Question

Free Response Questions Please round all numerical answers to the nearest four decimal places

1. Answer the following questions if the average cost function is: AC=q^2-24q+10

(b) what level of production is the AC function minimized?

(c) If this firm is operating in a competitive market, what is its price at long run equilibrium?

(d)How much profit does the firm earn at the long run equilibrium?

(Please show the steps for how you get the answer. Thank you so much!)

Answer 1

1. AC = q² - 24q + 10

b) When AC is minimized, then d(AC)/dq = 0

Or, 2q - 24 +0 = 0

Or, 2q = 24

Or, q = 12

Therefore, at q = 12, AC is minimized.

C) if this firm is operating in a competitive market, then the long run equilibrium price will be equal to minimum AC so that each firm earns zero economic profit in long run.

AC is minimized when q = 12.

Therefore, at q = 12, AC = (12)² - (24*12)+10 = - $134.

So, the long run equilibrium price will be - $134.

D) A profit maximizing perfectly competitive firm produces at the point where price is equal to MC. In long run equilibrium, it produces at the point where AC is at it's minimum. Because, MC cuts AC at it's minimum point, so, in Long run equilibrium, if the firm produces at that point, then at the profit maximizing output level, the price will be equal to minimum AC and therefore total revenue will be equal to total cost. Each firm therefore will earn zero economic profit at LR equilibrium and there will be no entry or exit.