To determine the optimal output level for a perfectly competitive firm, we need to find where the firm maximizes its profit. This happens when the firm's total revenue (TR) equals its total cost (TC), or when the firm maximizes its profit.
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Calculate the Total Cost (TC): Total Cost is the sum of Fixed Cost (FC) and Variable Cost (VC).
- TC = FC + VC
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Calculate the profit:
- Profit = Total Revenue (TR) - Total Cost (TC)
Let's calculate for each output level:
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For 0 workers (Output = 0):
- FC = $100, VC = $0
- TC = $100 + $0 = $100
- TR = $0
- Profit = $0 - $100 = -$100
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For 10 workers (Output = 300):
- FC = $100, VC = $90
- TC = $100 + $90 = $190
- TR = $150
- Profit = $150 - $190 = -$40
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For 20 workers (Output = 800):
- FC = $100, VC = $295
- TC = $100 + $295 = $395
- TR = $400
- Profit = $400 - $395 = $5
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For 30 workers (Output = 1,200):
- FC = $100, VC = $490
- TC = $100 + $490 = $590
- TR = $600
- Profit = $600 - $590 = $10
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For 40 workers (Output = 1,500):
- FC = $100, VC = $670
- TC = $100 + $670 = $770
- TR = $750
- Profit = $750 - $770 = -$20
Now, let's summarize the profits for each output level:
- Output = 0: Profit = -$100
- Output = 300: Profit = -$40
- Output = 800: Profit = $5
- Output = 1,200: Profit = $10
- Output = 1,500: Profit = -$20
The maximum profit occurs at an output of 1,200 units, with a profit of $10.
Therefore, the firm should choose to produce at:
d. The firm should choose to produce 1,200 units of output.
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