Differential bargaining games as microfoundations for production functions
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.
This volume is dedicated to the 80th anniversary of academician V. M. Matrosov. The book contains reviews and original articles, which address the issues of development of the method of vector Lyapunov functions, questions of stability and stabilization control in mechanical systems, stability in differential games, the study of systems with multirate time and other. Articles prepared specially for this edition.
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.
Mathematical models of nonlinear systems of a certain class allow them represented as linear systems with nonlinear state feedback. In other words, let make the appropriate coordinate transformation of the original dynamic model. Such a transformation, using Lyapunov functions, a number of studies used to determine the parameters of regulators to ensure the asymptotic stability properties of the nonlinear system, ie guaranteeing bounded trajectories emanating from the initial states of the system. For linear systems, there is a powerful and convenient mathematical apparatus allows the synthesis of optimal controls, but this unit is not applicable or partially applicable for nonlinear systems. Unlike prior work in this paper for nonlinear systems linearizable feedback as in the synthesis of optimal control problems with quadratic performance applied the method based on the use of the Riccati equation with parameters depending on the state.
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.
The monograph presents the results of calculations of the human capital dynamics and structure for the Russian economy in 1991-2012 years, using the method of accumulated costs by analogy with the calculation of the fixed capital volume. Analysis of the human capital contribution implemented on the basis of the production function model; original mathematical-statistical methods providing stability and economic interpretability of the results developed.