Answer to Question #203551 in Microeconomics for Rida Awwal

Question

A firm operates in a perfectly competitive market. The market price of its product is 4

birr and the total cost function is given by TC=1/3Q^3-5Q^2+20Q+50

, where TC is the

total cost and Q is the level of output.

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

POINTS TO NOTE

$P = 4 birr$ , $TC = 1/3*Q^3 - 5Q^2 + 20Q + 50.$

$TC=1/3∗Q3−5Q2+20Q+50.$

SOLUTION

A) The firm produce at P = MC to maximize its profit:

$MC = Q^2 - 10Q + 20,MC=Q2−10Q+20$ ,

Q² - 10Q + 20 = 4,Q2−10Q+20=4,

Q² - 10Q + 16 = 0,Q2−10Q+16=0,

Q1 = 8 units, Q2 = 2 units.

B) The level of profit at equilibrium is:

$TP = TR - TC$ = 4*8 - (1/3*8³ - 5*8² + 20*8 + 50) = -28.67.TP=TR−TC=4∗8−(1/3∗83−5∗82+20∗8+50)=−28.67.

The profit at Q = 2 is lower, so it is not a profit-maximizing quantity.

C) $TR = 4*8 = 32$ ,

TC = 1/3*8³ - 5*8² + 20*8 + 501/3∗83−5∗82+20∗8+50 = 60.67.

= 60.67

 

D) The minimum price is required by the firm to stay in the market is:

$P = AVC = VC/Q$

= 1/3*8 ² - 5*8 + 20 = 1.33.

=1.33.