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 - 10 q² + 60 q + W

where,

Q = number of sandwiches

W = daily wages paid to workers

The wage, which depends on total industry output, equals: W = 0.3 Nq

where,

N = number of firms.

Assume that the market demand is:

Q^D = 900 - 5 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

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.

TC = q³ - 15q² + 90q + W = q³ - 15q² + 90q + 0.2Nq, W = 0.3 Nq

Q = number of sandwiches

W = daily wages paid to worke

N = number of firms

Q^D = 900 - 5 P

.for the long run equilibrium, P = AC = MC.

AC = TC/q

= q² - 15q + 90 + 0.2N

MC = dTC/dq = 3q² - 30q + 90 + 0.2N

AC and MCare equating:-

q² - 15q + 90 + 0.2N

= 3q² - 30q + 90 + 0.2N

2q² = 15q

q = 15/2

q= 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

->Then N increases, P increases.

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

supply by the market (QS) = N x q = N x 7.5

QD = QS,

193.75 - 3N = 7.5N

10.5N = 193.75

N = 18.45 ~ 18 firms

(4)Q = 18 x 7.5 = 135 .

(5)P = 33.75 + 0.2N = 33.75 + 0.2 x 18 = 33.75 + 3.6

= 37.35