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 estimated marginal revenue function for the firm?

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 estimated marginal revenue function for the firm?

Quizplus · Accepted Answer

The marginal revenue (MR) function is derived from the inverse demand function. Solving for P in the demand function and differentiating with respect to Q gives MR = 78 - 0.004Q.

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 $Q _ { d } = 39,000 - 500 P + 0.4 M - 8,000 P _ { R }$