Equilibrium of a production economy with non-compact attainable allocations set

Advances in Nonlinear Analysis

article

Senda Ounaies¹  Jean-Marc Bonnisseau¹  Souhail Chebbi³ 

[1] Centre d’économie de la Sorbonne, Université Paris 1, 106–112 Boulevard de l’Hôpital;Department of Mathematics, College of Science, University El-Manar;Department of Mathematics, College of Science, King Saud University

关键词: Production economy;    non-compact attainable allocations;    quasi-equilibrium;    nonlinear optimization;   

DOI  :  10.1515/anona-2017-0234

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

In this paper, we consider a production economy with an unbounded attainable set where the consumers may have non-complete non-transitive preferences. To get the existence of an equilibrium, we provide an asymptotic property on preferences for the attainable consumptions and we use a combination of the nonlinear optimization and fixed point theorems on truncated economies together with an asymptotic argument. We show that this condition holds true if the set of attainable allocations is compact or, when the preferences are representable by utility functions, if the set of attainable individually rational utility levels is compact. This assumption generalizes the CPP condition of [N. Allouch, An equilibrium existence result with short selling, J. Math. Econom. 37 2002, 2, 81–94] and covers the example of [F. H. Page, Jr., M. H. Wooders and P. K. Monteiro, Inconsequential arbitrage, J. Math. Econom. 34 2000, 4, 439–469] when the attainable utility levels set is not compact. So we extend the previous existence results with non-compact attainable sets in two ways by adding a production sector and considering general preferences.

【 授权许可】

CC BY