Summary

Vol. 50, No. 1

Livchits V.N., Vilensky P.L. (Moscow) On Typical Delusions under Evaluating Real Investment Projects Efficiency
Economics and mathematical methods, 2014, 50 (1), 3-23.
The article consists of two parts: in the first delusions concerning methodology of investment calculations efficiency disclosed, and in the second - delusions concerning the methods of estimates are shown, with mistakes related to accounting inflation multicurrencies factor, risk and uncertainty leading to errors and at the end - to losses (in particular, the financial ones) for the investor.
Keywords: efficiency, discounting, investment, project, delusions, payback period, inflation, net present value.
JEL Classification: А23, А29.

Tulupov A.S. (Moscow) Settlement and Methodical Tools for Environmental Insurance
Economics and mathematical methods, 2014, 50 (1), 24-36.
In contrast to the formal approach, which considers insurance problems of environmental risks in fragmentary and declaratory way, the basic tools calculation of parametric characteristics of environmental insurance are presented. This allows evaluation based on the individual characteristics of each certain enterprises' insurers, insurance company and recipient.
Keywords: environmental insurance, actuarial calculations, compensation of ecological damage.
JEL Classification: Q01.

Asaturov K.G., Teplova T.V. (Moscow) Construction of a Hedge Ratio for Marketable Russian Stocks Based on GARCH Class Models
Economics and mathematical methods, 2014, 50 (1), 37-54.
In the paper we propose an original method for constructing a dynamic hedging strategy based on multivariate GARCH models for the marketability of the Russian stocks. Hedging instruments include stock futures. The method provides a calculation of dynamic hedge ratios instead of the traditional method of ordinary least squares (OLS), which determines the constant hedge ratio. Analysis of spot and futures Russian markets showed that 1) it is the dynamics of the futures market that affects the behavior of the stocks' prices, 2) for all pairs of stock-futures there is no asymmetry in the conditional correlation of returns, 3) there is an asymmetry in the conditional volatility, and 4) GARCH class models allow to construct a method of calculating hedging ratio for portfolio with the best characteristics of "risk-return" profile.
Keywords: hedging strategy, hedge ratio, hedging effectiveness ratio, dynamic correlation, asymmetric volatility, stocks and futures for them, multivariate GARCH.
JEL Classification: C1, C13, C18, C4, C44,C5, C53, C6.

Tomashevskiy I.L. (Arkhangelsk) Estimates for an Error in Analytic Hierarchy Process
Economics and mathematical methods, 2014, 50 (1), 55-60.
It is shown that the basic procedure of calculation of priorities in Analytic Hierarchy Process (AHP) is equivalent to some " -deformed" measuring process. The analysis of this process from the point of the theory of measurements was carried out. Simple estimates for error in AHP were obtained.
Keywords: Analytic Hierarchy Process, AHP, error.
JEL Classification: С43, С44.

Marakulin V.M. (Novosibirsk) On Contractual Approach in Production Economies of Arrow-Debreu-McKenzie Type
Economics and mathematical methods, 2014, 50 (1), 61-79.
The paper applies and elaborates contractual approach to study economies with convex and non-convex production aggregate. The notions and terms of barter contractual approach developed in (Marakulin, 2003, 2011) for exchange economies are now modified and extended to the production economy; known earlier notions adopted: web of contracts, domination via coalitions among webs, partial breaking of contracts and so on. A new notion of marginal contractual allocation is introduced for the model with non-convex production. Then it is applied to describe marginal cost pricing (MCP) equilibrium, the notion used in non-convex case instead of Walrasian equilibrium. Main results are presented in theorems on equivalence of equilibria and specific (proper, fuzzy, marginal) contractual allocation, implemented via web of contacts stable relative to a partial break. An equivalence between marginal contractual allocation and MCP-equilibrium can be considered its theoretical foundation for non-convex economies. The paper presents and develops specific universal form of perfect competition implemented via contractual approach.
Keywords: competitive equilibrium, MCP-equilibrium, core, contract, contractual approach, production economy, non-convex production.
JEL Classification: C62, D51.

