5. Suppose that the market for painting services is perfectly competitive. Paint

Question

5. Suppose that the market for painting services is perfectly competitive. Painting companies are identical; their long-run cost functions are given by TCC)603 a) Find the long-run equilibrium quantity (q) and price (P) in this industry. Round answers to one decimal. b) If market demand is Q 8,00 0-20P, find the equilibrium total industry output (Q). c) Assuming again that all painting companies are identical, find the equilibrium number of firms. 6. Explain why marginal revenue does NOT equal price for a firm with market power.

Explanation / Answer

(5)

(a) In long run equilibrium, P = MC = AC

MC = dTC(Q)/dQ = 18Q2 - 60Q + 200

AC = TC(Q)/Q = 6Q2 - 30Q + 200

Equating,

18Q2 - 60Q + 200 = 6Q2 - 30Q + 200

12Q2 = 30Q

2Q = 5 [Assuming Q is non-zero, dividing by 6Q]

Q = 2.5 (Firm output)

P = AC = (6 x 2.5 x 2.5) - (30 x 2.5) + 200 = 37.5 - 75 + 200 = 162.5

(b) Substituting value of P in market demand function,

QD = 8,000 - (20 x 162.5) = 8,000 - 3,250 = 4,750 (Industry output)

(c) Equilibrium number of firms = Industry output / Firm output = 4,750 / 2.5 = 1,900

NOTE: As per Chegg Answering Policy, first question has been answered.

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