To determine the marginal cost of increasing production from 5,000 units to 6,000 units, we need to follow these steps:
1. Identify the relevant data:
- Output at 5,000 units (5 thousand)
- Output at 6,000 units (6 thousand)
- Fixed cost: \[tex]$2000 (fixed and doesn't change)
- Variable cost at 5,000 units: \$[/tex]200
- Variable cost at 6,000 units: \[tex]$300
2. Calculate the total cost for each output level:
- Total cost for 5,000 units = Fixed cost + Variable cost for 5,000 units
\[
\text{Total cost for 5,000 units} = \$[/tex]2000 + \[tex]$200 = \$[/tex]2200
\]
- Total cost for 6,000 units = Fixed cost + Variable cost for 6,000 units
[tex]\[
\text{Total cost for 6,000 units} = \$2000 + \$300 = \$2300
\][/tex]
3. Calculate the change in cost when increasing from 5,000 units to 6,000 units:
- Change in total cost = Total cost for 6,000 units - Total cost for 5,000 units
[tex]\[
\text{Change in total cost} = \$2300 - \$2200 = \$100
\][/tex]
4. Calculate the marginal cost:
- Marginal cost is the change in cost per additional unit produced. Since we are considering thousands of units, we calculate it per thousand units (1,000 units).
[tex]\[
\text{Marginal cost} = \frac{\text{Change in total cost}}{\text{Change in output (in thousands)}}
\][/tex]
- Change in output = 1,000 units (from 5,000 to 6,000 units, which is 1 thousand)
[tex]\[
\text{Marginal cost} = \frac{\$100}{1} = \$100
\][/tex]
Therefore, the marginal cost of increasing production from 5,000 units to 6,000 units is \[tex]$100. The correct answer is:
\[
\boxed{\$[/tex]100}
\]
