Question

Consider a company where Q=200-5P; MC=AC=50

A) compute the competitive P and Q.

B) compute the consumer surplus

C) compute Qm, Pm, CSm, profit in monopoly market

Answer 1

Q = 200 - 5P

This will be drawn as the below diagram where MC = 50. MC is above the vertical intercept of demand curve which cannot be true.

Demand curve must be: P = 200 - 5Q whose diagram is drawn below:

a) Competitive equilibrium occurs when MC = Demand

At this price is 50 and 30 units are produced.

b) Consumer surplus is area of portion A + B + C + D + E whose sum is (1/2) * (200 - 50) * (30 - 0) = 2,250

c) Monopoly equilibrium occurs when MR = MC. At this point, price charged is 125 and units produced are 15. Consumer surplus is area of portion A + B whose sum is (1/2) * (200 - 125) * (15 - 0) = 562.5

Profit is area of portion C + D whose sum is [(125 - 50) * (15 - 0)] = 1,125

Deadweight loss in monopoly is area of portion E whose sum is (1/2) * (125 - 50) * (30 - 15) = 562.5