Question

Suppose that the potential customers for hair braiding in a city believe that all hair braiding is identical and that the market is perfectly competitive. Hair braiding requires special skills so the supply of workers in this industry is upward-sloping, and the wages earned by hair braiders increase as the industry output increases.

Firms in this market face the following total cost:

TC = Q3 ?8Q2 + 20Q + W

where Q is the number of hair braidings and W is the daily wage paid to workers. The wage, which depends on total industry output, equals W = 0.1NQ, where N is the number of ?rms. Market demand is:

QD = 500?20P

(f) If the demand changed to QD = 1,000?10P what would be the new long-run competitive equilibrium and does this support your prediction about the long-run supply curve from part (a)?

EDIT:

Question 7

Suppose that the potential customers for hair braiding in a city believe that all hair braiding is identical and that the market is perfectly competitive. Hair braiding requires special skills so the supply of workers in this industry is upward-sloping, and the wages earned by hair braiders increase as the industry output increases. (Total 12 Marks)

Firms in this market face the following total cost:

TC = Q3 ?8Q2 + 20Q + W

where Q is the number of hair braidings and W is the daily wage paid to workers. The wage, which depends on total industry output, equals W = 0.1NQ, where N is the number of ?rms. Market demand is:

QD = 500?20P

(f) If the demand changed to QD = 1,000?10P what would be the new long-run competitive equilibrium and does this support your prediction about the long-run supply curve from part (a)?

My apologies, some of the symbols didnt copy over properly.

Answer 1

TC = Q³ - 8Q² + 20Q + 0.1NQ

New demand function: QD = 1,000 - 10P

10P = 1,000 - QD

P = 100 - 0.1QD

In part (a) Average total cost (AC) = TC/Q

AC = Q² - 8Q + 20 + 0.1N

As output rises, AC initially falls, reaches a minimum (lowest) point and starts rising. Therefore, long run industry supply curve is predicted to be U-shaped.

(f)

In long run equilibrium, Price = ATC = MC

MC = dTC/dQ = 3Q² - 16Q + 20 + 0.1N

So,

3Q² - 16Q + 20 + 0.1N = Q² - 8Q + 20 + 0.1N

2Q² - 8Q = 0

Q - 8 = 0 (Dividing by 2Q)

Q = 8

P = AC = (8 x 8) - (8 x 8) + 20 + 0.1N = 20 + 0.1N

Market supply (QS) = Number of firms x Firm output = N x 8

When QD = 500 - 20P,

In market equilibrium, quantity demanded equals quantity supplied.

500 - 20P = 8N

500 - 20 x (20 + 0.1N) = 8N

500 - 400 - 2N = 8N

10N = 100

N = 10

Price = AC = 20 + (0.1 x 10) = 20 + 1 = 21

When QD = 1,000 - 10P, equating new QD with QS,

1,000 - 10P = 8N

1,000 - 10 x (20 + 0.1N) = 8N

1,000 - 200 - N = 8N

9N = 800

N = 89

Market quantity = 8 x 89 = 712

From market demand function,

712 = 1,000 - 10P

10P = 288

P = AC = 28.8 (new long run equilibrium price)

Therefore, as Q increases (due to an increase in demand), AC increases (since P is higher). Therefore, the long run supply function is upward rising and not U-shaped.