Answer to Question #297256 in Macroeconomics for sara

Question

A firm's total-revenue and total-cost functions are

TR=4Q

TC=0.040¹-0.90³ + 100+5

(a) Determine the best level of output. b) Determine the total profit of the firm at its

Answer 1

a) A monopoly firm maximizes profit by producing at the point where MR = MC.

For this firm, TR= 40

Therefore,MR = $\frac{d(TR)}{dQ}$ = 4

And, TC = 0.04Q³ - 0.9Q² + 10Q + 5

Therefore, MC = $\frac{d(TC)}{dQ}$ = 0.12Q² - 1.8Q + 10

Setting MR = MC,we get

0.12Q² - 1.8Q + 10 = 4

0.12Q² - 1.8Q + 6 = 0

Multiplying both sides by 0.12 we get,

Q² - 15Q + 50 = 0

Q² - (10 + 5)Q + 50 = 0

Q² - 10Q + 5Q + 50 = 0

Q(Q - 10) - 5(Q-10) = 0

Q = 10 OR Q = 5

The firm will maximize profit by producing 10 or 5 units. 10 will be the best level because it is greater than 5 units.

b) When Q = 10, TR = (4 × 10) = 40 and TC = 0.04(10)³ - 0.9(10)² + (10 × 10) + 5

= 40 - 90 + 100 + 5 = 55

Therefore, total profit at this best level of output is (TR - TC) = (40 - 55) = -15

There is a loss of $15