To determine the output level a perfectly competitive firm should produce, we need to consider where marginal cost (MC) equals marginal revenue (MR), which in a perfectly competitive market is equal to the price.
First, we should calculate total cost (TC) for each level of output:
- Total Cost (TC) = Fixed Cost (FC) + Variable Cost (VC)
- We know FC is constant at $100 for all output levels.
Now let's compute TC for each output level:
- For 0 workers (output = 0):
- TC = FC + VC = 100 + 0 = $100
- For 10 workers (output = 300):
- TC = 100 + 90 = $190
- For 20 workers (output = 800):
- TC = 100 + 295 = $395
- For 30 workers (output = 1,200):
- TC = 100 + 490 = $590
- For 40 workers (output = 1,500):
- TC = 100 + 670 = $770
Next, determine profits at each output level:
- Profit = Total Revenue (TR) - Total Cost (TC)
Now, calculate the profit for each level:
- For 0 output:
- TR = $0, TC = $100 -> Profit = 0 - 100 = -100
- For 300 units:
- TR = $150, TC = $190 -> Profit = 150 - 190 = -40
- For 800 units:
- TR = $400, TC = $395 -> Profit = 400 - 395 = +5
- For 1,200 units:
- TR = $600, TC = $590 -> Profit = 600 - 590 = +10
- For 1,500 units:
- TR = $750, TC = $770 -> Profit = 750 - 770 = -20
The firm should choose to produce the output level that maximizes profit. Based on the calculations:
- Profit at 800 units = +5
- Profit at 1,200 units = +10
Thus, the output level that maximizes profit is 1,200 units.
Therefore, the firm should choose to produce 1,200 units of output.
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