Summary

Vol. 54, No. 1

Shulgin S.G., Zinkina J.V., Andreev A.I., Korotayev A.V. Measuring country-to-country cultural distance through individual differences in values and its influence on the global trade
Economics and mathematical methods, 2018, 54 (1), 3-25.
      Sergey G. Shulgin - Cand. Sc. (Economics), Deputy director at the International Research Laboratory for Demography and Human Capital, Russian Academy of National Economy and Public Administration; Russia, Moscow, sergey@shulgin.ru
      Julia V. Zinkina - Cand. Sc. (History), Senior Research Fellow at the International Research Laboratory for Demography and Human Capital, Russian Academy of National Economy and Public Administration, Moscow, Russia; Research Fellow at the Laboratory for Monitoring the Risks of Socio-Political Destabilization, National Research University - Higher School of Economics; Russia, Moscow, juliazin@list.ru
      Alexey I. Andreev - Cand. Sc. (Biology), Deputy Dean at the Faculty of Global Processes, Moscow State University named after M.V. Lomonosov; Russia, Moscow, andreev@fgp.msu.ru
      Andrey V. Korotayev - Doctor Sc. (History), Professor, Head of the Laboratory for Monitoring the Risks of Socio-Political Destabilization, National Research University - Higher School of Economics, Moscow, Russia; Leading Researcher at the International Research Laboratory for Demography and Human Capital, Russian Academy of National Economy and Public Administration; Russia, Moscow, akorotayev@gmail.com

Abstract. The paper proposes a method for measuring the country-to-country cultural distance. This method is based on the analysis of the differences in values of individuals residing in these countries. These differences are assessed through an innovative ensemble of five metrics (Mahalanobis distance, Euclidean distance, L-distance, as well as normalized versions of Euclidean and L-distances), - the MELNN ensemble, compiled through factor analysis. For each individual we find "neighbors in values", i.e. other individuals with possibly closest MELNN scores. We proceed to build a network interaction model on the basis of MELNN scores so that we could differentiate between the "neighbors in values" of different orders (direct neighbors, neighbors' neighbors etc.). Analyzing the closeness of each individual from any single country to the individuals from different countries eventually allows to define the cultural distance between these countries. We use the obtained values of country-to-country cultural distances in a gravity model, where they prove it to be a significant factor influencing the structure of bilateral trade.
Keywords: global trade; values; world value survey; cultural distance; neighbors in values; metrics ensemble; MELNN; Mahalanobis distance; Euclidean distance; L-distance; gravity model.
JEL Classification: F14, F60.
This study was supported by the Russian Science Foundation (project 15-18-30063).

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Anderson J.E. (1979). A Theoretical Foundation for the Gravity Equation. The American Economic Review, 69, 1, 106-116.
Bergstrand J.H. (1985). The Gravity Equation in International Trade: Some Microeconomic Foundations and Empirical Evidence. The Review of Economics and Statistics, 67, 3, 474-481.
Bergstrand J.H. (1989). The Generalized Gravity Equation, Monopolistic Competition, and the Factor-Proportions Theory in International Trade. The Review of Economics and Statistics, 71, 1, 143-153.
Butayeva K.O., Weber S., Davydov D.V. (2016). Language, Culture, Migration, Conflicts: Economic Projection. Vestnik Moskovskogo Universiteta. Seriya 6: Ekonomika, 1, 3-21 (in Russian).
Cyrus T.L. (2012). Cultural Distance and Bilateral Trade. Global Economy Journal, 12, 4, 1-25.
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Drogendijk R., Slangen A. (2006). Hofstede, Schwartz, or Managerial Perceptions? The Effects of Different Cultural Distance Measures on Establishment Mode Choices by Multinational Enterprises. International Business Review, 15, 4, 361-380.
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Grafarend E.W. (2006). Linear and Nonlinear Models: Fixed Effects, Random Effects, and Mixed Models. Berlin, New York: Walter de Gruyter.
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Kaasa A., Vadi M., Varblane U. (2016). A New Dataset of Cultural Distances for European Countries and Regions. Research in International Business and Finance, 37, 231-241.
Kandogan Y. (2012). An Improvement to Kogut and Singh Measure of Cultural Distance Considering the Relationship Among Different Dimensions of Culture. Research in International Business and Finance, 26, 2, 196-203.
Kirkman B.L., Lowe K.B., Gibson C.B. (2006). A Quarter Century of Culture's Consequences: A Review of Empirical Research Incorporating Hofstede's Cultural Values Framework. Journal of International Business Studies, 37, 3, 285-320.
Santis G. de, Maltagliati M., Salvini S. (2014). How Close? An Attempt at Measuring the Cultural Distance between Countries. Working Papers. Warsaw: Institute of Statistics and Demography. Warsaw School of Economics.
Shenkar O. (2001). Cultural Distance Revisited: Towards a More Rigorous Conceptualization and Measurement of Cultural Differences. Journal of International Business Studies, 32, 3, 519-535.
Tadesse B., White R. (2010). Does Cultural Distance Hinder Trade in Goods? A Comparative Study of Nine OECD Member Nations. Open Economies Review, 21, 2, 237-261.
Thomson G.H. (1951). The Factorial Analysis of Human Ability. London: London University Press.
Tinbergen J. (1962). Shaping the World Economy; Suggestions for an International Economic Policy. New York: Twentieth Century Fund. VanDerWal, J, Falconi, L., Januchowski, S., Shoo, L., and Storlie, C. (2014). SDM Tools: Species Distribution Modelling Tools: Tools for Processing Data Associated with Species Distribution Modelling Exercises. R-package version 1.1-221. Available at: http://CRAN.R-project.org/package=SDMTools (accessed: July 2016).
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Weber S., Gabzhevich D., Ginzburg A.I., Ginzburg V., Savvateyev A.V., Filatov A.Yu. (2009). Linguistic Diversity and Its Influence on Economic and Political Decisions. Journal of the New Economic Association, 3-4, 28-53 (in Russian).
Zinkina J.V., Shulgin S.G., Korotayev A.V. (2016). Evolution of Global Networks: Patterns, Trends, Models. Moscow: Lenand (in Russian).

Received 28.07.2016

Dementiev V.E., Evsukov S.G., Ustyuzhanina E.V. Pricing model in the market for network goods in terms of duopolistic competition
Economics and mathematical methods, 2018, 54 (1), 26-42.
      Viktor E. Dementiev - Сorrespondent member of Russian Academy of Sciences, Doct. Sc. (Economics), Professor, Central Economics and Mathematics Institute, Russian Academy of Sciences, Deputy Director, Russia, Moscow; vedementev@rambler.ru
      Sergey G. Evsukov - Cand. Sc. (Economics), Central Economics and Mathematics Institute, Russian Academy of Sciences, senior researcher, Russia, Moscow; sg 7777@yandex.ru
      Elena V. Ustyuzhanina - Doct. Sc. (Economics), Plekhanov Russian University of Economics, Head of the Department, Russia, Moscow; dba-guu@yandex.ru

Abstract. The article is devoted to analyzing peculiarities of pricing in the markets for network goods. Such markets are usually oligopolies. This is due to the double economies of scale: when the size of the network increases, the consumer value of such a good rises whereas cost per unit falls. As a result, the singularity of pricing in the market for network goods is the interdependence of prices, demand, the achieved size of a network and consumer values. On the basis of the model of a duopoly, we consider the distribution of the effect of the output of new network goods between generator and imitator. Generator is an agent, who offers to the market a fundamentally new product, imitator is an agent, who may quickly reproduce innovation. The peculiarities of the proposed model include taking two types of investment (direct and precautionary) as well as the scale of the consumer value into consideration. The dynamic of changes in the value of a good is a logistic function where the dependent variable is the number of consumers (instead of time). Generator has to take into account the threat of entering the market imitator, since the outcome time of the imitator affect the amount and distribution of total benefit. That is why generator is beneficial at the stage of formation of network to set low prices for products. The low price in the initial period let to increase quickly the growing demand for a network good. The lower this price in the initial period, the sooner it is possible to increase the growing demand for a network good. This may mean that the imitator will fail to receive a large share of the benefits.
Keywords: network goods, pricing, duopoly, sunk costs, indirect costs, generator, imitator.
JEL Classification: D46, G30, C12.
The article was prepared with the financial support of RFBR (project 17-06-00080) "The comparative analysis of pricing strategies at the network markets based on the economic and mathematical modelling".

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Afanasyeva K.E., Shiryaev V.I. (2007). Prediction of Regional Mobile Communication Markets. Problems of forecasting, 5, 97-105 (in Russian).
Antipina O.N. (2009). Theoretical Bases of Pricing in the Markets for Information Goods and Technologies. Problems of the new economy, 4, 12-22 (in Russian).
Bass F.A. (1969). New Product Growth Model for Consumer Durables. Management Science, 15, 89-113.
Cabral L.M.B., Salant D.J., Woroch G.A. (1999). Monopoly Pricing with Network Externalities. International Journal of Industrial Organization, 17, 199-214.
Chen J. (2016). How Do Switching Costs Affect Market Concentration and Prices in Network Industries? The Journal of Industrial Economics, 64, 2, 226-254.
Christensen K. (2015). The Innovator's Dilemma. As for New Technologies Die Strong Company. M.: Alpina Publisher (in Russian).
Dementiev V.E. (2008). The Advancing Strategy in Conditions of Oligopoly Competition in the Markets for New Products. Theory and Practice of Institutional Transformations in Russia. Moscow: CEMI, Russian Academy of Sciences, 10, 5-10 (in Russian).
Economides N., Himmelberg Ch. (1995). Critical Mass and Network Size with Application to the US FAX Market. Discussion Paper EC-95-11. Stern School of Business. N.Y.: New York University.
Fligstein N. (2013). The Architecture of Markets. Economic Sociology of Capitalist Societies of the XXI Century. Moscow: Publishing house "National Research University - Higher School of Economics" (in Russian).
Fudenberg D., Tirole J. (2000). Pricing a Network Good to Deter Entry. The Journal of Industrial Economics, 48, 4, 373-390.
Goolsbee A., Klenow P.J. (2000). Evidence on Learning and Network Externalities in the Diffusion of Home Computers. NBER Working Paper, W7329.
Katz M. L., Shapiro C. (1986). Technology Adoption in the Presence of Network Externalities. The Journal of Political Economy, 94, 4, 822-841.
Kucharavy D., Guio R. de (2007). Application of S-Shaped Curves. TRIZ-Future Conference 2007: Current Scientific and Industrial Reality. Nov. 2007. Frankfurt, 81-88.
Litwin N.D., (2003). Modeling of Price Discrimination in e-Commerce. Proceedings of the Far Eastern State Technical University, DFU, 135, 89-98 (in Russian).
MacKie-Mason J.K., Varian H.R. (1995). Pricing Congestible Network Resources. IEEE Journal on Selected Areas in Communications, 13, 7, 1141-1149.
Makarov V.L. (2002). About Mathematical Models of Competition between Enterprises. Economic Science of Modern Russia, 1, 5-9 (in Russian).
Onkar S.G., Sigarev A.S., Ustyuzhanina E.V. (2016). Model of Dynamic Pricing of Network Goods in a Monopoly Provider. Financial Analytics: problems and solutions, 30 (312), 2-18 (in Russian).
Pleschinskiy A.S. (2017). Analysis of Competition and Cooperation in the Development of Technological Innovation in Manufacturing Industries. Economics and Mathematical Methods, 3, 38-58 (in Russian).
Pleschinskiy S.A., Zhiltsova E.S. (2013). Analysis of the Results of Modernization of Production in Conditions of Oligopoly Competition the Innovator and his Pursuer. Economics and Mathematical Methods, 1, 88 -105 (in Russian).
Saaskilahti P. (2016). Buying Decision Coordination and Monopoly Pricing of Network Goods. Journal of Economics & Management Strategy, 25, 2, 313-333.
Semenychev V.K., Korobetskaya A.A. (2012). The Product Life Cycle Model Based on a Fractional-Rational Trend with Arbitrary Asymmetry. Economics and Mathematical Methods, 48, 3, 106-112 (in Russian).
Sigarev A.V. (2016). Online Shopping. Features of Pricing in Electronic Markets. The Modern Economy: Concepts and Models of Innovative Development. Materials of VIII International scientific-practical conference, REU them. G.V. Plekhanov, 121-125 (in Russian).
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Ulph D., Vulkan N. (2000). Electronic Commerce and Competitive First-Degree Price Discrimination. UCL and University of Bristol, February.

