Answer to Question #283901 in Microeconomics for abrham

Question

Suppose the perfectly competitive firm’s cost function is TC=Q³-21Q²+600Q+1820 and its AR=600. (2Pts)                         

    a. What is the profit maximization level of output?

b.     What is the maximum of profit or minimum of loss?

Answer 1

a. P = MR = MC

$(TC=Q3-21Q2+600Q+1820)'=3Q^2-42Q+600$

With perfect competition , AR = MR

$3Q^2-42Q+600=600$

$3Q^2-42Q=0$

$Q(3Q-42)=0$

Q=0

3Q-42=0

Q=14

b. In conditions of perfect competition, the marginal income is equal to the price of the goods. Therefore, the rule MR = MC can be presented in another form: P = MR = MC, or P = MS. That is, in conditions of perfect competition, profit maximization (loss minimization) is achieved when the volume of production corresponds to the point of equality of marginal costs and price.