Markovian equilibrium in infinite horizon economies with incomplete markets and public policy

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

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

We develop an isotone recursive approach to the problem of existence, computation, and characterization of nonsymmetric locally Lipschitz continuous (and, therefore, Clarke-differentiable) Markovian equilibrium for a class of infinite horizon multiagent competitive equilibrium models with capital, aggregate risk, public policy, externalities, one sector production, and incomplete markets. The class of models we consider is large, and examples have been studied extensively in the applied literature in public economics, macroeconomics, and financial economics. We provide sufficient conditions that distinguish between economies with isotone Lipschitz Markov equilibrium decision processes (MEDPs) and those that have only locally Lipschitz (but not necessarily isotone) MEDPs. As our fixed point operators are based upon order continuous and compact nonlinear operators, we are able to provide sufficient conditions under which isotone iterative fixed point constructions converge to extremal MEDPs via successive approximation. We develop a first application of a new method for computing MEDPs in a system of Euler inequalities using isotone fixed point theory even when MEDPs are not necessarily isotone. The method is a special case of a more general mixed monotone recursive approach. We show MEDPs are unique only under very restrictive conditions. Finally, we prove monotone comparison theorems in Veinott's strong set order on the space of public policy parameters and distorted production functions.

Original languageEnglish (US)
Pages (from-to)505-544
Number of pages40
JournalJournal of Mathematical Economics
Volume41
Issue number4-5 SPEC. ISS.
DOIs
StatePublished - Aug 2005

Fingerprint

Incomplete Markets
Public Policy
Infinite Horizon
Economics
Lipschitz
Monotone
Fixed point
Competitive Equilibrium
Externalities
Production Function
Fixed Point Theory
Equilibrium Model
Sufficient Conditions
Successive Approximation
Macroeconomics
Nonlinear Operator
Comparison Theorem
Compact Operator
Infinite horizon
Decision process

Keywords

  • Lattice Programming
  • Markovian equilibrium
  • Monotone methods

ASJC Scopus subject areas

  • Economics and Econometrics
  • Applied Mathematics

Cite this

Markovian equilibrium in infinite horizon economies with incomplete markets and public policy. / Datta, Manjira; Mirman, Leonard J.; Morand, Olivier F.; Reffett, Kevin.

In: Journal of Mathematical Economics, Vol. 41, No. 4-5 SPEC. ISS., 08.2005, p. 505-544.

Research output: Contribution to journalArticle

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