Practice
Monopoly: MR = MC
A monopoly’s marginal revenue from its demand schedule, its profit-maximizing output and price, and its profit.
The skill
A monopoly chooses the quantity where marginal revenue equals marginal cost, then charges the highest price buyers will pay for that quantity, read from the demand schedule. Selling one more unit means lowering the price on every unit, so marginal revenue is less than the price; find it as the change in total revenue. The most common mistake is setting the price equal to marginal cost, or reading the price from the marginal revenue column. A monopoly's price is always above its marginal cost.
A worked example
A monopoly faces the demand schedule below, so selling more units means charging a lower price for all of them. Its total cost of zero units is $50.
| Quantity | Price ($) | Total cost ($) |
|---|---|---|
| 1 | 95 | 64 |
| 2 | 89 | 75 |
| 3 | 83 | 91 |
| 4 | 77 | 113 |
| 5 | 71 | 143 |
| 6 | 65 | 180 |
| 7 | 59 | 225 |
| 8 | 53 | 279 |
What price does the monopoly charge to maximize profit, in dollars?
Solution
- Total revenue is price × quantity, and marginal revenue is the change in total revenue: 1st unit: 95, 2nd unit: 83, 3rd unit: 71, 4th unit: 59, 5th unit: 47, 6th unit: 35, 7th unit: 23, 8th unit: 11.
- Marginal cost of each unit, from total cost: 1st unit: 14, 2nd unit: 11, 3rd unit: 16, 4th unit: 22, 5th unit: 30, 6th unit: 37, 7th unit: 45, 8th unit: 54.
- Marginal revenue is above marginal cost through unit 5 and below it after, so the monopoly produces 5 units.
- It charges the highest price at which 5 units sell: $71, above the marginal cost of unit 5 ($30).
- Profit = 355 − 143 = $212.
Answer: 71