**Balatsky E.V.** (Moscow) *
Reproduction cycle and tax burden
*
IN the article, a methodology is stated of estimating the maximum permissible level of tax burden for legalentities where the economic structure can effect extended reprodution. The methodology has been tested on Russian statistical data. Analyzed are Laffer's effects as applicable to the aggregate tax burden. An approach is developed to estimating nominal and effective tax burden and the corresponding experimental calculations have been carried out. Foreign investment potentialities for stimulating economic growth in the recipient country are discussed and the role of fiscal, investment and technological factor in this process is shown. Disclosed are shortcomings of the modern tax system of Russia.

**Bagrinovsky K.A., Prokopova V.S.** (Moscow) *
A new approach to analysis of inter-industry exchange equivalence
*
Three concepts of inter-industry exchange (HE) equivalence are considered. One of them corresponds to the payment according to labor principle, the second - to equal rate of return on capital advanced in different industries under inter-industry competition of capital. The third concept of HE equivalence is connected with simultaneous influence of the two above-named principles.

**Malyshev V.L.** (Moscow) *
"The rules of the game" and transaction prices
*
The article deals with problems of introducing relationships, peculiar to institutional norms of behavior in the real economic mechanism of manufacturers' activity. In this case, initial parameters are estimated gross effect of the use the product at the customer's (the upper limit of prices).

**Goussev A.A., Kozmenko S.N., Kozmenko O.V.** (Moscow, Sumy) *
Emergency situations: economic damage and investments in the prevention
*
More exactly defined is the terminology applied in investigation of economic problems of emergency situations of nature and anthropogenous origin. Methods of probability and value estimation of economic damage and first of all - of indirect one. Methodological grounds of managing emergency situations at different stages of their development are considered. Also the problem of rationalizing the allocation of limited investment resources for anti-catastrophe purposes among several regions of a certain territory is considered and an appropriate methodology is suggested.

**Glazyrina I.P., Glazyrin V.V.** (Tchita) *
Ecological debt and information support of decision-making procedures
*
Some issues of state regulation of nature use in resource-type regions are considered These territories
possess vast stocks of natural resources, including renewable ones, and indisputable "potential of
sustainable development". However, economic processes observed during the transition period have not
yielded the expected economic result in spite of comsiderable "extraction of nature capital" and, at the same
time, have resulted in essential degradation of ecosystems. Not the last role was played by orientation
of the state policy in the field of managing natural resources towards mechanisms of decentralized markets. In the paper, a transition is suggested to another model of nature use regulation developed on the
basis of the ecological debt concept and providing for a more active position of the state. An algorithm is considered whose function is to minimize the ecological debt. Described is a scheme of constructing an information system to support decisions on the basis of this algorithm.

**Dorofeyev E.A.** (Sankt-Peterburg) *
Floating coupon rate bonds: pricing principle
*
The paper presents the rules for circulation of floating coupon rate bonds and their theoretical pricing is studied on the basis of an arbitration model. Original results are also stated on the applicability of this model to the Russian OGSZ market.

**Malyutina M.S.** (Moscow) *
Macroeconomic aspects of the pension system reform: analysis of the generations intersection model
*
The article deals with studying macroeconomic aspects of the pension reform. A model is considered of two intersecting generations economy and it is shown that transition to a cumulative pension system for an economy with shortage of capital can essentially increase the rate of savings and stimulate economic growth. Pareto non-worsening transition to a new pension system can be achieved only if general efficiency of the economy increases due to a reform.

**Kleiner G.B., Piontkovsky D.I.** (Moscow) *
Multi-factor production functions with constant marginal factor substitution elasticity
*
A new characteristic of multi-factor production functions is introduced. It is in a certain sense dual to pair elasticity of factor substitution - so-called proportional growth elasticity, which is production scale elasticity of marginal substitution rate. Multi-factor production functions are investigated with constant elasticities of substitution and proportional growth for given (or all) pairs of factors. It is shown that the class of such production functions is broad enough. In particular, it contains the class of Cobb-Douylas functions, although it does not include (except degenerate variants) Solow and Mukerji functions. A full desctiption of such functions, depending of three or four factors. Also some sufficient conditions are stated for the case of arbitrary number of factors. In addition, a full classification is given of quasiseparable
functions with this condition. The behavior of isoquantas of such functions from the point of view of production with unlimited growth of one of the factos.

