A producer of Quidditch brooms employs 400 units of labor at $\$ 10$ each, and the rental rate of capital is $\$ 200$. 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) 40
(B) 10
(C) 30
(D) 50
(E) 20

Question

A producer of Quidditch brooms employs 400 units of labor at $\$ 10$ each, and the rental rate of capital is $\$ 200$. 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) 40
(B) 10
(C) 30
(D) 50
(E) 20

Accepted Answer

∻Solution∻ ‖ a ⋮ Marginal Product of Capital (MPK): The marginal product of capital is the additional output produced by employing one more unit of capital. The table provides the MPK for different quantities of capital. ‖ ‖ b ⋮ Marginal Revenue Product of Capital (MRPK): To maximize profit, the firm should employ capital until the marginal revenue product of capital equals the rental rate of capital. The MRPK is calculated as $MRPK = MPK imes P$, where $P$ is the price of the output. ‖ ‖ c ⋮ Rental Rate of Capital: The rental rate of capital is given as $200$. ‖ ‖ d ⋮ Comparison: Compare the MRPK with the rental rate of capital for each quantity of capital to determine the optimal amount of capital to employ. ‖ ‖ e ⋮ Calculation: Since the price of the output is not provided, we assume it is constant. The firm should employ capital until the MPK is equal to the rental rate of capital. ‖ ∻Answer∻ ⚹ The firm should employ 40 units of capital to maximize profit. ⚹ ∻Key Concept∻ ⚹ Marginal Revenue Product of Capital (MRPK) ⚹ ∻Explanation∻ ⚹ The firm should employ capital until the marginal revenue product of capital equals the rental rate of capital. In this case, 40 units of capital is the optimal amount to maximize profit. ⚹◊What is the relationship between the marginal product of capital and the quantity of capital employed in the production process?⍭ Generate me a similar question◊

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