Suppose that in Omaha the daily demand functions for Pepsi and Coke are given by:

Q_P = 45 – 250P_P + 200P_C and Q_C = 45 – 250P_C + 200P_P

where Q is in thousands of cans per day, P_P is the price of a can of Pepsi, and P_C is the price of a can of Coke.

a). Assume each firm has the same cost function C_i = 0.3*q_i, that is, each firm has a constant marginal cost of $0.30 per can. Derive (i.e., do not use formulae) and sketch the best response functions for these firms. (Put Coke’s price on the horizontal axis.)

b). Solve for the equilibrium prices, quantities, and profits.

c). Now suppose that Pepsi’s marginal cost falls to $0.24 per can. Find the new best response functions and illustrate them on your graph from part a.

d). Find the new equilibrium prices, quantities and profits. (Solve for Pepsi’s new price first, to the nearest penny, and then find Coke’s price.) How do these market results differ from part b? Do these differences make sense? Explain.