Firms A and B are duopolists with constant marginal cost 10. The only prices they can charge are 20 or 15. If both price at 20, each sells to eight customers; if both charge 15, each sells to ten customers. If one firm charges 20 and the other 15, the low-price firm gets 20 customers and the high-price none. The game is to be played once and prices must be chosen simultaneously.

c) Suppose that the game is to be played twice. In the first period marginal cost is 20 but it is known to fall to 10 in the second period. Before first period prices are chosen, A and B both announce that "if we sell to anyone in the second period at a lower price than we charge in the first period, we will give the first period buyers a rebate equal to the difference". Given these announcements, show that there is a subgame perfect equilibrium in which both firms charge 20 in each period.

d) Assume now that the setup is the same as in c) but firms cannot make the rebate announcement, by how much is their profit reduced relative

to c)?