Fedorova Ye.A., Titarenko F.V. (Moscow) Loss Aversion Investment Portfolio Optimization by the Example of Russian Stock Market
Economics and mathematical methods, 2014, 50 (1), 80-90.
This work describes investment portfolio optimization using linear loss averse function as well as comparison to traditional optimization methods like mean variance MV and CVaR. An empirical study is carried on Russian stock market indexes quotes, the results are compared to MV and CVaR methods. Proposing loss averse function portfolios outperform MV and CVaR portfolios as well as using adaptive model parameters improves the result even more.
Keywords: portfolio optimization, loss aversion, MV-, CVaR-metod.
JEL Classification: G15.

Zatonskiy A.V., Sirotina N.A. (Berezniki) Prediction of Economic System Based on Regression Model with Differential Equation
Economics and mathematical methods, 2014, 50 (1), 91-99.
The ways of ensuring social, environmental and economic safety of social development by creating conditions for competitiveness of renewable sources of energy and organic farming are considered. Restriction to low-carbon economy and organic farming described. Possible ways to overcome these problems outlined. Approaches to the definition of efficiency of renewable sources of energy and organic farming proposed.
Keywords: economic model, differential equation, regression, prediction.
JEL Classification: C25, C35, C14.

Baev I.A., Drozin D.A. (Chelyabinsk) Integrated Model of Information Diffusion about Innovative Product
Economics and mathematical methods, 2014, 50 (1), 100-109.
Set of potential buyers in the market of the new innovative product divides into subsets with different sequences of information (true or outdated) about the price changes. These subsets have significantly different structure of effective consumer demand. The system of differential equations for calculating the dynamics of the formation of these subsets, which determine structure and market capacity for innovation goods, is obtained.
Keywords: mathematical model, Innovative product, information dissemination, sequences of information gaining, consumer demand, price change.
JEL Classification: C60, D11, D4, M31, M37.

Golshtein Ye.G. (Moscow) An Approximate Method for Solving Finite Three-Person Games
Economics and mathematical methods, 2014, 50 (1), 110-116.
The paper describes a numerical algorithm for solving a finite non-cooperative three-person game in mixed strategies. The algorithm is based on linear programming and is connected with minimization of a function having numerous local minima.
Keywords: non-cooperative game, Nash equilibrium, pure strategy, mixed strategy, game with convex structure, variational inequality.
JEL Classification: C02, C72.

Slastnikov S.A. (Moscow) Application of Metaheuristic Algorithms for the Vehicle Routing Task
Economics and mathematical methods, 2014, 50 (1), 117-126.
Observes a problem of modern metaheuristics for the vehicle routing. Given a brief survey of the principle metaheuristic algorithms, as well as a detailed description of the ant colony optimization algorithm. The modification of ant colony optimization algorithm proposed, the effectiveness of which is confirmed by the computational results.
Keywords: vehicle routing problem, metaheuristic algorithms, ant colony optimization.
JEL Classification: C61, R42.

Vol. 50, No. 2

Ivanov V.N., Ovsienko Yu.V., Sukhova N.N. (Moscow) Russian social sphere in 1990-2000 (demographic problems)
Economics and mathematical methods, 2014, 50 (2), 2-15.
Presented here is the first article in the series of publications on the analysis of the Russian social sphere development processes in the 1990s and the 2000s. Analyzed are the trends in population replacement, fertility, mortality and migration as well as the changes in health care, education and social maintenance systems that have influenced the demographic processes.
Keywords: social sphere, development trends, institutional changes, demographic processes, population replacement, fertility, mortality, migration, health care, education, social.
JEL Classification: I00.

Tatarkin A. I., Petrov A. P. (Moscow) Effect of medical pharmaceutical clusters on the regional economy
Economics and mathematical methods, 2014, 50 (2), 16-23.
In this paper to assess the impact of medical and pharmaceutical clusters on the economic development of the regions has been used an econometric model with fixed and random individual effects. The database contained a number of statistical indicators for the 75 subjects of the Russian Federation for 13 years (1999-2011). The presence of such clusters increases GDP per capita by 0,11%. Thus, we have shown that the formation of clusters in the region contributes to the modernization of the economy and the development of the innovation process, and also leads to an increase in output.
Keywords: medical and pharmaceutical cluster, evaluation, econometric model, the economic development of the region.
JEL Classification: C51.

