A monopolist can produce at constant average and marginal costs of AC = MC = 5. The firm faces a market demand curve given by Q = 53 - P.[M-30]

a)Calculate the profit-maximizing price-quantity combination of the monopolist's profits.

b)Suppose a second firm enters the market. Let q₁ be the output of the firm 1 and q₂ the output of the firm 2. Market demand now is given by q₁+q₂ = 53 - P. Assuming firm 2 has the

same costs as firm 1, calculate the profits of firm 1 and 2 as functions of q₁ and q_2.

c)Suppose each of these two firms chooses its level of output so as to maximize profits on the assumption that the other's output is fixed. Calculate each firm's reaction function which expresses desired output of one firm as a function of the other's output.

d)On the assumption in part (c), what is the only level of q₁ and q₂ with which both the firms will be satisfied (what q₁ , q₂ combination satisfies both reaction curves)?

e)With q₁ and q₂ at equilibrium level specified in part (d), what will be the market price, the profits for each firm, and the total profits earned?

f)Suppose now there are n identical firms in the industry. If each firm adopts the Cournot strategy toward all its rivals, what will be the profit-maximizing output level for each firm? What will be the market price? What will be the total profits earned in the industry? (All these will depend on n.)