**Polterovich V.M.** (Moscow) *
Strategies of the institutional reforms. Promising trajectories
*
This is the first part of the research devoted to the problem of the choice of institutional reform strategies. A strategy is defined as a planned trajectory of institutional changes in time. Three types of strategies are compared: shock therapy, gradual growing, and interim institution strategy. A concept of a promising trajectory is introduced; this is a trajectory that has good chances to be successful since it meets a number of requirements. A promising trajectory has to be agreed with technological, resource and institutional constraints, and should provide built-in mechanisms to stimulate planned institutional changes and to prevent dysfunctions and institutional traps. In particular, such a trajectory has to take into account national cultural peculiarities, static and dynamic institutional complementarities, and political decision making mechanisms. It is necessary to restrain redistributive activities and envisage compensations to those who could lose due to reforms. Institutional changes have to be supported by measures directed to form positive institutional expectations, and by government policies stimulating economic growth. In the second part of the work, proposed analytical tools are implemented to compare reforms in Russia and China.

**Shokhor S.L.** (Moscow) *
About the influence of optionality on a choice of investment decisions
*
The optional approach to the analysis of investment efficiency in the conditions of uncertainty is considered. The short reference of the main points of the theory of real options is given. The approach to the estimation of capital investment projects which provides a possibility of representing a project as a sequence of trivial investment decisions is proposed. The number of additional prepositions about the properties of this sequence is made, allowing to consider different levels of controllability of the project. Correspondence between the parameters determining an estimation of an option as a financial instrument and parameters of the project is proposed. The influence of administrative flexibility on economic value of the project is shown.

**Bulgakov V.K., Bulgakov O.V.** (Khabarovsk) *
Modeling the dynamics of the aggregated economic parameters for the regional economic systems in Russia
*
The authors propose a new class of production functions (

**Egorova N.Ye., Khachatrjan S.R.** (Moscow) *
Application of the differential equations for the analysis of dynamics of the small enterprises development using credit-investment resources
*
The economic-mathematical models grounded on the solution of the common differential equations, describing various methods of investment in small business (self-financing, the state support, crediting) are presented. Models allow to research dynamics of small enterprises development depending on the selected investment strategies: "pure" (one investment resource) and "mixed" (mixed financing schemes) and also to describe the conditions of credits availability.

**Arkin V.I., Slastnikov A.D.** (Moscow) *
Tax holidays optimization in the stochastic model of a new enterprise creation
*
In the framework of the model of "wait to invest" that describes behavior of a potential investor wishing to invest into the project of a new enterprise creation, we construct the model of investment attraction by tax holidays. In the paper we obtain and analyze optimal tax holidays which give maximum expected discounted tax payments from a future enterprise into the regional budget.

**Kuchaev A.I., Pomansky A.B.** (Moscow) *
Share auction
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Share auction (simultaneous sale of large shares) as an alternative to the sale of the large companies is researched. Besides the increase of a number of participants because of weakening budget constraints, the auctioneer has a possibility to increase income owing to an additional competition for the right to control the company.

**Mednitsky V.G., Mednitsky Yu.V., Tsurkov V.I.** (Moscow) *
Decomposition approach to the solution of the optimization problems for the production systems structures
*
The authors describe the relations between the optimization of the production systems and the estimation of economic efficiency of those discrete elements, from the sets of which one may compose the production structures. These relations have been found in search of algorithms for the optimal solutions of some problems of the stochastic linear programming with the mixed-integer variables.

**Rodionov M.M.** (Moscow) *
About one descriptive model of granting credit limits
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Aggregate risk of a credit portfolio is often a subject of trade. Before discussing the terms of transaction a seller and a buyer have to reach an agreement on how to participate in individual losses in the portfolio. Such an agreement changes distribution of total loss of each party for the given credit portfolio. A model of such an agreement on participation in individual losses is described. Equation for calculation of credit limits in case of power functions of utility is given. The outcomes of the model are compared with a common practice in factoring and credit insurance.

