**Smolyak S.A.** (Moscow) *
Project Efficiency Evaluation under Fuzzy Probabilistic Uncertainty
*
The structure of efficiency criteria for investment projects whose effect is random variable with unprecisely known distribution is studied. By this the various possible distributions of effect have various "degrees of possibility" and are formalized as fuzzy distributions.

**Denisov V.I.** (Moscow) *
Possible Lines of Production Support and Their Socioeconomic Evaluation
*
In the paper, proposed are a complex of new tools, not used before, to encourage home production development, a methodology of comparative evaluation of different lines of producers support, of variants
of interests harmonization in economic interactions in conformity with projected socioeconomic effects
from their realization at the level of enterprises, industries, and the national economy.

**Shagalov G.L.** (Moscow) *
Problems of Determining the Rationality of CIS Countries Exchange Rate Policies
*
The paper deals with problems associated with determining the rationality of exchange rate policy in
CIS countries. The purchasing-power parity (PPP) indices and the official exchange rates of European
CIS countries (Russia, Belarus', Ukraine Moldova) in 1992—1998 are compared. The effect of exchange
rate policy of these countries upon dynamics of external economic sphere macroeconomic indices is investigated.

**Maksimov V.A., Nekrasova I.V.** (Rostov-na-Donou) *
Forecasting Return on Investment in the Stock Market
*
In the paper, the possibility of using factor models to forecast return on investment in the sock market
in investigated. As factors, market profitability index, enterprises' capitalization volume, and book-to-market ratio were taken. Testing one-factor and three-factor models shows that the latter explains the
income formation process with more reliability.

**Kruchinin L.A., Smorgonsky A.V.** (Moscow) *
Price Dynamics in a System of Interacting Enterprises
*
The paper deals with a model of interaction of a large number of enterprises connected by mutual supplies under a stable production process. The significant model parameters are determined and their bifurkation values, determining the moment of emergence of a tendency to unlimited growth of production
prices, are found. The dynamycs of the enterprises' economic indices under different conditions of their
work is investigated.

**Latyshev N.V., Moushkov A.Yu., Tyulin A.E.** (Tver) *
On the Efficiency of Development of Complicated Special-Purpose Systems
*
In the article, a method is described of forming a rational plan of socioeconomic development of a region
with taking into account interests of development of a regional industrial complex, participating in development and production of special-purpose systems.

**Bat'kovsky A.M., Korobov S.P., Khroustalyov E.Yu.** (Moscow) *
An Optimization Method of Defense Expenditures under Hard Budget Constraints
*
The process of management of armed forces building and development under specific conditions of severe shortage of funds in considered. A methodological approach to solving optimization problem of
planning limited resources in the interests of defense budget formation is suggested.

**Levin V.L., Levin M.I.** (Moscow) *
A Model of Indivisible Goods Privatization under Corruption
*
In the work, a model of privatization of indivisible goods under corruption conditions is proposed. The
basis of our considerations is new concepts of regular, strong regular and maximum equilibria. The primary variant of this model was studied in [1]. In this work, the assumptions made in [1] are considerably
weakened and that makes it possible to cover a more general case.

**Goubanov V.A., Kovaldzhy A.K.** (Moscow) *
Season Fluctuations Separation on the Basis of Variational Principles
*
A distribution-free procedure for separating "season waves" (cycles) from arbitrary time series based on
variational principles is considered. In its initial statement, the problem is not correct in Tikhonov's
sense. A regularization suggested separates a class of solutions for which the problem becomes correct.
It is shown that the existence of singularities in the initial realization leads to trend "noising". The preciseness of "season wave" restoration depending on series parameters is estimated. Numerical results
for model series and a number of macroeconomic indices are presented.

