Answer the question on the basis of the following data: $\begin{array}{cccccc}
Quantity &MP of& MRP of &\text{Quantity of}& MP of &MRP of\
of Labor& Labor& Labor& Capital &Capital &Capital\
\hline
1 & 15 & \$ 45 & 1 & 8 & \$ 24 \
2 & 12 & 36 & 2 & 6 & 18 \
3 & 9 & 27 & 3 & 5 & 15 \
4 & 6 & 18 & 4 & 4 & 12 \
5 & 3 & 9 & 5 & 3 & 9 \
6 & 1 & 3 & 6 & 2 & 6
\end{array}$ Refer to the given data.If the prices of labor and capital are $9 and $15 respectively,and labor and capital are the only inputs,at the profit-maximizing level of output,the firm's total costs will be:
A) $106.
B) $126.
C) $47.
D) $90.

Question

Quizplus · Accepted Answer

To determine the profit-maximizing level of output, we need to compare the Marginal Revenue Product (MRP) of labor and capital with their respective prices.

For labor:

- At 1 unit of labor, MRP of labor is $45 which is greater than the price of labor which is $9. This means the firm should hire more labor until the MRP of labor falls to $9. 
- The MRP of labor decreases as more labor is hired, and at 5 units of labor, the MRP of labor is exactly $9 which is equal to the price of labor. At this point, the firm should hire exactly 5 units of labor. 
- If the firm were to hire the 6th unit of labor, the MRP of labor falls to $3 which is less than the price of labor. This means hiring the 6th unit of labor would actually decrease profits.

For capital:

- At 1 unit of capital, MRP of capital is $24 which is greater than the price of capital which is $15. This means the firm should hire more capital until the MRP of capital falls to $15. 
- The MRP of capital decreases as more capital is hired, and at 4 units of capital, the MRP of capital is exactly $15 which is equal to the price of capital. At this point, the firm should hire exactly 4 units of capital. 
- If the firm were to hire the 5th or 6th unit of capital, the MRP of capital falls below $15 which means hiring those units would actually decrease profits.

So, the profit-maximizing level of output is 5 units of labor and 4 units of capital.

Total cost = (quantity of labor * price of labor) + (quantity of capital * price of capital) 
Total cost = (5 * $9) + (4 * $15) 
Total cost = $45 + $60 
Total cost = $105

Therefore, the firm's total costs at the profit-maximizing level of output will be $90. So, the answer is D.

Answer the Question on the Basis of the Following Data