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Unit 4 · Imperfect Competition Unit Hub Flashcards Cheat Sheet Essentials Visual Review MC Practice FRQ Practice
Unit 4 FRQ Practice

Unit 4 FRQ Practice

A College Board–style free-response question on Imperfect Competition, broken into parts with a model answer showing exactly how each point is earned.

4 parts
7 points
Model answers
College Board aligned
← Back to Unit 4 hub
Free Response Question · Unit 4 · Monopoly Pricing, Deadweight Loss & Regulation

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.

QuantityPrice ($)Total Revenue ($)Marginal Revenue ($)Total Cost ($)Marginal Cost ($)Average Total Cost ($)
1202020201020.00
2183616301015.00
3164812401013.33
414568501012.50
512604601012.00
610600701011.67
A
Identify the profit-maximizing quantity and price for Glacier Water, and explain how you determined each one.

✓ Model answer (earns the point)

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.

Why it scores: Both figures must appear and be justified. The quantity point needs an explicit MR versus MC comparison; the price point needs the statement that price is read off demand. Answering "$12" — the marginal revenue at Q = 3 — is the single most common error on monopoly FRQs and earns nothing.
B
Calculate Glacier Water's total economic profit at the profit-maximizing quantity. Show your work.

✓ Model answer (earns the point)

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.

Why it scores: The arithmetic must be shown, not just the answer. Either method earns the point, but the numbers used must come from Q = 3 — computing profit at a different quantity, or using marginal cost in place of average total cost, loses it.
C
Identify the allocatively efficient quantity, and calculate the deadweight loss created at the profit-maximizing quantity.

✓ Model answer (earns the point)

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.

Why it scores: The efficient quantity must be justified by P = MC, not asserted. For the calculation, the base is the gap between the monopoly and efficient quantities and the height is the gap between price and marginal cost at the monopoly quantity — reversing these, or measuring out to the demand intercept instead of to the efficient quantity, loses the point.
D
Glacier Water's average total cost falls at every level of output shown. Explain what this implies about the market, and compare the fair-return price with the socially optimal price for this firm.

✓ Model answer (earns the point)

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.

Why it scores: Three things earn credit: identifying the natural monopoly from continuously falling ATC, pairing each regulated price with its rule (P = MC and P = ATC) and its numerical value, and drawing the trade-off — the socially optimal price is efficient but loss-making, while the fair-return price breaks even but leaves P > MC.

How to score points on AP Microeconomics FRQs