A Dynamic System Of The Equilibrium Solution Existence And Uniqueness Of Analysis

In the Dynamic Economic systems composed of many agents, we often use Recursive method and optimal principle of dynamic programming to (SP)(i.e. sequential problem) and (FE)(i.e. functional equations) to analyze system equilibrium. But in the systems with some distortion or cxternelities there is no common way to deal with the Equilibrium problem.In this paper, I consider an infinitely lived dynamic economy with stochastic technology shocks. Under suitable assumption, the equilibrium problem of this economy can be transformed into solving a functional equation( q(x)H'[q(x)] = ).When the shocks of each period are serially independent, It is easy to show the existence and uniqueness of (FE) by pure analysis. But if the shocks of each period are serially correlated, the problem considered is more complicated. In the light of different state space, four fixed point theorems are considered. Define an operator T ( (Tf)(x)= ) on the functions space. Insection 4.1, Banach's fixed point theorem is applied to T to show the existence and uniqueness of equilibrium solution. If the state space is finite (i.e. let the state space X={ xl ,x1,....., xm}), then operator T abovetakes the form Tlf = . Brouwer's fixed pointtheorem show the existence of equilibrium solution of this operator in section 4.2. Schauder fixed point theorem is an extension of Brouwer's fixed point theorem to infinite dimensional spaces. Finally, I present a fixed theorem that applies when the operator T on the functions space is monotone. The monotonicity leads to a constructive method for locating fixed points and a computationally useful method for establishing existence and uniqueness of the Competitive Equilibrium.