Two firms produce differentiated products. The demand for each firm’s product is as follows:  Demand for Firm 1: q1(p1

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Two firms produce differentiated products. The demand for each
firm’s product is as follows:
 Demand for Firm 1: q1(p1, p2) = 20 – 2p1 + p2
 Demand for Firm 2: q2(p1, p2) = 20 – 2p2 + p1
Both firms have the same cost function: c(q) = 5q. Firms compete
by simultaneously and independently choosing their prices and
then supplying enough to meet the demand they receive.
Please compute the best response function for firm 1.
Please compute the best response function for firm 2.
Please compute the Nash equilibrium prices.
Please compute the Nash equilibrium profit per firm.
Suppose both firms raise their prices by 20% above their Nash
equilibrium levels. Please compute the profit per firm for these
higher prices. Are profits higher or lower than the Nash
equilibrium profits?
Why is it difficult to keep prices 20% above the Nash
equilibrium prices?