The marginal product of capital of producing 2,991 units of output (find point A)in the table below is:
$$\begin{array}{l}
\text { Production Function far God } \mathbf { X }\
\begin{array} { l l l l l }
L ^ { * } & K & Q & M _ { K } = ( \Delta Q / \Delta K ) & \begin{array} { l }
\mathbf { M P } _ { K } = ( Q / K ) \
\text { Mverage }
\end{array} \
\text { Labor } & \text { Capital } & \text { Output } & \begin{array} { l }
\text { Product of } \
\text { Capital }
\end{array} & \begin{array} { l }
\text { Product of } \
\text { Capital }
\end{array} \
9 & 0 & 0 & - & - \
9 & 10 & 57 & 5.7 & 5.70 \
9 & 20 & 324 & 26.7 & 16.20 \
9 & 30 & 657 & 33.3 & \mathbf { B } \
9 & 40 & 1,072 & 41.5 & 26.80 \
9 & 50 & 1,524 & 45.2 & 30.48 \
9 & 60 & 1,976 & 45.2 & 32.93 \
9 & 70 & 2,391 & 41.5 & 34.16 \
9 & 80 & 2,724 & 33.3 & 34.05 \
9 & 90 & 2,991 & \mathbf { A } & 33.23 \
9 & 100 & 3,048 & 5.7 & 30.48 \
9 & 110 & 3,016 & - 3.2 & 27.42 \
9 & 120 & 2,945 & - 7.1 & 24.54
\end{array}
\end{array}$$

Question

The marginal product of capital of producing 2,991 units of output (find point A)in the table below is:
$$\begin{array}{l}
\text { Production Function far God } \mathbf { X }\
\begin{array} { l l l l l } 
L ^ { * } & K & Q & M _ { K } = ( \Delta Q / \Delta K ) & \begin{array} { l } 
\mathbf { M P } _ { K } = ( Q / K ) \
\text { Mverage }
\end{array} \
\text { Labor } & \text { Capital } & \text { Output } & \begin{array} { l } 
\text { Product of } \
\text { Capital }
\end{array} & \begin{array} { l } 
\text { Product of } \
\text { Capital }
\end{array} \
9 & 0 & 0 & - & - \
9 & 10 & 57 & 5.7 & 5.70 \
9 & 20 & 324 & 26.7 & 16.20 \
9 & 30 & 657 & 33.3 & \mathbf { B } \
9 & 40 & 1,072 & 41.5 & 26.80 \
9 & 50 & 1,524 & 45.2 & 30.48 \
9 & 60 & 1,976 & 45.2 & 32.93 \
9 & 70 & 2,391 & 41.5 & 34.16 \
9 & 80 & 2,724 & 33.3 & 34.05 \
9 & 90 & 2,991 & \mathbf { A } & 33.23 \
9 & 100 & 3,048 & 5.7 & 30.48 \
9 & 110 & 3,016 & - 3.2 & 27.42 \
9 & 120 & 2,945 & - 7.1 & 24.54
\end{array}
\end{array}$$

Quizplus · Accepted Answer

The marginal product of capital (MPK) is calculated as the change in output divided by the change in capital. Looking at the table, we can see that the MPK goes from 33.3 when K=30 to A when K=90. Therefore, the change in output is A-657=234, and the change in capital is 60 (from 30 to 90). Thus, the MPK is 234/60=3.9. Therefore, A is the correct answer.

The Marginal Product of Capital of Producing 2,991 Units of Output