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Question
Microeconomics
Posted 9 months ago

A producer of Quidditch brooms employs 400 units of labor at $10\$ 10 each, and the rental rate of capital is $200\$ 200. The marginal product of different units of labor used to produce Quidditch brooms are shown in this table.
\begin{tabular}{ll} 
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) 10
(B) 20
(C) 50
(D) 30
(E) 40
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Answer from Sia
Posted 9 months ago
Solution
a
Marginal Product of Capital (MPK): The marginal product of capital is the additional output produced by using one more unit of capital
b
Marginal Revenue Product of Capital (MRPK): To maximize profit, the firm should employ capital until the marginal revenue product of capital (MRPK) equals the rental rate of capital. MRPK is calculated as the marginal product of capital (MPK) multiplied by the price of the output
c
Rental Rate of Capital: The rental rate of capital is given as $200
d
Calculation: Since the price of the output is not provided, we assume it to be constant. The firm should employ capital where MPK equals the rental rate of capital
e
Comparison: Compare the MPK values with the rental rate of capital to determine the optimal quantity of capital


Quantity of CapitalMarginal Product of Capital (MPK)108200208000307800407600507400
\begin{aligned}
&\text{Quantity of Capital} & \text{Marginal Product of Capital (MPK)} \\
&10 & 8200 \\
&20 & 8000 \\
&30 & 7800 \\
&40 & 7600 \\
&50 & 7400 \\
\end{aligned}


Since the rental rate of capital is 200,thefirmshouldemploycapitalwhereMPKisclosestto200, the firm should employ capital where MPK is closest to 200. In this case, none of the MPK values are close to $200, but we can infer that the firm should employ the highest quantity of capital where MPK is still significantly higher than the rental rate.
Answer
50
Key Concept
Marginal Product of Capital (MPK)
Explanation
The firm should employ the quantity of capital where the marginal product of capital (MPK) is closest to the rental rate of capital to maximize profit. In this case, employing 50 units of capital provides the highest MPK that is still significantly higher than the rental rate.

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