A firm in Madison is currently producing 100 units of output per day. The manager reports to the owner that producing the 100th unit costs the firm $5. The firm can sell the 100th unit for $5. The firm should continue to produce 100 units in order to maximize its profits (or minimize its losses).

Question

BlackTom AI · Accepted Answer

Profit is maximized where marginal revenue (MR) equals marginal cost (MC), so producing the 100th unit at MR = MC is optimal.

1) Relevant concepts:
- Marginal cost (MC): additional cost of producing one more unit (here, $5 for the 100th unit).
- Marginal revenue (MR): additional revenue from selling one more unit (here, price received for the 100th unit = $5).
- Profit maximization rule for a competitive firm: choose output where MR = MC (subject to the shutdown rule that price must cover average variable cost).

2) Step-by-step reasoning:
- Given MC(100) = $5 and MR(100) = $5, compare MR and MC at the margin.
- If MR > MC, producing an extra unit increases profit; if MR < MC, producing an extra unit decreases profit.
- When MR = MC, producing the extra unit makes no change in profit — the firm is at a local optimum.

3) Calculation (intermediate steps):
- Marginal profit from the 100th unit = MR − MC = $5 − $5 = $0.
- Since the marginal profit is zero, producing the 100th unit neither raises nor lowers profit, meaning output is optimal at that margin.

4) Why this is correct:
- The equality MR = MC is the fundamental first-order condition for profit maximization. Producing where MR = MC ensures there is no incremental gain or loss from changing output by one unit.

5) Why the other option (False) is incorrect:
- Claiming the firm should not produce 100 units contradicts the MR = MC rule. Only if additional information showed price ($5) is below average variable cost would the firm shut down; no such information is given.

6) Conclusion:
- Given MC = $5 and MR = $5 for the 100th unit and no indication of a shutdown condition, the firm should continue producing 100 units. Final answer: True.

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