Suzanne is the monopoly seller of an illegal product in a particular city. Her marginal cost is $13 per unit and she has no other costs. She faces a demand curve of P = 112–q, and she charges the same price to all her clients. Unfortunately for Suzanne, in the city there is a corrupt government official who has the power to shut Suzanne’s operation down. This official, however, is willing to take a bribe and let Suzanne continue to sell. What is the highest bribe that Suzanne is willing to pay? [Hint: she wants to be at least as well off as having to stop operating]

[Round your answer to 2 decimal points when necessary]

Question

Suzanne is the monopoly seller of an illegal product in a particular city. Her marginal cost is $13 per unit and she has no other costs. She faces a demand curve of P = 112–q, and she charges the same price to all her clients. Unfortunately for Suzanne, in the city there is a corrupt government official who has the power to shut Suzanne’s operation down. This official, however, is willing to take a bribe and let Suzanne continue to sell. What is the highest bribe that Suzanne is willing to pay?  [Hint: she wants to be at least as well off as having to stop operating]

[Round your answer to 2 decimal points when necessary]

BlackTom AI · Accepted Answer

First, restating the scenario: Suzanne is a monopolist selling an illegal product with marginal cost MC = 13 and no other costs. Demand is P = 112 − q, and she charges a single price. The corrupt official can shut her down but may accept a bribe to allow operation. The bribe is the maximum amount Suzanne would pay to continue operating, ensuring she is at least as well off as if she stopped.

Option analysis:
- Compute the profit if Suzanne operates without a bribe. For a monopoly with P = 112 − q, total revenue TR = Pq = (112 − q)q = 112q − q^2. Marginal revenue MR = dTR/dq = 112 − 2q. Setting MR = MC gives 112 − 2q = 13, so q* = 49.5. The corresponding price is P* = 112 − q* = 62.5.
- Profit at this output (without bribe) is (P* − MC) × q* = (62.5 − 13) × 49.5 = 49.5 × 49.5 = 2,450.25. This is Suzanne’s operating profit before any bribe.
- If Suzanne stops producing, her profit is 0 (no revenue, no costs).
- The highest bribe she would be willing to pay is the amount that leaves her indifferent between continuing to operate and stopping, i.e., bribe = operating profit = 2,450.25.

Why the other considerations don’t change this:
- If she produced more or less than q*, profit would be lower because MR ≠ MC, so the maximum profit occurs at q* where MR = MC, making 2,450.25 the maximum attainable profit before a bribe.
- The bribe cannot exceed this maximum profit, or she would be worse off than stopping (profit would be negative after paying the bribe).

Conclusion (numerical result): the highest bribe Suzanne is willing to pay equals 2,450.25, rounded to two decimals as required.

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