Question

A producer of fixed proportion goods X and Y (Q = Qx = Qy) has marginal costs and revenues of MC = 10 Q, MRX = 150 - 6 QX, MRy = 30 - 4 Qy. The producer should produce how many units?

a. Qx =9, Qy=9
b. Qx = 9, Qy = 7.5
c. Qx = 10, Qy = 10
d. Qx = 9, Qy=0

Answer 1

The producer should produce 9 units of goods X and 9 units of goods Y.

Step-by-step explanation:

In order for the producer to determine the optimal quantity of units to produce, they need to find the intersection point between marginal cost (MC) and marginal revenue (MR) for both goods X and Y. This is because the profit-maximizing level of output occurs where MR equals MC.

Given the marginal cost equations, MC = 10Q, MRX = 150 - 6QX, and MRy = 30 - 4Qy, we can set MC equal to MRX and solve for QX. This gives us 10Q = 150 - 6QX. Solving for QX, we find QX = 9. Similarly, setting MC equal to MRy and solving for Qy gives us Qy = 9.

Therefore, the producer should produce 9 units of goods X and 9 units of goods Y.

Answer 2

a. Qx =9, Qy=9

Step-by-step explanation:

As per the given data

Q = QX = QY

MRX = 150 - 6QX = 150 - 6Q

MRY = 30 - 4QY = 30 - 4Q

MC = 10Q

Now calculate the Marginal revenue as follow

MR = MRX + MRY

MR = 150 - 6Q + 30 - 4Q

MR = 150 + 30 - 6Q - 4Q

MR = 180 - 10Q

The Equilibrium of the producer will be

MR = MC

180 - 10Q = 10Q

180 = 10Q + 10Q

180 = 20Q

Q = 180 / 20

Q = 9

As we know

Q = Qx = QY

Hence, the value of Qx and QY is 9