The Effect of Used Markets with Endogenous Replacement of Durable Goods

The purpose of this paper is to examine the effect of used asset markets for a particular class of durable goods markets where replacement and trading ages are endogenous, and where the imperfect substitutability between new and used goods results from the heterogeneity of buyers. Durable goods are assumed to be like automobiles: the quality of the service declines with the age of the durable, but the time at which the durable is traded and replaced with a new one is a choice variable for the owner. As in my earlier work on heterogeneous buyers [3], it is assumed that the decline in service value with age is lower for some buyers, so that these buyers will specialize in used assets in the presence of used markets. However, this paper departs from previous work by allowing the retirement age and the age at which goods are traded in the used market to be endogenously determined. This extension has important implications because it will be shown that retirement age (durability) will be affected by the presence of used asset markets. This paper examines the question of whether a competitive industry will favor a ban on used markets. Previous authors [2; 6; 8] have examined this question in markets where durable goods are like textbooks: the used asset markets exist because the length of the demand for services by the purchaser is less than the lifetime of the durable. In these models, the presence of a used asset market is equivalent to a lengthening of the lifetime of the good. However, in the model of this paper, the opening of a used asset market results in uniformity of the lifetime of the durable good, since all of the oldest durables will be held by the user type that places the highest value on old durables. This uniform retirement age with the used market will be shown to lie between the retirement ages adopted by the two user types when there are no used markets. Thus, the average age of the stock of durables could rise or fall with the introduction of used markets. Second, the model of this paper allows for the analysis of restrictions on used markets that raise the cost of used market transactions but do not eliminate trading. It will be shown that the effects of a per unit tax on used market transactions will differ from that of an ad valorem tax because of the greater incentive created by an ad valorem tax to postpone used market transactions. This result is in the spirit of Barzel's [1] result that the form of the tax is important because different types of taxes may affect characteristics of the good in different ways. In the present context, goods