An industry consists of two Cournot firms selling a homogeneous product with a market demand curve given by P = 100 - Q1 - Q2. Each firm has a marginal cost of $10 per unit.
a) Find the Cournot equilibrium quantities and price.
b) Find the quantities and price that would prevail if the firms acted "as if" they were a monopolist (i.e., find the collusive outcome).
c) Suppose Firms 1 and 2 sign the following contract. Firm 1 agrees to pay Firm 2 an amount equal to T dollars for every unit of output it (Firm 1) produces. Symmetrically, Firm 2 agrees to pay Firm 1 an amount T dollars for every unit of output it (Firm 2) produces. The payments are justified to the government as a cross licensing agreement whereby Firm 1 pays a royalty for the use of a patent developed by Firm 2, and similarly, Firm 2 pays a royalty for the use of a patent developed by Firm 1. What value of T results in the firms achieving the collusive outcome as a Cournot equilibrium?
d) Draw a picture involving reaction functions that shows what is going on in this situation.