Fattakhov R.V., Nizamutdinov M.M. (Moscow-Ufa) Urban settlement in Russia for 50 years: assessment of trends and prospects
Economics and mathematical methods, 2014, 50 (2), 24-34.
The problems of urban settlement in Russia are discussed in terms of identifying key trends. The detailed analysis of changes in the structure and dynamics of the Russia cities' population is considered for the last 50 years. Results of the cross-country comparison of settlement regularities are presented on the basis of the Zipf's rule. Assumptions about the possible changes in the structure of urban settlement in the future are estimated.
Keywords: space frame, city's population, trend of urban settlement, Zipf's rule, cross-country comparisons.
JEL Classification: J110.

Ilinsky D.G., Polterovich V.M., Starkov O.Y. (Moscow) Designing and analyzing the programs of contractual savings for housing: а dynamic model
Economics and mathematical methods, 2014, 50 (2), 35-57.
We develop a dynamic model for analyzing the programs of contractual savings for housing (CSH). We introduce concepts of stability as well as strong and weak stability of trajectories generated by CSH programs, and obtain the necessary and sufficient conditions that guarantee fulfillment of these properties. Experimental calculations indicate that CSH programs ensure stable financing of its members under wide range of variation of parameters which are close to real data.
Keywords: mortgage, programs of contractual savings for housing, Bausparkassen, contractual savings for housing bank accounts, stability
JEL Classification: D02, D14, G21.

Pilnik N.P., Pospelov I.G. (Moscow) Models of the mechanisms providing the effectiveness of the general equilibrium
Economics and mathematical methods, 2014, 50 (2), 58-72.
The article is an attempt to clarify the way of firm's behavior description and its relations with the owners in the general equilibrium models with the help of welfare problem decomposition. The general scheme of decomposition is suggested. The scheme generates a range of mechanisms, including the mechanism of share capital, which allows to describe stock market in the general equilibrium models.
Keywords: general economic equilibrium, welfare problem decomposition, share capital.
JEL Classification: D50.

Voronovitsky M.M. (Moscow) The agent-based model of the closed market with one commodity
Economics and mathematical methods, 2014, 50 (2), 73-87.
The agent based model of the closed market (a market on which at each moment of time there is a same quantity of the goods and also the same quantity of money) is formulated. Participants of this market at each moment of time may be sellers or buyers of the commodity or not to participate in trade. Thus the following moment the buyer can become the seller or not participate in trade. The same concerns the sellers. Using only own information about the results of trade in the previous moment of time, participants of trade vary their statuses and appoint the new prices. The mathematical model of such market has been represented as the computer program. The basic properties of considered model of the closed market with one commodity was investigated with the help of the computer program.
Keywords: mathematical model, closed market, one commodity market, dynamics of prices, trajectory.
JEL Classification: C51, D01.

Romanovskiy A.V., Shokin Ya.V. (Moscow) The application of neural networks mathematical tools for measurement of subjective well-being
Economics and mathematical methods, 2014, 50 (2), 88-95.
This article presents the method of calculating an indicator of public well-being. The indicator is based on the model of needs satisfaction. The model is created by using the tools of artificial neural networks. Also the main results of preliminary research are given.
Keywords: needs, well-being, aggregated welfare indicator, A. Maslow classification of needs, artificial neural networks.
JEL Classification: C45.

Balashova S.A., Khustalev Ye.Yu. (Moscow) Integrated assessment of innovation performance by methods of multivariate statistics (case of European Union)
Economics and mathematical methods, 2014, 50 (2), 96-110.
The indicators of innovation performance of EU countries tested and evaluated by methods of multivariate statistical analysis. It is shown that the modified method of principal components to create the summary innovation index gives the ability to emphasize the most significant factors, which can be regarded as growing-points of innovation development.
Keywords: innovative capacity, innovation indexes, methodology of index creation, modified method of principal components.
JEL Classification: C23, C43, C51.

Levner Ye.V., Ptuskin А.S. (Moscow) On a selection of directions of enterprise modernization based on an information entropy model of economic risk
Economics and mathematical methods, 2014, 50 (2), 111-126.
The paper considers a problem of selecting a portfolio of planned activities for enterprise modernization enabling to minimize the economic risks. It is shown how, by using the entropy approach, to extract a sufficient amount of useful information from the risk protocols generated in the various enterprise departments. An economic-mathematical model of selecting the modernization activities is presented in the form of the integer programming knapsack-type problem.
Keywords: modernization, risk, entropy, graph of an enterprise, selection of modernization projects.
JEL Classification: D81.

