A firm sells two goods X and Y)that are related in consumption.The estimated demand and cost conditions are: What are the profit-maximizing levels of output for the two goods?
A) = 20, = 10
B) = 41, = 24
C) = 56, = 24
D) = 51, = 74
E)none of the above

Question

A firm sells two goods X and Y)that are related in consumption.The estimated demand and cost conditions are:  What are the profit-maximizing levels of output for the two goods?
A) = 20, = 10 
B) = 41, = 24 
C) = 56, = 24 
D) = 51, = 74 
E)none of the above

Quizplus · Accepted Answer

To find the profit-maximizing levels of output for goods X and Y, we need to use the following formulas:

MRx = 10 - 0.5Qx - 0.2Qy 
MCx = 20 
MRy = 8 - 0.2Qx - 0.1Qy 
MCy = 10

Setting MRx = MCx, we have:

10 - 0.5Qx - 0.2Qy = 20 
-0.5Qx - 0.2Qy = 10 
-5Qx - 2Qy = 100

Setting MRy = MCy, we have:

8 - 0.2Qx - 0.1Qy = 10 
-0.2Qx - 0.1Qy = 2 
-2Qx - Qy = 20

Solving these two equations simultaneously, we get:

Qx = 51 
Qy = 74

Therefore, the profit-maximizing levels of output for goods X and Y are 51 and 74, respectively. The answer is D.

A Firm Sells Two Goods X and Y)that Are Related