**Perminov S.B., Vaschilko T.V.** (Moscow) *
Econometric Cross-Impact Analysis of Share Prices in Stock Market Technological Sector
*
In the article, a method of identification of statistical, causal relationships between share prices and stock
market indices as a tool for their forecasting is considered. As a statistical base of calculations, series of
daily quotations for 1991-1999 for some major companies and of stock indices are used. To evaluate
the influence. Granger's test is applied. It is shown that the application of this approach is especially advisable when a great number of market participants is considered and it is necessary, first of all, to establish the fact itself of the existence of causal relationship. In this case, the method suggested makes it
possible to identify market leaders and to essentially narrow the domain of possible regressors search in
a more detailed statistical analysis.

**Ilyichev V.G., Ilyicheva V.V.** (Rostov-na-Donou) *
On the Problem of Apartments Exchange Modeling
*
A mathematical formalization of the problem of searching mutually beneficial apartment exchanges is
suggested. The focus of investigation is the matrix of scalar products of weight vectors, describing the
clients' preferences, and vectors of apartments' characteristics.

**Pugachev V.F., Pitelin A.K.** (Moscow) *
National economy evaluation of investment projects
*
Quantitative relationships between market values and national economy evaluations of investment
project efficiency are investigated. A technique is proposed of determining industry effect multipliers
(IEM) by means of an interindustry simulation model of the Russian economy. Results of calculations
for different variants of economic policy are presented. Approximate methods of calculating investment
project effect multipliers (IPM) are developed. Recommendations are given on regulation of investment
by the state.

**Asanov A.A., Borisenkov P.V., Larichev 0.I., Naryzhny E.V., Roizenzon G.V.** (Moscow) *
The TSIKL multi-criteria classification method and its application to analyze credit risk
*
A problem of testing banks' credits depending on their riskness is discussed. The problem is studied as
that of milti-criteria classification. A new method to solve it (the TSIKL method) is proposed. The effectiveness of the method proposed is proved. A procedure is described of applying the method to the
practical problem in question.

**Volkonsky V.A., Kouzovkin A.I.** (Moscow) *
Fuel and energy prices. Investment. Budget
*
The authors consider the problem of rationality of energy carriers price levels and of the corresponding
financial flows. A comparison with the USA and countries of Western Europe is given. Estimated costs
and incomes for the gas and oil industries with taking into account sales in the domestic market and export, as well as changes in resources for investment and in rental income under the suggested changes
in prices are presented.

**Pakhomova E.A., Veselova D.E.** (Dubna) *
The development of the housing in Russia and an econometric analysis of the flat market in Moscow
*
The authors consider qualitative characteristics of the Russian quarter market. The present condition of
the hosing sphere is evaluated and an econometric analysis of the flat market in Moscow is given. The
influence of random and dummy variables upon a flat's price prediction is tracked.

**Khroustalyov E.Yu., Tsymbal V.I.** (Moscow) *
On the mechanism of economic support
of military construction
*
A number of rules is substantiated according to which the mechanism of economic support of military
construction should function. The main procedures have been developed for coordination of the budget
process in the RF with processes of military construction administration and implementation of the military reform. Formulations of problems and possible methodological approaches to their solution are
stated within the framework of the target program budget planning of transformations in the Russian
military system.

**Vygon G.V.** (Moscow) *
Determining the fundamental value of oilfields: the real options method
*
A model is suggested to calculate the fundamental value of fields of different categories of oil on the
basis of the real options method. This approach allows to evaluate the significance of optimal management under high oil prices volatility and to take into account such specific features of oil companies as
the qualitative difference of oil fields by the degree of their development and the dependence of extraction dynamics on the degree of depletion.

