Question

If P=36-Q is the inverse demand curve and AC=MC=12 then under a monopolist CS=........, PS=........ and DWL=............

Answer 1

Profit is maximized where marginal revenue is equal to marginal cost

Marginal revenue can find out from the demand curve by doubling the coefficient of Q

Demand Function

P = 36 - Q

Marginal Revenue Function

MR = 36 - 2Q

Equating both MR and MC

36 - 2Q = 12

Q = 12

To find the profit-maximizing price we will use this quantity in demand function.

P = 36 - Q

P = 36 - 12

P = 24

Hence the monopoly will produce 12 units at a price of $24

In the above graph, the red triangle represents consumer surplus hence the area of this triangle will be the consumer surplus.

Area = 1/2 x base x height

Area = 1/2 x 12 x 12

Area = 72

Hence the consumer surplus will be $72

In the above graph, the blue triangle represents the deadweight loss hence the area of this triangle will be the deadweight loss.

Area = 1/2 x base x height

Area = 1/2 x 12 x 12

Area = 72

Hence the deadweight loss will be $72

In the above graph, the yellow rectangle represents the producer surplus hence the area of this rectangle will be the producer surplus.

Area = L x B

Area = 12 x 12

Area = 144

Hence the producer surplus will be $144