**Zikina A.V.** (Omsk) *
Consequent optimization for multi-criteria task
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The author examines the influence of all the levels of priorities on the decision using the method of consequent concessions for the case of consequent optimization of multi-criteria tasks. Applies the mechanism of generalized decisions for parametric systems.

**Korkhin A.S.** (Ukraine) *
Linear regression and two disparity-inequalities
*
The author analyses the linear regression with the arbitrary finite number of parameters. These parameters are estimated with two linear disparities of general type. The factors on the left and the right-side disparities are known. No instructions for disparities for the specific sample are demanded. Gives the ratios for the estimation of matrix of average square (powers) of errors of the parameters of regression and remainder dispersions.

**Polterovich V.M.** (Moscow) *
Strategies of the institutional reforms. China and Russia
*
This is the second part of the work devoted to the problem of the choice of institutional reform strategies. In the first part a concept of a promising trajectory was introduced. This is a trajectory that has good chances to be successful since it meets a number of requirements; their list was discussed in detail. In this paper, proposed analytical tools are used to compare reforms in Russia and China. It is shown that China had no significant advantages with respect to initial conditions. However, Chinese reformers, in contrast to the Russian ones, followed theoretical recommendations and choosed promising trajectories as their strategies. This observation explains the difference in the reform outcomes, and may be also considered as evidence in favor of the theory suggested.

**Goncharenko A.B.** (Moscow) *
Two approaches to modeling the population mobility
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The author gives the comparative analysis of two "pull-push" models (attraction and repulsion between the groups) - the gravitation model, based on the distance between the groups, and the model connecting the inter-group flows with the comparative quality of life in these groups. The results prove the possibility of complex modeling the population mobility based on both grounds.

**Ivanov P.M.** (Nal'chik) *
Stable regional development: concept and operational model
*
The author proposes the concept of stable regional development, based on Le Chatelier principle in the thermodynamic equilibrium, as well as on the principle of flexibility and adaptability of the regional system. The operational model of regional development of adaptive system with the identificator is being built. It allows to immediately reacting to any system perturbances threatening the loss of the quality of life in the region. The adaptive system with the identificator is based on the economic-mathematical model of regional development being included in the feedback loop of regional operation system.

**Belenky V.Z.** (Moscow) *
The operation of ratio-conjugate and its application in linear-homogenous models of economics
*
The author describes the mathematical tools based on the operation of ratio-conjugation in the space of convex linear homogenous monotone functions. In these spaces the RC-operation is much more conten-sive and informative than the known Jung-Fenchel operation of conjunction (additive) in the convex analysis. It is shown that the RC-tool is an effective instrument for the analysis of linear homogenous models of the economy, in particular in the Neiman-Gale models, as well as in the theory of aggregation.

**Gurvich Ye.Ò., Andryakov A.D.** (Moscow) *
The mechanisms of financial crisis in Russia
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A "hostage effect" giving the government the opportunity to impose a part of costs of financial crisis mitigation on investors is introduced and analyzed. It is shown that the framework of the "hostage effect" model traditional approaches to preventing the crisis within the model describing the "hostage effect" may have negative consequences. The authors analyze the mechanisms of the financial crises in Russia in 1998, and give the explanations of the results of IMF credits for Russia before the culmination of the crisis.

**Abramov A.P.** (Moscow) *
Turnpike, prices and the free enterprises
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The article describes the financial mechanism using which a multisectoral economy can work in accord without a control center. The sectors define a volume of output in a planned period based on the maximum profit, thus the cost of production depends on a volume of sales. The existence of dynamic system of the prices retaining economy on a turnpike is proved.

**Golstein Ye.G.** (Moscow) *
Minimization of quasi-convex functions, using imperfect data
*
The article describes the Oracle-type method for the minimization of quasi-convex Lipschitz-continues function with the errors in the Oracle's responses. The method is based on the cuttingplane procedure where the search of clipping center is reduced to the task of linear and quadratic programming problems. For every iteration the auxiliary polyhedron is constructed, some expansion of which depends on the number of Oracle's errors and contains the required minimum. A number of iterations is found, necessary for finding the e-minimum point of the function, that depends on the characteristics of a class of the minimizing functions and the Oracle's errors. The author specifies the method for convex and differen-tiable quasi-convex functions.

