Initially, three firms produce homogeneous products. Consider a market with inverse demand per period given by P = 140 - Q. Each firm faces a marginal cost of 20 per unit. As well, each firm faces a fixed cost per period of 500. Firms are Cournot competitors, simultaneously choosing quantities.

a) What are the Cournot equilibrium quantities, and the corresponding price and profits? Show your work and explain your answer.

(b) Now, suppose that firms 1 and 2 merge. The merged firm continues to face a marginal cost of 20 per unit. The merged firm faces a fixed cost of 700. Is the merger profitable for the merging parties?