Question

11. Kites are manufactured by identical firms in a perfectly competitive environment. Each firm’s long run average cost and marginal cost of production are given by:

AC = Q + 100/Q and MC = 2Q where Q is the number of kites produced.

a) In long run equilibrium, how many kites will each firm produce? (2 pts)

b) What will the price of kites (P) be? (1 pt)

c) Suppose the demand for kites is given by formula Q = 8000 - 50*P.

How many kites will be sold and how many firms will there be in kite

industry? (2 pts)

12. Continuing from question 11, suppose the demand for kites unexpectedly rises to

Q = 9000 – 50*P.

In the short run it is impossible to manufacture any more kites than those already in existence (i.e. your answer to 11c).

Worth 1 pt each:

a) What will the new price of kites be?

b) How much profit will each kitemaker earn?

c) In the long run, what will the price of kites be?

d) How many firms will enter the kitemaking industry and how much profit will they earn in the long run?

Answer 1

11)

a) in the long run P = min (AC)

AC would be minimum when d(AC)/dQ = 0:

1 - 100/Q² = 0

Firm would produce = 10 kites

b) Price of kites = ATC (when Q = 10) = 10 + 100/10 = 20

c) Demand = 8000 - 50 x 20 = 7000

Number of firms = Demand/production by 1 firm = 7000/10 = 700 firms

12)

Demand: 9000 - 50P

Supply of 1 firm : Q = P/2 (same as marginal cost curve)

Supply (Qs) = 700 x Q = 350P

9000 - 50P = 350P

P = 22.5

(Q = 9000 - 50 x 22.5 = 7875)

b)

Q (each firm) = 7875/700 = 11.25

Profit = P x Q - TC

Profit (each firm) = ((22.5 x 11.25) - (11.25² + 100) = 26.5625

c)

In the long run, P = 20 (calculated in the same way as above)

d)

Demand = 8000 (when P = 20)

Number of firms = 8000/10 = 800 firms

Profit (long run) = 0