A Monetary Theory with Non-Degenerate Distributions

56 Pages Posted: 28 Mar 2011

See all articles by Guido Menzio

Guido Menzio

University of Pennsylvania - Department of Economics; National Bureau of Economic Research (NBER)

Shouyong Shi

Pennsylvania State University

Hongfei (Amy) Sun

Queen's University

Multiple version iconThere are 2 versions of this paper

Date Written: March 15, 2011

Abstract

Dispersion of money balances among individuals is the basis for a range of policies but it has been abstracted from in monetary theory for tractability reasons. In this paper, we fill in this gap by constructing a tractable search model of money with a non-degenerate distribution of money holdings. We assume search to be directed in the sense that buyers know the terms of trade before visiting particular sellers. Directed search makes the monetary steady state block recursive in the sense that individuals' policy functions, value functions and the market tightness function are all independent of the distribution of individuals over money balances, although the distribution affects the aggregate activity by itself. Block recursivity enables us to characterize the equilibrium analytically. By adapting lattice-theoretic techniques, we characterize individuals' policy and value functions, and show that these functions satisfy the standard conditions of optimization. We prove that a unique monetary steady state exists. Moreover, we provide conditions under which the steady-state distribution of buyers over money balances is non-degenerate and analyze the properties of this distribution.

Keywords: Money, Distribution, Search, Lattice-heoretic

JEL Classification: E00, E4, C6

Suggested Citation

Menzio, Guido and Shi, Shouyong and Sun, Hongfei, A Monetary Theory with Non-Degenerate Distributions (March 15, 2011). Available at SSRN: https://ssrn.com/abstract=1794276 or http://dx.doi.org/10.2139/ssrn.1794276

Guido Menzio

University of Pennsylvania - Department of Economics ( email )

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Shouyong Shi (Contact Author)

Pennsylvania State University ( email )

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Hongfei Sun

Queen's University ( email )

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