Question

Consider a competitive firm with total costs given by TC(q) = 100 + 10q + q 2 The firm faces a market price p = 50.

(d) Find the profit-maximizing level of output q^*. At this level of output, what are TR, TC, ATC, and π?

(e) Graph the ATC, AVC, MC, and MR curves in a single graph, and indicate the profit-maximizing level of output. If there are profits, shade the region corresponding to profit and label it.

Answer 1

Answer : d) Given,

TC(q) = 100 + 10q + q^2

MC (marginal Cost) = $\Delta$TC / $\Delta$q

=> MC = 10 + 2q

For competitive firm the profit-maximizing condition is P = MC. So,

50 = 10 + 2q

=> 50 - 10 = 2q

=> 40 = 2q

=> q = 40 / 2

=> q = 20

Therefore, here the profit-maximizing output level is 20 units.

TR = P * Q = 50 * 20 = $1,000

TC = 100 + (10 * 20) + (20)^2

=> TC = $700

ATC = TC / q = 700 / 20

=> ATC = 35

Profit ($\dpi{50} \prod$) = TR - TC = 1,000 - 700

=> $\dpi{50} \prod$ = $300.

e) In the following picture's diagram the ATC, MC, AVC and MR curves are drawn. Here the firm earns profit. The profit area is shown by the shaded area in the following picture's diagram.

Price ($) 96 PROFITTA Co o 20 Quantity