We present a dynamic quantity setting game, where players may continuously adjust their quantity targets, but incur convex adjustment costs when they do so. These costs allow players to use quantity targets as a partial commitment device. We show that the equilibrium path of such a game is hump-shaped and that the final equilibrium outcome is more competitive than its static analog. We then test the theory using monthly production targets of the Big Three U.S. auto manufacturers during 1965-1995 and show that the hump-shaped dynamic pattern is present in the data. Initially, production targets steadily increase until they peak about 2-3 months before production. Then, they gradually decline to eventual production levels. This qualitative pattern is fairly robust across a range of similar exercises. We conclude that strategic considerations play a role in the planning phase in the auto industry, and that static models may therefore under-estimate the industry's competitiveness.
Caruana, Guillermo and Liran Einav. “Production Targets.” Rand Journal of Economics 39, 4 (Winter 2008): 990-1017. citation courtesy of