On the existence and computation of an equilibrium in an economy with constant returns to scale production
The problem of finding an equilibrium in an economy with nonlinear constant returns to scale production activities is considered. In the first part of the paper it is shown by a constructive argument that there exists an equilibrium under the condition that there is no production without input. Under this condition there exists a price vector such that all nonlinear production activities make negative profits. It can be shown that starting from such a prime vector there exists a path leading to an equilibrium pair of prices and activity levels. In the second part of the paper the authors consider the problem of the computation of an equilibrium. In the literature several algorithms have been proposed for solving the equilibrium problem in case of linear production activities. Amongst these algorithms are simplicial methods and a method which solves the problem by solving a sequence of linear variational inequality problems. The authors adapt these methods for solving the equilibrium problem in an economy with nonlinear technologies. The simplicial method follows approximately the path defined in the constructive proof of the existence of an equilibrium in such an economy. This method is globally convergent. The sequence of solutions to the linear variational inequality problems may not converge. Moreover, at each iteration the set of feasible prices (non positive profit for each technology) is a subset of the set of feasible prices in the linear approximation of the problem and hence the solution to the linear variational inequality problem does not need to be feasible. If so, a subproblem has to be solved to find a feasible starting price vector for the next iterate of the sequence.
sequence of linear variational inequality problems
scientific article; zbMATH DE number 464841
scientific article