model of the Czech Republic. Ministry of Finance of the Czech Republic. Working Paper 2/2009.
Stork Z. (2011). A DSGE Model of the Czech Economy: a Ministry of Finance Approach. Prague: Ministry of Finance, Czech Republic.
Sugata G., Pal S. (2004). The Effect of Inequality on Growth: Theory and Evidence from the Indian States. Review of Development Economics, 8 (1), 164-177.
Suvorov A.V. (2001). Incomes and Consumption of the Population: Macroeconomic Analysis and Forecasting. Moscow: MAKS Press (In Russian).
Thorbecke E. (2000). The Use of Social Accounting Matrices in Modeling. In: "IARIW, 26th General Conference of The International Association for Research in Income and Wealth". Cracow, Poland, 27 August. Available at: http://www.iariw.org/papers/2000/thorbecke.pdf (accessed: May 2017).

Received 04.08.2016

Skarzhinskaya E.M., Tzurikov V.I. Model of collective actions. Part 2: Leading coalition
Economics and mathematical methods, 2017, 53 (4), 89-104.
      Elena M. Skarzhinskaya - Doct. Sc. (Economics), Professor, Professor at Nekrasov Kostroma State University, Kostroma, Russia; yelena.skarzhinsky@gmail.com
      Vladimir I. Tzurikov - Cand. Sc. (Physics & Maths), Doct. Sc. (Economics), Associate professor, Professor, Kostroma State Agricultural Academy, Kostroma; tsurikov@inbox.ru

Abstract. A group of agents able to generate consolidated income by specific private investments (efforts) is considered. A strictly convex function that increases as the value of the investment of each agent increases is used as the value of the expected consolidated income. The agents are familiar with the relation of the expected income to the size of investments. At the same time, each team member pursues only the individual interests and aims to maximize his/her own gain. It is assumed that there may be a small group of agents (coalition) within a team who enjoy a fairly high level of confidence in the other team members and have no other means of influencing their behavior. In order to maximize its own gain and based on its members' chosen investment strategy, the coalition determines the distribution rule for the consolidated income for all the team members and gives them all the necessary information about this rule and the amounts of their own investments. Agents who are not members of the coalition and who consider this information reliable will accept the coalition's proposal if the amount of the expected individual gain for each agent exceeds its expected value in an alternative option in the form of the Nash equilibrium. Conditions determining the size and structure of the coalition are found within the model, and when these conditions are met, the Stackelberg equilibrium is Pareto superior to the Nash equilibrium. Connections are made between the individual characteristics of the coalition members and the integral characteristics of every team member both with the coalition size and structure, as well as with the corresponding investment amounts and the values of consolidated and individual gains.
Keywords: collective actions, specific investments, leading coalition, Stackelberg equilibrium, coordination, income distribution.
JEL Classification: C02, D23.

      REFERENCES (with English translation or transliteration)
Holmstrom B. (1982). Moral Hazard in Teams. The Bell Journal of Economics, 13, 2, 324-340.
Kapeljushnikov R.I. (2010). The Multiplicity of Institutional Worlds: The Nobel Prize in Economic Sciences-2009. Preprint WP3/2010/02 (Part 1). Moscow: NRU HSE (in Russian).
M?nard C. (2004). The Economics of Hybrid Organizations. Journal of Institutional and Theoretical Economics, 160, 3, 345-376.
Olson M. 1965. The Logic of Collective Action. Public Goods and the Theory of Groups. Cambridge: Harvard University Press.
Skarzhinskaja E.M., Tsurikov V.I. (2014). On the Efficacy of Collective Action. Russian Management Journal, 12, 3, 87-106 (in Russian).
Skarzhinskaja E.M., Tsurikov V.I. (2017). Collective Action Model. Part 1: Equilibrium, Justice, Efficiency. Economics and Mathematical Methods, 53, 2, 118 -133 (in Russian).
Williamson O.I. (1996). The Economic Institutions of Capitalism: Firms, Markets, Relational Contracting. Saint Petersburg: Lenizdat (in Russian).