**Gavrilets Yu.N., Efimov B.A.** (Moscow) *
A game-theoretical model of aims forming in a reference group
*
The article deals with a model of forming opinions of members of a collective under influence of certain social and psychological factors. It is assumed that each participant strives for adjusting his (her) aims in such manner that a certain functional (an analogue of "psychological energy" cost) be at minimum level. In this case. the interaction process is modeled by a certain iterative procedure of exit to the state of equilibrium (in Nash's sense) of a special game of m persons. The existence of game equilibrium in the generalized game and convergence of the iterative process to this equilibrium are proven. Sufficient conditions of uniqueness and Pareto optimality of the game equilibrium have been found. Given is an analytical expression of the game equilibrium for a special class of such games.

**Kossachyov Yu.V.** (Moscow) *
Examining the stability of a dynamicmodel of financial and industrial corporate structure
*
A dynamic model is investigated of interaction of enterprises within the framework of a corporate financial and industrial group with vertical integration. The availability of credit and shareholder ties. At the same time. the bank, investing in decrease of the manufacturer's unit cost, occupies a dominating position. Dynamic stability is connected with arriving at equilibrium situation in a differential game. It is shown that in meeting certain conditions, each enterprises of the group gets the maximum guaranteed result, exceeding the analogous result in the case of independent activity which determines economic incentive of the participation in the group during the whole period.

**Pugachev V.F., Pitelin A.K.** (Moscow) *
National economic evaluation of currency
*
Numerical interrelations between financial and national economic efficiency of economic decisions are
investigated. A methodology for calculating effect multipliers (EM) with the use of a simulation model
of the Russian economy is suggested. Magnitudes of currency effect multipliers (CEM) are calculated
for various economic policy variants. The influence of (CEM) upon investment evaluation is analyzed.

**Varshavsky A.E.** (Moscow) *
Modeling non-payments and money demand in the barter economy
of Russia
*
On the basis of analysis of main indicators and factors of non-payments and barter expansion, it is shown
that the non-payments reflect systemic changes in the Russian economy connected with changes in financial
turnover functioning. The results of the analysis are used for specification and estimation of parameters
of econometric models, including two models: those of effective demand and non-payments.
The inclusion of non-payment factors in the model of effective demand distinguishes it from others.
A rather simple aggregated macro-economic model has been developed which is described by a system
of linear equations and with the use of it analytical relations have been obtained, allowing to estimate
the influence of non-payments upon GDP and to develop justified recommendations on stabilization of
the Russian economy.

**Afanasyev A.A.** (Moscow) *
An equilibrium model of the money-and-barter economy
*
Investigated are some macro-economic causes of the rise of barter in a monetary economy which include
monetary and strict tax policy of the state. On the basis of a dynamic equilibrium model, two cases of
barter are analyzed. In the first case, the barter appears as a response to a strict monetary policy of the
state which is characterized by low rates of money supply growth. In the second one - in response to a
soft monetary policy of the state which is characterized by high rates of money issue. Considered are
conditions of the existence of money-and-barter equilibrium as well as several numerical examples. In
conclusion, it is shown that the first case is peculiar to a postplanned economy and the second - to a
market one.

**Solntsev V.N., Kholodilin K.A.** (St.-Peterburg) *
On manifestations of long-term tendencies
in the modem economic crisis in Russia
*
The paper tries to estimate the scale of current economic crisis in Russia and to reveal the combination
of the factors contributing to it. The latter include transformational factors (those related to the transition
process) and evolutionary ones (forces inherited from the previous development path of the economy).
The conclusions of the paper are based on the analysis of the empirical data using a brand-new statistical
technique - Caterpillar method.

**Guriyev S.M., Pospelov I.G., Shaposhnik D.V.** (Moscow) *
A model of general equilibrium
in the presence of transaction costs and money substitutes
*
Within the framework of the model of general equilibrium with transaction costs and money substitutes
[1], equilibrium is considered with non-payments that are treated as mutual credit of enterprises. It is
shown that the equilibrium with non-payments differs from the equilibrium with barter considered in
[1]. Equilibria with non-payments turn out to be inefficient and, in the case of general state, they are non-unique.
It is shown that in an economy with transaction costs and money substitutes, enterprises get incentives
to integration which are interpreted as one of explanations of financial-and-industrial groups
formation.

