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Macroeconomics
Posted 3 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) 50
(B) 10
(c) 30
(D) 20
(E) 40

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Answer from Sia
Posted 3 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 $200, we need to find the quantity of capital where MPK is closest to this value
c
Comparison of MPK and Rental Rate: - At 10 units of capital, MPK is 8200,whichismuchhigherthantherentalrate.At20unitsofcapital,MPKis8200, which is much higher than the rental rate. - At 20 units of capital, MPK is 8000, still higher than the rental rate. - At 30 units of capital, MPK is 7800,closerbutstillhigherthantherentalrate.At40unitsofcapital,MPKis7800, closer but still higher than the rental rate. - At 40 units of capital, MPK is 7600, which is now lower than the rental rate. Therefore, the firm should employ 30 units of capital, where MPK is just above the rental rate
Answer
C) 30
Key Concept
Marginal Product of Capital (MPK)
Explanation
The firm should employ the amount of capital where the MPK is equal to or just above the rental rate of capital to maximize profit. In this case, it is 30 units of capital.$

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