Question

The market demand curve is P = 90 − 2Q, and each firm’s total cost function is C = 100 + 2q 2 .

(d) (2 points) Verify that the monopoly price and quantity satisfy the monopolist’s rule of thumb for pricing.

(e) (3 points) What is the monopolist’s factor markup of price over marginal cost?

(f) (4 points) How does the monopolist’s factor markup of price over marginal cost compare to that of a perfectly competitive firm?

Answer 1

Solutiom :

(d) Verify that the monopoly price and quantity satisfy the monopolist’s rule of thumb for pricing.

When Q = 11.25, MC = 4 x 11.25 = 45

Monopoly pricing rule, using Lerner Index (LI), is

- 1 / E = (P - MC) / P

- 1 / E = - 1 / - 3 = 1/3

1/3 = (P - 45) / P

P = 3P - 135

2P = 135

P = 67.5, which satisfies the value derived in part (c).

(e) What is the monopolist’s factor markup of price over marginal cost?

Mark-up over MC = (P - MC) / MC

= (67.5 - 45) / 45

= 22.5 / 45

= 0.5

(f) How does the monopolist’s factor markup of price over marginal cost compare to that of a perfectly competitive firm?

For a perfectly competitive firm, P = MC, therefore Markup = zero.

As a result, monopoly markup is always higher than perfectly competitive firm's markup.