Question

In: Economics

Suppose that the market for gourmet deli sandwiches is perfectly competitive and that the supply of...

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?

Solutions

Expert Solution

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


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