Received 12.04.2016

Tomashevskii I.L. Multicriteria decision making with criteria-alternative interactions
Economics and mathematical methods, 2017, 53 (4), 105-113.
Igor' L. Tomashevskii - Cand. Sc. (Physics & Maths), Associate Professor at School of Information Technologies and Automation Systems, Northern (Arctic) Federal University; Russia, Arkhangelsk, i.tomashevskii@gmail.com

Abstract. Multicriteria decision making models need to evaluate a finite set of alternatives concerning multiple criteria and to evaluate each criteria and all the alternatives. If criteria of importance depend essentially on the alternatives then the second problem is very difficult. In this article, we propose some algorithm to obtain criteria weights from a set of local criteria weights for each alternative. This algorithm is based on criteria-alternatives interactions and derived weights as the solution of the eigenvector problem for some interaction matrix. The obtained criteria-alternatives interaction algorithm may be used to modify any original MCDM method based on an additive scalar criterion. If criteria are independent from alternatives, the criteria-alternatives interaction algorithm automatically takes the original form.
Keywords: decision analysis, MCDM, AHP, criteria weights, preference.
JEL Classification: С44, D7, D81.

REFERENCES (with English translation or transliteration)
Anokhin A.M., Glotov V.A., Pavel'ev V.V., Cherkashin A.M. (1997). Methods for Determination of Criteria Importance Coefficients. Automatika i Telemekhanika, 8, 3-35 (in Russian).
Barron F.H. (1992). Selecting a Best Multiattribute Alternative with Partial Information about Attribute Weights. Acta Psychologica, 80, 91-103.
Barzilai J., Golany B. (1994). AHP Rank Reversal, Normalization and Aggregation Rules. INFOR, 32, 57-64.
Belton V., Gear A. (1983). On a Short-Coming of Saaty's Method of Analytic Hierarchies. Omega, 11, 228-230.
Belton V., Gear A. (1985). The Legitimacy of Rank Reversal - A Comment. Omega, 13, 143-144.
Belton V., Stewart T.J. (2002). Multiple Criteria Decision Analysis: An Integrated Approach. Boston: Kluwer Academic Publishers.
Choo E.U., Schoner B., Wedley W.C. (1999). Interpretation of Criteria Weights in Multicriteria Decision Making. Computers & Industrial Engineering, 37, 527-541.
Edwards W., Barron F.H. (1994): SMARTS and SMARTER: Improved Simple Methods for Multiattribute Utility Measurement. Organization behavior and human processes, 60, 306-325.
Ehrgott M. (2005). Multicriteria Optimization. Heidelberg: Springer Berlin.
Gantmakher F.R. (1988). Theory of Matrices. Moscow: Nauka (in Russian).
Hesham K.A., Salih O.D. (2008). Assigning Cardinal Weights in Multi-Criteria Decision Making Based on Ordinal Ranking. Journal of Multi-Criteria Decision Analysis, 15, 125-133.
Hwang C.L., Yoon K. (1981). Multiple Attribute Decision Making-Methods and Applications. A State of the Art Survey. Berlin, Heidelberg, New York: Springer Verlag.
Lootsma F.A. (1999). Multi-Criteria Decision Analysis via Ratio and Difference Judgement. Dordecht: Kluwer Academic Publishers.
Lotov A.V., Pospelova I.I. (2008). Multi-Criteria Decision-Making Problems. Moscow: MAKS Press (in Russian).
Miettinen K. (1999). Nonlinear Multiobjective Optimization. Boston: Kluwer Academic Publishers.
Podinovskiy V., Potapov М. (2013). Weighted Sum Method to Analyze Multi-Criteria Decision-Making Problems: pro et contra. Business Informatics, 3, 41-48 (in Russian).
Podinovskiy V.V. (2007). Introduction to the Importance Factors Theory in Multicriteria Decision Problem. Moscow: Fizmatlit (in Russian).
Podinovskiy V.V., Nogin V.D. (2007). Pareto Optimal Solutions of Multicriteria Problems. Moscow: Fizmatlit (in Russian).
Rosenthal R.E. (1985). Principles of Multiobjective Optimization. Decision Sciences, 16, 133-152.
Saaty T. (1980). The Analytic Hierarchy Process. New York: McGraw-Hill.
Saaty T. (1994). How to Make a Decision - the Analytic Hierarchy Process. Interfaces, 24, 19-43.
Schoner B., Wedley W. (1989). Ambiguous Criteria Weights in AHP: Consequences and Solutions. Decision Sciences, 20, 462-475.
Schoner B., Wedley W., Choo E. (1993) A Unified Approach to AHP with Linking Pins. European Journal of Operational Research, 64, 384-392.
Stillwell W.G., Seaver D.A., Edwards W. (1981). A Comparison of Weight Approximation Techniques in Multiattribute utility Decision Making. Organizational Behavior and Human Performance, 28, 62-77.
Triantaphyllou E. (2002). Multi-Criteria Decision Making Methods: A Comparative Study. Boston: Kluwer Academic Publishers.
Wang Y., Luo Y. (2009). On Rank Reversal in Decision Analysis. Mathematical and Computer Modelling, 49, 1221-1229.