Received 02.08.2017

Aivazian S.A., Afanasiev M.Yu., Kudrov A.V. The method of comparing the regions using the technical efficiency estimates with account of production structure
Economics and mathematical methods, 2018, 54 (1), 43-51.
      Sergei A. Aivazian - Deputy Director, Central Economic and Mathematics Institute of the Russian Academy of Sciences, Moscow, Russia; aivazian@cemi.rssi.ru
      Mikhail Yu. Afanasiev - Head of Laboratory, Central Economic and Mathematics Institute of the Russian Academy of Sciences, Moscow, Russia; miafan@cemi.rssi.ru
      Aleksander V. Kudrov - Senior Research Fellow, Central Economic and Mathematics Institute of the Russian Academy of Sciences, Moscow, Russia; kovlal@inbox.ru

Abstract. The author propose the method of ranking the regions' economy using the technical efficiency estimates. It is assumed that such estimates can be theoretically justified using the production capacity model constructed for a group of regions with homogeneity properties. At the same time, technical efficiency evaluations are not comparable for the regions from different homogeneous groups. It is quite natural to build a common model for all the regions to obtain comparable estimates. However, the ranks of the estimates of technical efficiency for the regions of a certain group obtained from such a model do not necessarily correspond to the ranks of estimates obtained from the group model. In this case, the ranking of all the regions by estimates of the general model is not entirely correct. The method presented in this paper makes it possible, with the usage of the optimization model, to obtain corrected estimates that are minimally different from those obtained from the general model, whose ranks correspond to the ranks of the estimates obtained from group models. Based on the adjusted estimates, the main problem is solved - general rating is constructed, corresponding to the ratings of the regions of each homogeneous group.
Keywords: regional economy, econometric modeling, stochastic frontier, technical efficiency estimation.
JEL Classification: C12, C51, R15.
The work was supported by the Russian Science Foundation (project 17-18-01080).

      REFERENCES (with English translation or transliteration)
Aivazian S.A., Afanasiev M.Yu. (2014). Development of Production Capacity on the Basis of the Stochastic Frontier Concept: Methodology and Results of Empirical Analysis. Moscow: KRASAND (in Russian).
Aivazian S.A., Afanasiev M.Yu., Kudrov A.V. (2016a). Models of Productive Capacity and Technological Efficiency Evaluations of Regions of the Russian Federation Concerning the Output Structure. Economics and Mathematical Methods, 52, 1, 28-44 (in Russian).
Aivazian S.A., Afanasiev M.Yu., Kudrov A.V. (2016b). Clusterization of Russian Regions Based on the Industry Production Structure. Applied Econometrics, 41, 24-46 (in Russian).
Aivazian S.A., Fantaccini D. (2014): Econometrics-2. Moscow: Infra-M (in Russian).

Received 03.05.2017

Kovalenko A.G. In search of equilibrium state at the spatial dispersed markets with imperfect competition of a uniform product
Economics and mathematical methods, 2018, 54 (1), 52-68.
      Alexey G. Kovalenko - Doctor of physical and mathematical sciences, Professor, Associate professor, Federal public autonomous educational institution of the higher education "Samara national research university under the name of the academician S.P. Korolev", Samara; alexey.gavrilovich.kovalenko@rambler.ru

Abstract. The author analyzes the dispersed economic systems - dispersed markets. Subjects of these markets are producers, consumers and dealers of a uniform product. Goods from the producer reach consumers by means of a commodity-money exchanges. Models of the dispersed markets with the perfect competition are described as the systems of the nonlinear equations of the theory hydraulic networks. To create the models of the imperfect competition subjects at the markets are described as extreme tasks. Balance ratios of an exchange (balance condition) of the subjects are also described by extreme tasks. We receive the new network game - a theoretical task unknown earlier. It describes interaction of the subjects both in the local markets of knots of a network, and between the subjects of markets of various knots. Changing leaders of exchange at the local markets, we receive a full range of structures of interaction of the economic system subjects' - from the markets of perfect competition to the markets of centralized management. Algorithms of search of equilibrium state are given for the structures in concern. Implementation of these the algorithms for the computer gives the tool to analyze the specific economic systems of the considered type.
Keywords: structures of the single-product spatial dispersed market, the imperfect competition of the dispersed markets, network tasks of the theory of games, models and methods of search of conditions of balance.
JEL Classification: L13.

      REFERENCES (with English translation or transliteration)
Galperin V.M. Ignatyev S.M., Morgunov V.N. (2000). Microeconomics. General edition by Galperin V.M. Saint Petersburg: Economic school (in Russian).
Hachаturov V.R., Solomatin A.N., Zlotov A.V., Bobylev V.N., Veselovskii V.E., Kovalenko A.G., Kosachev Yu.V. et al. (2015). Planning and Design of Development of Oil and Gas Extraction Regions and Fields: Mathematical Models, Methods, Application. Khachaturov V.R. (ed.). M.: URSS:LENAND (in Russian).
Kleyner G.B. (2015). The State - the Region - Branch - the Enterprise: Framework of System Stability of Economy of Russia. Part 1. Economy of Region, 2, 50-58 (in Russian).
Kovalenko A.G. (1990). Elements of Convex Vector Programming. Kuibyshev: Kuibyshev state university (in Russian).
Kovalenko A.G. (1999). About Mathematical Modeling of the Dispersed Market. Economics and Mathematical Methods, 35, 3, 108-115 (in Russian).
Kovalenko A.G. (2001). Mathematical Models of Interindustry Balance in the Conditions of the Dispersed Market. Economics and Mathematical Methods, 37, 2, 92-106 (in Russian).
Kovalenko A.G. (2012). To a Question of Interrelation of the Dispersed Market Decentralized Multigrocery Spatial and the Centralized Management of this Economic System. Magazine of the economic theory, Russian Academy of Sciences, Office of social sciences, economy Section, 3, 148-154 (in Russian).
Kovalenko A.G. (2013). Mathematical Models and Methods of the Analysis of the Dispersed Markets. Development of mathematical models and methods of the theory of hydraulic networks, methods of optimization and multicriteria analysis. Saarbr?cken: Palmarium Academic Publishing (in Russian).
Kovalenko A.G., Hachаturov V.R, Kalimoldayev M.N. (2012). Models of the Dispersed Market of the Imperfect Competition: Problems of their Development, Application in Management of Regional Economy. Problem of Informatics, 4, 18-23 (in Russian).
Makarov V.L. (1999). Computable Model of the Russian Economy (RUSEC). Preprint WP/99/069. Moscow: TSEMI RAS (in Russian).
Merenkow A.P., Khasilew W.Ya. (1985). Theory of Hydraulic Circuits. Moscow: Nauka (in Russian).
Nikaido H. (1972). Convex Structures and Economic Theory. The Institute of Social and Economic Research. Osaka University, Osaka, Japan. New York, London: Academic Press (in Russian).
Polterovich V.M. (1998). Crisis of the Economic Theory. Economic Science of Modern Russia, 1, 46-66 (in Russian).
Ponkin E.V., Manicheva A.S. (2010). Imitating Modeling of the Dispersed, Multiagent Market of Grain. The Bulletin of Novosibirsk State University, 2, 8, 54-64 (in Russian).
Tirole J. (1988). The Theory of Industrial Organization. Cambridge: MIT.
Vasin A.A. Vasina P.A. (2004). Markets and Auctions of Uniform Goods. Preprint. Moscow: NES (in Russian).

Received 26.09.2016

Marakulin V.M. Perfect competition without Slater condition: the equivalence of non-standard and contractual approach
Economics and mathematical methods, 2018, 54 (1), 69-91.
      Valeriy M. Marakulin - Doctor Sc. (Physics & Maths.), Assistant professor, Institute of Mathematics named after Sobolev, Siberian Branch of the Russian Academy of Sciences, Novosibirsk State University, Novosibirsk, Russia; marakulv@gmail.com

Abstract. In the neoclassical Arrow-Debreu model under the conditions of perfect competition every allocation from the core allows price decentralization, i.e. it is an equilibrium allocation. Moreover, espetially in the conditions, under which the core and equilibria coincise and are called perfect competition. However, in all the known models of perfect competition the theorem of the core coincidence and equilibria is proved exclusively under the survival assumption, which implies that Slater's condition for consumer's problem is fulfilled. How important is this additional requirement and what will happen if it is discarded? The paper is addressing this problem. The classical Debreu-Scarf approach is analyzed and is compared with the contractual model of perfect competition developed early by the author. It is shown that the most accurate model of this is provided by the contractual approach; namely, this is a concept of fuzzy contractual allocation which provides stability with respect to the signing of a new contract and an asymmetric partial break of already existing ones. Under weak assumptions, it is proved that these allocations coincide with those with nonstandard prices. In this case implemented allocations generally are different from the elements of the classical core in perfect competition conditions (Edgeworth equilibria). However, in the case when model assumptions (indecomposability) provide the survival assumption for non-standard equilibria, the contractual approach coincides with the classical one.
Keywords: equilibrium with random prices, survival assumption (Slater condition), perfect competition, fuzzy core, fuzzy contractual allocations, Edgeworth equilibria.
JEL Classification: C62, D51.

      REFERENCES (with English translation or transliteration)
Aliprantis C.D., Brown D.J., Burkinshaw O. (1989). Existence and Optimality of Competitive Equilibria. Berlin, New York: Springer-Verlag.
Anderson R.M. (1992). Non-Standard Analysis with Applications to Economics. In: Hildenbrand W., Sonnenschein H. (eds.). "Handbook of Mathematical Economics". Vol. IV. Amsterdam: North-Holland, 2145-2208.
Aumann R.J. (1964). Markets with a Continuum of Traders. Econometrica, 32, 1-2, 39-50.
Brown D.J., Robinson A. (1975). Nonstandard Exchange Economies. Econometrica, 43, 41-55.
Davis M. (1977). Applied Nonstandard Analysis. New York: Wiley.
Debreu G., Scarf H.E. (1963). A Limit Theorem on the Core of an Economy. International Economic Review, 4, 235-246.
Hildenbrand W. (1974). Core and Equilibria of a Large Economy. Princeton/New Jersey: Princeton University Press.
Konovalov A.V., Marakulin V.M. (2006). Equilibria without the Survival Assumption. Journal of Mathematical Economics, 42, 198-215.
Loeb P.A. (2000). An Introduction to Non-Standard Analysis. In: Loeb P.A., Wolff M. (eds.) "Nonstandard Analysis for the Working Mathematician". Dordrecht: Kluwer Academic Publishers.
Marakulin V.M. (1988). An Equilibrium with Nonstandard Prices and Its Properties in Mathematical Models of Economy. Preprint No. 18. Novosibirsk: IM SB of USSR Academy of Sciences (in Russian).
Marakulin V.M. (2011). Contracts and Domination in Competitive Economies. Journal of the New Economic Association, 9, 10-32 (in Russian).
Marakulin, V.M. (2012). An Abstract Equilibrium Analysis of Economic-Mathematical Models. Novosibirsk: SB Russian Academy of Science Publisher (in Russian).
Marakulin V.M. (2013). On the Edgeworth Conjecture for Production Economies with Public Goods: A Contract-Based Approach. Journal of Mathematical Economics, 49, 3, 189-200.
Marakulin V.M. (2014). On Contractual Approach for Arrow-Debreu-McKenzie Economies. Economics and Mathematical Methods, 50 (1), 61-79 (in Russian).
Rashid S. (1987). Economies with Many Agents: An Approach Using Nonstandard Analysis. Baltimore: Johns Hopkins University Press.

