Question

1. Suppose firms in a perfectly competitive, constant cost (i.e., flat LR supply curve), industry face monthly demand given by Qp = 1000 - P and have access to a production technology that yields a cost function TC(Q:) = 40? + 100Qi + 100 where Q denotes units produced per month. Assume the only difference between short-run and long-run costs is T C(0) = 100 in the short run and TC(O) = 0 in the long run (which is consistent with all inputs being flexible, except a $100 building lease, for example) (a) Suppose the industry currently has 100 firms. What are the short-run equilibrium price and quantity ? (b) What is the long-run equilibrium price for this industry? (c) How many firms will operate in this industry in the long run? (d) Suppose the government grants a monthly lump-sum subsidy to each firm that manufactures the product. If this lump-sum subsidy equals $36 per month, what would be the new long-run equilibrium price for the industry? (e) Compare consumer surplus in the long-run equilibrium before the subsidy with the long-run equilibrium after the subsidy. What is the change in consumer surplus? (f) How much does the subsidy cost the government? Is it a good idea ? Explain why or why not?

Answer 1

Hi! Welcome to Chegg!

Due to presence of Chegg policy, I am answering first four parts.

1.

a.

Let firm i quantity be Qi

Q = 100 Qi

Short run equilibrium in perfect competitive market occurs at:

P = MC

dTC 1000 - 1000i => = 8Qi + 100

900 = 108 Qi

Qi = 8.3333

With 100 firms,

Q = 100 X 8.33 = 833.33

P = 1000 - 833.33 = 166.67

b.

In perfectly competitive industry, equilibrium occurs at:

P = min(AC)

AC = - 4Qi + 100 + load

To find minimum of AC, we have:

DAC doi = 4-100

Qi = 5

Minimum AC = 20 + 100 + 20 = 140

Long run equilibrium price = 140

c.

Let number of firms be n.

Demand: Q = 1000 - P

nQi = 1000 - 140 = 860

5n = 860

n = 172

d.

Lump-sum subsidy will reduce costs as follows:

TC = 4Q_i² +100Qi + 100 - 36

AC = 1Qi +100 +

To find minimum of AC, we have:

DAC dai = 4-

Qi = 4

Long run price = 16 + 100 + 16 = 132

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