Question

Sub King and GyroMart are the only two sandwich shops in town.
Their goods are imperfect substitutes. Careful research has found that the demand
function for the two firms are
q1 = 30 − 3p1 + 2p2,
and
q2 = 30 − 3p2 + 2p1.
In other words, while the price of Gyros affects demands for subs, consumers do
not simply buy the cheapest item, some are willing to pay more to get a sub, and
some are willing to pay more to get a Gyro. The marginal cost of production
for each firm is zero. Assume the firms are engaged in differentiated Bertrand
competition
1. Find the best-response functions for firm Sub King and GyroMart

2. Find the differentiated Bertrand Nash equilibrium outcome. What are the
profits of each firm?

3. Is this outcome efficient? Explain your answer.

4. Suppose that the firms merge, so now they set prices jointly. What prices
should the merged firm choose to maximize total profits? What are postmerger profits? Compare them with Bertrand profits. (Hint: Write out
total profits of the merged firm and find marginal profits with respect to
both prices, i.e., ∂π/∂p1 = 0 and ∂π /∂p2 = 0. Then solve the resulting system of 2 equations for p1 and p2 by substituting one into the other.)

5. What are the main features of the Cournot competition model and the Betrand competition model, respectively? Given examples of industries in our
real life that are suitable to fit Cournot competition and Betrand competition, respectively, and explain why.

Answer 1