Question

The demand schedule in a perfectly competitive market is given by P = 93 – 1.5Q (for Q ≤ 62) and the long-run cost structure of each company is:

Total cost:	256 + 2Q + 4Q2
Average cost:	256/Q + 2 + 4Q
Marginal cost:	2 + 8Q

Q. New companies will enter the market at any price greater than:

8

61

88

Please clarify the calculation

Answer 1

The long run competitive equilibrium occurs at the point where MC = AC = P for each company.

Set MC = AC

2 + 8Q = 256/Q + 2 +4Q

2 + 8Q - 2 - 4Q = 256 / Q

4Q = 256 / Q

4Q² = 256

Q² = 256 / 4

Q^{2 =} 64

Q = (64)^0.5

Q = 8

In perfect competition, P =MC

P = 2+8Q

P = 2 + 8 (8)

P = 66

Any price above 66 result into an economic profit because P = MC > AC. Hence, new companies will enter the market.

Answer: Price should be greater than 66.