Suppose an industry consists of two firms that compete in prices. Each firm produces

one product. The demand for each product is as follows:

q1 = 25 - 5p1 + 2p2

q2 = 25 - 5p2 + 2p1

The cost functions are C(qi) = 2 + qi for i = 1; 2.

(a) Are the products produced by these firms homogenous or differentiated?

(b) Find the best response function for each rm.

(c) How does the price firm 1 sets change with its belief about the price of its competitor's product?

(d) What are the Nash equilibrium prices?

(e) What is the percentage markup of price over marginal cost here (this is called the Lerner index)? Do the firms have market power? Why does the Bertrand paradox of zero variable duopoly profits apply here?

(f) Suppose the firms merged. What is the new price of products 1 and 2?

(g) Explain intuitively why the price is higher under monopoly than under Bertrand duopoly?

(h) Are total monopoly profits higher or lower than the sum of Bertrand duopoly profits? Why or why not?