Comparative Statics of Oligopoly Equilibrium in a Pure Exchange Economy

Somdeb Lahiri

doi:10.4236/me.2011.22012

Abstract

In this paper we consider an oligopoly and we are concerned with the effect of entry in the market of buyers and/or sellers on the price of the good being sold and the pay-offs/utilities of the buyers and sellers. The major results obtained in this paper are the following: 1) Given the number of buyers both individual as well as aggregate offers go up as the number of sellers increases. Further, the price of Y decreases, each buyer is better off and each seller is worse off as the number of sellers increases. 2) Given the number of sellers, the price of Y increases, each buyer is worse off and each seller is better off as the number of buyers increases. 3) As the economy is replicated the equilibrium price decreases. The sequence of equilibrium prices thus obtained converges to the competitive equilibrium price of the original economy. 4) As the economy is replicated the buyers are better off. The sequence of consumption bundles of the buyers converges to the consumption bundle of the buyers at the competitive equilibrium of the original economy. 5) As the economy is replicated the sellers are worse off. The sequence of consumption bundles of the sellers converges to the consumption bundle of the sellers at the competitive equilibrium of the original economy.

Highlights

We consider a general equilibrium model with two goods, i.e. money (X) and an infinitely divisible good (Y), where buyers are initially endowed only with X and sellers are initially endowed only with Y
The major results obtained in this paper are the following: 1) Given the number of buyers both individual as well as aggregate offers go up as the number of sellers increases
The sequence of consumption bundles of the buyers converges to the consumption bundle of the buyers at the competitive equilibrium of the original economy

Summary

Introduction

We consider a general equilibrium model with two goods, i.e. money (X) and an infinitely divisible good (Y), where buyers are initially endowed only with X and sellers are initially endowed only with Y. If buyers behave strategically we have a simple version of a strategic market game due to Shubik [1], Shapley [2] and Shapley and Shubik [3] that is discussed in Gabszewicz and Michel [4] The latter class of models has been studied in [5]. We discuss similar issues for an oligopoly assuming that buyers and sellers have Cobb-Douglas utility functions. Further our use of Cobb-Douglas utility functions allows us to obtain sharper results than what Amir and Bloch [7] do, albeit in a different market structure. In particular we are able to go beyond the questions addressed in earlier investigations for bilateral oligopoly and claim that buyers are unconditionally better off and sellers are unconditionally worse off as the economy is replicated. It just makes the analysis simpler without sacrificing any major implication

The Model

Oligopoly Equilibrium

Findings

Conclusions