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Suppose there are two firms in a market producing differentiated products. Both firms have MC=0. The...

Suppose there are two firms in a market producing differentiated products. Both firms have MC=0. The demand for firm 1 and 2’s products are given by:

q1(p1,p2) = 5 - 2p1 + p2

q2(p1,p2) = 5 - 2p2 + p1

a. First, suppose that the two firms compete in prices (i.e. Bertrand). Compute and graph each firm’s best response functions. What is the sign of the slope of the firms’ best-response functions? Are prices strategic substitutes or complements?

b. Solve for the Nash equilibrium prices and quantities when the two firms play Bertrand. Calculate the firm’s profits.

c. Next, assume firms compete in quantities (i.e. Cournot). Solve for firm 1 and 2’s inverse demand functions (i.e. solve the demand equations for p and write as a function of q).

d. Compute and graph each firm’s best response functions. What is the sign of the slope of the firms’ best-response functions? Are quantities strategic substitutes or complements?

e. Solve for the Nash equilibrium prices and quantities when the two firms play Cournot. Calculate the firm’s profits. f. Compare the market outcomes in parts (a) and (c). Is the equilibrium outcome more competitive under price or quantity competition?

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