The Applications Of Nonlinear Analysis In Production Theory

In this thesis,we intend to study production theory in economics,using nonlinearly analytical methods.This thesis is divided into three chapters.Itis organized as follow:In chapter 1, we consider Shephard input and output functions. First of all,we extend some useful mathematical properties, which can, in a sense, disclosethe essence of these functions. Along this line, we will discuss their dual functionsin the following parts.In chapter 2, we aim at specifying shortage functions in term of functionalmeaning, and related price vectors as well, which are able to achieve the maxi-mum profits. At first, we introduce upper bounded functions, a class of concavefunctions, which enable the production sets to be represented by them. Secondly,after a properly linear operation, the shortage function can be recognized as in-deed the outcome of this operation on the upper bounded function. At the end,falling back on conical theory, we introduce a category of set-valued maps, whichcan shed light on thinking on macroscopical view.In chapter 3, utilizing set-valued analysis, a production sets can be recognizedas the graph of some set-valued map. In the light of this, we make a overall research to this problem during this chapter. Moreover, we introduce, so tospeak,a the dual map, which can be used to seek the optimum price vectors.