Consider a market with two goods, each of which is an imperfect substitute for the other. The inverse demand function (Price as a function of quantity) for each firm is given by (as a function of the quantity by the two firms)
P1(q1,q2)=30-2q1-q2 Firm1
P2(q1,q2)=30-q1-2q2 Firm 2.
Both firms can produce as much as they want, but must make quantity decisions simultaneously. Both firms have a marginal cost of 0.
Using the same techniques that we covered for solving Cournot competition with homogenous goods, determine the best response function for each player, as a function of the quantity produced by the other.
b) Given this, solve for the equilibrium quantity by each player, the market price for each player's good, and the profits made by each player.
c) If the firms had undifferentiated products, the market demand function would be the following:
P(Q) = 30 - 2Q
The equilibrium quantity is for each firm to sell 5 units. How does this compare with your answer in part (b)? Explain why firms find it profitable to change their quantities in this way.