Firm 1 and firm 2 produces homogeneous information goods and compete in price. They face the same and constant
marginal cost of production, that is MC_1 = MC_2 = $1 . Below are their demand functions:
Firm 1: Q_1 = 50 - 4P_1 + P_2
Firm 2: Q_2 = 50 - 4P_2 + P _1
a. If the firms colludes with each other, what are the profit maximizing prices, (P_1)∗ and (P_2)∗ ?
b. If they set their price simultaneously, What is the Nash equilibrium prices? Why?
c) If both firms have simultaneously priced their own information good at their marginal cost already and they are determining a new price level. Explain why cutting the price is a dominated strategy. Design a game to prove that both firms will not be willing to raise their product prices anymore. Briefly explain the game.
(Assuming that both firms can choose from either keeping the price unchanged or increasing the price of the products by $1)