Refer to the following:
A firm with market power faces the following estimated demand and average variable cost functions:
$Q _ { d } = 39,000 - 500 P + 0.4 M - 8,000 P _ { R }$
$A V C = 30 - 0.005 Q + 0.0000005 Q ^ { 2 }$
where
$Q _ { d }$ is quantity demanded, P is price, M is income, and
$P _ { R }$ is the price of a related good. The firm expects income to be $40,000 and
$P _ { R }$ to be $2. Total fixed cost is $100,000.
-What is the profit-maximizing choice of output?

Question

Refer to the following:
A firm with market power faces the following estimated demand and average variable cost functions:
 $Q _ { d } = 39,000 - 500 P + 0.4 M - 8,000 P _ { R }$ 
 $A V C = 30 - 0.005 Q + 0.0000005 Q ^ { 2 }$ 
where
 $Q _ { d }$ is quantity demanded, P is price, M is income, and
 $P _ { R }$ is the price of a related good. The firm expects income to be $40,000 and
 $P _ { R }$ to be $2. Total fixed cost is $100,000.
-What is the profit-maximizing choice of output?

Quizplus · Accepted Answer

The profit-maximizing choice of output is 8,000 units. This is because at this output level, the marginal revenue (MR) equals the marginal cost (MC). The MR is the change in total revenue resulting from a one-unit increase in output, and the MC is the change in total cost resulting from a one-unit increase in output. At an output level of 8,000 units, the MR is $20 and the MC is $20. Therefore, the firm will maximize its profits by producing 8,000 units.

Refer to the Following: a Firm with Market Power Faces Qd=39,000−500P+0.4M−8,000PRQ _ { d } = 39,000 - 500 P + 0.4 M - 8,000 P _ { R }Qd​=39,000−500P+0.4M−8,000PR​

Refer to the Following:
a Firm with Market Power Faces $Q _ { d } = 39,000 - 500 P + 0.4 M - 8,000 P _ { R }$