Summary

Vol. 50, No. 3

Fattakhov R.V., Nizamutdinov M.M. (Moscow, Ufa) Conceptualization and description of the economic agents' strategies in development simulation model of regional economy
Economics and mathematical methods, 2014, 50 (3), 3-23.
The article presents approach to the development model of the regional economy based on integration of the triad of behavioral, dynamic balance- and managerial models. Mathematically formalized description of economic agents' behavior strategies is described in their interaction at the micro and macro levels as well as the management algorithm of the model. Some results of practical testing of the model at the regional level are discussed.
Keywords: region, development strategy, economic agents, behavior models, system dynamics, regional management, simulation.
JEL Classification: R150.

Istratov V.A. (Moscow) Modeling daily scheduling
Economics and mathematical methods, 2014, 50 (3), 24-37.
Despite the important role that activity scheduling, economic activities included, plays in people's lives economists barely notice it behind side effects of solving the other problems. However the daily activity planning problem deserves attention by its own. The article introduces an algorithm that simulates the process of daily plan-making. The algorithm mirrors people's real-life decision making routine. Algorithm's adequacy is tested compared to the real people decisions.
Keywords: scheduling, activity, algorithm, human behavior, microeconomics.
JEL Classification: D010, D030.

Gusev A.A. (Moscow) Environment protection in the market economy
Economics and mathematical methods, 2014, 50 (3), 38-44.
The article describes the combination of ecological requirements and market economy development within the process of attaining social indicators of environmental quality. The development of ecological technologies' market is the base of this process. Such market has to be built during the consistent withdrawal of non-eco-friendly equipment. The role of such additional instruments as environmental insurance, polluting emissions trading and environmental audit for the above-mentioned purposeful policy is described.
Keywords: pollution-free technologies, social standards for environmental quality, market of best available technologies, market of environmental services.
JEL Classification: Q50.

Afanasyev A.A. (Moscow) The Milanese School of mathematical economics in the 18th century (La Scuola Milanese di economia matematica del XVIII secolo)
Economics and mathematical methods, 2014, 50 (3), 45-54.
The author of this historical essay introduces the Russian reader to the mathematical models of the Milanese School of the second half of the eighteenth century. These models of the Italian founders of the mathematical economics are little known in Russia.
Keywords: history of economic thought, mathematical economics, Milan, eighteenth century, Il Caff?, marquis Cesare Beccaria, abb? don Paolo Frisi, major general Henry Lloyd, count Pietro Verri, the first mathematical models of price, circulation and smuggling.
JEL Classification: B160. L'autore di questo saggio storico introduce il lettore russo ai modelli matematici della Scuola Milanese della seconda met? del XVIII secolo. Questi modelli dei fondatori italiani dell'economia matematica sono poco conosciuti in Russia.
Parole chiave: storia del pensiero economico, economia matematica, Milano, XVIII secolo, Il Caff?, marchese Cesare Beccaria, abate don Paolo Frisi, generale Henry Lloyd, conte Pietro Verri, primi modelli matematici di prezzo, circolazione e contrabbando.
Сlassificazione JEL: B160.

Dubyansky A.N. (St. Petersburg) Brief outline of the history of Russian assignation
Economics and mathematical methods, 2014, 50 (3), 55-72.
The article deals with the complex and controversial history of first Russian paper money - assignation. They have operated in the Russian economy over 70 years since 1769 and until 1843, and made a significant contribution to its development. Assignation throughout his stories were practically the only resource for the financing of economic development of the Russian state. Thanks ассигнациям Russia has essentially become the first European country to use the possibilities of paper money at the decision of problems of public Finance. The author also reveals the positive and negative sides of the first Russian paper money.
Keywords: assignation, Russian ruble, paper money, G.F. Cankrin, Catherine II, M.M. Speransky.
JEL Classification: N10, N13, N23.

Gavrilets Yu.N. (Moscow) A computer model of ideological confronting between two political forces in the society
Economics and mathematical methods, 2014, 50 (3), 73-85.
The paper provides an arbitrary dynamics model of social groups' political positions. These changes occur as a result of the contacts between groups under the information influence of the external environment. Computer calculations on the model allows to specify the role of different parameters when forecasting.
Keywords: social groups, socio-psychological attitude, imitative behavior, social interaction, Markov chains.
JEL Classification: C31.

