Question

A firm’s long-run average cost curve is estimated by the equation: AC = 1,000 – 1.4Q + .005Q2 . What is the lowest price per unit sold that would prevent the firm from shutting down in the long run? Hint: Write the answer to two decimal places. Hint two: Total cost (C) is just AC multiplied by Q. Selected Answer: [None Given] Response Feedback: Review the discussion about the long run shut down problem in the Chapter Six slides

Answer 1

The lowest price per unit that would prevent the firm from shutting down in the long run is that price which is equal to minimum AC.

AC is minimum when it is equal to MC.

AC = 1,000 - 1.4Q + 0.005Q²

TC = AC * Q = (1,000 - 1.4Q + 0.005Q²) * Q = 1,000Q - 1.4Q² + 0.005Q³

Calculate MC -

MC = dTC/dQ = d(1,000Q - 1.4Q² + 0.005Q³)/dQ = 1,000 - 2.8Q + 0.015Q²

Equating AC and MC,

1,000 - 1.4Q + 0.005Q² = 1,000 - 2.8Q + 0.015Q²

1.4Q = 0.010Q²

Q = 1.4/0.010

Q = 140

AC = 1,000 - 1.4Q + 0.005Q²

AC = 1,000 - (1.4 * 140) + [0.005 * (140)²]

AC = 1,000 - 196 + 98

AC = 902

The minimum AC is $902.

So,

The lowest price per unit sold that wouold prevent the firm from shutting down in the long run is $902.