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The paper presents a normative mathematical model of Kazakhstan economy with distressed assets in the banking sector. The model contains a lot of unspecified parameters which are not defined directly by the data of economic statistics. A method of identification of the model parameters is a type of global optimization problem. Parallel calculations are used for estimation of model parameters by statistical data of the Kazakhstan economy 2000–2017.

A simplest multi-sector dynamic model for regional economy is a normative balance mathematical model, but it contains a lot of unspecified parameters which are not defined directly by the data of economic statistics. Only confidence intervals for the unknown parameters can be computed from the statistical data. This work presents a method for estimation of the model parameters by application of parallel computations on multi-processors systems and by some heuristic algorithms. They determine the unknown parameters of economic model by indirect way, comparing time series for macro indexes calculated by model with statistical time series for these indexes. A new wavelet based measure of similarity was used. The use of the method is illustrated by the parameter estimation of a macroeconomic model of Kirov (Vyatka) Region of Russia for 2000-2006. The each production sector shadow money stock grows due to sale of shadow final product to households and as intermediate product to other sectors. Calibrated model is used for estimation of the Regional Government economic politics in particular for politics of regional economic integration.

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). Solution of an optimal problem on cohort total number of livestock gives the age limit for the operation of animals, the volume of the credits for the farm, the speed of slaughter, and the conditions of the farm purchase of young animals. The integral equation for the equilibrium price of young animals is obtained. A steppe ecosystem model based on a carbon cycle is constructed. The model takes into account some external influences. It is taken into account that the maintenance of animals damages the nature. Numerical experiments on the obtained ecological- economic model with the rational expectations is solved with the help of the highly productive calculations on the supercomputer MVS 1000M. On the basis of base scenario the developments of processes in several alternatives are built and calculated. One of scenarios demonstrates a regime in which the area of natural pastures is reduced by the virtue of external human activity. }

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. 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.

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).

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 ia used for investment in education, (ii) the production level depends on the education level, and (iii) the pollution ia directly prportional 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 complitly 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 yhe quality of life can be improved by descrease 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.