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]
