2019, Set 2, Question 2 · 5 points
2019 AP Microeconomics FRQ 2 (Set 2) answers
Per-unit tax on hats and tax incidence
Use a labeled graph to identify the after-tax consumer price, quantity and tax revenue. Compare price and revenue when demand is perfectly inelastic, and predict how cutting the tax changes producer surplus.
Skip to the worked answer and scoring (try the question first if you can)
This exam had three free-response questions in a 60 minute section (10 minutes of reading and 50 of writing), with about half the time suggested for Question 1 and the rest split evenly between Questions 2 and 3. The current exam has 3 free-response questions in 60 minutes. The skills these questions practice still count.
Lessons this question draws on
1 Read the question
The question is College Board's, from the 2019, Set 2 exam. It starts on page 3 of the PDF. College Board no longer posts this exam, so it opens from the copy of College Board's PDF that the Internet Archive saved on December 20, 2025.
2 Write your answer
Answer each part the way you would on the exam, in full sentences, with your work shown. Your writing saves as you type.
3 Score it
Score your answer against College Board's scoring guidelines, one point at a time. Give yourself a point only when your answer says what the guideline asks for.
Scoring guidelines (PDF, page 5) What the exam readers saw (Chief Reader report)
4 Worked answer and scoring
Here is how a response that earns full credit could read, part by part, and what College Board's scoring guidelines look for, put in our own words. Open a part once you have written your own answer to it. The scoring guidelines PDF above is the official word on every point.
Read the graph first. Before the tax, Demand meets Supply at W. The tax shifts supply up by the tax per unit, so buyers now trade where Demand meets Supply + Tax, at S, and sellers keep the price on the original Supply curve at that quantity, at Z. The vertical gap SZ is the tax on each hat.
Part a 2 points
Model answer
(i) After the tax, the market settles where Demand crosses Supply + Tax, at point S. Consumers pay P3, and the quantity sold is Q2.
(ii) Tax revenue is the tax per hat times the number of hats sold. Sellers keep P1 (point Z, on Supply at Q2), so the tax per hat is P3 − P1, and revenue is the rectangle P1P3SZ, which equals (P3 − P1) × Q2.
What earns each point
- Consumers pay P3, and the after-tax quantity is Q2. Buyers face the supply curve with the tax added, so the new equilibrium is S. Naming the point S instead of its price and quantity, or reading off W or X, does not give the values asked for.
- Tax revenue is the area P1P3SZ, that is (P3 − P1) × Q2. The height of the rectangle is the tax per unit, the gap between what buyers pay (P3) and what sellers keep (P1), and its width is the quantity actually taxed, Q2.
Part b 2 points
Model answer
(i) Higher. With demand perfectly inelastic at Q3, buyers purchase Q3 whatever the price. Supply + Tax at Q3 is at point X, so consumers pay P4, above P3.
(ii) Higher. The tax per hat is the same vertical distance between Supply and Supply + Tax, but now it is collected on Q3 hats instead of Q2. With downward-sloping demand, the tax raised the price and cut purchases from Q3 to Q2. With perfectly inelastic demand the tax does not cut the quantity bought at all, and Q3 is greater than Q2, so revenue, (P4 − P2) × Q3, is larger than (P3 − P1) × Q2.
What earns each point
- Higher. Buyers who will take Q3 at any price pay the full tax on top of the price sellers need at Q3: P4 instead of P3.
- Higher, because perfectly inelastic demand keeps the quantity at Q3 after the tax, while the downward-sloping demand in (a) let it fall to Q2, and Q3 is greater than Q2. Revenue is the tax per unit times the units taxed. The tax per unit has not changed, so the comparison turns on quantity. A higher price by itself does not explain more revenue, because the government collects the tax, not the price.
Part c 1 point
Model answer
Producer surplus stays the same. With demand perfectly inelastic at Q3, buyers bear the whole tax: sellers receive P2, the price on the original Supply curve at Q3, and sell Q3, whatever the tax. Cutting the tax lowers only the price consumers pay. The price sellers keep and the quantity they sell do not change, so the area above Supply and below P2 out to Q3 is unchanged.
What earns the point
- Stays the same, because sellers still receive P2 and still sell Q3; equally, because consumers bear all of the tax. Producer surplus depends only on the price sellers keep and the quantity they sell. When demand cannot respond, any change in the tax lands entirely on buyers.
Common mistakes
From what the exam readers reported seeing in 2019 students' answers, in our words:
- Giving the after-tax outcome as point S itself, or as P4 and Q3, or as P2 and Q3, instead of the price P3 and the quantity Q2 read off the axes.
- Tax revenue named as the area P2P4XW or P2P3ST instead of P1P3SZ.
- A consumer price that stays the same or falls after the per-unit tax is imposed.
- Higher tax revenue asserted with no reason given.
- Lower tax revenue because the price rises.
- Unchanged tax revenue on the grounds that producers bear the whole tax.
- Unchanged producer surplus with no explanation.
- Producer surplus said to rise, or to fall, when the tax is cut.
Question, scoring guidelines and Chief Reader report: College Board, from the Internet Archive. The title, summary and worked answer are ours.