Universal Theory of Equilibrium in Models with Complementarities

Tarun Sabarwal

No 202312, WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS from University of Kansas, Department of Economics

Abstract: We develop a universal theory of equilibrium for models with complementarities on partially ordered sets (posets), unifying lattice-based theories used widely in economics and other disciplines and poset-based theories useful to study stochastic systems in many settings. Our theorems for extremal equilibria, structure of equilibrium set, and monotone comparative statics (MCS) of equilibrium generalize both types of theories in a unified manner. This extends to new theorems for MCS of the infimum equilibrium set, supremum equilibrium set, full equilibrium set, and isotone equilibrium set, and to a universal theory of order approximation of equilibria as well. As an application, we show new, deeper structural features of equilibrium in the canonical isotone stochastic dynamic economy with correlated shocks due to Hopenhayn and Prescott (1992).

Keywords: Complementarities; Equilibrium; Fixed Point; Poset; Monotone Comparative Statics; Stochastic System. (search for similar items in EconPapers)
JEL-codes: C02 C60 C62 C70 D70 (search for similar items in EconPapers)
Pages: 53 pages
Date: 2023-11, Revised 2023-11
New Economics Papers: this item is included in nep-dge, nep-gth and nep-mic
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