**Ziljakov Ye.G.** (Belgorod) *
Adaptive definition of the relative importance of the objects based on the qualitative pare comparisons
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The author proposes the variation method for data processing for the paired qualitative comparisons of the objects to define their relative importance in the form of their positive weights without a priori development of the scales of propositions. The interpretation of the elements of paired comparisons matrix in the functional form of weights is used as a base of the method.

**Ustuzanina Ye.V.** (Moscow) *
Privatization: the lessons in history
*
Within the last twenty years we have been witnessing the struggle of two tendencies: the privatization of economic activity and etatization, whose essence is keeping the bureaucratic pressure on the economy. The history of Russian privatization can be divided into five stages: spontaneous privatization, official privatization, redistribution of participation, corporate wars, interference of government. The survey of legislative innovations and enforcement practice at every stage is given in the article.

**Tarasova N.A.** (Moscow) *
Modeling and forecasting the hidden (and shadow) elements of employment and incomes
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The article offers the methods of modeling and forecasting the hidden (and shadow) elements on different levels of structurization of population and their incomes: function layers, social and socio-economic (profit) groups of population. These elements reflect opacity of incomes of the population. These elements are: shadow employment of employees and the other employed (herein called "businessmen" or "business owners") and shadow incomes of shadow employed and hidden incomes of officially employed.

**Makarov V.L., Vasiliev V.A.** (Moscow, Novosibirsk) *
Information equilibrium. I: Existence
*
The following series of articles deals with the existence and coalitional stability of information equilibrium - an analogy of Walrasian equilibrium, introduced by V.L.Makarov for the economies with externalities. The first article presents general information equilibrium existence theorem, similar to that proved by T.C.Bergstrem and A.Mas-Colell for the classic competitive equilibrium. The basic tool, applied by the authors, is so-called information extension of the initial non-autonomous economy, closely linking exchange models with and without externalities.

**Movshovich S.M.** (Moscow) *
Procedures of bilateral bargaining
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We consider multistep negotiations to make a deal between a buyer and a seller. Their information about each other is incomplete, the number of steps is limited, there is no discount. The protocol of negotiation is formalized as a game. It is shown that a maximum of an expected payoff doesn't depend on a number of steps in games where the players make their moves either in turns or simultaneously. In both types of game the results are unsatisfactory. The mechanism of negotiation is offered that leads to essentially more fair and efficient result.

**Yershov E.B.** (Moscow) *
Implicitly-superperfect price and quantity Divisia indexes
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The family of Superperfect Divisia price and quantity indexes (Yershov, 2003), which includes Fisher and Montgomery indexes as special cases, is extended. For such indexes commodity prices are linear functions of parameter

The facts that (1) implified Tornquist indexes are implicitly-superperfect, and (2) implified Laspeires and Paashe indexes cannot be represented in the form of Divisia indexes are proved. Comparative analysis of Fisher, Montgomery and Tornquist indexes is provided. Knowledge about paths, which generate implicitly-superperfect Tornquist indexes, allows to introduce new class of Divisia

**Lebedev S.S., Sedova S.V.** (Moscow) *
The Decomposition method of integer programming
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New integer programming method, based on the decomposition of the variants' graph, is presented. It is described for the special charge problem, but can be easily modified for the general problem of the linear integer programming.

**Ashepkov L.Ò., Kossogorova I.B.** (Vladivostok) *
The interval task of linear programming
*
The article summarizes the research of the common interval task of linear programming. Such tasks can be used for many economic applications; for example, in the models of forecast planning expert estimations, prognoses or design accounts of the future manufacturing metrics are used (value of production, inventories of resources, technological specifications etc.). Arising uncertainty and lack of the information on allocation of input data in the set intervals hinder application of well developed theory of parametric linear programming, stochastic optimization and demands the other approaches. The authors' approach is based on idea of finding one "comprehensible" solution for all parametric set of tasks of the linear programming generated by "harmless" assumption of input data.

