**Pleschinsky A.S., Lasarev I.A.** (Moscow) *
Vertical inter-company operations in the markets with the domineering position of the some economic agents
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A model of sequential oligopolies is developed, taking into account the strategic nature of the firm's interactions in the product markets, imperfections in financial markets, and the effects of fiscal policy on firm's decisions. The "leader – follower" strategic interaction in quantity choice of the output is studied, and an explicit solution is obtained in the case of constant marginal cost and linear demand. The analysis also examines the effect of a firm's dominant position on: the prices and quantities of intermediate and final goods depending on the competitive environment; the level of organization of the financial system; and the parameters of fiscal policy.

**Katyshev P.K., Chernavsky S.Ya., Eismont O.A.** (Moscow) *
The estimate of the costs function in the agricultural production in Russia
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The authors analyze the costs function of the Russian agricultural enterprises. Behavior of the Russian agricultural enterprises corresponds to minimization of production costs, while the labor, fuels and electricity are statistically significant, while the fertilizes – insignificant production factors. The authors got the relevant price elasticity estimates of the production factors demand and of the agricultural output.

**Zeltukhin P.S., Lavrinov G.A., Khrustalev Ye.Yu.** (Moscow) *
Method of an estimation of the volumes of financing effecting high technology armaments
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A method of estimation of volumes of financing of high technology armaments ensuring increase of veracity of received values is described using a complex of a broader spectrum of parameters of military and technical requirements of the state.

**Zavelsky M.G., Pekarsky A.V.** (Moscow) *
Methods to improve efficiency of investment decisions at the stock market
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The authors analyze the results of testing their new indicators of the stock exchange market. They use the real market information (of the USA and Russia markets). These indicators will help to take better investment decisions.

**Zakharova Ye.A.** (Chelyabinsk) *
Structural shifts in inter-branch relations of the Russian agro-industrial complex for 1995–2003
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Some changes of the agro-industrial complex inter-branch relations structure took place in agriculture during the years of reform. There is a calculation of structural shifts effectiveness in the Russian agro-industrial complex for 1995 – 2003 in this article. Information of input-output tables was a basis for such calculation. Technological and structural components of branch changes were revealed. Moreover, agricultural products final demand shifts were calculated in compare others branches.

**Yegorova N.Ye.** (Moscow) *
Models and methods of express-analysis in choosing the schemes of taxation of the small business
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The author proposes the economic and mathematical instruments of express-analysis for selecting the mode of taxation of small businesses. The method is based on dichotomial approach used in the well-known

**Zotov V.V., Presniakov V.F., Rastolniy V.V.** (Moscow) *
The terms and concepts of business-process reengineering
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The history of business-process concept and the role of business-processes in enterprise functioning are described. It is noted that current discord hinders adequate evaluation of reengineering-project effectiveness in conceptualizing this term. The characteristics of technological systems and hierarchy of production structures and their dominating assets are described in connection with institutional factors of economic environment. The authors propose to interpret business-process reengineering as the continuous process of optimizing external and internal transaction costs which form transaction configuration of an enterprise in meeting business purposes.

**Andreev M.Yu., Pospelov I.G.** (Moscow) *
Stochastic ideal exchange model and actually infinite low prices
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Stochastic dynamic ideal exchange model with incomplete markets is considered. It is shown that at the certain realizations of an equilibrium trajectory and at a certain moment a full depreciation of monetary savings (default) occurs.

**Berezhnoy A.Ye.** (Moscow) *
The evolution of multi-tenors economic system
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The article presents a mathematic model of multi-tenors (multi-structural) economic system. Development of innovation technological tenors as well as of a stationary economy was described. The task of optimal management of the process of development was described and solved. It is shown that the fluctuations of economic indexes are immanent of the multi-tenors economy. The economic cycle is a result of development of innovative technological systems. A model shows the reasons for cycle formation.

**Nemitkina V.V.** (Moscow) *
Application of the optimization methods for the analysis and control of the information risks
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The article describes the mathematical model of correlation between the information risk and the amount of financing the information security measures. A model is the basis for optimization the task of allocation of the finance between the separate measures of protecting the information to lower the general risk. The author proposes a model of optimal economic amount of financing to provide information security.

**Kogalovsky M.R., Parinov S.I.** (Moscow) *
Metrics of the on-line information spaces
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The authors discuss the problems of a new branch in Sciences — metrics of the online information spaces, which arise from moving of socio-economic activities into online virtual environment. The particular focus of this article is online scientometrics based on the Socionet statistic services.

