Question

A firm operates in a perfectly competitive market. The market price of its product is 4
1
birr and the total cost function is given by TC= Q 3  5Q 2  20Q  50 , where TC is the
3
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) Find TR & TC
D) What minimum price is
required by the firm to stay
in the market?

Answer 1

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

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

$MC = Q^2 - 10Q + 20,$

$Q^2 - 10Q + 20 = 4,$

$Q^2 - 10Q + 16 = 0,$

Q1 = 8 units, Q2 = 2 units.

B) The level of profit at equilibrium is:

$TP = TR - TC = 4*8 - (1/3*8^3 - 5*8^2 + 20*8 + 50) = -28.67.$

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

C) TR = 4*8 = 32,

TC = $1/3*8^3 - 5*8^2 + 20*8 + 50$ = 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.