### 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 language | English (US) |
---|---|

Pages (from-to) | 75-98 |

Number of pages | 24 |

Journal | Journal of Economic Theory |

Volume | 139 |

Issue number | 1 |

DOIs | |

State | Published - Mar 2008 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Economics and Econometrics

### Cite this

*Journal of Economic Theory*,

*139*(1), 75-98. https://doi.org/10.1016/j.jet.2007.05.009

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

Research output: Contribution to journal › Article

*Journal of Economic Theory*, vol. 139, no. 1, pp. 75-98. https://doi.org/10.1016/j.jet.2007.05.009

}

TY - JOUR

T1 - A qualitative approach to Markovian equilibrium in infinite horizon economies with capital

AU - Mirman, Leonard J.

AU - Morand, Olivier F.

AU - Reffett, Kevin

PY - 2008/3

Y1 - 2008/3

N2 - 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.

AB - 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.

KW - Equilibrium comparative statics

KW - Lattice programming

KW - Markovian equilibrium

KW - Order theoretic fixed point theory

KW - Stochastic growth

UR - http://www.scopus.com/inward/record.url?scp=38849169723&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38849169723&partnerID=8YFLogxK

U2 - 10.1016/j.jet.2007.05.009

DO - 10.1016/j.jet.2007.05.009

M3 - Article

AN - SCOPUS:38849169723

VL - 139

SP - 75

EP - 98

JO - Journal of Economic Theory

JF - Journal of Economic Theory

SN - 0022-0531

IS - 1

ER -