Two firms where the price of a product is a consequence of the total production. Let D denote the market demand potential and q_i the quantity firm j (j = 1, 2) brings to market. p = D q_1 q_2, where (p) final retail price. The two firms incur the same unit production cost dented by c. they differ in terms of their production yield. Firm 1 has a 100% yield. Whereas Firm 2 yield level of (where < 1). In the case of Firm 2, to produce q2 units, this firm needs to start a batch of q2/ units. The production cost applies to all units in the batch.

(a) Assuming that both parties move simultaneously, find the equilibrium quantities for both parties. Also, what is the equilibrium market price?

(b) Assuming that Firm 2 moves first, find the equilibrium quantities for both parties. What is the equilibrium market price?

(c) Compare the equilibrium prices and joint (total) profits across both cases.