Refer to the following:
$$\begin{array} { l }
P _ { X } = 666 - 0.5 Q _ { X } - 2 Q _ { Y } \
P _ { Y } = 484.5 - 1.5 Q _ { Y } - 0.25 Q _ { X } \
M C _ { X } = 20 + 2 Q _ { X } \
M C _ { Y } = 4 + Q _ { Y }
\end{array}$$
-What are the profit-maximizing prices for the two goods?
A) $P _ { X }$ = $375,$P _ { y }$ = $284
B) $P _ { X }$ = $423,$P _ { y }$ = $712
C) $P _ { x }$ = $166,$P _ { y }$ = $324
D) $P _ { X }$ = $481,$P _ { y }$ = $588

Question

Refer to the following:
 $$\begin{array} { l } 
P _ { X } = 666 - 0.5 Q _ { X } - 2 Q _ { Y } \
P _ { Y } = 484.5 - 1.5 Q _ { Y } - 0.25 Q _ { X } \
M C _ { X } = 20 + 2 Q _ { X } \
M C _ { Y } = 4 + Q _ { Y }
\end{array}$$
-What are the profit-maximizing prices for the two goods?
A) $P _ { X }$ = $375,$P _ { y }$ = $284
B) $P _ { X }$ = $423,$P _ { y }$ = $712
C) $P _ { x }$ = $166,$P _ { y }$ = $324
D) $P _ { X }$ = $481,$P _ { y }$ = $588

Quizplus · Accepted Answer

The profit-maximizing prices are found by setting the marginal cost equal to the marginal revenue for each good. The marginal revenue for good X is:MRx = P - 0.5 = 666 - 0.5Qx - 2Qy - 0.5Setting this equal to the marginal cost of good X, we get:20 + 2Qx = 666 - 0.5Qx - 2Qy - 0.5Solving for Qx, we get:Qx = 222Substituting this back into the demand equation for good X, we get:Px = 666 - 0.5(222) - 2Qy = 375The marginal revenue for good Y is:MRy = P - 1.5 = 484.5 - 1.5Qy - 0.25Qx - 1.5Setting this equal to the marginal cost of good Y, we get:4 + Qy = 484.5 - 1.5Qy - 0.25Qx - 1.5Solving for Qy, we get:Qy = 166Substituting this back into the demand equation for good Y, we get:Py = 484.5 - 1.5(166) - 0.25(222) = 284Therefore, the profit-maximizing prices are Px = $375 and Py = $284.

Refer to the Following -What Are the Profit-Maximizing Prices for the Two Goods? A)

Refer to the Following -What Are the Profit-Maximizing Prices for the Two Goods?
A)