Question

Suppose a perfectly competitive firm with total cost function given as:
TC= 400+20Q-2Q2+2
3Q
3.
A. Find profit maximizing level of output and the maximum profit if the average revenue
equals $180.
B. Calculate the shutdown level of output and price.

Answer 1

A. The maximum profit of a firm operating in conditions of perfect competition is determined by the identity: P = MS.

МС =(TC)'= 20 - 4Q+69Q^2

Let's find the volume of output that maximizes the company's profit.

The price according to the condition is equal to P = 180.

Р = МС

180=20 - 4Q+69Q^2

69Q^2-4Q-160=0

Q=1.55

Then you need to calculate the total revenue:

$TR (40) = 1.55 * 180 = 279$

and total costs:

$TC = 20-4Q+69q^2=20-4\times1.55+69(1.55)^2=179.5725$

maximum profit=TR-TC=279-179.5725=99.4275

B. The volume of production, at which the total costs are equal to the total income (TR=TC), does not bring the company either profit or loss, i.e. there is zero profit

TR=TC

TR-TC=0

180Q- 400+20Q-2Q2+23Q^3=0

23Q^3-2Q^2+200Q-400=0

Q=1.5753