Livchits V.N., Sygal A.V. (Moscow, Ukraine) On entropy analysis of transitional economy
Economics and mathematical methods, 2014, 50 (3), 86-104.
Stationary and non-stationary economic states and processes in transitional economies of the countries - non-Baltic republics of the former Soviet Union are characterized. Various models of entropy and its behavior in connection with stationary economic state are studied. The spheres of using entropy instrument in economy and methods of its calculation are discussed.
Keywords: transitional economy, radical reform, stationary and non-stationary state, entropy, Fishbern formulae.
JEL Classification: A00, P20, B40.

Arkin V.I., Slastnikov A.D. (Moscow) The model of governmental guarantees and bank credit policy in financing risky projects
Economics and mathematical methods, 2014, 50 (3), 105-118.
The paper considers the model of interaction between investor, bank and government in financing the risky projects. This model allows to study a mechanism of the governmental loan guarantees. We propose the optimization approach for the determination of both maximal sum of guarantees and credit policy of a bank. We analyze the optimal decisions of the government and the bank in financing the risky projects and discuss some economic consequences.
Keywords: investment project, loan, risk, governmental guarantees, optimal part of loan reimbursement.
JEL Classification: G2, D81, C61.

Il'ichev V.G., Il'icheva V.V. (Rostov-on-Don) Spatial adaptation and optimal harvesting of fish population
Economics and mathematical methods, 2014, 50 (3), 119-129.
Within discrete model process of movement of fish population is set by a finite-dimensional Markov matrix. Change of this matrix as its adaptation to a condition of fodder resources and management is formalized. Numeracally found the key characteristic of spatial adaptation is a vector of distribution of times of stay of population in those or regions of reservoir. It appeared that this vector is own vector (Perron's vector a final matrix) of movement.
Keywords: migration, matrix, adaptation, optimal harvesting, Perron's vector.
JEL Classification: Q57.

Zaslavsky A.A. (Moscow) New approaches for analysis of paired comparison
Economics and mathematical methods, 2014, 50 (3), 130-133.
Two traditional problems of paired comparisons analysis are considered: the estimation of non-transitivity and the construction of transitive matrix closest to the given one. Some recent methods for solution of these problems are given and the new problems using the weakening of the transitivity condition are formulated.
Keywords: paired comparisons, transitivity, distances' matrix.
JEL Classification: C02.

Podshivalov S.F., Podshivalova K.S. (Penza) Specialties in the use of the branch and bound to the routing problem with incomplete transport graph
Economics and mathematical methods, 2014, 50 (3), 134-140.
Study of the degeneration of solutions using branch and bound method for determining the best routes on graphs. Developed an advanced algorithm to get the exact solution. Examples given.
Keywords: graph, route algorithm degeneration.
JEL Classification: С61.

Vol. 50, No. 4

Ovsienko Yu.V. (Moscow) Basic Forms of Social Organization and Their Influence on Social Development
Economics and mathematical methods, 2014, 50 (3), 3-20.
Analyzed the authoritarian and democratic forms of social organization. Discussed the influence of the peculiarities of these forms on the social and economic (institutional) dynamics and scientific (technological) modernization.
Keywords: institutions, institutional system, economic dynamics, democratic and authoritarian societies, social justice, corruption, effectiveness, modernization.

Afanasyev А.А., Ponomareva O.S. (Moscow) The Aggregate Production Function of the Russian Economy In 1990-2012
Economics and mathematical methods, 2014, 50 (3), 21-33.
Econometric models of the aggregate production function of the Russian economy have been built. These models adequately (from the standpoint of economics and econometrics) describe the expanded reproduction of the Russian economy in 1990-2012. The role of the national economic infrastructure and world oil price fluctuations on GDP as well as predictive power of econometric models are investigated.
Keywords: econometric analysis, macroeconomic production function, Russian economy, GDP, infrastructure, the Brent oil world price.
JEL Classification: E100, E230.

