5. Suppose two firms compete over prices in the market for soft drinks. Firm 1 produces Coke and Firm 2 produced Pepsi. Consumers see those drinks close, but not perfect substitutes. The demand for Coke is therefore given by 30 C Cp q pp =+ , and the demand for Pepsi is given by 30 p pC q pp =+ , where qC is the quantity of Coke, qP is the quantity of Pepsi, pC the price charged by Firm 1 and pP is the price charged by Firm 2. For simplicity, the marginal cost is assumed to be zero for both firms.

a) Find the Nash equilibrium of this differentiated Bertrand competition. How much profit does each firm earn in equilibrium? Now suppose that Firm 1 sets the price first (i.e., Firm 1 is a Stackelberg leader); Firm 2, after observing Firm 1's price, chooses the price.

b) Find the equilibrium of this Stackelberg price competition. What is the profit of each firm?