Answer to Question #282710 in Macroeconomics for Ethio

Question

Suppose that the firm operates in a perfectly competitive market. The market price of its product is $10. The firm estimates its cost of production with the following cost function: TC= -4Q2+Q3 + 10Q + 2

A) What level of output should the firm produce to maximize its profit?

B) Determine the level of profit at equilibrium.

C) What minimum price is required by the firm to stay in the market?

Answer 1

A) The firm should produce such level of output for which P = MC to maximize its profit.

$MC = TC'(Q) = 3Q^2 - 8Q + 10,$

$3Q^2 - 8Q + 10 = 10,$

$3Q^2 - 8Q = 0,$

Q(3Q - 8) = 0,

Q = 0 (does not satisfy conditions) or Q = 8/3 = 2.67 units.

B) The level of profit at equilibrium is:

$TP = 10×2.67 - (-4×2.67^2 + 2.67^3 + 10×2.67 + 2) = 7.48.$

C) The minimum price of P = AVC is required by the firm to stay in the market.