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Stationary Equilibrium in a Market for Durable Assets

John Rust

Abstract

This paper presents a dynamic model of consumer trading on the primary, secondary, and scrap markets for a stochastically deteriorating durable good in a stationary economy with perfect information and no transaction costs. We explicitly model the trading process by tracking each durable from its "birth" in the primary market, through its sequence of owners in the secondary market, until its "death" in the scrap market. We prove that a stationary equilibrium tests, characterize the distribution of consumer holdings of durables, and show that equilibrium asset prices are shadow prices to a particular regenerative optimal stopping problem. We show that each heterogeneous agent equilibrium is observationally equivalent to a homogeneous agent equilibrium. We derive a differential equation for equilibrium rental rates, and a functional equation which links rental rates to asset prices. These equations show precisely how the structure of durable prices and rental rates embody the functional form and population distribution of preferences and the technological characteristics of durable goods.