Received 29.03.2017

Malakhov D.I., Pilnik N.P., Radionov S.A. Correcting the system of balance sheets as a basis of general economic equilibrium models
Economics and mathematical methods, 2018, 54 (1), 92-109.
      Dmitrii I. Malakhov - Master of Economics, National Research University Higher School of Economics, Faculty of Economic Sciences, Department of Applied Economics, Lecturer, Intern Researcher; Russia, Moscow, d.malakhow@gmail.com
      Nikolai P. Pilnik - Cand. Sc. (Economics), National Research University Higher School of Economics, Faculty of Economic Sciences, Department of Applied Economics, Assistant Professor; Senior Researcher, Dorodnicyn Computing Centre, RAS, Researcher; Russia, Moscow, u4d@yandex.ru
      Stanislav A. Radionov - Cand. Sc. (Economics), National Research University Higher School of Economics, Faculty of Economic Sciences, Department of Applied Economics, Intern Researcher, Lecturer; Dorodnicyn Computing Centre, RAS, Junior Researcher; Russia, Moscow, saradionov@edu.hse.ru

Abstract. The article analyzes one of the specific reasons for the low accuracy of the overall economic equilibrium models: the discrepancy model balances their statistical counterparts. We consider three types of balance sheet ratios: financial balance, balance sheet and profit and loss balance. Relation between these balances is described by such variables as "own capital" and "retained earnings". A method by which one can solve the problem in conscious disregard of the model of statistical variables, while maintaining the validity of the balance sheet ratios, is proposed. It is shown that due to the introduction of a model of a small number of additional variables, it is possible to adapt the sometimes excessively detailed statistics for a particular model and its system of indicators, so that at the model level and balance equality is persisted. In the model of a firm-manufacturer (part of general equilibrium model) it is shown that it is possible to restore the entire system of balance sheet ratios, containing information on the cash flow statement, revaluation and balance sheet accounts at the proper recording of financial balance sheets in the model. In the presented model, a firm maximizes the utility of dividend flow at basic prices by controlling the trajectories of output, investment, cash balances, the volume of accumulated debt and currency reserves. Optimal firm behavior is described by a system of differential and algebraic equations, as well as the complementary slackness conditions resulting Lagrangian functional variation on the primal and dual variables. It is shown how important is the transformation of the financial balance in the equation of the dynamics of the company's net assets.
Keywords: general equilibrium, model of the firm, description of the production, financial balance, balance sheet.
JEL Classification: С68.
The study was carried out with the financial support of the Russian Science Foundation (project 14-11-00432).

      REFERENCES (with English translation or transliteration)
Andreev M., Vrzheshch V.P., Pilnik N., Pospelov I., Khokhlov M., Zhukova A., Radionov S. (2014). Intertemporal General Equilibrium Model of Russian Economy Based on National Accounts Desagregation. Journal of Mathematical Sciences, 197, 2, 175-236.
Christiano L.J., Eichenbaum M., Evans C.L. (2005). Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy. Journal of political Economy, 113, 1, 1-45.
Gerali A., Neri S., Sessa L., Signoretti F.M. (2010). Credit and Banking in a DSGE Model of the Euro Area. Journal of Money, Credit and Banking, 42, s1, 107-141.
Gertler M., Karadi P. (2011). A Model of Unconventional Monetary Policy. Journal of monetary Economics, 58, 1, 17-34.
Gertler M., Kiyotaki N. (2010). Financial Intermediation and Credit Policy in Business Cycle Analysis. Handbook of monetary economics, 3, 11, 547-599.
Pilnik N.P., Pospelov I.G. (2009). Описание целей деятельности фирмы в динамической модели общего равновесия. Moscow: VTs RAN (in Russian).
Pilnik N.P., Pospelov I.G., Radionov S.A., Zhukova A.A. (2014). The Intertemporal General Equilibrium Model of the Economy with the Product, Money and Stock Markets. International Journal of Computational Economics and Econometrics, 4, 1-2, 207-233.
Pilnik N.P., Stankevich I.P. (2015). Dynamic Model of the Interaction of the Firm and Its Owners. Mathematical Models and Computer Simulations, 27, 1, 65-83 (in Russian).
Pospelov I.G. (2001). Economic Agents and Systems of Balances. Preprint WP2/2001/03 Seria WP2 "Quantitative analysis of the economy". Moscow: National Research University Higher School of Economics (in Russian).
Pospelov I.G. (2003). Models of Economic Dynamics, Based on the Balance of Forecasts of Economic Agents. Moscow: VTs RAN (in Russian).
Pospelov I.G., Pospelova I.I., Khokhlov М.А., Shipulina G.E. (2006). New Principles and Methods of Development of Macro Models of the Economy and a Model of Modern Russian Economy. Moscow: VTs RAN (in Russian).

Received 02.03.2016

Kurmanova S.M. System analysis of discounting function properties in stationary and non-stationary economies
Economics and mathematical methods, 2018, 54 (1), 110-119.
      Sataney M. Kurmanova - post-graduate student, Federal Research Center "Computer science and Control" of RAS, Institute of System Analysis; Russia, Moscow, satanei8989@mail.ru

Abstract. The article is devoted to the system analysis of discounting methods in economic and financial systems under various macroeconomic environments. Appropriate definitions of stationarity and non-stationarity are given. For the first time the immanent properties and corresponding models of the time factor influence on financial flows in stationary and non-stationary conditions are considered. The most common methods of time factor accounting for simple and complex percentages are analyzed; the correctness of the compound interest and the mismatch of the simple percentage method to a number of specified required properties is proved. Mathematical formalization models of the indicated properties of weighting (discounting) functions are given. Theorems on the invariance, ranking of stationary financial systems on a discounting time base are proved. A number of statements (theorems) are developed; they are useful for analyzing the dynamics of financial flows distributed over time and may be used in assessing the comparative effectiveness of alternative investment projects with different immanent dynamics of financial flows.
Keywords: stationary and non-stationary economies, financial systems, time factor, weighting function, discounting function.
JEL Classification: C02, G02, G11, G17.

      REFERENCES (with English translation or transliteration)
Baturina N.A. (2009). Historical Aspects of the Discount Rate Genesis. Economist's guide, 9, 127-136 (in Russian).
Endovitsliy D.A. (2001). Complex Analysis and Control of Investment Activities. Moscow: Finansy i statistika (in Russian).
Ershov E.B. (2011). Situational Theory of Price Index and Quantity. Moscow: RNOR (in Russian).
Kantorovich L.V. (1959). Economic Calculation of the Best Use of Resources. Moscow: AS USSR edition (in Russian).
Livchits V.N. (1984). Optimization in Planning and Design. Moscow: Ekonomika (in Russian).
Livchits V.N. (2013). System Analysis of the Non-Stationary Economy of Russia (1992-2013). Moscow: LENAND (in Russian).
Livchits V.N., Livchits S.V. (2010). System Analysis of the Non-Stationary Economy of Russia (1992-2009): Market Reforms, Crisis, Investment Policy. Moscow: PoliPrintServis (in Russian).
Newell A., Shaw J.C., Simon H.A. (1964). A Variety of Intelligent Learning in a General Problem Solver. In: "Self-Organizing Systems". Moscow: Mir (in Russian).
Prokhorov Y.V., Rosanov Y.А. (1973). Calculus of Probabilities. Moscow: Nauka, Fizmatlit (in Russian).
Pugachev V.F. (1968). Optimization of Planning (Theoretical Problems). Moscow: Ekonomika (in Russian).
Samuelson P.A., Nordhaus W.D. (1997). Economics. Moscow: Binom-Kio-Rus (in Russian).
Samuelson Paul A. (2002). Foundations of Economic Analysis. St. Petersburg: Economic School (in Russian).
Smolyak S.A. (2002). Evaluation of the Investment Projects Effectiveness under Risk and Uncertainty (the Theory of the Expected Effect). Moscow: Nauka (in Russian).
Smolyak S.A. (2006). Discounting Cash Flows in the Tasks of Evaluation of the Investment Projects Effectiveness and the Value of the Property. Moscow: Nauka.
Vilenskiy P.L., Livchits V.N., Smolyak S.A. (2015). Evaluation of the Investment Projects Effectiveness: Theory and Practice: Work book. М.: PoliPrintServis (in Russian).
Zhevnyak A.V. (2010). Mathematical Theory of Discounting Cash Flows. Mathematical Theory of Credit. Ryazan': Rinfo (in Russian).

Received 11.03.2017

Baljabin V.A., Zaslavsky A.A. Construction of regular paired comparisons matrix. Results of calculating experiments
Economics and mathematical methods, 2018, 54 (1), 120-124.
      Victor A.Baljabin - magister, Moscow Power Energetic Institute, Russia, Moscow, viktorbalyabin@mail.ru
      Alexey A. Zaslavsky - Ph.D (Techn.), senior researcher, Central Economic and Mathematics Institute, Russian Academy of Sciences, Russia, Moscow; zasl@cemi.rssi.ru

Abstract. The construction of transitive matrix closest to the given one is a traditional problem of paired comparisons analysis. But the condition of transitivity seems to be too strong for paired comparisons with draws. Earlier the authors proposed to use the condition of regularity, which is the weakening of the transitivity. Note that, in contrast to the traditional problem, any theoretical results allowing to find a regular matrix closest to the given one are not known. Hence the research and the analysis of heuristic algorithms for this problem are of interest. Several algorithms based on quantitative assessment of non-regularity proposed by the authors and the results of calculating experiments are discussed in the paper. The most effective of proposed algorithms solves the problem for matrices by 3 minutes, and so can be used in the paired comparisons analysis.
Keywords: paired comparisons, transitivity, regularity, distances matrix.
JEL Classification: C02.

      REFERENCES (with English translation or transliteration)
David H.A (1949). The Method of Paired Comparisons. Chapel Hill: Univ. of North Carolina.
Gil'burd М. М. (1988). On Heuristic Methods of Obtaining the Median in Group Choice Problem. Automation and Remote Control, 7, 131-136 (in Russian).
Kemeny J.G., Snell J.L.(1963). Mathematical Method in the Social Sciences. New York: Blaisdell.
Prigarina T.A., Chebotarev P.Yu. (1989). Methods of Expert Estimations by the Example of the Preference Detecting Problem. Working paper. M.: CEMI (in Russian).
Zaslavskii A.A. (2007). Geometry of Paired Comparisons. Automation and Remote Control, 3, 181-186 (in Russian).
Zaslavskii A.A. (2014). New Approaches for Analysis of Paired Comparisons. Economics and mathematical methods, 50, 3, 130-133 (in Russian).
Zaslavskii A.A., Frenkin B.R. (2009). Mathematics of Tournavents. Moscow: MCCME (in Russian).
Zaslavskiy A.A., Shevlyakova A.N. (2010). Geometric Method for Analysis of Paired Comparisons. Computational Experiment. MPEI Bulletin, 6, 5-12 (in Russian).

Received 03.07.2017

Sigal A.V. About the effectiveness of portfolios found using the game-theoretic method
Economics and mathematical methods, 2018, 54 (1), 125-144.
      Anatoliy V. Sigal - Doct. Sc. (Economic), Associate Professor, Professor at Department of Business-Informatics and Math Modeling, V.I. Vernadsky Crimean Federal University. Institute of Economics and Management; Russia, Simferopol, ksavo3@gmail.com

Abstract. The article discusses the features, advantages and disadvantages of using the concept of the combined application of statistical and antagonistic games to determine the portfolio structure in different information situations that has the lowest level of economic risk. Special attention is given to substantiation of the appropriateness of game-theoretic methods for finding the portfolio structure, which has the lowest level of economic risk, and to the substantiation of the effectiveness of portfolios, the structure of which is found using the game-theoretic method. The essence of the combined application of statistical and antagonistic games lies in identification of the initial statistical game modeling a management decisions with an antagonistic game, whose payoff matrix coincides with the payoff matrix of the initial statistical game. In the article, antagonistic games are defined as finite matrix games, i.e. games of two persons with zero-sum. Statistical and antagonistic games have the same formal structure. This fact gives the theoretical and practical options to apply combinations of statistical and antagonistic games. Under certain circumstances, solving the corresponding antagonistic game leads to finding the structure of the portfolio that has the lowest level of risk (under certain conditions, for any valid probability distribution of the economic environment states).
Keywords: statistical game, antagonistic game, information situation, portfolio structure, economic risk, portfolio effectiveness.
JEL Classification: C720.

      REFERENCES (with English translation or transliteration)
Blackwell D., Girshick M.A. (1958). Theory of Game and Statistical Decisions. Moscow: Inostrannaja literature (in Russian).
Livchits V.N., Sigal A.V. (2014). On Entropy Analysis of Transitional Economy. Economics and Mathematical Methods, 50, 3, 86-104 (in Russian).
Markowitz H.M. (1952). Portfolio Selection. Journal of Finance, March, 7, 1, 77-91.
Markowitz H.M. (1959). Portfolio Selection: Efficient Diversification of Investments. N.Y.: John Wiley & Sons.
Neumann J. von, Morgenstern O. (1944). Theory of Games and Economic Behavior. Princeton: Princeton Univ. Press.
Neumann J. von (1928). Zur Theorie der Gesellschaftsspiele. Mathematische Annalen, 100, 295-320.
Sigal A.V. (1998a). Fundamentals of the Modern Portfolio Theory of the Securities. Simferopol: Crimean Economic Institute of the Kyiv National Economic University (in Russian).
Sigal A.V. (1998b). The Application of the Theory of Games in the Portfolio Theory. Machine Information Processing 61. Kiev: Kiev National Economic University, 154-160 (in Ukrainian).
Sigal A.V. (2014). Theory of Games for Decision-Making in Economics. Simferopol: DIAIPI (in Russian).
Sigal A.V. (2015). Combined Application of Statistical and Antagonistic Games in Portfolio Theory. Audit and Financial Analysis, 6, 91-112 (in Russian).
Syudseter K., Strem A., Berck P. (2000). Mathematical Handbook for Economists. St.-Petersburg: Economic School (in Russian).
Trukhaev R.I. (1981). Models of Decision-Making in Conditions of Uncertainty. Moscow: Nauka (in Russian).
Vorobyov N.N. (1985). Theory of Games for Economists-Cybernetics. Moscow: Nauka (in Russian).
Wald A. (1945). Statistical Decision Functions which Minimize the Maximum Risk. Ann. of Math., 46, 265-280.
Wald A. (1949). Statistical Decision Functions. Ann. Math. Statist., 20, 2, 165-205.
Wald A. (1950). Statistical Decision Functions. N.Y.: John Wiley & Sons.
Wald A. (1960). Sequential Analysis. Moscow: Fizmatgiz (in Russian).

