CAPACITY CONSTRAINTS AND VOLUNTARY OUTPUT CUTBACK IN DYNAMIC COURNOT COMPETITION

This paper considers Cournot competition in which duopolists play a qu antity-setting game with sticky prices and capacity constraints, A fee dback (subgame-perfect) equilibrium is derived and analyzed, With suff icient differentiability, the paper shows the existence and the unique ness of symmetric feedback equilibrium. We show that there arises a ra nge of constraints defined by two threshold values in which the firms' outputs are below the constraint level in the steady state. Yet the o utputs depend nontrivially on the constraint. For outside observers, t he constraint does not seem to be binding. But the constraint is bindi ng in that a marginal change in the level of capacity constraint affec ts firms' steady-state outputs. The result implies that under this con straint the firms cut back their steady-state outputs voluntarily more than stipulated by the constraint. We also show that the procedure to construct a constrained solution from an unconstrained solution by tr uncation may not always be appropriate. This paper's analysis utilizes the concept of connectable points associated with the solutions to th e auxiliary equation of the Hamilton-Jacobi-Bellman equation. Since th e concept of connectable points and their characterization does not di rectly rely upon the linear-quadratic structure of this game, the meth od can be modified and applied to other differential games with restri ctions on the control space(s).