Question

Suppose that the market for gourmet deli sandwiches is perfectly competitive and that the supply of workers in this industry is upward-sloping, so that wages increase as industry output increases. Delis in this market face the following total cost: TC = q³ - 15 q² + 90 q + W where,

Q = number of sandwiches

W = daily wages paid to workers

The wage, which depends on total industry output, equals: W = 0.2 Nq where, N = number of firms.

Assume that the market demand is: QD = 700 - 15 P

1. What is the long-run equilibrium output for each firm?

2. How much does the long-run equilibrium price change as the number of firms increases?

3. What is the long-run equilibrium number of firms?

4. What is the total industry output?

5. What is the long-run equilibrium price?

Answer 1

TC = q³ - 15q² + 90q + W = q³ - 15q² + 90q + 0.2Nq

(1)

In long run equilibrium, P = AC = MC.

AC = TC/q = q² - 15q + 90 + 0.2N

MC = dTC/dq = 3q² - 30q + 90 + 0.2N

Equating AC and MC,

q² - 15q + 90 + 0.2N = 3q² - 30q + 90 + 0.2N

2q² = 15q

q = 15/2 = 7.5

(2)

P = AC = (7.5)² - 15 x 7.5 + 90 + 0.2N = 56.25 - 112.5 + 90 + 0.2N = 33.75 + 0.2N

Therefore, as N increases, P increases.

(3)

QD = 700 - 15 x (33.75 + 0.2N) = 700 - 506.25 - 3N = 193.75 - 3N

Market supply (QS) = N x q = N x 7.5

Since QD = QS,

193.75 - 3N = 7.5N

10.5N = 193.75

N = 18.45 ~ 18 firms

(4)

Q = 18 x 7.5 = 135 (Industry output)

(5)

P = 33.75 + 0.2N = 33.75 + 0.2 x 18 = 33.75 + 3.6 = 37.35