Received 12.05.2016

Vol. 54, No. 2

Central Economics and Mathematics Institute RAS - 55

N.A. Trofimova Per aspera ad astra. CEMI is 55
Economics and mathematical methods, 2018, 54 (2), 3-19.
      Natalia A. Trofimova - Cand. Sc. (Economics), Associate Professor, Leading scientific researcher, Central Economics and Mathematics Institute, Russian Academy of Sciences, Nakhimovskii prospekt, B. 47, Moscow, 117418, Russia; nataly_trofimova@mail.ru

Abstract. The article is devoted to the study of the history of creation and analysis of the scientific activity of the CEMI RAS. The main goal of the CEMI RAS was the introduction of mathematical methods and computer technology into the practice of management and planning, the creation of a theory of optimal management of the national economy. The article analyzes the main stages in the development of the scientific activity of the Institute, it is emphasized that the whole history of the Institute's activity is the history of the struggle for the modernization of the national science, the introduction of the newest methods for solving the main social and economic tasks. The main point of the article - characteristics of the main directions of scientific activity both of the Institute and its Divisions. The main scientific research of CEMI is, and will be, computer and mathematical modeling of both the society as a whole and the economy itself, including models of artificial societies, computable models of general economic equilibrium and their practical use in making economic and political decisions at all levels of the national economy. The article concludes that CEMI has everything necessary for effective work in new conditions.
Keywords: CEMI Academy of Sciences of the USSR, CEMI RAS, system of optimal economic functioning, social modeling, digital economy, N.P. Fedorenko, V.L. Makarov.
JEL Classification: C02, B31, A12.
DOI: 10.7868/S0424738818020012
The author is grateful to Academician V.L. Makarov and Dr. Sc. A.A. Afanasiev for help and useful comments in the preparation and writing of this jubilee article.

      PUBLICATIONS ABOUT CEMI RAS (AS USSR):
Fedorenko N.P. (1999). Remembering the Past, Looking to the Future. Moscow: Science.
Kutateladze S.S., Makarov V.L., Romanovsky I.V. (2001). Scientific Heritage of L.V. Kantorovich (1912-1986). Siberian Journal of Industr. Math., 4(2), 3-17.
On the other Side of the Moebius Strip (2013). The First Book. Moscow: CEMI RAS.
CEMI - 50 Years (2013). (CEMI and EMM - 50 Years Together). Economics and Mathematical Methods, 49(4), 3-4;
Anniversary booklet "CEMI-50" (2013). Saint Petersburg: Nestor-History.
Katsenelinboygen A.I. (2007). About Time. About People. About Myself. Moscow: Hermitage Publishers.

Received 12.12.2017

Academician Valery L. Makarov Scientific School
Economics and mathematical methods, 2018, 54 (2), 20-28.
DOI: 10.7868/S0424738818020024

Afanasiev А.А., Vorontsov А.А. Modified computable general equilibrium model of the Russian economy with the gas industry RUSEC - PAO "GAZPROM"
Economics and mathematical methods, 2018, 54 (2), 29-49.
      Anton А. Afanasiev - Doct. Sc. (Economics), Professor at National Research University - Higher School of Economics (NRU-HSE) in 2011-2017; Leading Researcher, Central Economics and Mathematics Institute, Russian Academy of Sciences, Nakhimovskii prospekt, 47, 117418 Moscow, Russia, aanton@cemi.rssi.ru
      Aleksandr A. Vorontsov - master program 1st year student at Faculty of Computer Sciences, National Research University - Higher School of Economics (NRU-HSE); Kochnovskii proezd, 3, 125319 Moscow, Russia aavorontsov@edu.hse.ru

Abstract. Forecasting the key macroeconomic indicators and evaluating their variance, influenced by a change in natural monopolies' tariffs is the key priority of any country. Computable general equilibrium (CGE) models are used for economical processes modeling and predicting macroeconomic indexes. CGE model of RUSEC-GAZPROM was designed in 2003 by CEMI RAS to estimate an impact of home natural gas prices change on key Russian macroeconomic indicators. The main purpose of this article is to show a modification of the initial version of RUSEC-GAZPROM by specifying economical agents' behavior. This modification will allow researchers to investigate how the changes in home natural gas prices affect Russian macroeconomic indicators when gas production volumes are endogenous. There is a description of initial RUSEC-GAZPROM model, and its modification - RUSEC - PAO "GAZPROM" - as well as the description of model calibration process. The research also shows the experiments made with the modified model, which demonstrate a reaction of the main Russian macroeconomic indicators on the change in home gas prices. The result of this research contains the modified version of RUSEC-GAZPROM and completed experiments with it. Modified RUSEC-GAZPROM model may be useful to Gazprom corporation, its subsidiaries and the Russian Government to find an effective strategy of regulating natural monopolies' tariffs.
Keywords: CGE model, Russian economy, gas industry, Gazprom, internal natural gas prices, macroeconomic indicators, experiments, scenario calculations.
JEL Classification: C53, L71, Q35, Q41, Q47.
DOI: 10.7868/S0424738818020036
The article was based on the results of a bachelor's degree thesis performed in the spring of 2017 at the National Research University "Higher School of Economics" by the fourth-year bachelor student of the Faculty of Business and Management Alexander A. Vorontsov under the scientific supervision of the University Professor, Doctor of Economic Sciences Anton A. Afanasyev. This study carried with the financial support from 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)
Afanasiev А.А. (2013). Modelling of Money Circulation Processes in the Economy with the Gas Industry. Moscow: CEMI RAS (in Russian).
Chernavskii S. (2015). Reform in the Russian Power Sector: Achievements and Failures. In: "Report to the 27th European Conference on Operation Research: Area Game, Theory, Mathematical Economics: Mathematical Models in Macro- and Microeconomics". Glasgow. University of Strathclyde.
Chernavskii S., Eismont O. (2012). How to Sell Russian Gas to Europe Via Ukraine. OPEC Energy Review, 36, 1, 87-103.
Chernavskii S.Ya. (2010). Anti-Crisis Measures and Modernization of the Energy Sector. In: Polterovich V.M. (ed.) "The strategy of modernization of the Russian economy". Saint Petersburg: Aleteiya, 356-419 (in Russian).
Chernavskii S.Ya. (2011). The Market of Associated Petroleum Gas in Russia. In: Kleiner G.B. (ed.) "Mesoeconomics of Development." Moscow: Nauka, 108-137 (in Russian).
Chernavskii S.Ya. (2012). Institutional Trajectory of the Development of Associated Petroleum Gas Markets in Russia. In: Yasin E.G. (ed.) "XIII April International Scientific Conference on the Problems of Development of the Economy and Society". Book 1. Moscow: HSE Publ., 540-550 (in Russian).
Chernavskii S.Ya. (2012). Russia's Gas Market: Reforming Trends. Journal of the New Economic Association, 4 (16), 157-160 (in Russian).
Chernavskii S.Ya. (2013). Reforms in the Regulated Sectors of the Russian Energy Industry. Moscow, Saint Petersburg: Nestor-Istoriya (in Russian).
Chernavskii S.Ya. (2013). The Problems of Increasing the Efficiency of the Russian Gas Industry. EKO, 8 (470), 57-78 (in Russian).
Chernavskii S.Ya. (2014). Successes and Failures of the Russian Energy Market Reforms. Journal of the New Economic Association, 3, 165-168 (in Russian).
Chernavskii S.Ya. (2015). Successes and failures of reforming the Russian energy sector. In: "Proceedings of the Open Seminar Economic Problems of the Energy Complex". Moscow: INP (in Russian).
Chernavskii S.Ya. (2016). Problems of Increasing Overall Efficiency in the Russian Gas Sector. Problems of Economic Transition, 58, 2, 142-161.
Chernavskii S.Ya., Eismont O.А. (2010). Is Russia Favored by the Gas Cartel (on the Example of the European Gas Market)? Journal of the New Economic Association, 1-2, 127-149 (in Russian).
Katyshev P.K., Chernavskii S.Ya., Eismont O.А. (2012). Estimation of the Cost Function of Electricity Production in Russia. In: "XII International Scientific Conference on the Problems of Development of the Economy and Society". Book 4. Moscow: HSE Publ., 120-130 (in Russian).
Katyshev P.K., Peresetsky A.A., Chernavskii S.Ya., Eismont O.А. (2004). The Impact of Higher Tariffs on Natural Gas and Electricity on the Russian Economy. In: Yasin E.G. (ed.) "Competitiveness and modernization of the economy". Book 1. Moscow: HSE, 250-268 (in Russian).
L'vov D.S., Chernavskii S.Ya. (2000). On the Reform of the Electric Power Industry in Russia. Economic Science of Contemporary Russia, 2, 53-60 (in Russian).
Makarov V.L. (1999). Computable General Equilibrium Model of Russian Economy. Moscow: CEMI RAS (in Russian).
Makarov V.L., Afanasiev et al. (2003). Evaluation of the Impact of Gas Prices on the Main Macroeconomic Indicators of the Russian Economy. In: Chernavsky S.Ya. (ed.) "Analysis of price elasticity of demand for natural gas in Russia: Report" 2 edition. Moscow: CEMI RAS (in Russian).
Makarov V.L., Afanasiev А.А., Losev А.А. (2011). Computable Simulation Model for Money Circulation in the Russian Economy. Economics and Mathematical Methods, 47, 1, 3-27.
Makarov V.L., Chernavskii S.Ya., Eismont O.А. (2014). Reforming the Russian Electric Power Industry: Theory and Practice. In: Petrakov N.Ya. (ed.) "Modernization and Economic Security of Russia". Vol. 4. Moscow, Saint Petersburg: Nestor-Istoriya, 53-77 (in Russian).
Makarov V.L., Filkin M.Ye., Tsveta'eva Z.N., Chernavskii S.Ya. (2016). Design and Analysis of Reforms in the Russian Energy Sector. In: "Modernization and Economic Security of Russia". Vol. 6. Moscow, Saint Petersburg: Nestor-Istoriya, 154-206 (in Russian).

Received 21.11.2017

Red'ko V.G., Sokhova Z.B. A model of interaction between investors and producers in a transparent economic system
Economics and mathematical methods, 2018, 54 (2), 50-61.
      Vladimir G. Red'ko - Doct. Sc. (Physics and Mathematics), PhD, Deputy Director of Center of Optical Neural Technologies of Scientific Research Institute for System Analysis, Russian Academy of Sciences; Nakhimovskiy prospekt, 36, build. 1, Moscow, 117218, Russia; vgredko@gmail.com
      Zarema B. Sokhova - Junior Researcher at Scientific Research Institute for System Analysis, Russian Academy of Sciences; Nakhimovskiy prospekt, 36, build. 1, Moscow, 117218, Russia; zarema_s@mail.ru

Abstract. The paper presents a model of transparent economic system, economic community that consists of investors and producers. There is information exchange between investors and producers. The model describes effective distribution of capital by the investors. Each investor takes into consideration activity of other investors. The investors and producers exchange information about their capital, intentions, and profit; this information is open for all community members. The information exchange makes the possibility to create a decentralized system of interaction within the community of investors and producers. The iterative process is an important element of the model. The iterative process helps each investor to take into account decisions of other investors. The model was investigated by means of computer simulation. The results of computer simulation demonstrate the effective interaction of investors and producers in the economic community. The iterative process was thoroughly investigated. At each iteration, any investor informs producers about its intention to invest a certain capital in one or another producer. Producers take into account these intentions at recalculation of their capitals. It is shown that the iterative process converges after a sufficiently large number of such iterations. It is also shown that the presence of iterations can lead to more effective cooperation in the economic community than similar cooperation, but without iterations.
Keywords: investors, producers, competition, information exchange in economic community, iterative process, decentralized system, collective behavior.
JEL Classification: С63.
DOI: 10.7868/S0424738818020048
This work was partially financially supported by the Russian Foundation for Basic Research (project 16-01- 00223).
The authors sincerely thank the leaders of the scientific seminars Sergey Malkov and Igor Pospelov for the opportunity to discuss first versions of this paper at seminars. The authors thank the anonymous reviewer for useful comments that helped to improve the paper.

