Duopoly Competition

Consider a market for phone service, in which there are two phone service providers that serve the DC area. They both have cost curves of C(q) = 2 q. The inverse demand function for the market is P(Q) = 14 - Q.

a. Assume that both firms decide on quantity simultaneously. Solve for the Cournot equilibrium firm quantities, price, and market quantity.

b. Assume that firm 1 chooses quantity and then firm 2 responds. Solve for the Stackelberg equilibrium firm quantities, price, market quantity, and profits for each firm. Is there a first mover advantage? Explain briefly.

c. Now suppose that the demand functions for each firm are q1 = 7 - 1 2 p1 + 1 4 p2 and q2 = 7 - 1 2 p2 + 1 4 p1. Solve for the Nash-Bertrand equilibrium prices, firm quantities, and market quantity.