To determine the short-run profit-maximizing level of output for the firm, we need to follow these steps:
1. Calculate the profit at each level of output. Profit is determined by subtracting the Total Cost from the Total Revenue at each output level.
Let's compute the profit for each level of output based on the table:
- For an output of 1:
[tex]\[ \text{Profit} = \text{Total Revenue} - \text{Total Cost} = 6 - 4 = 2 \][/tex]
- For an output of 2:
[tex]\[ \text{Profit} = \text{Total Revenue} - \text{Total Cost} = 12 - 6 = 6 \][/tex]
- For an output of 3:
[tex]\[ \text{Profit} = \text{Total Revenue} - \text{Total Cost} = 18 - 9 = 9 \][/tex]
- For an output of 4:
[tex]\[ \text{Profit} = \text{Total Revenue} - \text{Total Cost} = 24 - 13 = 11 \][/tex]
- For an output of 5:
[tex]\[ \text{Profit} = \text{Total Revenue} - \text{Total Cost} = 30 - 20 = 10 \][/tex]
2. Identify the output level that yields the maximum profit. Comparing the calculated profits:
- Output 1: Profit = 2
- Output 2: Profit = 6
- Output 3: Profit = 9
- Output 4: Profit = 11
- Output 5: Profit = 10
The highest profit is 11, which occurs at an output level of 4 units.
Therefore, the short-run profit-maximizing level of output for the firm is:
4