      REFERENCES (with English translation or transliteration)
Bakhtizin A.R. (2007). Hybrid of Agent Based Model with 5 Income Groups of Households and CGE Model of Russian Economy. Artificial Societies, 2, 2, 30-75 (in Russian).
Burkov V.N., Danev В., Yenaleev A.K., Naneva Т.В., Podval'nyi L.D., Yusupov B.S. (1988). Competition Mechanisms in Allocation of Limited Resources. Automation and Remote Control, 11, 142-153 (in Russian).
Burkov V.N., Novikov D.F. (1999). The Theory of Active Systems: Status and Prospects. Moscow: Sinteg (in Russian).
Burtsev M.S., Turchin P.V. (2006). Evolution of Cooperative Strategies from First Principles. Nature, 440, 1041-1044 (in Russian).
Claes R., Holvoet T., Weyns D. (2011). A decentralized Approach for Anticipatory Vehicle Routing Using Delegate Multiagent Systems. IEEE Transactions on Intelligent Transportation Systems, 12, 2, 364-373.
Holvoet T., Valckenaers P. (2007). Exploiting the Environment for Coordinating Agent Intentions. In: "Environments for Multi-Agent Systems III. Lecture Notes in Artificial Intelligence". Berlin: Springer, 4389, 51-66.
Polterovich V.M. (2015). From Social Liberalism Towards the Philosophy of Collaboration. Social Sciences and Modernity, 4, 41-64 (in Russian).
Polterovich V.M. (2016). Positive Collaboration: Factors and Mechanisms of Evolution. Russian Journal of Economics, 3, 1, 24-41 (in Russian).
Red'ko V.G., Burtsev M.S., Sokhova Z.B., Beshlebnova G.A. (2007). Modeling Competition with Evolution of a Multi-Agent System. Artificial Societies, 2, 2, 76-89 (in Russian).
Tsetlin M.L. (1969). Automaton Theory and Modeling of Biological Systems. Moscow: Nauka (in Russian) (Tsetlin M.L. (1973). Automaton Theory and Modeling of Biological Systems. New York: Academic Press (English edition)).
Varshavsky V., Pospelov D. (1988). Puppets without Strings. Moscow: Mir Publishers (English edition).
Varshavsky V.I. (1973). Collective Behavior of Automata. Moscow: Nauka (in Russian).

Received 03.02.2017

Aivazian S.A., Brodsky B.E. Retrospective analysis of structural changes in SEM (simultaneous equation) models with varying structure. Part 1.
Economics and mathematical methods, 2018, 54 (2), 62-70.
      Sergei A. Aivazian - Doctor of Science Physics-Mathematics, Deputy Director Central Economics and Mathematics Institute, Russian Academy of Sciences, Nakhimovskii prospekt, B. 47; Moscow, 117418, Russia; aivazian@cemi.rssi.ru
      Boris E. Brodsky - Doctor of Science Physics-Mathematics, Head of Lab. Central Economics and Mathematics Institute, Russian Academy of Sciences, Nakhimovskii prospekt, B. 47, Moscow, 117418, Russia; bbrodsky@yandex.ru

Abstract. This article is devoted to the study of the problem of retrospective analysis of structural changes in SEM (simultaneous equation) models with varying structure. We consider main assumptions about statistical dependence of observations: strong mixing and -weak dependence conditions, as well as the main criteris for effectiveness of a method of retrospective analysis. A new nonparametric method of retrospective detection of structural changes is proposed which does nor require knowledge about distributuinal laws of data and its statistical properties are studied. We formulate theorems about convergence to zero of type 1 and type 3 error probabuilities for the proposed method with an increasing sample size. Results of the simulation sudy of the proposed method are given in the second part of the paper. Unlike earlier published papers, this article considers the problem of macroeconometric modeling with account of structural changes in data. Here we consider the method for the retrospective detection of multiple structural changes in data, simulation study of this method, as well as applications to the problems of macroeconometric modeling with account of structural changes in data. In particular, we consider the macromodel of the USA economy proposed by L. Klein (the structural change in the year 1929 is detected) and the disaggregated model of the Russian economy (quarterly data in 1995-2016s). Here we detect two instants of structural changes in 2002 and 2010. Results of the simulation study wittness about the fact that the proposed method can effectively detect structural chsnges in SEM models.
Keywords: SEM model, econometric analysis, retropective method, structural change, type 1 error, type 2 error.
JEL Classification: C30, C51.
DOI: 10.7868/S042473881802005X
This study was supported by the Russian Foundation for Basic Research (project 15-01-03359).

      REFERENCES (with English translation or transliteration)
Aivazian S.A. (1959). A Comparison of Optimal Properties of the Neuman-Pearson and the Wald Sequential Probability Ratio Test. Theory of Probability and Its Applications, 4, 86-93 (in Russian).
Andrews D.W.K. (1993). Tests for Parameter Instability and Structural Change with Unknown Change Point. Econometrica, 61, 821-856.
Andrews D.W.K., Ploberger W. (1994) Optimal Tests When a Nuisanse Parameter Is Present Only under the Alternative. Econometrica, 62, 1383-1414.
Ango Nze P., Doukhan P. (2004). Weak Dependence. Models and Applications in Econometrics. Economic Theory, 20, 995-1045.
Bai J., Lumsdaine R., Stock J. (1998). Testing for and Dating Common Breaks in Multivariate Time Series. Review of Economic Studies, 65, 395-432.
Bradley R. (2005). Basic Properties of Strong Mixing Conditions. A Survey and Some Open Questions. Probability Surveys, 2, 107-144.
Brodsky B.E. (2006). Retrospective Analysis of Structural Changes in Econometric Models. Economics and Mathematical Methods, 46, 4 (in Russian).
Brodsky B.E., Darkhovsky B.S. (2000). Non-Parametric Statistical Diagnosis. Problems and Methods. Dordreht: Kluwer Academic Publishers.
Brodsky, B.E., Darkhovsky B.S. (1993). Non-Parametric Methods in Change-Point Problems. Dordrecht: Kluwer Academic Publishers.
Brown R.L., Durbin J., Evans J.M. (1975). Techniques for Testing the Constancy of Regression Relationships over Time. Journal of Royal Statistical Society, Series B, 37, 149-192.
Chu C., Stinchcombe M., White H. (1996). Monitoring Structural Change. Econometrica, 64, 1045-1065.
Cs?rg? M., Horv?th L. (1988). Invariance Principles for Change-Point Problems. J. of Multivar. Analysis, 27, 151-168.
Cs?rg? M., Horv?th L. (1997). Limit Theorems in Change-Point Analysis. Chichester: Wiley.
Doukhan P., Louhichi S. (1999). A New Weak Dependence Condition and Applications to Moment Inequalities. Stochastic proceses and their Applications, 84, 313-342.
Girshick M.A., Rubin H. (1952). A Bayes Approach to a Quality Control Model. Ann. Math. Statist, 23 (1), 114-125.
Hinkley D.V. (1969). Inference about the Intersection in Two-Phase Regression. Biometrika, 56 (3), 495-504.
Klein L. (1950). Economic Fluctuations in the United States 1921-1941. Cowles Foundation. New York: John Wiley.
Maddala G., Kim I. (1998). Unit Roots, Cointegration, and Structural Change. Cambridge: Cambridge Univ. Press.
Page E.S. (1955). A Test for a Change in a Parameter Occuring at an Unknown Point. Biometrika, 42, 523-526.
Petrov V.V. (1972). Sums of Independent Random Variables. Moscow: Nauka (in Russian).
Ploberger W., Kramer W. (1992). The CUSUM Test with OLS Residuals. Econometrica, 60, 271-285.
Ploberger W., Kramer W., Kontrus K. (1989). A New Test for Structural Stability in the Linear Regression Model. Journal of Econometrics, 40, 307-318.
Shiriayev A.N. (1963a). On Optimal Methods in Sequental Detection Problems. Theory of probability and its applications (TPA), 8, 26-51 (in Russian).
Shiryaev A.N. (1961). Detection of Spontaneous Effects. Doklady USSR, 135, 799-201 (in Russian).
Shiryaev A.N. (1963b). Detection of Change-Points in Technological Process, I. Theory of probability and its applications (TPA), 8, 3, 264-381 (in Russian).
Shiryaev A.N. (1963c). Detection of Change-Points in Technological Process, II. Theory of probability and its applications (TPA), 8, 4, 431-443 (in Russian).
Shiryaev A.N. (1965). Some Precise Formulas in Change-Point Problems. Theory of probability and its applications (TPA), 10, 2, 380-385 (in Russian).
Tartakovsky A.G., Nikiforov I., Basseville M. (2014). Sequential Analysis: Hypothesis Testing and Change-Point Detection. N.Y.: CRC Press. Zacks S. (1983). Survey of Classical and Bayesian Approaches to the Change-Point Problem. Recent Advances in Statistics. N.Y, 245-269.
Zeileis A., Leisch F., Kleiber C., Hornik F. (2005). Monitoring Structural Change in Dynamic Econometric Models. Journal of Applied Econometrics, 20, 99-121.

Received 29.06.2017

Kurochkin S.V. Dynamic features of the Treynor-Black model
Economics and mathematical methods, 2018, 54 (2), 71-88.
      Sergey V. Kurochkin - Cand. Sc. (Mathematics), Associate professor, Federal Research Centre "Computer Science and Control" of Russian Academy of Sciences, Dorodnicyn Computing Centre, Russia, Senior researcher; National Research University - Higher School of Economics, Associate professor, Russia, Moscow; skurochkin@hse.ru, kuroch@ccas.ru

Abstract. The Treynor-Black (TB) model seems to be the first active portfolio managenent model to give the direct answer to the problem of how a portfolio manager should incorporate analysts' estimates in her/his portfolio structure. Concerning the assets' returns probabilities distributions W. Sharpe Diagonal Model was taken here as an assumption. In this article I analyze the qualitative dynamics of the stock market under the dynamic version of the TB model, assuming all the investors apply the TB model to their portfolios. A similar assumption is made in CAPM, where market stability and pricing relations are deduced supposing all investors have equal access to information and use Modern Portfolio Theory in their portfolio decisions. I also show, how one should recalculate analysts' target prices to alphas in TB model. The study of the related dynamic system reveals that the TB model produces stable pricing only for the big companies: about 10% market capitalization and more. These findings are then compared to the empirical data on market/target (the latter according to analysts' consensus forecasts) prices for the Russian Blue Chips. It turns out that actual price dynamics usually shows steady gaps between target and market price while the model price should increasingly oscillate around the target. The likely interpretation is: the market does not trust analysts' forecasts.
Keywords: portfolio management, Treynor-Black model, dynamic system, stability.
JEL Classification: G11.
DOI: 10.7868/S0424738818020061

      REFERENCES (with English translation or transliteration)
Black F., Litterman R. (1992). Global Portfolio Optimization. Financial Analysts Journal, 48, 5, 28-43.
Bodie Z., Kane A., Marcus A. (2014). Investments. N.Y.: McGraw Hill.
Bradshaw M., College B., Huang A. (2013). Analyst Target Price Optimism around the World. Midwest Finance Association 2013 Annual Meeting Paper. Available at: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2137291 (accessed: April 2017).
Cvitanic J., Lazrak A., Martellini L., Zapatero F. (2006). Dynamic Portfolio Choice with Parameter Uncertainty and the Economic Value of Analysts' Recommendations. The Review of Financial Studies, 19, 4, 1113-1156.
Damodaran A. (2016). Investment Valuation. M.: Alpina (in Russian).
Fama E. (1965). The Behavior of Stock Market Prices. Journal of Business, 38, 34-105.
Katok A., Hasselblatt B. (2005). A First Course in Dynamics. M.: MCCME (in Russian).
Kurochkin S.V. (2014). If the Go Away. What Well Be Russian Stock Market in the Absence of Foreign Investors? Rynok tsennyh bumag, 8, 57-59 (in Russian).
Moscow Exchange (2014). MICEXINDEXCF index. Available at: http://www.moex.com/ru/index/MICEXINDEXCF/constituents/ (accessed: April 2017, in Russian).
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Sberbank (2017). Dividends. Official Site. Available at: http://www.sberbank.com/ru/investor-relations/share-profile/dividends (accessed: April 2017, in Russian).
Standard and Poors (2017). S&P 500. Available at: http://us.spindices.com/indices/equity/sp-500 (accessed: April 2017).
Stowe J., Robinson T., Pinto J., McLeavy D. (2002). Analysis of Equity Investments: Valuation. N.Y.: Wiley and Sons.
Treynor J., Black F. (1973). How to Use Security Analysis to Improve Portfolio Selection. Journal of Business, 46, 1, 66-86.
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Zhongzhi H. (2007). Incorporating Alpha Uncertainty into Portfolio Decisions: A Bayesian Revisit of the Treynor-Black Model. Journal of Asset Management, 8, 3, 161-175.

