Sia
Question
Macroeconomics
Posted 6 months ago
A producer of Quidditch brooms employs 400 units of labor at each, and the rental rate of capital is . The marginal product of different units of labor used to produce Quidditch brooms are shown in this table.
\begin{tabular}{ll}
\hline Quantity of Capital & Marginal product of capital \\
\hline 10 & 8200 \\
20 & 8000 \\
30 & 7800 \\
40 & 7600 \\
50 & 7400
\end{tabular}
How much capital should the firm employ to maximize profit?
Choose 1 answer:
(A) 30
(B) 10
(C) 50
(D) 20
(ㄷ) 40
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Answer from Sia
Posted 6 months ago
Solution
a
Profit Maximization Condition: A firm maximizes profit by employing capital up to the point where the marginal product of capital (MPK) equals the rental rate of capital
b
Calculation of Profit Maximizing Capital: Given the rental rate of capital is $200, the firm should employ the quantity of capital where MPK is closest to this value
c
Comparison of MPK with Rental Rate: The MPK for 10 units of capital is 8200, which is significantly higher than the rental rate. As we increase the quantity of capital, the MPK decreases. We need to find the quantity of capital where MPK is just equal to or falls below the rental rate of $200
d
Determining the Optimal Quantity of Capital: By examining the table, we see that the MPK for 20 units of capital is 8000, which is still higher than the rental rate. For 30 units of capital, the MPK is 7800, which is also higher. However, for 40 units of capital, the MPK is 7600, and for 50 units, it is 7400. Since the rental rate is $200, and we assume a linear interpolation between the quantities of capital, the closest MPK to the rental rate without going below it would be slightly less than the MPK for 40 units of capital
Answer
(D) 20
Key Concept
Marginal Product of Capital (MPK) and Rental Rate of Capital
Explanation
The firm should employ the quantity of capital where the MPK is equal to the rental rate of capital to maximize profit. In this case, it is the quantity of capital where MPK is just above $200, which corresponds to 20 units of capital.
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