Question

1. There are identical firms with cost function ?(?) = ? 2 + 100. The market demand is given by the following inverse demand function ? = −0.02? + 220. The industry is a constant cost industry. This is a competitive market where each firm takes the price as given, with $5 per unit tax levied on the producers.

a) Calculate the firm’s MC, AC, AVC and supply ?(?). Graph the cost curves and the supply on a graph.

b) What is the long-run market supply curve? Graph the long-run market supply with the market demand on a graph. Explain how you come to your conclusion.

c) How many firms operate in the long-run? Explain why you will not see a more or smaller number of firms in the long run.

d) What is the short-run market supply if there are 50 firms? What is the profit in the short-run with 50 firms in the market? What is the consumer surplus, producer surplus, and the total welfare in the short run with 50 firms?

g) What is the consumer surplus, producer surplus, and the total welfare in the long-run?

Answer 1

A)TC=q^2+100

After tax,TC=q^2+5q+100

MC=2q+5

AC=q+5+100/q

AVC=q+5

Supply function is nothing but MC function,

P=2q+5

Q=0.5p-2.5

B)Long run supply will be horizontal at minimum average cost.

Minimum average cost is where average cost is Equal to MC

Q+5+100/q=2q+5

Q^2=100

Q=10

AC=10+5+100/10=25

So long run supply will horizontal at p=25

C) Long run market output,

25=220-0.02q

Q=195/0.02=9750

Number of firms= total market output/ each firm output=9750/10=975

Because ,there is zero economic Profit at this number of firms ,so no firms want to exit or enter the market , so number of firms remain fixed at this level.

D) individual firm supply:Q=0.5p-2.5

short run market supply;Q=50(0.5p-2.5)=25p-125

P=q/25 +5=0.04q +5

Equilibrium,

0.04q+5=220-0.02q

Q=215/0.06=3583.33

P=220-0.02*3583.33=148.33

Each firm output=3583.33/50=71.66

ATC=71.66+5+100/71.66=78.05

Profit of each firm=(148.33-78.05)*71.66=5035.8

CONSUMERs surplus=1/2*3583.33*(220-148.33)=128,408.6

Producer surplus=1/2*3583.33*(148.33-5)=256,799.3

Total welfare=128,408.6+256.799.3=385,207.9