**Pleschinsky A.S.** (Moscow) *
The equilibrium transfer prices under vertical interaction
of production economic agents
*
The author considers the relations between the supplier's and the consumer's net profit and amount of
transfer, rate for intra-group transactions and own circulating assets. The values of the transfer price
mechanism parameters are determined for which total production agents' profit is maximum. Formulae
are obtained to calculate .rates for intra-group transactions and transfer for which the supplier and the
consumer have positive net profit increments in relation to its maximum value in the case of using market prices. It is proved that transfer prices effects for the supplier, the customer and the state are positive
for any relationships between own means of production agents and their needs of circulating assets when
the financial market is well developed and for a solvent supplier and/or when the consumer's funds are
insufficient in the case of a non-developed financial market. A model of equilibrium transfer price mechanism is proposed. It is shown that the equilibrium set is the set of optimal - by the total net profit maximization criterion - agents; states with rates for intra-group transactions providing non-negative effects
for the supplier and the consumer. When using the equilibrium mechanism of transfer prices and reinvesting profit, the agents function on a stationary trajectory and it gives total net profit, equal - ceteris
paribus - to maximum net profit of a vertically integrated firm consisting of these agents.

**Kovalenko A.G.** (Samara) *
Interindustry balance mathematical models under a dispersed market
*
The author considers mathematical models of a multi-product market consisting of interlocking dispersed markets. The static model describes a multi-product market in an equilibrium state. Methods of
searching for an equilibrium state based on mathematical methods of hydraulic circuits are proposed.
The dynamic model of a dispersed market is a sequence of its interlocked equilibrium states. The model
allows - with taking into account consumption of irreproducible resources - to forecast the development
of market subjects over time, to simulate competition among them and governing impacts on the system
to regulate market relations.

**Belen'ky V.Z., Aroushanyan I.I., Trofimova N.A., Frenkin B.R.** (Moscow) *
A polyproduct dynamic interindustry model of the national economy with an optimizable foreign trade block
*
The article completes a cycle of methodological research on developing a dynamic interindustry model
which, unlike traditional tools, takes into account the specific features of the modem situation in the
Russian economy. The central idea of the work is optimization of the foreign trade block on the basis of
the maximum economic growth principle.

**Fomin A.S.** (Moscow) *
Price-formation policy analysis when developing a queueing system
*
The article deals with analysis of a price-formation policy where maximum profit is ensured for the developer whereas maximum conservation of budget is ensured for the customer.

**Vasilyev A.N.** (Kiev ) *
A self-organizing model of the labor market
*
The mechanism of labor market functioning is considered as an example of economic model of self-organization. To describe dynamics if such a process, a differential equation is suggested and the main properties of its solutions are analyzed. It is established that this economic system has two stationary states and only one of them is stable. The results obtained are analyzed from the point of view of modem economic ideas about the nature and character of the problem of employment.

**Ivanova N.Yu., Orlov A.I.** (Moscow) *
Economic and mathematical modeling of a small business
(a review of approaches)
*
Two interlocked problems are discussed. What economic and mathematical methods and models can the
head of a small organization use in his (her) work? What economic and mathematical methods can describe dynamics of small organizations? The authors use their experience of administering small organizations, teaching small entrepreneurship and scientific studying small business.

**Glouschenko K.P.** (Novosibirsk) *
Spatial behavior of price levels
*
With the use data on price levels for foodstuffs and manufactured goods from regions of Western Siberia for 1994-1998, the author investigates whether a convergence to a single price takes place. Theoretical grounds for econometric models used for testing the observance of the law in the strong and the weak forms. Estimates are given of the degree of convergence of regional price levels to the average for Russia and to other regions' price levels, as well as magnitudes of thresholds on the way to interregional exchange.

**Bagrinovskii K.A., Goroshko I.V.** (Moscow) *
Concerted control in a social organization-system
*
The authors study possibilities of improving activity of social organization-systems and concerted controlling them. With the use of home affairs authorities as an example, specific problems of harmonization are considered and approaches to their solution are formulated. Special attention is paid to a topical problem of harmonizing interests of local and federal authorities in matters related to home affairs authorities'terms of reference.

**Frolova L., Kauzhena D.** (Riga) *
Environment protection and business in Latvia
*
In the article, the results of a poll where enterprises answered a number of questions concerning interaction between invironment protection and business are analyzed. The base of the analysis are strategic, organizational and technological factros, each of them is characterized by seven indicators. To find the necessary equilibrium among these factors, the comparison method and the evaluation method are used. The technology of equilibrium model formation suggested in the article is a step-by-step process. The results of analytical calculations with the equilibrium model show that Latvia reached the 52.4-percent balance between environment protection and business. This means that the trends of business development in Latvia are positive and they are aimed at using soft technologies.