Received 15.02.2017

Gol'shtein E.G., Malkov U.H., Sokolov N.A. Hybrid method for solving bi-matrix games
Economics and mathematical methods, 2018, 54 (2), 89-103.
      Evgeny G. Golshtein - chief researcher, doctor of physico-mathematical Sciences, prof., Central Economics and Mathematics Institute, Russian Academy of Sciences, Nakhimovskii prospekt, B. 47, Moscow, 117418, Russia; golshtn@cemi.rssi.ru
      Ustav H. Malkov - leading researcher, candidate of physico-mathematical Sciences, Central Economics and Mathematics Institute, Russian Academy of Sciences, Nakhimovskii prospekt, B. 47, Moscow, 117418, Russia; malkov@cemi.rssi.ru
      Nikolay A. Sokolov - leading researcher, candidate of physico-mathematical Sciences, Central Economics and Mathematics Institute, Russian Academy of Sciences, Nakhimovskii prospekt, B. 47, Moscow, 117418, Russia; sokolov@cemi.rssi.ru

Abstract. In order to find optimal mixed strategies of a bi-matrix game one can use the approximate algorithm for solving bi-matrix games (2LP-algorithm) and/or the Lemke-Howson algorithm (LH-algorithm). When solving a bi-matrix game the 2LP-algorithm provides finding the global minimum of the Nash function by processing (numerous) local minima of the same function. The point is that every successive (alternating) minimization of this function with respect to one of the two variables (while the other variable is fixed) can be easily reduced to a linear programming problem. By making use of a trial of the initial pure strategies and solving two linear programs at each iteration the 2LP-algorithm either establishes the game's exact solution (if a complementarity slackness condition holds) or finds an approximation to the set of Nash points (when the complementarity slackness condition is slightly broken). The algorithm is very easy to implement, however, it loses its efficiency whenever the payoff matrices are scarce and/or (mutually) linearly dependent on each other. On the contrary, the LH-algorithm reduces the bi-matrix game to the solution of a related linear equations system. Starting from the basis of the unit vectors, the method makes simplex-type steps aiming to decrease the number of broken complementarity slackness conditions. As a rule (but not always) the algorithms finds the exact solution of the game. The proposed hybrid method uses the LH-algorithm to re-optimize an approximate solution produced by the 2LP-algorithm starting with the basis of the latter. The efficiency of the Lemke-Howson algorithm and the proposed hybrid approach has proved to be about the same. Moreover, the hybrid method has managed to find exact solutions to several test games for which both the 2LP- and LH-procedures failed.
Keywords: bi-matrix games, convex structures, pure strategies, mixed strategies, Nash points, Nash function, complementarity slackness condition, Lemke-Howson algorithm, hybrid method.
JEL Classification: C02, C72.
DOI: 10.7868/S0424738818020073

      REFERENCES (with English translation or transliteration)
Golshtein E.G., Malkov U.H., Sokolov N.A. (2013). A Numerical Method for Solving Bimatrix Games. Economics and Mathematical Methods, 49, 4, 94-104.
IBM ILOG CPLEX Optimization Studio (2011). Available at: http://www-03.ibm.com/software/products /ru/ibmilogcpleoptistud, свободный. Загл. с экрана. Яз. англ. (дата обращения: июль 2017 г.).
Lemke C.E., Howson J.T. jr. (1964). Equilibrium Points of Bimatrix Games. Journal of the Society for Industrial and Applied Mathematics, 12, 778-780.
MATLAB (2012). The Language of Technical Computing. Available at: http://www.mathworks.com/products /matlab/, свободный. Загл. с экрана. Яз. англ. (дата обращения: июль 2017 г.).

Received 24.05.2017

Istratov V.A. The goal-structure approach to qualitative valuation
Economics and mathematical methods, 2018, 54 (2), 104-126.
      Victor A. Istratov - Cand. Sc. (Economics), Leading researcher, Central Economics and Mathematics Institute, RAS, Nakhimovskii prospekt, B. 47, Moscow, 117418, Russia; Saint-Petersburg State University, Researcher, Universitetskaya naberezhnaya, B. 7-9, Saint-Petersburg, 199034, Russia; istratov@cemi.rssi.ru

Abstract. The author analyses qualitative valuation: while being frequently used in economic literature, very little attention is paid to the study of qualitative estimates themselves. As a consequence, qualitative assessments are often inconvenient to use because of the vagueness of their wording, which, in turn, generates discrepancies and misunderstandings. In addition, the ambiguity of the wording leads to the impossibility of comparing qualitative estimates, or substantially limits this possibility. Both ambiguity and incomparability are detrimental to the prospects for qualitative valuation as a scientific tool. In the current situation, it is necessary to develop a unified formulation approach (a language) to qualitative assessments to make them unambiguous and comparable. The author makes an attempt to formalize and standardize the presentation of qualitative values, and to find a method for their submission and formulation that differs from those already available. The article contains an overview of the approaches to qualitative assessments adopted in several areas of knowledge that are close to the computational economy and simulation modeling: in particular, in the economics, in artificial intelligence, and the others. The approach proposed in the article takes into account the goals with which a qualitative estimate is used. It involves the interpretation of a qualitative assessment as a complex element which structure plays the key role in understanding and applying the value. Qualitative assessment in this approach is not opposed to quantitative, and in some cases they are combined. The proposed approach may be useful in computer simulation of human behavior and socio-economic interactions.
Keywords: qualitative value, quality, economic valuation.
JEL Classification: A10, Y80.
DOI: 10.7868/S0424738818020085

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Received 04.05.2017

Vol. 54, No. 4

Nikonova A.A. Evolution of innovation mode within economic dynamics
Economics and mathematical methods, 2018, 54 (4), 3-28.
Affiliation: Central Economics and Mathematics Institute, Russian Academy of Science, Moscow, Russia; E-mail: prettyal@cemi.rssi.ru
The article was prepared with the financial support of the Russian Foundation for Humanities (since 2016 - Russian Fund for Basic Research) (project 15-02-00229(a)).

Abstract. We demonstrated how the models of creation knowledge and technology had been changing while manufacturing was transformed. The key factors and structure models to innovate were investigated in the context of economic and technological dynamics. The arguments were given for the modern generation of innovation models to support paramount importance of such driving forces as knowledge, motivated actors, skillful organization, and innovative culture. Fundamental requirements from the side of the new economy have been formulated for such models as well as in relation to Russia. Character of the contemporary innovation wave, as well as the global structural and economic shifts and crisis in the world economy define the directions of innovation strategy and organization and economic mechanisms to regulate innovation activity. According to the system economic theory, which was developed in CEMI RAS, methodology and ways to control innovation should be chosen adequately the peculiarities of the socio-economic and scientific-technical dynamics, taking into account external factors and internal features of economic systems at macro, meso and micro level. Based on the results of the analysis of contemporary scientific-technological and economic trends and findings of leading home and foreign researchers, we proposed the design for the special model to generate innovation on the base of innovation ecosystem concept. We proposed several measures to implement such mode in the Russian economy taking into consideration regulatory and economics uncertainty.
Keywords: new technology, knowledge, market, management, communication, collaboration.
JEL Classification: O32.
DOI: 10.31857/S042473880003316-6

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The Global Innovation Index 2015 (2015). Geneva: Cornell University, INSEAD, WIPO, 2015. Available at: file:///C:/Users/ПК/Downloads/gii-full-report-2015.pdf (accessed: April 2017).
The Global Innovation Index 2017 (2017). Geneva: Cornell University, INSEAD, WIPO, 2017. Available at: file:///C:/Users/ПК/Downloads/gii-full-report-2017.pdf (accessed: July 2017).
Wessner С.W. (2004). Entrepreneurship and the Innovation Ecosystem. Policy Lessons from the United States, 2004. Available at: http://papers.econ.mpg.de/egp/discussionpapers/2004-46.pdf (accessed: April 2017).

Pitelin A.K. On the fair scale of progressive taxation
Economics and mathematical methods, 2018, 54 (4), 29-40.
Affiliation:Central Economics and Mathematics Institute, Russian Academy of Sciences; Russia, Moscow, E-mail: pitel@cemi.rssi.ru

Abstract. This article concerns some problems associated with the progressive taxation of personal incomes. The main focus of the paper is the development of progressive tax scale meeting the principle of justice. The taxes are considered fair, if all the taxpayers have been withdrawn the same proportion of utility from their earnings. The utility of money spent for consumption, which is characterized by marginal utility decrease, is meant. This utility is presented in the article by the logarithmic function, which arguments are the ratios of incomes of the citizens to the subsistence level. The particular way of building smooth tax functions satisfying the above formulated rule of fair taxation is proposed. It is proved, that the implementation of such functions requires just progressive taxation. And, after that, a procedure of forming multi-layered scales approximating these smooth tax functions is also presented. A few concrete examples of fair progressive scales are shown. A curious fact is marked that the scale of the progressive income tax adopted in France with good accuracy corresponds to the proposed methodology. In the final part of the article some rules for application of such scales taking into account citizen's marital status are shortly discussed, as well as some other questions relating to the possible transition from the currently used in Russia flat scale to a progressive scale of taxation of personal incomes.
Keywords: taxpayers, income, subsistence level, utility function, justice, progressive taxation, multi-layered scale.
JEL Classification: D63, H20, H21.
DOI: 10.31857/S042473880003317-7

      REFERENCES (with English translation or transliteration)
Graborov S.V. (2015). Majority Optimization of Taxes, Transfers, Prices and Wages. Economics and Mathematical Methods, 53, 2, 80-96 (in Russian).
Graborov S.V. (2015). Optimization of Budget Incomes and Expenses by Majority Rule. Working Paper # WP/2011/286. Moscow: CEMI RAS (in Russian).
Graborov S.V., Pitelin A.K. (2017). Majoritarion Optimality of Direct and Indirect Taxation on Citizens. Economics and Mathematical Methods, 53, 2, 24 - 39 (in Russian).
Persson T., Tabellini G. (2000). Political Economics: Explaining Economic Policy. London: The MIT Press.
Rawls J. (1995). A Theory of Justice. Issued by Novosibirsk University (in Russian).
Roemer J. (1999). The Democratic Political Economy of Progressive Income Taxation. Econometrica, 67, 1, 1-19.