**Yanovsky L.P.** (Voronej) *
A dynamic model of survival of a large enterprise with rentseeking
management
*
In the paper, a dynamic model of behavior of a large firm in a transition economy is studied. Unlike the
famous Baumol's model [I], large firms in a transition period maximize not only total sales volume but
also, at the same time, the firm's managers maximize their total income. The degree of maturity of the
transition economy is taken into account through weight coefficients in the integrand of the objective
functional. Obtained are conditions of a firm's downfall and conditions of a firm's stabilization depending
on the managers' behavior.

**Vygon G.V., Pomansky A.B.** (Moscow) *
Analysis of relationship between technological efficiency
and companies' market capitalization
*
In this paper, we suggest to use the well-known Data Envelopment Analysis (DEA) for identifying
undervalued companies within a homogeneous group. This approach may be useful for testing the hypothesis
about the stock market efficiency. Capitalization dynamics is considered of the 13 largest oil-and-gas
corporations for the first quarter of 1999. For 61 trading day at NYSE, the corresponding efficiency
coefficients were calculated. The analysis of the coefficients obtained has shown that the stock
market in the USA on the average is a weak-form efficient one. However, the approach suggested, in
principle, allows identifying companies that at some moment turn out to be undervalued as compared
with the others from the same group.

**Belenky V.Z., Smirnov V.N.** (Moscow) *
Optimal management structure in a two-parametric
one-dimensional stochastic model of investing (the case of exponential distribution)
*
The model considered in the work represents one of rare cases when it is possible to obtain a detailed
description of optimal management synthesis. Earlier, a variant of the model was investigated where the
required investment volume, being described as a random variable had a uniform distribution. In this
work this distribution is given as exponential. As a result of it five different types of optimal strategy
have been obtained. It is shown that the possible number of fixed points increases up to two (earlier,
there was one point at the most).

**Ovsienko Yu.V., Roussakov V.P., Soukhova N.N.** (Moscow) *
Labor pension in the accumulation form
*
The process is considered of forming an individual's pension fund in the accumulation form through a
pension tax evenly paid off during the period of work. Expressions have been obtained for estimating
the average amount of the pension fund and of pensions depending on the corresponding tax rates and
interest income under different variants of wages dynamics. Corresponding variant calculations have
been carried out. Identified is the dependence of pension on the duration of work and pension periods.

**Kicha I.V., Tokarev V.V.** (Moscow) *
Transition from indicators to macroeconomic ones
*
Established is and analytical dependence of macro-economic indicators on industrial average specific
technicoeconomic characteristics and on labor force for quasi-balanced economic dynamics modes. The
formulae obtained can be used for theoretical and applied analysis of the state and prospects of the national
economy without time-taking calculations of development paths on multi-industry models.

**Volchkova N.A.** (Moscow) *
Integration of bank and industrial capital in export sectors
*
A mathematical model of integration of an industrial enterprise, operating in an export industry and a
financial firm is suggested. It is shown that under oligopolistic competition in an international market,
such integration may be mutually beneficial for them. The cause of it consists in non zero oligopolistic
profit made in an international market at the expence of export. It is shown that under certain conditions
imposed on the group ownership structure, the interest rate for loans given to the enterprise by the financial
firm will be lower than the world level.

**Dementyev N.P.** (Novosibirsk) *
On income, expenditure and savings indicators
*
Investigations [1,2] are continued on formation, transformation and use of inflation tax in a money and
credit system, encompassing finances of government, population and enterprises, as well as the banking
system of Russia. The main attention is paid to population finances.

**Anikonov D.S., Tsitsiashvili G.Sh.** (Vladivostok) *
Issues of improving the procedure of mutual debts set-off
*
Considered is a problem of mutual debts cleaning-off of

**Lavlinsky S.M.** (Novosibirsk) *
Production sharing agreement and stable development of a territory
rich in raw materials
*
For a resource-type region under transition period conditions, two basic nature-use models are compared:
a license agreement and an individual tax scheme of "Production Sharing Agreement" type. It
cleared up which of the models and under what conditions within a fixed time horizon ensures a stable
development path for the territory.

