Question

Question 2: Consider an industry where firms have the following cost function: C(q) = 200 + 20*q + 0.02*q2 Consumer Demand is given by: P(Q) = 100 – 0.02*Q

(a) Work out the equilibrium price and quantity if you are told that the industry is a monopoly.

(b) Suppose, instead that there is free entry in this industry and firms enter and behave as in perfect competition. How many firms will enter the industry in the long-run?

Answer 1

a)

Monopoly Profit Maximization condition:

MR = MC

C(q) = 200 + 20q + 0.02Q^2

MC= 20+0.04Q

P= 100 - 0.02Q

TR = 100Q - 0.02Q^2

MR = 100 - 0.04Q

MR = MC

100 - 0.04Q = 20 +0.04Q

80 = 0.08Q

Q = 80/0.08

= 1000

P = 100 - 0.02*1000

= 80

b)

Q =200 + 20q + 0.02Q^2

AC = 200/Q +20 + 0.02Q

On differentiating and putting equal to zero.

0.02 - 200/Q^2 = 0

200 = 0.02Q^2

Q^2 = 10000

Q = 100

P = AC = MC

= 20+0.04(100)

= 20 - 4

= 16

Total output:

16 = 100 - 0.02Q

Q = 84/0.02

= 4200

Number of firm = 4200/100

= 42

Thus, extra 41 firms will enter the industry.