Question

A uniform pricing monopolist has the following cost function and faces the following demand curve for its product:

C(y) = 20y

P(y) = 100 - y

(a) Find the monopolist quantity, price, and deadweight loss relative to the perfectly competitive outcome. Draw a diagram labeling the perfectly competitive outcome as A, and the monopolist outcome as B. Be sure to include the marginal cost and marginal revenue curves in your diagram.

(b) There are two possible scenarios for the monopolist:

i. The government sets a price ceiling of $40/unit in which case the monopolist does not invest in any R&D because it is wary of future government regulation.

ii. There is no government regulation, so then the monopolist invests in R&D which then changes the cost function so that MC = 0. Which scenario has higher welfare (ignore the cost of R&D for producer surplus)? Which scenario do the consumers prefer? Explain.

(c) For plan (i), the marginal revenue curve features a discontinuity at some Q. Explain intuitively why the marginal revenue curve has this discontinuity.

(d) Go back to your solution in part a. Suppose now the government allows one other identical firm to enter this market and firms compete on quantity. Let x equal to value of marginal revenue at the monopolist output when there is only one firm. Claim: If the two firms each produce half the monopoly quantity, then MR = x for both firms at the current level of output. Is this claim true, false, or uncertain? Explain your reasoning.

Answer 1

(a)

(1) Perfectly competitive outcome

A perfect competitor maximizes profits by equating price with marginal cost (MC), where

MC = dC(y) / dy = 20

Equating price with MC,

100 - y = 20

y = 80

P = MC = $20

(2) Monopoly

A monopolist will maximize profit by equating marginal revenue (MR) with MC.

P = 100 - y

Total revenue (TR) = P x y = 100y - y²

MR = dTR/dy = 100 - 2y

Equating with MC,

100 - 2y = 20

2y = 80

y = 40

P = 100 - 40 = $60

(3) Deadweight loss in monopoly

DWL = (1/2) x Difference in price x Difference in output

= (1/2) x $(60 - 20) x (80 - 40) = (1/2) x $40 x 40

= $800

(4) Graph

In following graph, D, MR and MC are demand, marginal revenue and marginal cost curves.

Perfectly competitive equilibrium is at point A where price (Demand) intersects MC, with price Pc and quantity Qc.

Monopoly equilibrium is at point B where MR intersects MC, with price Pm and quantity Qm.

Deadweight loss is the area of triangle ABC.