We consider the problem of a government that wishes to promote replacing old cars with new ones via a vehicle scrappage program. Since these programs increase consumer's willingness to pay for a new car, manufacturers (or dealers) could respond strategically by raising their prices. In a two-period game between government and a manufacturer, we find equilibrium prices and subsidy levels. Our results demonstrate that price levels are increasing over time and are higher than in the benchmark case where no subsidy is offered. Further, if consumers act strategically, then the equilibrium price levels will be higher than in the scenario where they behave myopically.