**Pozamantir E.I., Tischenko T.I.** (Moscow) *
Transport and economy: dynamic model of investment formation, usage and influence on volume and quality of production
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The main provisions of transport investment and its influence on the dynamics of the country's economic development in sectoral aspect are stated. Interindustry connections are described with the help of a modified model of dynamic input-output balance. Its specific features are: representation of each product by three positions corresponding to quality gradations; transport services' differentiation of quality gradations according to the character of consumers' demands; age structure of basic production assets of transport and other industries' influence on the volumes of services and goods related to the highest quality category; dividing production costs into parts proportional to the volumes of output and basic production assets; relations between dynamics of assets' age structure and investment volumes; dependence of direct costs coefficients on the age structure of assets and export share in the volume of product's realization; influence of gross added value on the total volume of products' final usage and its distribution.

**Itskhoki O.Ye.** (Moscow) *
Asymmetric price rigidity and the optimal rate of inflation
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The author studies the long-run optimal rate of inflation. We argue that various frictions in the functioning of markets may well lead to the optimality of a positive long-run inflation. The paper studies optimal long-run inflation in the environment with asymmetric price rigidity, when prices are more rigid downwards than upwards. We prove two main theoretical results. First, asymmetric price rigidity does not affect the expected equilibrium level of output in an environment with forward looking price setting by firms. Second, in the conditions of asymmetric price rigidity, it is optimal to choose a positive rate of inflation. Numerical calibration of the model suggested that the optimal rate of inflation falls within 2%.

**Eismont O.A.** (Moscow) *
Provision of the natural resources and endogenous growth in closed economy
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The paper investigates the relations between natural resource abundance, market structure, knowledge accumulation and economic growth, using a two-sector model of a closed economy with an imperfectly competitive resource sector. The obtained results contradict the common notion that resource abundance is detrimental to economic growth. It is found that the rate of knowledge accumulation is positively related to resource scarcity, while there is an inverse relationship between resource scarcity and growth. Claimed that it is Dutch Disease or similar effects, characteristic for an open economy, rather than resource abundance

**Borodin K.G.** (Moscow) *
Evaluation of agrifood market
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In the article specific aspects, connected with quantitative evaluation of condition of agrifood production market, are considered. The author also suggests the method, allowing to correctly fulfill quantitative evaluation within the limits of a posteriori approach. In contrast to known methods, this one takes into account the static comparative advantages in the production of certain goods and permits to fulfill an integral evaluation of agrifood market.

**Akayev A.A.** (Moscow) *
Analysis of solutions of general equations of microeconomic dynamics
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The general differential equation, describing the joint interaction of long-term economic growth and cyclical fluctuations of business activity, was derived for the first time. The equation has an integrated nonlinear investment accelerator that supports the persistent fluctuations in the economics. The scheme of approximate solution of derived nonlinear equation of macroeconomic dynamics by means of separation of business cycles with high fluctuations from slow-changing trend trajectory using averaging-out method of Krylov–Bogolyubov–Mitropolsky is suggested.

**Nakoryakov V.Ye., Gasenko V.G.** (Novosibirsk) *
Partial derivative equations in macroeconomics
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The systems of partial derivative equations of hyperbolic type for aggregate demand (AD) and aggregate supply (AS) as functions of two independent variables (time and price index) are suggested for macroeconomics. It is shown that two mechanisms have great influence on dynamics of AD and AS curves: kinetics, or the velocity, of equilibrium setting between AS and AS curves and cinematic waves of inflation and deflation. The current values of aggregate demand, aggregate supply and price index can be calculated within the model for both cases of crossing and not crossing AD and AS curves.

**Tsarkov V.A.** (Moscow) *
Ferhulst dynamics and capital growth dynamics for the economy
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The author analysis the general model of capital reproduction. He got the equation of capital growth at the certain points in time, in proportion to the cycle of capital return in the process of its reproduction. He states that with the nonlinear profit capitalization function the dynamics of capital growth is equal to Ferhulst dynamics, describing the population growth in Nature. The author formulates the hypothesis of the fractal economy, where exponential growth of the capitalist economy may become cyclic and even chaotic considering the level of marginal efficiency of the reproduction process.

**Belenky V.Z., Ketova K.V., Sabirova O.R.** (Moscow) *
Stationary states in the dynamic models with bounded trajectories
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The problem of finding stationary states in dynamic models with bounded trajectories is considered. Its solution is given on the base the "secular" equation for the fixed-points of optimal strategy, previously developed by the authors. For two variants of model (monoproduct – section 2, and multiproduct – section 3) the finite explicit formula for searched states is obtained.

**Zikhina A.V., Kaneva O.N., Ogorodnikov S.B.** (Omsk) *
The two-phase task of the stochastic programming for shaping securities portfolio structure
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The stochastic approach is used for the account and risk analysis in the portfolio model. The model is built up on the two-phase task of the stochastic programming.

