Question

Suppose that the firms in the Cournot oligopoly decide to collude. The corresponding demand curve for the monopolist is given by P= 100-20 where MR = 100-4Q; MC = 4, TC = 4Q Solve for the cartel (total) output, price, and profit. O Q* = 42; p* = 25; Profit = 1152 O Q* = 4; p* = 92; Profit = 352 O Q* = 48; P* = 24; Profit = 1152 O Q* = 24; p* = 52; Profit = 1152

Answer 1

Answer

The correct answer is (d) Q* = 24; P* = 52, Profit = 1152.

In order to maximize profit a monopolist produces that quantity at which MR = MC

where MR = Marginal revenue = 100 - 4Q, MC = Marginal Cost = 4

Thus MR = MC

=> 100 - 4Q = 4

=> Q = 24

Hence Profit maximizing Output(Q*) = 24.

Demand is given by : P = 100 - 2Q and as Q = 24 => P = 100 - 2*24 = 52

Hence Profit maximizing Price(P*) = 52.

Profit = TR - TC

where TR = Total Revenue = Price*Quantity = P*Q - Total Cost)i.e. TC)

=> Profit = 52*24 - 4Q = 52*24 - 4*24 = 1152

Hence Maximum profit earned is 1152

Hence, the correct answer is (d) Q* = 24; P* = 52, Profit = 1152.