There are two firms in the cement industry, Acme and Bollard. The demand curve for cement is given by q = 450 - 0.25p. Each firm has one manufacturing plant and each firm i has a cost function C(qi) = qi^2, where qi is the output of firm i.
a. Derive Acme's and Bollard's reaction functions.
b. If Acme and Bollard formed a cartel, what would industry output, price and profits per firm be?
c. What is the Cournot level of output for each firm? How much profits would each firm receive at this equilibrium?
d. Now suppose that Acme is the Stackelberg leader in this industry and Bollard is the Stackelberg follower. What will output and profits for each firm be at this equilibrium?