Question

Consider two sellers (“1” and “2”) of brand new, still in the box iPhone X’s. Online

inverse demand for these iPhones is given by P(Q) = 60 ? Q. The two sellers compete by choos-

ing prices, so we have Bertrand competition with identical products. Because the products are

truly identical, consumers only buy from whichever seller has a lower price. If they charge the same prices, half purchase from one seller and half purchase from the other. Assume further that only integer prices are feasible, so the sellers cannot undercut each other by pennies. These sellers

of iPhones acquire the phones from Apple at a cost of 20 per phone.

a) Write out seller 1’s best response function.

(b) Create a 3x3 payoff matrix showing the payoffs for each seller if they were restricted to

only choosing the following prices: 19, 20, or 21.

(c) On the same payoff matrix, circle all pairs of payoffs that correspond to Nash equilibrium

strategies of the sellers.

Answer 1