Refer to the data in the accompanying table.

\begin{tabular}{|c|c|c|}
\hline
Output & \begin{tabular}{c}
Marginal \\
Revenue
\end{tabular} & \begin{tabular}{c}
Marginal \\
Cost
\end{tabular} \\
\hline 0 & - & - \\
\hline 1 & [tex][tex]$\$[/tex]16[tex]$[/tex] & [tex]$[/tex]\[tex]$10$[/tex][/tex] \\
\hline 2 & [tex][tex]$\$[/tex]16[tex]$[/tex] & [tex]$[/tex]\[tex]$11$[/tex][/tex] \\
\hline 3 & [tex][tex]$\$[/tex]16[tex]$[/tex] & [tex]$[/tex]\[tex]$13$[/tex][/tex] \\
\hline 4 & [tex][tex]$\$[/tex]16[tex]$[/tex] & [tex]$[/tex]\[tex]$17$[/tex][/tex] \\
\hline 5 & [tex][tex]$\$[/tex]16[tex]$[/tex] & [tex]$[/tex]\[tex]$21$[/tex][/tex] \\
\hline
\end{tabular}

If the firm's minimum average variable cost is [tex][tex]$\$[/tex]10$[/tex], the firm's profit-maximizing level of output would be

A. 2
B. 3
C. 4
D. 5



Answer :

To find the firm's profit-maximizing level of output, we need to compare the marginal revenue (MR) with the marginal cost (MC) at each output level. The profit-maximizing level of output is when marginal revenue is greater than or equal to marginal cost and stops just before marginal cost exceeds marginal revenue.

Let's analyze each output level:

1. Output = 1:
- Marginal Revenue (MR) = \[tex]$16 - Marginal Cost (MC) = \$[/tex]10
Since MR (\[tex]$16) > MC (\$[/tex]10), producing 1 unit is profitable.

2. Output = 2:
- Marginal Revenue (MR) = \[tex]$16 - Marginal Cost (MC) = \$[/tex]11
Since MR (\[tex]$16) > MC (\$[/tex]11), producing 2 units is also profitable.

3. Output = 3:
- Marginal Revenue (MR) = \[tex]$16 - Marginal Cost (MC) = \$[/tex]13
Since MR (\[tex]$16) > MC (\$[/tex]13), producing 3 units continues to be profitable.

4. Output = 4:
- Marginal Revenue (MR) = \[tex]$16 - Marginal Cost (MC) = \$[/tex]17
Since MR (\[tex]$16) < MC (\$[/tex]17), producing 4 units is not profitable.

5. Output = 5:
- Marginal Revenue (MR) = \[tex]$16 - Marginal Cost (MC) = \$[/tex]21
Since MR (\[tex]$16) < MC (\$[/tex]21), producing 5 units is also not profitable.

Thus, the firm's profit-maximizing level of output is the highest output level where MR remains greater than or equal to MC, which occurs at:

Output = 3

Therefore, the firm's profit-maximizing level of output is:

[tex]\[ \boxed{3} \][/tex]