suppose that the demand curve for antimacassars is p = 51 - Q/900.The firm's profit-maximizing output is closest to
A)16,875 antimacassars.
B)5,625 antimacassars.
C)3,712.50 antimacassars.
D)11,250 antimacassars.
E)2,812.50 antimacassars.

Question

Quizplus · Accepted Answer

To find the profit-maximizing output, we need to use the marginal revenue (MR) and marginal cost (MC) approach.

First, let's find the MR:

MR = dTR/dQ = p(1+dQ/dS)

where dQ/dS is the inverse of the demand equation:

dQ/dS = 1/900p

Substituting this into the MR equation:

MR = p(1+1/900p) = p + 1/900

Now, let's assume the cost of producing each antimacassar (MC) is a constant $10.

To maximize profit, the firm should produce at the output where MR = MC.

MR = MC 
p + 1/900 = 10 
p = 899/90

Substituting this back into the demand equation:

Q = 900p/(899) 
Q = 11,250

Therefore, the firm's profit-maximizing output is 11,250 antimacassars.

Suppose That the Demand Curve for Antimacassars Is P =