A College Board–style free-response question on Imperfect Competition, broken into parts with a model answer showing exactly how each point is earned.
Glacier Water is the only provider of piped water in an isolated town, protected by a government-granted franchise. It has a large fixed cost and a constant marginal cost of $10 per unit. The table shows its demand and cost data.
| Quantity | Price ($) | Total Revenue ($) | Marginal Revenue ($) | Total Cost ($) | Marginal Cost ($) | Average Total Cost ($) |
|---|---|---|---|---|---|---|
| 1 | 20 | 20 | 20 | 20 | 10 | 20.00 |
| 2 | 18 | 36 | 16 | 30 | 10 | 15.00 |
| 3 | 16 | 48 | 12 | 40 | 10 | 13.33 |
| 4 | 14 | 56 | 8 | 50 | 10 | 12.50 |
| 5 | 12 | 60 | 4 | 60 | 10 | 12.00 |
| 6 | 10 | 60 | 0 | 70 | 10 | 11.67 |
The profit-maximizing quantity is 3 units and the price is $16.
Quantity comes from the MR = MC rule. Marginal revenue exceeds marginal cost through the third unit (MR = $12 > MC = $10), but on the fourth unit MR = $8 falls below MC = $10. The firm therefore stops at Q = 3, the last unit that adds more to revenue than to cost.
Price comes from the demand schedule, not from marginal revenue. At Q = 3, buyers are willing to pay $16, so that is the price the monopolist charges.
Total economic profit = total revenue − total cost.
At Q = 3: TR = $48 and TC = $40, so profit = $48 − $40 = $8.
Equivalently, per-unit profit = P − ATC = $16 − $13.33 = $2.67, and $2.67 × 3 ≈ $8.
Allocative efficiency requires P = MC. Marginal cost is constant at $10, and price equals $10 at Q = 6, so 6 units is the allocatively efficient quantity.
Deadweight loss is the triangle between the demand curve and marginal cost, running from the monopoly quantity out to the efficient quantity:
DWL = ½ × base × height = ½ × (6 − 3) × ($16 − $10) = ½ × 3 × $6 = $9.
Average total cost falling across the entire relevant range means economies of scale persist throughout, so a single firm can serve the whole market at lower cost than several firms could. Glacier Water is a natural monopoly.
The socially optimal price sets P = MC = $10 (Q = 6). This is allocatively efficient, but at that output average total cost is $11.67, which is above the $10 price — the firm takes a loss and would need a subsidy to stay in business. This is the general natural-monopoly problem: because ATC is still falling, marginal cost lies below average total cost, so efficient pricing cannot cover total cost.
The fair-return price sets P = ATC = $12 (Q = 5). The firm earns exactly zero economic profit and needs no subsidy, and output is higher than the unregulated monopoly's 3 units. But price still exceeds marginal cost ($12 > $10), so some deadweight loss remains and the outcome is not allocatively efficient.