It is a common practice for governments to offer scrappage subsidies in order to stimulate the early removal of used cars and modify the distribution of vehicle holdings. In this paper, we analyze the market implications of such subsidies when producers have market power and face competition from a secondary used car market. One key result is that, with market power, a subsidy can induce scrappage even if it pays less than the price of a used car in the absence of the subsidy. We provide a full characterization of the effects of scrappage subsidies on primary and secondary markets for the case of a monopoly, and show that the subsidy that maximizes aggregate welfare lowers prices in the used car market. Our results contrast with the predictions derived from a model with perfect competition.