Most studies of the demand for cars are designed to explain new purchases and assume that purchases are divided into net investment and replacement. Replacement is invariably identified with stock depletion, defined either as scrapping (determined by the length of life of a car) or as depreciation (determined by the decline in the price of a used car with age). Implicit in these theories is the assumption that the elasticity of substitution between the new and used car markets is rather high. This assumption is necessary to ensure that the price mechanism will induce consumers to buy new cars to make good the stock depleted by the scrapping or depreciation of used cars. Most empirical evidence indicates that this assumption is not justified and that new and used cars are poor substitutes, e.g. [1], [8] and [6]. Since the low degree of substitution between the two markets insulates new car purchases from the factors that influence the stock of used cars, stock depletion cannot explain replacement purchases of new cars. In this note an alternative approach will be suggested and its use illustrated by the case of new car sales in the US. The advantages of this approach are: (1) replacement is directly observable; (2) the assumption of perfect substitution between new and used car services is not necessary; and (3) it may help account for a series of implausible estimates of the depreciation rate that have been obtained from more orthodox models. It is generally accepted in the US automobile industry that new and used cars are bought by distinct groups. For instance, White in a recent study of the industry [6] says: New cars are not bought by a random selection of car owners but, instead, tend to be bought by a small group who buy new cars comparatively frequently and sell their used cars to the general public to hold. As an approximation, therefore, we can split buyers into two groups, those who buy their car new and those who buy it used, treating these groups as distinct. The demand of the new car buying group is primarily for replacement, since between 80 and 90 per cent of them trade-in or sell an old car when buying a new one; the average time from purchase to resale is between two and three years. This leads us to a definition of replacement as the process by which a consumer disposes of a car bought i years ago and purchases a new one. The existence of a well-developed second-hand market confirms that the replacement interval, i, is considerably shorter than the lifetime of a car, so that replacement does not equal scrapping. This replacement interval will vary between household and we shall observe a distribution of intervals, say c(i), which will determine the lag distribution generating replacement, U, from past purchases, Q; i.e.
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