Weak and strong optimality and increasing concave functions

摘要

In this paper we study the concept of the Pareto optimality allocations. The main characteristic of the equilibrium in exchange economy is given with the Pareto optimality criterion. We consider a mathematical model of an exchange economy and two definitions for Pareto optimality – weak and strong. The examining theorems are based only on the utility of the exchange goods and the increasing concave utility functions of the agents. We are examining a number of characteristics of the Pareto optimality allocations not using the fact of equilibrium.