**Perevalov Yu.V., Ghimadi I.E., Dobrodei V.V.** (Ekaterinburg) *
The effect of industrial enterprise privatization: methodology of analysis and come results
*
Analyzed are theoretical and methodological problems of evaluating the influence on enterprises' performance.
With the use of econometric models developed by the authors and of a data panel on 189 industrial
enterprises of the Sverdlovskaya Region for 1992-98, some hypotheses about positive privatization
effect are tested and confirmed.

**Glushkov I.N., Latyshev N.V., Ostapenko S.N.** (Tver) *
Comparative analysis and directions to
improve automated information systems ensuring the process of CTS development management
*
An analysis has been conducted of automated information systems (AISs) ensuring the process of analytical
data processing and decision-making support in the process of CTS development management.
Main directions of their improvement have been determined.

**Mednitzky V.G., Mednitsky Yu.V.** (Moscow) *
On coordination of local and global optimal plans
*
A specialized method is constructed of a concave optimization problem, describing one of possible approaches
to solving some problems of coordination (e.g. of optimal sectoral plans). Relations are investigated
between prices of products and objectively conditioned estimations [1] of local and global problems
as well as possibilities of the use of these estimations in economic mechanism functioning.

**Beklaryan L.A., Sotsky S.V.** (Moscow) *
On one model of agreement of an investment contract
*
The work deals with investigation of procedures of working out regional conditions of investment attraction.
As a participant, considered is the regional administration which establishes conditions in the
form of subsidies or assignments to the investor. In the model, all main factors, influencing agreement
of investment contract (opportunity cost of capital, risk, total assignments, indirect income (costs) associated
with investment in the given region) are taken into account.

**Mustafin A.T., Kantarbayeva A.K.** (Kazakhstan) *
On distribution of firms by sizes
*
A mathematical model is formulated of firms population development in terms of kinetic equation of
transfer for the function of enterprises distribution by sizes. The stationary distributions computed reveal
a prevalent statistical weight of small companies. The property of spectra of firm sizes makes it possible
to give a theoretical explanation to the well-known statistical fact that the overwhelming majority of jobs
in an economy are created by small firms.

**Zakharov V.V., Lezhnina E.A.** (St.-Peterburg) *
Stable agreements in the natural gas market in Europe
*
The article deals with the theory-of-games approach to regulation of the natural gas market in Europe.
To work out principles of preparation of a collective agreement for prices and volumes of gas supply, a
market model in the form of cooperative game is suggested. As the optimality principle,

**Kulaghin 0.A.** (St.-Peterburg) *
Method of local optimization for solving multi-criteria integer
programming problems
*
An interactive method is suggested which realizes the idea of local optimization of an unknown utility
function ("LPR"). It is assumed that the LPR preference relation satisfies a number of axioms. Under
these conditions, at each iteration of the method, a vicinity of feasible points is formed and within its
limits, the finite set of non-dominated solution made for LPR analysis is estimated. An example of
solving the problem is given.

**Kislitsyna 0.A.** (Moscow) *
Statistical methods of estimation of factors influencing the duration of
search for a job
*
A method of estimating the duration of search for a job with taking into account non-completeness of
observations based on modeling data of lifetime type. The method is adapted to information possibilities
and computer facilities of employment services which will enable them to actively develop systems of
measures, decreasing social tension associated with the loss of job and to efficiently use means allocated
for these purposes.

**Ovsienko Yu.V.** (Moscow) *
Institutional shifts in Russia and their economic and social consequences
*
In the article, the institutional changes that have taken place in Russia for the recent ten years are discussed. An attempt is made to ascertain those of them which, in the first place, have led to a social and
economic failure. Necessary conditions of effectiveness of institutional transformations are formulated.

**Volkonskii V.A., Koryaghina T.I.** (Moscow) *
The official and the shadow economy in reality and in statistics
*
A conceptual framework is suggested for investigation and statistical estimating of the shadow economy, which, for the last ten years, has become a factor commensurable with main processes that determine the future of Russian society. Special attention is paid to reflecting the shadow economy in the national accounts system. The growth of criminal business is considered in the context of classical and
modem problems of political economic theory.

