On the existence of equilibrium in a two-class economy with production

Abstract

This thesis considers a production economy which consists of distinct sets of workers and capitalists as agents. Both workers and capitalists provide labor for production of two distinct types of consumer goods, one of which is consumed by workers only and the other by capitalists only. Production of consumer goods involves a capacity constraint. Furthermore, firms are owned only by the capitalists. It is shown that there does not exist a Walrasian equilibrium for a large set of technological parameters with the above set of assumptions. First, an illustrative example is introduced and a condition which guarentees the non-existence of Walrasian equilibrium is derived in terms of technological parameters. Non-Walrasian equilibria are considered in this example for the cases in which there does not exist a Walrasian equilibrium in order to analyze the impact of non-existence result on efficiency. Sub-sequently, a generelization is carried out for the result of non-existence of Walrasian equilibrium. Non-existence of Walrasian equilibrium in this study is due to Arrow's corner which is a failure of lower hemicontinuity of the budget correspondence and upper hemicontinuity of the demand correspondence.