Question

2. Social Welfare Suppose the market of a good has linear market demand as Q 120-P. A firm in the (a) Find the profit-maximized price, output quantity, and profit of the firm under (b) Find the profit-maximized price, output quantity, and profit of the firm under c)Calculate the consumer surplus under the two cases and compare your results market has the total cost of production as C-200 perfect competition monopoly. What is the dead weight loss of the market due to monopoly? (d) Draw a graph with the demand curve, marginal cost curve, and marginal revenue curve to show how do you find the monopoly price and quantity. Label the con- sumer surplus under monopoly, the monopolist's profit, and the dead weight loss due to monopoly.

Answer 1

Q = 120 - P, so

P = 120 - Q

Marginal cost (MC) = dC/dQ = 20

(a)

A perfect competitor maximizes profit by equating price and MC.

120 - Q = 20

Q = 100

P = MC = 20

Profit = Q x (P - MC) = 100 x 0 = 0

(b)

A monopolist maximizes profit by equating MR with MC.

Total revenue (TR) = P x Q = 120Q - Q²

MR = dTR/dQ = 120 - 2Q

120 - 2Q = 20

2Q = 100

Q = 50

P = 120 - 50 = 70

Profit = 50 x (70 - 20) = 50 x 50 = 2500

(c)

From demand function, when Q = 0, P = 120 (Vertical intercept of demand curve).

Consumer surplus (CS) = Area between demand curve and price

CS with perfect competition = (1/2) x (120 - 20) x 100 = 50 x 100 = 5000

CS with monopoly = (1/2) x (120 - 70) x 50 = 25 x 50 = 1250

Deadweight loss = (1/2) x Difference In P x Difference in Q = (1/2) x (70 - 20) x (100 - 50) = (1/2) x 50 x 50 = 1250

(d)

In following graph, perfectly competitive outcome is at point E where Demand (D) intersects MC with price Pc and output Qc. In this case, CS is area AEPc. Monopoly outcome is at point G where MR intersects MC with price Pm and output Qm. In this case, CS is area AFPm. Profit equals area PcGFPm. Deadweight loss equals area EFG.

P, MR, Mc MC Gr MR