**Golshtein Ye.G.** (Moscow) *
The methods for solving the variational inequalities, using the imperfect data
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The connection between solving variational inequality and finding the fixed element of the point-toset mapping from convex compact to itself is established. Examples of variational inequalities relating to the convex optimization, convex antagonistic game, convex many-person non-coalition game, the problem to find equilibrium prices are given. We describe an iterative method of the Oracle type for solving variational inequality defined by the monotone mapping under Oracle mistakes. We set the requirement to Oracle mistakes which guarantee to find -solution to variation inequality (with given > 0). The upper-bound for number of iterations necessary for calculating -solution to variation inequality is obtained.

**Ovsijenko Yu.V., Rusakov V.P.** (Moscow) *
Correlation between the institutional systems' character and the mechanism of their creation
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The authors introduce the concept of institutional system as an aggregate of inter-related institutions, creating the norms for all the forms of relations among the individuals and the organizations in all the spheres of social life. Defined are its features, functions and effects on the socio-economic dynamics. It is shown that there is a spectrum of such systems, while institutional changes in each are influenced not only by the national traditions, but by the functioning social structure. Some specific peculiarities of the Russian institutional dynamics are considered.

**Tatarkin A.I.** (Ekaterinburg) *
Macroeconomic conditions and organizational institutions of stable regional development
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Using the statistical material and outcomes of foreign and Russian practice the author discloses the model variants of growing the role of macroeconomic environment and institutional mechanisms (the forms) in providing the stable, balanced and socio-oriented regional development in Russia. Disclosed are the options of restructuring of the interfederal relations in strating the levels of power, budget incomes and expenses, rules and regulations for joint ruling etc. The author marks the problem of developing the regional strategies of socio-economic development.

**Golovan S.V., Karminsky A.M., Peresetsky A.A.** (Moscow) *
Cost efficiency of Russian banks, taking into account the risk factors
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The paper analyses cost efficiency of Russian banks. Models of banks' production function are developed using stochastic production function approach. We consider several models, and the models of particular interest are models, which include asset quality and risk-preferences as factors. Analyzing the estimations, we reveal factors (bank's size, region, participation in deposit insurance system etc.) influencing efficiency.

**Kudryavtseva O.V.** (Moscow) *
Ecological efficiency at macro-level: material flow analysis, input-output intersectoral model and export of water in the Russian economy
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The article presents an analysis of indirect material flows (used natural resources are included in input-output tables). The model permits to study at the macrolevel ecological, economic and social aspects of the influence on the national economy as a whole. An "ecological" rucksack of Russian export is estimated (water is an example).

**Belov A.V.** (St.-Petersburg) *
The regional allocation of production factors in the Russian Federation: equity or efficiency?
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This paper presents a non-econometric estimation of the production function for the federal districts of Russia over the period from 1996 to 2004. The empirical results show that the regional allocation of employment does not correlate with the marginal productivity of labor, but the distribution of capital stocks to be closely connected to the marginal productivity of capital. In such an environment, alternative ways of allocating public investment can boost total output but usually also widen territorial income gaps. The promotion of both growth and equality simultaneously is possible in the case of sufficient income-elastic labor mobility and efficiency-oriented investment policy.

**Rudnik P.B.** (Moscow) *
Price competition and the market structure in high-tech industries
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Based on the well-known Shaked-Sutton model the author constructs a model of price equilibrium for the vertically differentiated market, including the premises that a group of consumers is present in the market who are not interested in buying one or several products of comparatively low quality. It is shown that this premise is a substantive factor in for generating price equilibrium.

**Brodsky B.Ye.** (Moscow) *
Models of economic exchange
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Unlike Walrasian theories of the general economic equilibrium based on the hypothesis of price-taking behavior of economic agents, all models of exchange considered in this paper use an assumption that agents actively form market prices of exchanged goods via adjusting subjective prices of these goods in the exchange process. The following models of exchange are considered: elementary economic exchange, "market failure" models, and general models of economic exchange based on the market prices of exchanged goods. Theorems are proved about existence of a stable equilibrium in these models of exchange described by dynamical systems of ordinary differential equations (volumes of demand and supply, market prices) under usual assumptions about inverse demand and supply functions.

**Korotayev A.V., Malkov A.S., Khaltourina D.A.** (Moscow) **
A compact mathematical model of the economic and demographic development of the Wbrld System ****(1-1973 CE)**

Extremely simple mathematical models are developed to account for 99.2-99.91% variation of economic and demographic macrodynamics of the World System during the major part of 2000 recent years of its history.

**Golshtein Ye.G.** (Moscow) *
On the monotony of mapping related to the non-antagonistic two-person game
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We consider a two-person game and an associated mapping which in its turn generates a variational inequality problem. The problem of finding the Nash points of the game is reduced to the solution of the above-mentioned inequality. However the mapping thus related to a non-antagonistic game need not be monotone, where as the standard numerical methods to solve variational inequality problems work well when the mapping in question is monotone. In our research we have revealed a series of classes of non-antagonistic two-person games which associated mappings generating the corresponding variational inequality problem, are monotone.