Answer to Question #282714 in Microeconomics 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

Solution:

A.). Profit maximizing output is where MR = MC

In a perfectly competitive market, P = MR = 10

MC = $\frac{\partial TC} {\partial Q}$ = -8Q + 3Q² + 10

10 = -8Q + 3Q² + 10

-8Q + 3Q² + 10 – 10 = 0

Q = 2.67

The level of output that the firm should produce to maximize its profit = 2.67

 

B.). Profit = TR – TC

TR = P Q = 10 x 2.67 = 26.7

TC = -4Q² + Q³ + 10Q + 2 = -4(2.67²) + 2.67³ + 10(2.67) + 2 = -7.129 +19.034 + 26.7 + 2 = 40.61

Profit = 26.7 – 40.61 = (13.9)

 

C.). The minimum price is where P = AVC

AVC = $\frac{VC} {Q}$ = -4Q² + Q³ + 10Q $\div$ Q = -4Q + Q² + 10

Substitute with Q value:

-4(2.67) + (2.67)² + 10 = -10.68 + 7.13 + 10 = 6.45

Q = 6.45

The minimum price is = 6.45