On the existence and computation of an equilibrium in an economy with nonlinear constant returns to scale production

In this paper we consider the problem of finding an equilibrium in an economy with non-linear constant returns to scale production activities. To find an equilibrium we propose an adjustment process in which the prices of the commodities and the activity levels of production adjust simultaneously. The process starts at a price vector at which each production activity has non-positive profit. We show that the process follows a path which connects the starting point with an equilibrium of the economy. From this it follows that the existence of a price vector at which each production activity has non-positive profit implies the existence of an equilibrium. The equilibrium can be computed by using a simplicial algorithm or by solving a sequence of Linear Variational Inequality Problems.

van der Laan, Gerard and Johannes Kremers (1993), On the existence and computation of an equilibrium in an economy with nonlinear constant returns to scale production, Annals of Operations Research 44 , 143-160