Question

All firms in a perfectly competitive industry have a long-run total cost function of T C(Q) = 36Q − 4Q² + 2Q³. The market demand curve is Q^D = 640 − 10P. The price of inputs is not affected by the industry output.

a) Find the (long-run) average cost and marginal cost curves.

b) What quantity will each firm produce in the long run?

c) What will be the market price in the long run?

d) What will be the total quantity supplied by all firms in the long run?

e) How many firms will operate in the industry in the long run?

f) Write down an expression for the long-run supply curve.

Answer 1

Long run total cost function is TC = 36Q – 4Q^2 + 2Q^3. Market demand is QD = 640 – 10P

a) Long run AC = TC/Q

AC = 36 – 4Q + 2Q^2

MC = dTC/dQ = 36 – 8Q + 3Q^2

b) In the long run P = MC = AC will result in a quantity of

36 – 4Q + 2Q^2 = 36 – 8Q + 3Q^2

4Q – Q^2 = 0

Q = 4 units

Long run quantity by each firm is 4 units.

c) Price = 36 – 8*4 + 3*4^2 = $52

d) Total quantity supplied = 640 – 10*52 = 120 units

e) Number of firms = 120/4 = 30 firms

f) Long run supply curve is P = $52