Question

1. (18pts) Suppose there are 100 firms in a perfectly competitive industry. Short run marginal costs for each firm are given by SMC = q + 2 and market demand is given by Qd = 1000-20P (5pts) Calculate the short run equilibrium price and quantity for each firm.. b. (3pts) Suppose each firm has a U-shaped, long-run average cost curve that reaches a minimum of $10. Calculate the long run equilibrium price and the total industry output.. (4pts) What is the long-run equilibrium output for each firm? What are the profits of each firm in the long run? Show that the short run equilibrium for each firm in part a is also the long run equilibrium. d. (2pts) Determine the consumer and producer surplus for the industry (in this case, the areas of the triangles). (4pts) Suppose now the market demand shifts upward to Qd = 1200-20P what will be the price and the total industry output in the new equilibrium? Will the shift in market demand change the number of firms in the long run? If so, how many firms will there be in the new long equilibrium? a. C. e. long run run

Answer 1

(a)

Firm's short sun supply curve is its SMC function, so

Firm's short run supply function: P = q + 2

Since there are 100 firms, Market supply (QS) = 100 x q

q = QS/100 = 0.01QS

P = 0.01QS + 2

0.01QS = P - 2

QS = 100P - 200 (Industry supply)

Equating industry demand and supply (Qd = QS),

1000 - 20P = 100P - 200

120P = 1200

P = 10

Q = (100 x 10) - 200 = 1000 - 200 = 800

q = Q / 100 = 800/100 = 8

(b)

In long run equilibrium, P = Minimum ATC = MC.

P = $10

From market demand function,

Qd = 1000 - (20 x 10) = 1000 - 200 = 800

(c)

For each firm, P = q + 2

10 = q + 2

q = 8

These results are identical as results derived above.

Since P = ATC in long run, firms earn zero profit in long run.

(d)

From market demand function, When Qd = 0, P = 1000/20 = 50 (Vertical intercept of demand curve).

Consumer surplus = Area between demand curve and price = (1/2) x (50 - 10) x 800 = 400 x 40 = 16,000

From market supply function, When QS = 0, P = 200/100 = 2 (Vertical intercept of supply curve).

Producer surplus = Area between supply curve and price = (1/2) x (8 - 2) x 800 = 400 x 6 = 2,400

NOTE: As HOMEWORKLIB Answering Policy, 1st 4 parts are answered.