To determine the marginal cost of producing the 45th unit of output, we need to follow a step-by-step process. Marginal cost is defined as the change in the total variable cost divided by the change in the output level. Here’s how to find it:
1. Identify the variable costs and outputs for relevant workers:
- For the second worker:
- Variable Cost = \[tex]$102
- Output = 35 units
- For the third worker:
- Variable Cost = \$[/tex]156
- Output = 45 units
2. Calculate the change in variable costs (ΔC):
[tex]\[
\Delta C = \text{Variable Cost for 3 workers} - \text{Variable Cost for 2 workers}
\][/tex]
[tex]\[
\Delta C = 156 - 102 = 54
\][/tex]
3. Calculate the change in output (ΔQ):
[tex]\[
\Delta Q = \text{Output for 3 workers} - \text{Output for 2 workers}
\][/tex]
[tex]\[
\Delta Q = 45 - 35 = 10
\][/tex]
4. Calculate the marginal cost (MC):
[tex]\[
\text{MC} = \frac{\Delta C}{\Delta Q}
\][/tex]
[tex]\[
\text{MC} = \frac{54}{10} = 5.4
\][/tex]
Therefore, the marginal cost of producing the 45th unit of output is [tex]\( \$ 5.40 \)[/tex].
The correct answer is:
[tex]\[
\$ 5.40
\][/tex]
