On the existence and computation of an equilibrium in an economy with constant returns to scale production
type: Item
instance of: scholarly article
title: On the existence and computation of an equilibrium in an economy with constant returns to scale production
zbMATH Open document ID: 0797.90010
DOI: 10.1007/BF02061064
author: Gerard van der Laan
author: Hans Kremers
published in: Annals of Operations Research
publication date: 1994-10-25T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 91B50
Mathematics Subject Classification ID: 90C90
Mathematics Subject Classification ID: 90-08
zbMATH DE Number: 464841
zbMATH Keywords: adjustment process
zbMATH Keywords: simplicial approximation
zbMATH Keywords: nonlinear constant returns
zbMATH Keywords: computation of an equilibrium
zbMATH Keywords: sequence of linear variational inequality problems
zbMATH Keywords: simplicial method
MaRDI profile type: Publication
cites work: Q3998344
cites work: Q5588318
cites work: Simplicial algorithms on the simplotope
cites work: The (2 n+1−2)-ray algorithm: A new simplicial algorithm to compute economic equilibria
cites work: A new simplicial variable dimension algorithm to find equilibria on the product space of unit simplices
cites work: An Adjustment Process for an Economy with Linear Production Technologies
cites work: A restart algorithm for computing fixed points without an extra dimension
cites work: Computation of economic equilibria by a sequence of linear complementarity problems
cites work: Q4070959
cites work: The Nonparametric Approach to Production Analysis
cites work: General economic equilibrium and variational inequalities
full work available at URL: https://doi.org/10.1007/bf02061064
OpenAlex ID: W1977491340
description: scientific article; zbMATH DE number 464841