This work builds a macro model for livestock farming based on aggregation of initial micro description for rational control of total number of vintage livestock (age cohorts). All variety of animal kinds is reduced to one by given recount coefficients. An optimal problem on co-hort total number of livestock (planning problem for life cycle of animals) is resolved. As a result the optimum age limit for the operation of animals, the optimum volume of the credits for the farm, the optimum speed of slaughter, and the optimum conditions of the farm pur-chase of young animals are determined. The integral equation for the equilibrium price of young animals, which contains forward-looking values of variables, is obtained. It means that for constructing of the model it is necessary to know how the farms forecast the prices. The problem is solved by the application of the rational expectations hypothesis: within the model framework all farms have the precise forecast of necessary prices on the planned period (they exploit available information without making systematic mistakes).
A steppe ecosystem model based on a carbon cycle with grazed animals as part of the ecosystem is constructed. The model takes into account some external influences. The pa-rameters of this model are identified on the basis of data on grassland ecosystems. Besides a model of credit-and-monetary system taking into account the organization of this system according to the Stanley Fischer currency board scheme with fixed exchange rate is constructed. In this case gold currency reserves change by the balance of payments.
In the description of full ecological- economic model it is taken into account that the maintenance of animals damages the nature. Balance relationships on the product market and on the labor market are carefully extracted for closing the model. In the description of interac-tion of livestock farming and ecosystem and government regulated mechanisms it is assumed that the tax rate per head of animal grows when the degradation level exceeds a limiting value established by the law, and the raw material price changes proportional to the remainder of its biomass stock.
Numerical experiments on the obtained ecological- economic model with the rational expectations are the complex computational problem, which is solved with the help of the highly productive calculations on the supercomputer MVS 1000M. Model is calibrated ac-cording to the Mongolian data. In the base scenario of the model calculations the basic indices of environment decrease down to 10% in one hundred years. Fluctuations of financial pa-rameters with the period in 36 years caused by price rational expectations are found out.
On the basis of base scenario the developments of processes in complex system of in-teraction of livestock farming and steppe ecosystem several alternative scenarios are built and calculated. The calculations showed that the specified system maintains also more rigid rela-tion to the level of the environment degradation than in the base scenario. In this case it is possible to improve all macro indexes of the studied system. It is shown also that an increase of efficiency of actions for rational use of available resources improves the steppe ecosystem state, enables to increase the output of final production and the incomes of the population. One of scenarios demonstrates a regime in which the area of natural pastures is reduced by the virtue of external human activity (for example, space activity).
The work is in part supported by the Russian Foundation of Basic Research (Grant 01-01-00114 and Grant 03-06-85600) and the Grant of the President of the Russian Federation for State Support of Leading Scientific Schools (no. SS 1843.2003.1).
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This paper presents new results of mathematical modeling of economy and environment interaction that continues paper . A model of mutual interaction of livestock farming - one in a two main agricultural branches - and natural pastures that are the essential part of livestock farming forage reserve is proposed. Macrodescription of livestock farming such as: total and vintage number of livestock, number of young animals, livestock outputs and production inputs, demand for credit, and profit - follows from the initial microdescription of rational managing of vintage livestock. This description forms a block "Economy" of the model of mutual interaction of livestock farming and natural pastures - natural vegetable coenoses.
 Olenev N.N., Petrov A.A., Pospelov I.G. A Model of Ecological Consequences of Economic Growth. Moscow: Mathematical Modelling. Vol. 10. Issue 8. 1998. P. 17-32.
This paper presents new results of mathematical modeling of economy and environment interaction . A model of mutual interaction of livestock farming - one in a two main agricultural branches - and natural pastures that are the essential part of livestock farming forage reserve is proposed. Results of numerical experiments and analysis of various scripts of livestock farming is described.
The work is in part supported by the Russian Foundation of Basic Research (Grant 01-01-00114) and the Program of State Support of Leading Scientific Schools (Grant 00-15-96118).
This paper gives a description of fertility influence on education level of population and its well-being. We carry out the consideration by a demographic model keeping age structure. We suppose that (i) a part of GDP is used for investment in education, (ii) the production level depends on the education level, and (iii) the pollution is directly proportional to the size of population. We are carrying on research on the dependence of average consumption on demographic structure of the population for an industrialised economy. In the model each age group of population has different skilled level determined by education and different level of potential labour productivity. The education level is completely determined by education expenditures. We have found the relation between the value of average consumption of population and the children-adults ratio, share of education expenditures in GDP. We have found that the quality of life can be improved by decrease of the population size not only ecologically but also economically.
