A qualitative approach to Markovian equilibrium in infinite horizon economies with capital

Leonard J. Mirman, Olivier F. Morand, Kevin Reffett

Research output: Contribution to journalArticle

31 Citations (Scopus)

Abstract

Using lattice programming and order theoretic fixpoint theory, we develop a new class of monotone iterative methods that provide a qualitative theory of Markovian equilibrium decision processes for a large class of infinite horizon economies with capital. The class of economies includes models with public policy, valued fiat money, monopolistic competition, production externalities, and various other nonconvexities in the production sets. The results can be adapted to construct symmetric Markov equilibrium in models with many agents and market incompleteness. As the methods are constructive, they provide the foundations for a rigorous analysis of numerical approximation schemes that study extremal Markovian equilibrium. Equilibrium comparative statics results relative to the space of economies are available. Of independent interest, we provide new conditions for preserving complementarity under maximization, and new generalized envelope theorems for nonconcave dynamic programming problems. Our fixed point algorithms are sharp, and are able to distinguish sufficient conditions under which Markovian equilibrium form a complete lattice of Lipschitz continuous, uniformly continuous and semicontinuous monotone functions as well as unique continuously differentiable equilibrium.

Original languageEnglish (US)
Pages (from-to)75-98
Number of pages24
JournalJournal of Economic Theory
Volume139
Issue number1
DOIs
StatePublished - Mar 2008

Fingerprint

Infinite horizon
Qualitative approaches
Non-convexity
Market incompleteness
Complementarity
Programming
Decision process
Production externalities
Monopolistic competition
Public policy
Fixed point
Comparative statics
Markov equilibrium
Fiat money
Envelope theorem
Dynamic programming
Approximation

Keywords

  • Equilibrium comparative statics
  • Lattice programming
  • Markovian equilibrium
  • Order theoretic fixed point theory
  • Stochastic growth

ASJC Scopus subject areas

  • Economics and Econometrics

Cite this

A qualitative approach to Markovian equilibrium in infinite horizon economies with capital. / Mirman, Leonard J.; Morand, Olivier F.; Reffett, Kevin.

In: Journal of Economic Theory, Vol. 139, No. 1, 03.2008, p. 75-98.

Research output: Contribution to journalArticle

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