Consider the following Cournot model.

• The inverse demand function is given by p = 30 –Q, where Q = q1 + q2.

• Firm 1’s marginal cost is $6 (c1 = 6). Firm 2 uses a new technology so that its marginal cost is $3 (c2 = 3). There is no fixed cost.

• The two firms choose their quantities simultaneously and compete only once. (So it’s a one-shot simultaneous game.)

Answer the following questions.

a. Derive Firm 1 and Firm 2’s reaction functions, respectively.

b. Solve the Nash equilibrium (q1 N, q2 N).

c. What is the equilibrium price and what is the profit level for each firm?

d. Suppose there is a market for the technology used by Firm 2. What is the highest price that Firm 1 is willing to pay for this new technology?

e. Now let’s change the setup from Cournot competition to Bertrand competition, while maintaining all other assumptions. What is the equilibrium price? 

f. Suppose the two firms engage in Bertrand competition. What is the highest price that Firm 1 is willing to pay for the new technology?