This paper builds a production function of skilled and unskilled labour for the economy that does not grow. The paper uses the constant elasticity of substitution production function (CES) of skilled and unskilled labour on the micro level as an important building stone. The paper obtains a production function on the macro level using the generalised Houthakker-Johansen model. The paper uses the macro production function as a core for description of production sectors in the model of Russian economy. Using Russian statistical data on output variables, this paper discussed the identification of new medium-run employment and wage equations of the model. The identification is based on the accuracy of fitting measured by the Theil's index and on the accuracy of direction measured by the correlation index. The paper shows that an employment problem of the skilled workers in Russia follows from the problem of absence of proper investments.
JEL classification: E22, E24, O33
Keywords: production function, skilled and unskilled labour, transition economy
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A general equilibrium model of transition period economy of Russian region is suggested. Qualitative special features of economic relations for 1996-1997 are described.
Print friendly version: http://www.ccas.ru/mmes/PREPR.HTM (in Russian)
An ecologo-economic model with market mechanisms of production regulation, exchange, and distribution is offered. For the description of the environmental processes a simplified model of ecosystem under external influence is used. The basis for the description of the economic processes is a life-cycle model of capital with reserve capacities. It was supposed, that the state forms ecological funds by raising the emission fees harmful waste and by payments for a natural resource used in production. An attempt to construct the description of mechanism of public influence on economic growth which would provide favorable evolution of the ecosystem is undertaken.
It is expounded some methods of mathematical modeling based on the methods of the system analysis of evolving economy /see Petrov, Pospelov and Shananin, (1996). "Essays on the Mathematical Modeling of Economics," Energoatomizdat, Moscow. 544p. (In Russian)/, and also some applications of this methods to applied investigation of transition period's problems. On the basis of the Russian economic model (1993-1995) it is discussed the methods of mathematical model's adaptation for a structure analysis of the economy. The purpose of the structure analysis is to give generalized estimations for variants of country's macroeconomic policy.
The description of influence of fertility on educational level of the population and on welfare is offered. The consideration will be carried out on an demographic model example, keeping the age structure.
Friendly version: http://www.geocities.com/nolenev/ORS09.html (in Russian)
The article sets forth the results of an investigation of the Russian economy after the reform of 1992 using mathematical models, for example, a model of inefficient inflationary equilibrium due to a lack of investments, which is characterized by the absence of savings. To get out of this situation, a plan is suggested for reorganizing economic relations to stimulate investments in production. The source of these investments is a restoration of the personal savings that were devalued by inflation in 1992.
A model of the investment policy of firms with reserve capacities is suggested. The aging of productive assets is taken into account. It is shown that the conceptions of a technology and a firm can be separated from each other and that the total production of firms can be described by means of an effective distribution of the total capacity among the technologies. The model gives rise to a new class of production functions.
The description of the ecology economic system with market mechanisms of regulation of production, exchange and distribution is offered. The processes in natural environment are described by model a wood ecosystem under external influence. It was supposed, that the state forms ecological funds, raising the tax from cost of unit of a product under some rate from unit rejection harmful waste and selling a natural resource used in production. Influence of parameters of dependence of the rate of the ecological tax from a level of pollution and cost of a natural resource from depletion of its on evolution of parameters of a condition of natural environment and production was studied. Numerical experiments have shown, that ecological control much depends on an initial condition of economy. The better economy on the eve of ecological crisis is balanced, the especially the rigid ecological policy can be applied. Thus stability of economic growth is not lost.
The closed multisector model of the market economy is considered. It is based upon the description of the long-term planning procedure used by firms. Numerical experiments show that the model gives qualitative description of the business activity cycle phases. Results of the investigation of one-sector version of the model are also presented. They include conditions of appearance and explicit expression of the period of weakly damping oscillations.
The mathematical description of economic activity of an industrial firm is offered. Process of occurrence and liquidation of firms is considered. It is supposed that new firm will be organized on extra means. It is supposed that firm is liquidated if sells all fixed capital. Conditions of occurrence and bankruptcy of firm are written out. The given microdescription of activity is included in a closed one-sector model of a market type economy. Preliminary results of the model research are shown.
The mathematical description of aging process of capacities of sector of the national economy is offered. It is supposed that in capacity aging process the output reduction is not accompanied by the appropriate reduction of working places. As a result the capacity aging causes reduction of productivity of labour on it. The current technological structure of sector is described by distribution of its capacities on size of labour input. A new class of production functions of sector is described. The production function turns out by integration of distribution of capacities on labour input. In a considered case it is complicated by deformation of distribution owing to change of labour input depending on durability of this capacity.