Question

Problem 1: The industry demand curve for a particular market is: Q = 2,000 - 4P. The firm's total costs is given by: TC = 200Q+0.750? For each of the three market cases below, you are to calculate: market output and price, consumer surplus, producer surplus, and deadweight loss. iii. Lerner Index of Monopoly Power. (a) Perfect Competition Single-Price (Pure) Monopoly First Degree Price Discrimination (c)

Answer 1

• Q = 2,000 - 4P, hence P = (2,000 - Q)/4 = 500 - 0.25Q
• MC = dTC/dQ = 200 + 1.5Q
• From demand function, when Q = 0, P = 500 (vertical intercept of demand curve)
• From MC function, when Q = 0, MC = 200 (vertical intercept of MC curve)
• Consumer surplus (CS) = area between demand curve and price
• Producer surplus (PS) = area between MC curve and price
• Deadweight loss (DWL) = (1/2) x Change in price x Change in quantity
• Lerner Index (LI) = (P - MC) / P

(a)

(i) Setting P = MC:

500 - 0.25Q = 200 + 1.5Q

1.75Q = 300

Q = 171.43

P = 500 - 0.25 x 171.43 = 500 - 42.86 = 457.14

(ii)

CS = (1/2) x (500 - 457.14) x 171.43 = 85.72 x 42.76 = 3,573.96

PS = (1/2) x (457.14 - 200) x 171.43 = 85.72 x 257.14 = 22,042.04

When P = MC, market efficiency is maximized, so DWL = 0

(iii)

LI = 0 [since P = 0]

(b)

(i)

TR = P x Q = 500Q - 0.25Q²

MR = dTR/dQ = 500 - 0.5Q

Setting MR = MC,

500 - 0.5Q = 200 + 1.5Q

2Q = 300

Q = 150

P = 500 - 0.25 x 150 = 500 - 37.5 = 462.5

(ii)

CS = (1/2) x (500 - 462.5) x 150 = 75 x 37.5 = 2,812.5

When Q = 150, MR = 500 - 0.5 x 150 = 500 - 75 = 425

PS = (1/2) x [(462.5 - 200) + (462.5 - 425)] x 150 = 75 x (262.5 + 37.5) = 75 x 300 = 22,500

DWL = (1/2) x (462.5 - 457.14) x (171.43 - 150) = (1/2) x 5.36 x 21.43 = 57.43

(iii)

MC = MR = 425

LI = (462.5 - 425) / 462.5 = 37.5 / 462.5 = 0.0811

(c)

With first-degree price discrimination, P = MC

(i)

P = 457.14

Q = 171.43 [From Part (a)]

(ii)

CS = 3,573.96

PS = 22,042.04

DWL = 0 [From Part (a)]

(iii)

LI = 0 [since P = MC]