Question

A firm has total cost function: ?(?) = ???? + ??? + ???

G) In a competitive market, what is the lowest price at which the firm will supply a positive quantity in long-run equilibrium?

H) In a perfectly competitive market, what price maximizes the firm’s profit?

I) How much output would the firm supply at the price in part H)

J) At what quantity is the firm’s marginal cost equal to its average cost?

Answer 1

Ans. Cost, c = 10y^2 + 50y + 250

G) Average Cost, AC = c/y = 10y + 50 + 250/y

The lowest price at which the firm will supply in long run is the minimum of AC, so, to minimize AC, we need to differentiate it with respect to y and equate the result to zero,

dAC/dy = 10 - 250/y^2 = 0

=> y = 5 units

So, minimum price = AC (at y = 5) = 10*5 + 50 + 250/5 = $150

H) Marginal Cost, MC = dc/dy = 20y + 50

At profit maximizing level,

MC = AC

=> 20y + 50 = 10y + 50 + 250/y

=> y = 5 units

Hence, price = $150

I) Output = 5 units

J) At AC = MC,

10y + 50 + 250/y = 20y + 50

=> y = 5 units