К теории оптимального экономического роста
Properties of increasing positively homogeneous functions are studied; in particular, their representations by use of tropical inner products with coefficients chosen from tropical support sets are described. An application to a model of economic complementarityand weak links is developed. It is shown that weak links do not necessary bound total factor productivity from below but in some cases constraint it from above.
Econometric models for forecasting natural gas production possess a number of significant advantages over their geological and engineering counterparts. They take into account much fewer factors, are substantially simpler and allow one to quickly formulate forecasts with acceptable accuracy. The results of natural gas production forecasting at OJSC Gazprom’s fields in the Tyumen region are evidence of this. Statistical data based on fixed production assets and cumulative production was taken into account in the calculations, power and exponential functions and regression analysis of time series were used as a mathematical tool.
In the present paper the game theory is applied to an important open question in economics: providing microfoundations for often-used types of production function. Simple differential games of bargaining are proposed to model a behavior of workers and capital-owners in processes of formation of a set of admissible factor prices or participants’ weights (moral-ethical assessments). These games result, correspondingly, in a factor price curve and a weight curve – structures dual to production function. Ultimately, under constant bargaining powers of the participants, the Cobb-Douglas production function is received.
The new economic-mathematical model based on complex variables theory and the new approach to complex variables usage in economics are suggested in the article. The comparison of modeling results of actual production processes using Cobb-Douglass production function and complex variables production function is conducted. It is shown that the instrumental base of economicmathematical methods can be widen with usage of complex variables theory.
Selected works of George Kleiner on economics and mathematics in occasion of his 70th birthday.