What price should a firm charge for a package of two shirts given a marginal cost of $2 and an inverse demand function P = 6 − 2Q by the representative consumer?
A) $2
B) $6
C) $8
D) $10

Question

Quizplus · Accepted Answer

To find the optimal price to charge for the package of two shirts, we need to use the profit-maximizing rule: set marginal cost equal to marginal revenue.

First, we need to find the revenue function from the inverse demand function:

P = 6 - 2Q 
Q = 3 - 0.5P 
Revenue = P x Q 
Revenue = (6 - 2Q) x Q 
Revenue = 6Q - 2Q^2

Next, we take the derivative of the revenue function to find the marginal revenue:

MR = d(6Q - 2Q^2)/dQ 
MR = 6 - 4Q

Setting marginal cost equal to marginal revenue:

MC = MR 
$2 = 6 - 4Q 
4Q = 4 
Q = 1

We can then use the inverse demand function to find the optimal price:

P = 6 - 2Q 
P = 6 - 2(1) 
P = $4

Since the package contains two shirts, the total price will be $8. Therefore, the best choice is C: $8.

What Price Should a Firm Charge for a Package of Two