There are three firms in the market for respirators and consumer demand is given byP= 300Qwhere Q=q1+q2+q3is the total output in the market.

The cost function of firm1 and firm2 is given by:

C1(q1) =F+ 12q1

C2(q2) =F+ 12q2

whereFis a fixed cost. Meanwhile firm 3 has a cost function given by C3(q3) =F+ 12q3

whereis a measure of firm 3's cost advantage or disadvantage. This means that if >1 then firm 3 is a high cost firm and if <1 then firm 3 is a low cost firm. Assume that the firms each choose their outputs to maximize profits (Cournot competition)

A) Find the Cournot equilibrium output for each firm, the product price and the profits of each of the three firms. For this to be an equilibrium, all three firms must at least cover their variable costs. Identify the constraint thatmust satisfy for this to be the case.

B)Suppose that= 1 and that when two firms merge, the merged firm's fixed cost isFwhere 12. Derive a condition onandFin order for a merger between firm 1 and 3 to be profitable. How do we interpret this condition?

C)Now suppose thatF= 0 and that when two firms merge, the merged firm's variable cost is the is the lower of the two firm's costs. Can a merger between firm 1 and 3 be profitable if1 such that firm 3 is a high cost firm? What are the profits of each firm after this merger? Derive a condition onin order for a merger between firm 1 and 3 to be profitable.