Consider two firms, A and B, which simultaneously set prices. Firm A has marginal cost of cA = 12, while Firm B has marginal cost of cB = 20.  Market demand in each period is given by Q (P) = 140 – P/2. Assume that consumers buy from the low cost firm if the firms charge the same price.

(a) Find the Nash Equilibrium that generates the maximum profits for each firm. In this case, what are the firms’ output levels and profits?

(b) What is Firm A’s monopoly price, output, and profits?  Same for Firm B.

(c) Suppose now the firms interact repeatedly over time, simultaneously setting prices in each period t=0, 1, 2… Suppose the two firms start to collude in the following way: In t = 0, both charge Firm B’s monopoly price, and Firm A gets 70% of the profits, while Firm B gets 30%. (In effect, Firm A shares 30% of its profits with Firm B.) In each subsequent period, they keep price and market shares unchanged unless one firm deviates.  If one firm deviates, then both firms charge the Nash equilibrium price from part (a) forever.  Calculate the smallest discount factors for Firm A and Firm B for which this is a Nash Equilibrium.

(a) Find the Nash Equilibrium that generates the maximum profits for each firm. In this case, whatare the firms’ output levels and profits?Q (P) = 140 – P/2P = 280 – 2QMR = 280 – 4QCA =…

 
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