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A large and a small firm A,B in a dying industry face declining inverse demand p(Q, t) = 10 -Q -t in periods t = 1,2, 3.... Firms have capacities kA = 4; kB = 2 and each firm produces at full capacity with marginal costs c = 2.5 as long as it stays in the market. In each period, firms simultaneously decide whether or not to exit.
After exiting, a firm cannot re-enter the market. The game ends when both firms have exited the game. Either firm aims to maximize the (non-discounted) sum of its profits until its exit.
(a) When do firms A and B exit in the unique subgame perfect equilibrium? (Hint: First establish at what time t profits turn negative as a function of the remaining firms, and then argue with generalized backward induction)
(b) Now assume that the small firm, B, is credit-constrained and is forced to exit in period t if its profits were negative in t-1. Show that now there exists a different subgame perfect equilibrium where firm B exits before firm A.
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