**Kossachiov Yu.V.** (Moscow) *
Efficiency of innovations-implementing corporate structure
*
On the base of analysis of a dynamic model of interaction between enterprises and a bank which are components of a vertically integrated corporate group, economic efficiency of the group is studied in introducing innovations permitting making new competitive products. With debt and equity relationships in the group taken into account, a model is optimized of intra-corporate equity financing of innovations. The stability of the dynamic model is secured by reaching the equilibrium state in a differential game. Conditions are established for preliminary selection of an innovation project for its efficient implementation.

**Andreyev G.I., Vitchinka V.V., Ostapenko S.N.** (Tver) *
A methodology of comparative evaluation of patterns for complex special-purpose systems
*
The authors propose a methodology of comparative evaluation of patterns included in a complex special-purpose system which satisfies the state's needs of defense. This methodology is designed for determining the adequacy of patterns to requirements for them and for evaluating prospects of their further development and their inclusion in short-term and long-term plans.

**Tiabin V.N.** (Obninsk) *
A complex of macroeconomic models of inflation
*
The authors propose a complex of macroeconomic models reflecting interrelationships among growth rate of price levels in the consumers' market, changes in output and unemployment level. The analysis of the model allowed to develop recommendations on ensuring control over inflation level and unemployment level, as well as on choosing the optimal level of overcoming crisis situations.

**Levin M.I., Levina E.A.** (Moscow) *
Modeling lobbying
*
The article presents a review of models of lobbying activity existing in literature. The models are classified by methods of research and subdivided into statistical and game-theoretic models.

**Beer K., Golshtein E.G., Sokolov N.A.** (Hemnitz (Germany), Moscow) *
A method of looking for the saddle-point of a function the domain of which is contained in a polyhedron
*
In the article, a method is described of looking for the saddle-point of a not necessary differentiable convex-concave function the effective set G

**Strotsev A.A.** (Rostov-na-Dony) *
A modified Braun method for solution of a "non-classic"-type matrix game
*
Diversity of decision-makers' preferences in economic problems has engendered diversity of decision-making criteria under uncertainty. Application of a number of criteria in forming a conflict situation model leads to changing the structure of traditional models which entails the impossibility of direct application of well-known iterative procedures to obtain the solution. A modification of the method proposed by Braun is considered for solving a mixed extension of matrix games with the purpose of its generalization for a wider class of problems. The connection of this approach with game processes of a more general type is shown.

**Kleiner G.B.** (Moscow) *
Economic and mathematical methods and economic theory
*
A new conception is suggested of the role and place of mathematical modeling in the system of theoretical and applied research which widens the traditional view of mathematical models only as of an instrument of economic analysis. The role of economic and mathematical modeling is substantiated as an independent scientific and applied line of scientific thought performing functions of the interlink in the "economic theory-economic policy-economic practice" ternary. Formulated are some problems associated with development of economic and mathematical and adjacent directions of research.

**Ovsienko Yu.V.** (Moscow) *
Socioeconomic changes in Russia on the eve of the Third Millenium
*
On the basis of analysis of official statistical data, quantitative evaluations of the changes in distribution of incomes of the polulation of Russia for the period of 1992-99. Their causes are discussed. It is shown that the dynamics of these changes have tended to moving away from the equilibrium.

**Perlamoutrov V.L., Troparevskaya L.E.** (Moscow) *
Financial flows and the real sector of the Russian economy
*
For securing investment influx into the real sector of the economy, systemic transformations are necessary, concerning developed market formation, releasing own sources of economic growth and extended
reproduction of domestic capital. Also necessary are government measures, reducing risks of financial
resources spillover from other spheres of the economy and promoting their concentration within strategic mainstreams of development.