Borodin K.G. Assessing the impact of food embargoes and economic sanctions on the commodity markets (the example of meat markets)
Economics and mathematical methods, 2018, 54 (4), 41-59.
Affiliation: All-Russian Institute of Agrarian Problems and Informatics after A.A. Nikonov, The Federal Research Center for Agrarian Economics and Social Development of Rural Territories - VNIIESH, Russia, Moscow; E-mail: borkg_cd@mail.ru

Abstract. The author developed a method allowing to quantify the consequences of the embargo and sanctions on the commodity markets, the basis of which was a partial equilibrium model. Other methodological components - geometrical interpretation of winning (loosing) producers and consumers, as well as the regression equations, allowing to determine the price of producers in the forecast period. The method has been tested on the meat markets (beef, pork, poultry). Estimates were made of changes in foreign trade, prices of producers and consumers, the dynamics of production, loss of budget, the losses of producers and consumers. The results showed that the markets with a high dependence on imports under the influence of the embargo and sanctions in the welfare of losing more than the markets with less dependence. The strongest pressure in these conditions domestic producers are experiencing in the beef market. Pork producers benefited from the rise in prices, but consumers suffered, as well as the budget from a sharp reduction in revenues in the form of import duties. Poultry market showed good stability and welfare under the embargo and sanctions due to the high competition, mainly between the large enterprises. The difference between the proposed method and those known earlier is that studies are usually limited to assessments of changes in foreign trade, while in this paper the author made a complex analysis. In addition, relevant estimates were obtained for producer and consumer prices, production dynamics, budget losses by source, winnings (losses) for producers and consumers.
Keywords: embargo, food imports, sanctions, consequences, meat markets.
JEL Classification: F14, F51, Q02, C51.
DOI: 10.31857/S042473880003319-9

      REFERENCES (with English translation or transliteration)
Antonova M., Zeller M. (2007). A Time Series Analysis of the Beef Supply Response in Russia: Implications for Agricultural Sector Development Policies. Available at: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.135.7259 (accessed: January 2017, in Russian).
Borodin K.G., Prokop'ev M.G., Strokov A.S. (2013). Assessing the Prospects for the Development of the Poultry Market in Russia in the Context of the Country's Accession to the World Trade Organization. Studies on Russian Economic Development, 2, 68-75 (in Russian).
Carone G. (1996). Modeling the U.S. Demand for Imports Through Cointegration and Error Correction. Journal of Policy Modeling, 18 (1), 1-48.
Caruso R. (2003). The Impact of International Economic Sanctions on Trade. An Empirical Analysis. Milan: Universit? Cattolica del Sacro Cuore di Milano. Available at: http://econwpa.repec.org/eps/it/papers/0306/0306001.pdf (accessed: January 2017).
Chung C., Zhang T., Peel D.S. (2009). Effects of Country of Origin Labeling in the U.S. Meat Industry with Imperfectly Competitive Processors. Agricultural and Resource Economic Review. December. Available at: http://ageconsearch.umn.edu/bitstream/59255/2/ARER%2038-3%20406-417%20Chung.pdf (accessed: January 2017).
Elsner K. (1999). Analyzing Russian Food Expenditure Using Micro-Data. IAMO discussion paper No. 23. Available at: http://ageconsearch.umn.edu/handle/14909 (accessed: January 2017).
Hufbauer G., Oegg B. (2003). The Impact of Economic Sanctions on US Trade: Andrew Rose's Gravity Model International Economics Policy Briefs. Number PB03-4. April. Available at: http://www.iie.com/publications/pb/pb03-4.pdf (accessed: January 2017).
Hupkova D., Bielik P. (2009). Estimating Demand Elasticities of Meat Demand in Slovakia. Available at: http://ageconsearch.umn.edu/bitstream/58030/2/Hupkova.pdf (accessed: January 2017).
Kutlina-Dimitrova Z. (2015). The Economic Impact of the Russian Import Ban: A CGE Analysis. European Commission. Trade. Chief Economist Note. Issue 3. December. Available at: http://trade.ec.europa.eu/doclib/docs/2015/december/tradoc_154025.pdf (accessed: January 2017).
Ovcharova L.N., Biryukova S.S., Ter-Akopov S.A., Vardanyan E.G. (2014). What Has Changed in the Incomes, Expenditures and Consumption of the Russian Population? Moscow: HSE (in Russian).
Rose A.K. (2002). Do We Really Know that the WTO Increases Trade? NBER Working Paper No. 9273. Cambridge: NBER (October).
Rose A.K., Reuven G. (2001). Does a Currency Union affect Trade? The Time Series Evidence. NBER Working Paper No. 8396. Cambridge: NBER (July).
Siptits S.O., Romanenko I.A., Strokov S.N., Evdokimova N.E., Abramov A.A. (2009). Long-Term Forecasts of the Development of Agro-Food Markets in Russia. Moscow: VIAPI: ERD (in Russian).
Song W. (2006). Import Demand Elasticities for Agricultural Products in Korea. Available at: http://www.apeaweb.org/confer/sea06/papers/song.pdf (accessed: January 2017).
Wang D., Parton K.A., Deblitz C. (2008). Impact of Potential Dairy-Beef Production on China's Beef Supply, Demand and International Trade. Australasian Agribusiness Review, 16, 18. Available at: http://www.agrifood.info/review/2008/Wang_Parton_Deblitz.pdf (accessed: January 2017).

Aivazian S.A.*, Brodsky B.E.** Retrospective analysis of structural changes in SEM (simultaneous equation) models with varying structure. Part 2.
Economics and mathematical methods, 2018, 54 (4), 60-70.
Affiliations: Central Economics and Mathematics Institute, Russian Academy of Sciences, Russia; * E-mail: aivazian@cemi.rssi.ru, ** E-mail: bbrodsky@yandex.ru
This study was supported by the Russian Foundation for Basic Research ((project 15-01-03359).

Abstract. This article is devoted to the study of the problem of retrospective analysis of structural changes in SEM (simultaneous equation) models with varying structure. We consider main assumptions about statistical dependence of observations: strong mixing and -weak dependence conditions, as well as the main criteris for effectiveness of a method of retrospective analysis. A new nonparametric method of retrospective detection of structural changes is proposed which does nor require knowledge about distributuinal laws of data and its statistical properties are studied. We formulate theorems about convergence to zero of type 1 and type 3 error probabuilities for the proposed method with an increasing sample size. Results of the simulation sudy of the proposed method are given the second part of the paper. Unlike earlier published papers, this article considers the problem of macroeconometric modeling with account of structural changes in data. Here we consider the method for the retrospective detection of multiple structural changes in data, simulation study of this method, as well as applications to the problems of macroeconometric modeling with account of structural changes in data. In particular, we consider the macromodel of the USA economy proposed by L. Klein (the structural change in the year 1929 is detected) and the disaggregated model of the Russian economy (quarterly data in 1995-2016s). Here we detect two instants of structural changes in 2002 and 2010. Results of the simulation study wittness about the fact that the proposed method can effectively detect structural chsnges in SEM models.
Keywords: SEM model, econometric analysis, retropective method, structural change, type 1 error, type 2 error.
JEL Classification: C30, C51.
DOI: 10.31857/S042473880003320-1

      REFERENCES (with English translation or transliteration)
Andrews D.W.K. (1993). Tests for Parameter Instability and Structural Change with Unknown Change Point. Econometrica, 61, 821-856.
Andrews D.W.K., Ploberger W. (1994) Optimal Tests When a Nuisanse Parameter Is Present Only under the Alternative. Econometrica, 62, 1383-1414.
Bai J., Lumsdaine R., Stock J. (1998). Testing for and Dating Common Breaks in Multivariate Time Series. Review of Economic Studies, 65, 395-432.
Brown R.L., Durbin J., Evans J.M. (1975). Techniques for Testing the Constancy of Regression Relationships over Time. Journal of Royal Statistical Society, Series B, 37, 149-192.
Klein L. (1950). Economic Fluctuations in the United States 1921-1941. Cowles Foundation. New York: John Wiley.
Maddala G., Kim I. (1998). Unit Roots, Cointegration, and Structural Change. Cambridge: Cambridge Univ. Press.
Ploberger W., Kr?mer W. (1992). The CUSUM Test with OLS Residuals. Econometrica, 60, 271-285.
Ploberger W., Kr?mer W., Kontrus K. (1989). A New Test for Structural Stability in the Linear Regression Model. Journal of Econometrics, 40, 307-318.

Golubkov V.V., Yakovets T.Yu. The forecast of demographic situation in Russia up to 2033
Economics and mathematical methods, 2018, 54 (4), 71-87.
Affiliations: V. V. Golubkov -ISA FRC CSC RAS, Russia, Moscow; e-mail: golvic@isa.ru; T.Y. Yakovets - International Institute P. Sorokin - N. Kondratiev, Russia, Moscow; e-mail: tzag@mail.ru.
This article was written with the financial support of the Russian Humanitarian Scientific Foundation (project 16-02-00229) "Socio-demographic evolution of Russia and other BRICS countries: patterns, trends and prospects.

Abstract. The brief description of the demographic model and modeling technique elaborated and used by the authors for investigating the trends of demographic development in Russia are given. The demographic model and the modeling technique are based on the using auto regression and regression analysis of time series for demographic indicators, simulation modeling and confidence intervals for model values of demographic indicators with taking into account a priori information and constraints on the model parameters and modeling process. On the basis of confidence intervals there were generated three scenarios of Russia's demographic development: Low, Medium and High. On the time period 2013-2033 the demographic model allows for the scenario variants to calculate one-year age structures for men and women, one-year age fertility, mortality and migration increase rates and all necessary for analysis integral demographic indicators. The results of the multivariate analysis of the demographic processes in Russia on time period 2013-2033 are described. In particular according to these results it was found that fertility and natural increase of the population will decrease generally because of the influence of demographic wave; the total population will increase generally due to the increase of migration; the population will grow old; the coefficient of demographic load on the population will grow at decreasing rate.
Keywords: demographic model, fertility, mortality, migration, age structures, modeling, forecast, demographic indicators, age fertility rates, age mortality rates, age net migration rates.
JEL Classification: J11.
DOI: 10.31857/S042473880003321-2

      REFERENCES (with English translation or transliteration)
Carter L., Lee R.D. (1992). Modeling and Forecasting U.S. Mortality: Differentials in Life Expectancy by Sex. International Journal of Forecasting 8, 3, 393-412.
Golubkov V.V., Krugliakv C.V. (2010). Construction of the Prognostic Two-Parametric Age Fertility Model by Russian Data. In: "Dynamics of heterogeneous systems". Proceedings ISA RAN, 53, 14, 2010, 87-99.
Heligman L., Pollard J.H. (1980). The Age Pattern of Mortality. Journal of the Institute of Actuaries, 107, 49-75.
Keilman N., Pham D.Q. (2000). Predictive Intervals for Age-Specific Fertility. European Journal of Population, 16, 41-66.
Rogers A. (1975). Introduction to Multiregional Mathematical Demography. N.-Y.: Wiley.
Schoen R. (1988). Modeling Multigroup Populations. N.-Y., L.: Plenum Press.
Vishnevsky A.G. (2012). Demographic Breakthrough or Circling? Part 1. Demoskop Weekly, 533-534, 1-29.

Kalashnikov P.V. Mathematical model of the optimal control process of the balance of the joint- distribution pension system
Economics and mathematical methods, 2018, 54 (4), 88-97.
Affiliation: Postgraduate student Far East Federal University, Vladivostok, Russia E-mail: pkalash_89@mail.ru

Abstract. The author describes how to build a dynamic actuarial balance model of the distribution component of the budget of the Pension Fund. In the course of the research, the analysis of the main characteristics of the actuarial estimation models of pension systems at the state level used in international practice is given. An analysis is made of the possibilities of applying the models in question within the framework of the mandatory pension insurance system of the Russian Federation. The author implements the construction of a dynamic actuarial model of the assessment of the balance of the joint-distribution pension system, taking into account the specifics of the socio-economic development and legislation of this state. The author offers a long-term forecast of the level of balance of contributions and benefits (associated with the formation of the insurance part of the labour old-age pension) which is based on the construction of actuarial models and using of statistical data. In the study the analysis of t controlling impacts to reduce the level of emerging budget deficit of Pension Fund of Russia in the long term is performed. The description of the combined and differentiated influence of the factors on consideration of the state of the pension system is also given. The novelty of the approach being implemented is the development of a set of control actions on the parameters of the actuarial basis that will allow the Russian pension system to be balanced in the long run and also to study the stability of the constructed model if the values of the considered values deviate from the main forecast values within the specified areas of change.
Keywords: budget deficit of the Pension Fund of the Russian Federation, an actuarial basis, control of the balance of the joint-distribution pension system.
JEL Classification: C63, H55.
DOI: 10.31857/S042473880003322-3

      REFERENCES (with English translation or transliteration)
Baskakov V.N. (2001): Insurance Against Accidents at Work: Actuarial Foundations. Moscow: Academia (in Russian). Bowers N. (2001). Actuarial Mathematics. Moscow: Janus-K (in Russian).
Holtzman R. (2001). Secured Old Age in the 21st Century: Pension Systems and Reforms in the International Perspective. Available at http://siteresources.worldbank.org/INTPENSIONS/Resources/Old_Age_Inc_Supp_Full_Rus.pdf (accessed: December 2016).
Kalashnikov P.V. (2015). Study of the Balance of the Budget of the Pension Fund of the Russian Federation. Saarbrucken: LAP Lambert Academic Publishing (in Russian).
Labor Office (2002). The ILO Pension Model, a Technical Guide. Available at: http://www.ilo.org (accessed: December 2016).
Simonenko V.N. (2010). Scenario of the Pension System Modeling in the Context of the Current State of the Economy. Bulletin of the Pacific State University, 4 (19), 145-152 (in Russian).
Smirnov I.V. (2004). Demography: A Training Manual. Kaluga: a branch of North-West Academy of Public Administration in Kaluga (in Russian).

