Market demand is given as Q_D= 60 - P.Market supply is given as Q_S= 3P.Each identical firm has MC = 3Q and ATC = 1.5Q.What is a firm's average total cost

Question

Quizplus · Accepted Answer

To find the optimal output level for a firm, we need to set marginal cost equal to market price. The firm's marginal cost is MC = 3Q, and in a perfectly competitive market, the price is equal to the market price which is equal to the marginal revenue, MR = P = 60 - Q, where Q is the total quantity produced by all the firms.

So, setting MC = MR, we get:

3Q = 60 - Q
4Q = 60
Q = 15

This means that each firm should produce 15 units of output.

To find the average total cost, we simply plug Q = 15 into the equation for ATC:

ATC = TC/Q = (1.5Q)/Q = 1.5

Therefore, the firm's average total cost is $1.50.

Since the market price is P = 60 - Q, and the firm's average total cost is $1.50, the firm earns a profit of:

π = (P - ATC)Q
π = (60 - 15 - 1.5) × 15
π = $675

Thus, the best choice for the firm is to produce 15 units of output at an average total cost of $1.50, which will result in a profit of $675.

Market Demand Is Given as QD = 60 - P

Market Demand Is Given as Q_D= 60 - P