**Smoliak S.A.** (Moscow) *
Interpolation of the function of several non-digital variables
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The article concerns the problems of restoration of the values of the functions of several variables using its precise or approximate values at random points. It is a common task of interpolation for the functions of digital variables. The author describes the problem arising in the assets valuation and in some other cases - the problem of restoration of functions for nominal or local variables. The heuristic optimization methods proposed, based on the formalization of the discrete analogue of the "smoothness" of the function.

**Trofimov G.Yu.** (Moscow) *
Economics and the neuroscience on the way of synthesis
*
The paper surveys the most recent results in the field of Neuroeconomics - a new discipline, an the interface between neurosciences and various fields of theoretical and applied economics. The main concepts and implications of this trend of research are related to the issues of individual choice under uncertainty, modeling of consumer utility, intertemporal preferences and to some examples of experimental games.

**Dementiev V.Ye.** (Moscow) *
A trap of technological adoption and the terms to overcome it in the two-sectors economic model
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The model of the economic development combining innovational and imitating processes is described. The sector of manufacture of knowledge is allocated. The model takes into account, that conditions of attraction of knowledge and technologies from abroad vary in the nonlinear image depending on a distance up to the leaders. It is shown, that orientation mainly on use of foreign technologies conducts to preservation of economic backwardness. At the same time, the model reveals limitation of independent technological development. The numerical variant of model illustrates opportunities of overcoming of the trap generated by the technological dependence.

**Akaev A.A.** (Moscow) *
Model of balanced economic growth for the steady reduction of poverty
*
In is shown, that the model of balanced economic growth is most applicable for the purposes of the steady long-term reduction of poverty. Parities for calculation of the guaranteed and potentially possible maximum rates of growth in economy in conditions close to balanced, are received. Forecast estimations of the rates of growth and reduction of poverty for 2006-2010 are calculated, using the example of development of the economy of the Kirghiz Republic.

**Makarov V.L., Vasil'ev V.A.** (Moscow, Novosibirsk) *
Information equilibrium. Coalition stability
*
The paper deals with some extremal properties of information equilibrium, including weak Pareto-opti-mality and coalitional stability w.r.t. representative fussy coalitions. A new concept of representative fuzzy core for exchange economies with externalities is introduced, and a corresponding core equivalence result is established. As a consequence, the famous Debren-Scarf theorem on shrinkability of the cores is extended to the case of information equilibrium.

The main results of the second part of the series of papers devoted to the information equilibrium are generalizations of the pioneering coalitional stability theorems, obtained by the authors.

**Katyshev P.C, Polterovich V.M.** (Moscow) *
Reform policies, initial conditions, and transformational recession
*
In this paper we formulate and substantiate a hypothesis that the magnitude of the transformational recession in transition economies in the last decade of XX century was determined not only by initial pre-reform conditions but also by privatization policies. Results of regression analysis that confirm this hypothesis are presented. It is shown that GDP decline during the first 9 years of reforms was the greater the more radical privatization at the start of reforms was. Our calculations also demonstrate that governments selected the starting speed of price and foreign trade liberalization taking into account the initial conditions. This observation may explain the non-significance of the speed of liberalization in the regressions.

**Belenky V.Z., Ketova K.V.** (Moscow, Izhevsk) *
The complete analytical decision of the macro-model of regional development for the exogenous demographic prognoses
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Considers the one-dimensional model of the regional development with the exogenous function of the prognosis of the human resources dynamics (for the infinite perspective). The authors use the two-steps approach: in the first step one can obtain the stationary model with the exponent growth of the human resources; in the second step one can generalize the obtained decision using the maximum principle. This technique allows to make the full mathematical analysis of the model.

**Brodsky B.Ye.** (Moscow) *
Retrospective analysis of structural breaks on the basis of econometric models
*
The problem of retrospective detection and estimation of structural changes in regression models and systems of simultaneous econometric equations is considered. The asymptotic lower bounds for the main performance criteria of estimation are proved. The asymptotically optimal methods for estimation of structural changes in regressions and systems of simultaneous equations are proposed under assumptions of dependent