TY - JOUR

T1 - General Equilibrium in a Heterogeneous-Agent Incomplete-Market Economy with Many Consumption Goods and a Risk-Free Bond

AU - Light, Bar

N1 - Publisher Copyright:
Copyright: © 2023 INFORMS.

PY - 2023/7/1

Y1 - 2023/7/1

N2 - We study a pure-exchange incomplete-market economy with heterogeneous agents. In each period, the agents choose how much to save (i.e., invest in a risk-free bond), how much to consume, and which bundle of goods to consume while their endowments are fluctuating. We focus on a competitive stationary equilibrium (CSE) in which the wealth distribution is invariant, the agents maximize their expected discounted utility, and both the prices of consumption goods and the interest rate are market-clearing. Our main contribution is to extend some general equilibrium results to an incomplete-market Bewley-type economy with many consumption goods. Under mild conditions on the agents’ preferences, we show that the aggregate demand for goods depends only on their relative prices and that the aggregate demand for savings is homogeneous of degree in prices, and we prove the existence of a CSE. When the agents’ preferences can be represented by a CES (constant elasticity of substitution) utility function with an elasticity of substitution that is higher than or equal to one, we prove that the CSE is unique. Under the same preferences, we show that a higher inequality of endowments does not change the equilibrium prices of goods and decreases the equilibrium interest rate. Our results shed light on the impact of market incompleteness on the properties of general equilibrium models.

AB - We study a pure-exchange incomplete-market economy with heterogeneous agents. In each period, the agents choose how much to save (i.e., invest in a risk-free bond), how much to consume, and which bundle of goods to consume while their endowments are fluctuating. We focus on a competitive stationary equilibrium (CSE) in which the wealth distribution is invariant, the agents maximize their expected discounted utility, and both the prices of consumption goods and the interest rate are market-clearing. Our main contribution is to extend some general equilibrium results to an incomplete-market Bewley-type economy with many consumption goods. Under mild conditions on the agents’ preferences, we show that the aggregate demand for goods depends only on their relative prices and that the aggregate demand for savings is homogeneous of degree in prices, and we prove the existence of a CSE. When the agents’ preferences can be represented by a CES (constant elasticity of substitution) utility function with an elasticity of substitution that is higher than or equal to one, we prove that the CSE is unique. Under the same preferences, we show that a higher inequality of endowments does not change the equilibrium prices of goods and decreases the equilibrium interest rate. Our results shed light on the impact of market incompleteness on the properties of general equilibrium models.

KW - Arrow-Debreu model

KW - Bewley models

KW - dynamic economies

KW - general equilibrium

KW - heterogeneous agents

UR - http://www.scopus.com/inward/record.url?scp=85169542457&partnerID=8YFLogxK

U2 - 10.1287/opre.2023.2442

DO - 10.1287/opre.2023.2442

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AN - SCOPUS:85169542457

SN - 0030-364X

VL - 71

SP - 1093

EP - 1111

JO - Operations Research

JF - Operations Research

IS - 4

ER -