Istratov V.A. Computer algorithm of social and personal norms formation
Economics and mathematical methods, 2018, 54 (4), 98-110.
Affiliation: Central Economics and Mathematics Institute, Moscow; Saint Petersburg State University, Saint Petersburg; E-mail: istratov@cemi.rssi.ru
This study was supported by the Russian Foundation for Basic Research (project 15-06-05877).

Abstract. The article offers a programming algorithm of modeling the formation of social norms based on personal ones. Different ways of social norm emergence are not considered in this work. An analysis of currently available computer implementations indicates the high relevance of such algorithms. The proposed algorithm dynamically generates personal and social norms which correspond to the actual model setting. In addition, norms can be dynamically changed or grow irrelevant and be erased without user interference. A norm in this algorithm is explicit, i.e. it is a rule of a certain type, which allows simple manipulations within the model framework as well as studying it without resorting to auxiliary calculations and interpretations. The norms formation algorithm is implemented as a software module extending a more general computer model of human behavior. In a series of computational experiments, in the overwhelming majority of cases, meaningful, logical, relevant social norms were formed. These experiments indicate the success and adequacy of the proposed norms formation algorithm.
Keywords: social norm, personal norm, behavior, computer simulation, algorithm, model, sanction.
JEL Classification: C63, D02.
DOI: 10.31857/S042473880003323-4

      REFERENCES (with English translation or transliteration)
Axelrod R. (1986). An Evolutionary Approach to Norms. The American Political Science Review, 80, 4, 1095-1111.
Cialdini R.B., Trost M.R. (1998). Social Influence: Social Norms, Conformity, and Compliance. In: Gilbert D.T., Fiske S.T., Lindzey G. (eds) "The handbook of social psychology"". Vol. 2. Boston: McGraw-Hill, 151-192.
Conte R., Castelfranchi C. (1995). Understanding the Functions of Norms in Social Groups through Simulation. In: Gilbert N., Conte R. (eds) "Artificial Societies: The Computer Simulation of Social Life". London: UCL Press, 252-267.
Cooter R.D. (1996). Decentralized Law for a Complex Economy: The Structural Approach to Adjudicating the New Law Merchant. University of Pennsylvania Law Review, 144, 5, 1643-1696.
Elster J. (1989). Social Norms and Economic Theory. Journal of Economic Perspectives, 3, 4, 99-117.
Horne C. (2001). Sociological Perspective on the Emergence of Social Norms. In: Hechter M., Opp K.-D. (eds) "Social norms". New York: Russell Sage Foundation, 3-35.
Istratov V.A. (2009). Agent-Based Model of Human Behavior: Can't Money Buy You Happiness? Economics and Mathematical Methods, 45, 1, 129-140.
Istratov V.A. (2016). Modelling Social Norm Emergence in Social Sciences. Economics and Mathematical Methods, 52, 4, 47-73.
Kenrick D.T., Li N.P., Butner J. (2003). Dynamical Evolutionary Psychology: Individual Decision Rules and Emergent Social Norms. Psychological Review, 110, 1, 3-28.
Latane B. (1996). Dynamic Social Impact: the Creation of Culture by Communication. Journal of Communication, 46, 4, 13-25.
Merdes C. (2017). Growing Unpopular Norms. Journal of Artificial Societies and Social Simulation, 20, 3. Available at: http://jasss.soc.surrey.ac.uk/20/3/5.html (accessed: 03.10.2017).
Nelson R.R., Sampat B.N. (2001). Making Sense of Institutions as a Factor Shaping Economic Performance. Journal of Economic Behavior & Organization, 44, 31-54.
Neumann M. (2008). Homo Socionicus: A Case Study of Simulation Models of Norms. Journal of Artificial Societies and Social Simulation, 11, 4. Available at: http://jasss.soc.surrey.ac.uk/11/4/6.html (accessed: 03.10.2017).
Opp K.-D. (2001). How Do Norms Emerge? An Outline of a Theory. Mind and Society, 2, 3, 101-128.
Savarimuthu B., Purvis Maryam, Cranefield S, Purvis Martin (2007). How do Norms Emerge in Multi-Agent Systems? Mechanism Design. The Information Science Discussion Paper Series, 2007, 1.
Schotter A., Schw?diauer G. (1980). Economics and the Theory of Games: A Survey. Journal of Economic Literature, 18, 2, 479-527.
Schwartz S.H. (1977). Normative Influences on Altruism. Advances in Experimental Social Psychology, 10, 221-279.
Veblen T. (2010). The Theory of the Leisure Class. [Veblen T. (1899). The Theory of the Leisure Class: An Economic Study of Institutions] Moscow: Librokom (in Russian).
Young H.P. (2008). Social Norms. In: Blume L., Durlauf S.N. (eds.) "The New Palgrave Dictionary of Economics", 7. New York: Palgrave, Macmillan, 647-651.

Druzhkov K.V., Eremin V.L. Public-private partnership - an actual form of implementation of infrastructure projects
Economics and mathematical methods, 2018, 54 (4), 111-115.
Affiliations: Druzhkov K.V. - National Research University of Information Technologies, Mechanics and Optics; Saint-Petersburg, Russia; E-mail:dkv83@mail.ru; Eremin V.L. - GSPA at Lomonosov Moscow State University; Moscow, Russia; E-mail:VladimirLE@anspa.ru

Abstract. This article is about actual form of cooperation between states and the corporate partners in big infrastructural economic projects - public-private partnership. The mechanism of public-private partnership helps states to optimize using of state budget resources on the implementation of important, but expensive projects in key areas of national economy. In long-term period, states can realize more socially significant projects. Private business in public-private partnership has an opportunity to realize major, long-term projects and to share risks of the project implementation with state partners. Without state participation, the implementation of such significant projects would be impossible because of the high cost of debt financing. The profitability of the project would be negative, because of the high level of risk, so the likelihood of completion of the project on time and with the necessary result would be minimal. The first experience of implementation of public-private partnership appeared long before the 20th century. Legal regulation of public-private partnership differs in different countries. In many countries there are special bodies for project management in public-private partnership. In the world practice public-private partnership projects are implemented in a wide range of industries from the construction of highways to hospitals. In the Russian practice of public-private partnership there are already a number of significant successful projects implemented. In this case, there are our own special problems and features.
Keywords: Public-private partnership, state procurement, concession, investment fund, private partner.
JEL Classification: H54.
DOI: 10.31857/S042473880003324-5

      REFERENCES (with English translation or transliteration)
Belitskaya A.V. (2013). Legal Regulation of Public Private Partnership. Monograph. Moscow: Statute (in Russian).
Delmon D. (2010). Public Private Partnership in Infrastructure: Practical Guide for Public Authorities. - Available at: http://www.fcpf.ru/upload/iblock/7ac/Jeff%20Delmon_PPP_russian.pdf (accessed: January, in Russian).
Emelianov Y.S. (2013). Public Private Partnership: Innovation and Investment. Moscow: World and Domestic Experience, Librokom (in Russian).
Kabashkin V.A. (2010). Public Private Partnership: International Experience and Russian Perspectives. Moscow: Delo (unpublished, accepted at the Editor) (in Russian).
Varnavskiy V.G., Klimenko A.V., Korolev V.A. (2010). Public Private Partnership Theory and Practice. Tutorial. Moscow: Publishing House of the State University - Higher School of Economics (in Russian).

Zinenko A.V. Catastrophe theory and price dynamics.
Economics and mathematical methods, 2018, 54 (4), 116-123.
Affiliation: Siberian State University of Science and Technology named after M.F. Reshetnev, Krasnoyarsk, Russia; E-mail: anna-z@mail.ru

Abstract. The paper is about finance markets research using non-classical non-linear dynamic methods. Classical time series (including market trends) prediction and analyses methods are based on mathematical statistics. These methods are based on linear and non-linear regression, moving averages and others. Statistical approach assumes that input data honors the normal distribution law. Practice shows that market trends data form normal distribution only on quiet market form and prediction of abrupt shifts is more valuable and important for market analytics. With the evolution of mathematics and social sciences, economists began to apply the differential calculus and its most complicated part - non-linear dynamics - long-known in physics. Starting with Benoit Mandelbrot 1960s works, scientists and analytics widely apply non-linear methods in market terms researches. Mandelbrot started with fractals and power laws; the researches nowadays also apply chaos and catastrophe theory. Catastrophe theory is a big mathematics nonlinear discipline. Catastrophe in terms of mathematics is a discontinuous shift of a system in response to small parameter change. In this paper we apply catastrophe theory to market quotes dynamics. We take market demand and supply as control parameters and trend reverse - as catastrophe. We constructed theoretical model and tested it on real data of property market.
Keywords: nonlinear dynamics, catastrophe theory, assembly-type catastrophe, condition variable, control parameters.
JEL Classification: G14.
DOI: 10.31857/S042473880003325-6

      REFERENCES (with English translation or transliteration)
Arnold V.I. (1990). Catastrophe Theory. Moscow: Nauka (in Russian).
Bodie Z., Marcus A. J., Kane A. (2005). Essentials of Investments. Moscow: Williams (in Russian).
Gilmor R. (1984). Applicable Catastrophe Theory. Moscow: Mir (in Russian).
Mandelbrot B. (2004). Fractals, Hazard and Finance. Moscow, Izhevsk: Reguljarnaja i Haoticheskaja Dinamika (in Russian).
Mandelbrot B., Hudson R. (2006). The (Mis)Behavior of Markets. Moscow: Williams (in Russian).
Mauboussin M. (2014). More Then You Know. Finding Financial Wisdom. Moscow: Alpina Publisher (in Russian).
Mlodinow L. (2011). The Drunkard's Walk. How Randomness Rules Our Lives. Moscow: Livebook-Gayatri (in Russian).
Peters E. (2000). Chaos and Order in the Capital Markets. Moscow: Mir (in Russian).
Peters E. (2004). Fractal Market Analyses. Moscow: Internet-trading (in Russian).
Stewart I. (1987). Catastrophe Theory and Its Applications. Moscow: Mir (in Russian).
Weatherall J. (2013). The Physics of Wall Street. A Brief History of Predicting the Unpredictable. Moscow: Mann, Ivanov i Ferber (in Russian).
Zinenko A.V. (2012). R/S Analyses on Stock Market. Business - Informatics, 3 (21), 21- 27 (in Russian).
Zinenko A.V. (2015a). Pareto Laws on Stock Exchange. Finance and Credit, 38, 11-19 (in Russian).
Zinenko A.V. (2015b). MICEX Index Dynamics Analyses With Modern Investment Theory. Krasnoyarsk: Sib SAU (in Russian).

Belousov F.A. Model of Nomads and Plowmen with a Limited Resource of Spatial Movement
Economics and mathematical methods, 2018, 54 (4), 124-131.
Affiliation: Central Economic and Mathematic Institute, Russian Academy of Sciences Address: Russian Federation, Moscow; e-mail: sky_tt@list.ru

Abstract. In the article (Belousov, 2017), the model with the simplest social structure was built and studied. In the model agents are divided into two types - nomads and plowmen, each of which is distinguished by its attitude to the method of production of the product. If plowmen can independently reproduce product, then nomads are not endowed with such skills, instead they have the ability to find such a product in the area, including taking it away from plowmen. In mentioned article, the question of extinction of one of the civilizations was studied, and the question of the coexistence of these civilizations in a single space during the observed period also was studied. The scientific novelty of this work lies in the development of the original model of nomads and plowmen and addition of new conditions associated with restrictions on movement of agents. In the new modification, agents are forbidden to move away from their place of birth beyond a certain exogenously specified distance during their lifetime. Due to the fact that the original model is rather the model of ancient society, its modification better reflects the socio-demographic processes that took place in ancient times. The ancient people, perhaps with rare exceptions, did not have the opportunity to travel long distances and they were somehow tied to their place of birth and permanent habitat. A series of experiments was carried out, the ranges of values of the parameter introduced into the model, under which different qualitative dynamics of the entire system is observed, were determined. The value of this work is added by the fact that the access to more productive computing power has allowed to carry out better calculations. Thus, in the initial model, calculations were carried out for a length of 4000 periods of model time; in the new model, this characteristic grew to 15,000 and 20,000 periods. Such growth of this indicator allows to reveal new qualitative dynamics not only in the new presented modification, but also in the original model of nomads and plowmen.
Keywords: artificial society, simulation modeling, agent-based modeling, extinction of civilizations, nomads, plowmen.
JEL Classification: С63.
DOI: 10.31857/S042473880003336-8

      REFERENCES (with English translation or transliteration)
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