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Abstract

The paper considers a private ownership economy in which economic agents could realize their aims at given prices, Walras Law is satisfied but agents’ optimal plans of action do not lead to an equilibrium in the economy. It means that the market clearing condition is not satisfied for agents’ optimal plans of action. In this context, the paper puts forward three specific adjustment processes resulting in equilibrium in a transformation of the initial economy. Specifically, it is shown, by the use of strict mathematical reasoning, that if there is no equilibrium in a private ownership economy at given prices, then, under some natural economic assumptions, after a mild evolution of the production sector, equilibrium at unchanged prices can be achieved.
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Abstract

We consider the Debreu private ownership economy in which all consumption plans belong to a proper linear subspace of the commodity-price space ℝl. This geometric property of consumption sets means that there is a dependency between quantities of some commodities in all consumption plans. Competitive mechanism makes producers adjust their plans of action to the same dependency. It results in the mild evolution of the production sector to offer production plans which are also contained in the given subspace of ℝl. Modified production system and the initial consumption system can form an economy in equilibrium. The aim of this paper is to model gentle changes of producers’ activity that give equilibrium in the Debreu economy with consumption system reduced to a proper subspace of ℝl without considering additional costs.
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