**Pleshchinskii A.S.** (Moscow) *
Dynamic efficiency of the equilibrium transfer prices mechanism
*
The object of investigation is the path of a supplier and a consumer functioning when they use the mechanism of equilibrium transfer prices and reinvest profits. Formulas have been obtained to calculate the
parameters of the equilibrium state. It is shown that the strategically optimal is the equilibrium path under the maximum permissible transfer rate. Under holding, where the permissible value of such a rate
can be larger, the agents' total net discounted income is increased in relation to the variant of equilibrium
path under economically independent enterprises vertical interaction.

**Golitshenko O.G.** (Moscow) *
Problems of regulating economic growth in macroeconomic models
*
The author considers the evolution of theory of economic growth from the Harrod-Domar model to the
"new neoclassical wave". It is shown that within the framework of the neoclassical theory (including
taking into account endogenous scientific and technical progress too) there is no reallocation of means
among production factors through which long-term growth could be achieved the rate of which were
not be determined by an extensive factor - the growth rate of volumes of labor used. Possibilities are
studied of modeling economic growth at the expense of the innovation component of development within the framework of the new neoclassical school. A model of production function is suggested, taking
in account the relationship between accumulated volume of technological knowledge, efficiency of labor and structure of fixed capital. Interrelationship is shown of this approach with those of the former
and the "new" neoclassical theory. For the class of models in question, factors of economic growth based
on innovations are studied and possibilities of realizing these factors are analyzed.

**Kotel'nikov V.P.** (Rostov-na-Donou) *
On distributions of the Cobb-Douglas production function values
*
A new solutions to the problem of identifying distribution of the Cobb-Douglas production function values the parameters and controlled variables of which are random vectors with correlated components.
The possibility is shown of using it to solve problems of multivariate combined distributions of considerable generality.

**Danilov V.I., Lang C.** (Moscow, Geneva) *
The gross substitutability property for piecewise linear
demand functions
*
The article deals with studying the gross substitutability property of demand generated by utilities, quasi-linear with respect to money. For piecewise functions the gross substitutability property is easily expressed in terms of the function tesselation. With the use of this criterion, it is shown that the gross substitutability emplies submodularity of the utility function and is equivalent to supermodularity of the Fenchel-conjugate function.

**Afanassiev A.A.** (Moscow) *
A model of natural inflation rate in an economy with a cost mechanism
of price formation and soft budget constraints for enterprises
*
The author presents a model of natural inflation rate that describes an economy, not governed by some
principles on which the quantity theory of money is based. Existence and uniqueness theorems have
been proven for equilibrium in the absence of nonpayments and nonrealized production stock, as well
as that of equilibrium existence in their presence.

**Levin V.L.** (Moscow) *
Model research of corruption under privatization
*
The author studies a closed equilibrium model of corruption under privatization. Unlike models described earlier (see [1], [2]), the scale coefficient of penalty functions acts as an endogenous variable,
determined from the condition of sum of bribes minimization. To organize bribe revealing checks, a
fixed amount of money is assigned and all additional expenditures connected with conducting these
checks are covered at the expense of penalties. The existence of stable equilibrium with minimum corruption level is established and its properties are described.

**Mitsel A.A., Kashtanova 0.V.** (Tomsk) *
On an algorithm of forming the optimal portfolio
of investment projects
*
The authors consider algorithms of solving a problem of choice of the optimal investment project portfolio on the basis of a model with loan and equity capital. An original algorithm is proposed for solving
the problem of portfolio optimization with loan capital. The results of the modeling are presented.

**Sedova S.V., Lebedev S.S.** (Moscow) *
A nodal vectors method for integer programming problems
with special relations between integer-valued and continuous variables
*
A new method of partially integer programming in which so-called nodal vectors of resolving multupliers are used to screen integer-valued variants is applied to special-type problems. The results of a computational experiment for a problem with fixed afterpayments are described.