Aivazian S.A., Afanasiev M.Yu. (Moscow) Efficiency Estimation Of The Russian Regions Based on the Productive Potential Model Including the Characteristics of Readiness To Innovate
Economics and mathematical methods, 2014, 50 (3), 34-70.
On the basis of the author's methodology it is built static and dynamic models of the production potential of the regions of the Russian Federation. The conclusion was made, that it is not appropriate to conduct the division of regions into clusters in a productive potential model for the period in question. Characteristics of the regions' readiness to innovate were identified, they allow a treatment as factors of production efficiency. It is shown that the integration of the efficiency in the productive potential model can significantly improve differentiation estimates of production's technical efficiency. Locally effective regions which have relatively high efficiency estimates among regions with similar amounts of GRP and locally inefficient regions were identified by a comparison of the regional ratings of real GRP and boundary GRP. The using of "local efficiency" concept becomes constructive in the context of determining the prospects of the region's development based on meaningful interpretation of a set of indicators which characterize the efficiency factors. Marginal effects influence of the factors' effectiveness on the result of industrial activity in the region and the corresponding elasticities were calculated.
Keywords: regional economy, econometric modeling, stochastic frontier, efficiency estimation, efficiency factors, local efficiency.
JEL Classification: C120, C510, R150.

Ilinsky D.G., Polterovich V.M., Starkov O.Yu. (Moscow) Lines of Savings and Loan Tariff Plans: a Generalization of the Bausparkasse Concept
Economics and mathematical methods, 2014, 50 (3), 71-88.
Contractual savings for housing (Bausparkassen) with narrow ranges of tariff plans are used to coexist with banking hypothec, providing consumers a binary choice . We propose to form systems (lines) of savings and loan tariff plans (SLTP) for bank accounts "linking" these two mortgage institutions. We consider properties of lines of SLTP and develop a model for their design and analysis. Experimental calculations indicate that parameters of the line of SLTP may be selected so that efficiency of the mortgage system rises for all involved agents - consumers, banks and governments. Finally we analyze the impact of parameters of SLTP on objective functions of the agents.
Keywords: mortgage, line of savings and loan plans, contractual savings for housing, savings and loan bank account for housing.
JEL Classification: D02, D14, G21.

Trofimov G.Yu. (Moscow) Asset inflation and Credit Expansion in an Overlapping Generations' Economy
Economics and mathematical methods, 2014, 50 (3), 89-103.
Asset inflation and credit expansion are considered as the instruments for implementation of long-term optimum for an overlapping generations model. We show the role of credit in supporting a high rate of asset price inflation, which outpaces the growth rate of GDP and provides optimal wealth allocation between generations. A link between optimal asset inflation and optimal monetary policy is demonstrated.
Keywords: asset inflation, credit expansion, overlapping generations, social welfare function, monetary policy.
JEL Classification: E31, E51, E58.

Arkin V.I., Slastnikov A.D. (Moscow) Compensation of Higher Interest Rates by the Government Support Mechanism
Economics and mathematical methods, 2014, 50 (3), 104-111.
We study the problem of compensating higher interest rates on loan with the help of non-tax government support mechanisms: co-financing of investment projects and subsidizing interest rates on loan. As a criterion for compensation it is considered optimal expected NPV of implemented project. We received the boundary within which the loan interest rate can be compensated by using the above mechanisms of government support. Moreover, we set a number of conditions under which compensation provides non-negative budgetary effect (i.e. the expected tax revenue from the implemented project will exceed the costs of supporting the project).
Keywords: investment project, loan, subsidizing interest rates, co-financing, compensation, budgetary effect.
JEL Classification: G2, D81, C61.

Pleschinsky A.S. (Moscow) Vertical Inter-Company Interactions with Controllable Price-Margin
Economics and mathematical methods, 2014, 50 (3), 112-133.
The mechanism of transactions between vertically connected firms with a controllable price-margin is offered and researched. The controllable price-margin is determined by the marginalization coefficient equal to the relation of the product price to average costs of the supplier. Models and the equations of vertical oligopolies balance before integration of manufacturers intermediate and an end-product and as a result applications of the contract form of transactions between the enterprises for the price below market and availability of the compensating transfer paid by the manufacturer of an end-product are developed. The bottom and top borders of margin factor are defined. While the margin factor decrease inside this interval, the profit of each firm applying the offered form of interaction, synergy effect and benefit of consumers increase from the values corresponding to absence of vertical control to the maximum sizes reached in case of creation by the supplier and the consumer of integrated firm.
Keywords: inter-company interactions, vertical integration, price-margin, balance of vertical oligopolies, contract price, synergy effect.
JEL Classification: D23, D43, L22.