Question

Suppose that a market could be either a monopoly or a competitive market.  Suppose that in either case the demand curve can be written as Qd= 100-2P.  Suppose further that the marginal cost of production is the same in either case.  This means that the supply curve in the competitive market is the same as the marginal cost curve for the monopoly.  So the supply curve is Qs= -20+P and, rearranging the terms, the marginal cost of the monopolist is MC= 20+Q.

1. What is the price and quantity in the market if the market is competitive?

2. What is the price and quantity in the market if the market is a monopoly?

3. How does the price and quantity compare between competition and monopoly?

4. What is the markup in the market is competitive?  What is the markup if the market is a monopoly? Calculate directly as P/MC.

5. What is the markup in the market is competitive?  What is the markup if the market is a monopoly?  Calculate using the elasticity of demand.  For competition, Ed= -infinity for the individual firm (ie. perfectly elastic demand because of a vast array of perfect substitutes).  For monopoly, calculate the elasticity of demand at the quantity and price that the monopoly produces.

Answer 1

SOLUTION:-

A) In perfect competition, P = MC

Or Qd = Qs

100-2P = -20+P

120 = 3P

P* = 40, Q* = 100-80 = 20

B) In Monopoly

MR = MC

2P = 100-Q

P = 50 - Q/2

MR = 50 - Q

So at eqm, 50-Q = 20 + Q

30 = 2Q

Q* = 15, P* = 50-7.5 = 42.5

C) So as compared to perfect Competition, in monoply,

Price is higher & Quantity is Lower

D) In perfect Competition P= MC

So markup = (P-MC)/P

= Zero

At Q = 15, MC = 20+15 = 35

In monoply = (42.5-35)/42.5 = .1764

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

So (P-MC)/P = 1/e

So in perfect competition, e = −∞

So (P-MC)/P = 0

In monopoly,

e = (P/Q)*dQ/dP

dQ/dP = -2

e = -42.5*2/15

= 5.667

Markup = 1/5.667 = .1764