Producers’ Adjustment Trajectories Resulting in Equilibrium in the Economy with Linear Consumption Sets

Abstract

We consider the Debreu private ownership economy in which all consumption
plans belong to a proper linear subspace of the commodity-price space R

l.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 R
l without considering additional costs.