**Movshovich S.M.** (Moscow) *
Public tax and inflation losses
*
Stationary equilibrium in a multi-period model of an economy, including a representative consumer,
producer and the state that sets taxes and determines the inflation rate is considered. The influence of
changes in tax rates and the inflation rate upon such economic indices, as investments and employment
is analyzed. Excess burdens of public losses per extra ruble of state budget revenues from tax collections
and money printing engendered by them are evaluated and compared with one another. It is shown that
the direction of inflation rate influence depends on the consumer's type whereas a tax always reduces
employment and investments. Under controllable inflation, close to zero, extra money issue losses are
close to zero and less than positive losses caused by raising the profit tax rate. Hence, small inflation is
an effective way to finance government expenditure. On the contrary, high inflation reduces real income
of the state.

**Astakhov A.S.** (Moscow) *
Has the methodology development resulted in more
accurate economic evaluations?
*
Some regularities of development of the methodology of production efficiency evaluation are analyzed.
Interactions of processes of development of conceptual bases, of basic model toolkit, evaluation criteria,
process-by-process factorial models, and information base are investigated. A general steady tendency
of lagging development of factorial "supporting" models and of information rebuilding and its inhibitory
impact on rates of theoretical development introduction have been revealed. It is shown that the development of methodology and model facilities exerted a rather complicated influence upon the criterion:
it began reflecting increasingly more indirect consequences of projects being implemented. At the same
time, that did not make it more reliable.

**Mikheeva N.N.** (Khabarovsk) *
Problems of using regional accounts in macro-economic analysis
*
An experience of applying the modem concept of macro-economic analysis - the national accounts system in investigating regional development is shown. Discussed are problems of building a system of regional accounts on the basis of the NAS-1993 methodology. The set of current accounts is represented
in the matrix form, convenient for formal analysis of the system of regional macro-economic indicators.
Examples are given of using a system of regional accounts when building matrices of social accounts.

**Kukushkin N.S.** (Moscow) *
The Nash equilibrium in games with additive aggregation
*
The article deals with strategic games where all the strategies are scalar and each player's gain depend
on his choice and on the sum of the partners' choice. A property of the payoff function is formulated and
two theorems of the Nash equilibrium existence in quasi-symmetrical games with this property: for continuous and for discrete sets of strategies. An interpretation is given for two well-known economic models those of Coumot oligopolistic competition and of ensuring social welfare with voluntary contributions.

**Beklaryan L.A., Sotskii S.V.** (Moscow) *
Optimization of the level of capital invested
in the problem in investment contract agreement
*
A problem is investigated of optimal control with phase constraints to which the problem of investment
contract agreement between an investor and a region is reduced. The existence and uniqueness of optimal control are proved. The behavior of the optimal trajectory (optimal level of capital invested) as the
solution to some implicit equation is analyzed. An algorithm is described of building the optimal control
is described. The behavior of the utility function and additional utility for an investor under the optimal
level of capital invested and the behavior of aggregate allocations depending on the region's characteristics are considered. On the basis of properties of the regions' and investors' characteristics, a breakup
of the regions and investors into groups is conducted in accordance with the level of their mutual attractiveness.

**Zulkarnayev I.U.** (Ufa) *
Mathematical modeling of vertical distribution
of government rights in a state and Coase's theorem
*
An approach to economic and mathematical modeling of distribution of state government functions
"along the vertical" is proposed as exemplified by two- and three-level modeling of two state-legal theories of state origin: the forced origin theory and the social-contract theory. Cause's theorem as applied
to the functions of state government which are regarded as objects of exchange between various state
bodies "along the vertical" is formulated and proved.

**Beer K., Golstein E.G., Sokolov N.A.** (Khemnitz, Moscow) *
On the use of the levels method for minimization
of convex functions with not all their values being finite
*
For a class of functions

**Zaslavskii A.A., Lebedev S.S.** (Moscow) *
A nodal vectors method for integer programming
*
A new method of mixed integer linear programming is described. An enumeration procedure generates
variants - vectors of fixed integer variables. The linear programming (LP) problem, corresponding to
some variant, determines the so-called nodal vector - the optimal solution to the dual LP problem. The
nodal vectors are used to construct bounds for other generated variants. As a result, the method rejects
most of the variants without solving the corresponding LP problems.