Received 26.09.2014

Maergoiz L.S., Khlebopros R.G. Mathematical model of optimal distribution of bonus funds
Economics and mathematical methods, 2017, 53 (4), 114-118.
      Lev S. Maergoiz - Doct. Sc. (Physics & Maths), Professor; Institute of Business Management and Economics, Siberian Federal University; Krasnoyarsk, Russia, bear.lion@mail.ru
      Rem G. Khlebopros - Doct. Sc. (Physics & Maths), Professor; Institute of Economics, Management and Environmental Studies, Siberian Federal University; International Scientific Centre of Investigations of Organism Extremal States, Presidium of Krasnoyarsk Science Centre, Siberian Branch, Russian Academy of Sciences; Russia, Krasnoyarsk

Abstract. An optimization mathematical model of the distribution of bonus funds between participants of a working collective is proposed, if there is a rating of categories of work fruits in the direction of growth of their quality, their labor-consuming nature (quality scale) and a numerical scale that characterizes the amount of work done to manufacture the products of each category (quantity scale). A description of the models based on the following principles of an optimal distribution of limited resource: the principle of proportionality inside any category; the minimization principle of the quadratic functional depending on differences ofthe resource densities for the neighboring categories according to the rating; "the direction principle". Its construction is illustrated on the example of the distribution of bonus funds in a research team. On the mathematical point of view this model does not differ from (worked out earlier) the distribution model of limited resource of social economic contents between consumers (people groups, which are under different conditions) in the presence of their rating and a numerical scale reflecting size of their needs.
Keywords: mathematical model, optimal distribution algorithm, extremal problem.
JEL Classification: А13.

      REFERENCES (with English translation or transliteration)
Gavrielets Yu.N. (1992). Compromise of Interests and Justice in Remuneration of Labour (Simulation Study). Econ. and Math. Methods, 28, 4, 16-28 (in Russian).
Gal'kova E.A., Maergoiz L.S., Khlebopros R.G. (2012). A Mathematical Algorithm of "Fair" Distribution of a Humanitarian Resource and Related Topics. Siberian Journal of Industr. Mathem., 15, 4(52), 71-77 (in Russian).
Gal'kova Ye.A., Maergoiz L.S. (2015). An Optimizational Mathematical Model of Two-Level Distribution of Limited Resources between Groups of People. Econ. and Math. Methods, 51, 3, 109-116 (in Russian).
Maergoiz L.S. (2014). Mathematical Algorithm of a "Just" Remuneration of Labour of a Research Team. In Proceedings "Mathematical Methods and Models in Investigation of Modern Economic and Social Problems". All-Russian Youth Research-to-Practice Conference, 14-15 November, 2014. Ufa: Bushkir State University. Part 1, 31-34 (in Russian).
Maergoiz L.S., Khlebopros R.G. (2014). Mathematical Algorithm of a "Just" Remuneration of Labour of a Research Team. Preprint. Krasnoyarsk: Siberian Federal University (in Russian).
Staroverov O.V., Kotel'nikova S.N. (2001). Modelling of Social and Economic Processes (Teaching Aid). Moscow: Moscow State Institute of Electronics and Mathematics (in Russian).

Received 13.09.2016