2019, Set 1, Question 2 · 5 points
2019 AP Microeconomics FRQ 2 (Set 1) answers
Spending a budget on water and another good
Use marginal benefit tables to find total benefit and consumer surplus, then use marginal benefit per dollar to show a bundle is not optimal and find the best one. Compute a cross-price elasticity after a price drop and classify the goods.
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 1 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.
Every number Dana needs is in the two marginal benefit columns. Total benefit adds up marginal benefits unit by unit, consumer surplus subtracts the price from each unit's marginal benefit, and the best bundle on a budget equalizes marginal benefit per dollar across the two goods.
Part a 1 point
Model answer
Total benefit is the sum of the marginal benefits of every unit bought. Two bottles of water give $24 + $18 = $42, and one unit of good X gives $24.
Total benefit = $24 + $18 + $24 = $66
What earns the point
- $66, with the sum of the three marginal benefits shown. Each row of the table is the extra benefit of one more unit, so the second bottle adds $18 on top of the first bottle's $24. Doubling $18, or taking only the second bottle's value, misses that the first bottle was also bought.
Part b 1 point
Model answer
Consumer surplus on each unit is its marginal benefit minus the $5 price. Add the three units:
($24 − $5) + ($18 − $5) + ($12 − $5) = $19 + $13 + $7 = $39
The same total comes from total benefit minus total spending: $54 − $15 = $39.
What earns the point
- $39, with the work shown unit by unit or as total benefit minus total spending. Surplus is what each unit is worth to Dana beyond what she pays for it. The table gives a value for each unit, so the surplus is a sum over units, not the area of a triangle under a straight demand line drawn through the table.
Part c 3 points
Model answer
(i) With water at $3 and good X at $6, the last bottle of water (the second) gives $18 ÷ $3 = 6 of benefit per dollar, while the last unit of good X (the fourth) gives $6 ÷ $6 = 1 per dollar. Water returns more benefit per dollar, so moving a dollar from good X to water raises Dana's total benefit. Her benefit is not at its maximum until the two ratios are equal.
(ii) Buy 4 bottles of water and 3 units of good X. That costs 4 × $3 + 3 × $6 = $12 + $18 = $30, the whole budget, and the last unit of each gives the same benefit per dollar: $6 ÷ $3 = 2 for water and $12 ÷ $6 = 2 for good X.
(iii) When good X falls to $3, both goods cost $3 and have the same marginal benefits, so the $30 buys 5 bottles of water and 5 units of good X (the fifth unit of each gives $3 ÷ $3 = 1 per dollar). Water rises from 4 bottles to 5.
Percentage change in water bought = (5 − 4) ÷ 4 = 25% Percentage change in the price of good X = ($3 − $6) ÷ $6 = −50% Cross-price elasticity = 25% ÷ (−50%) = −0.5
The elasticity is negative: a lower price of good X leads Dana to buy more water, so the two goods are complements. With the midpoint method the elasticity is (1 ÷ 4.5) ÷ (−3 ÷ 4.5) = −0.33, also negative.
What earns each point
- Not the best bundle, because water's marginal benefit per dollar (18 ÷ $3 = 6) is larger than good X's (6 ÷ $6 = 1). Choosing on a budget means comparing benefit per dollar, not benefit alone. Comparing $18 with $6 without dividing by the prices ignores that good X costs twice as much.
- 4 bottles of water and 3 units of good X. This bundle spends exactly $30 and leaves the marginal benefit per dollar equal at 2 for both goods. A bundle with equal ratios that costs more or less than $30 does not use the budget Dana has.
- Water rises to 5 bottles, the cross-price elasticity is 25% ÷ (−50%) = −0.5 (or −0.33 by the midpoint method), with the work shown, and the goods are complements. Cross-price elasticity puts the percentage change in the quantity of one good over the percentage change in the price of the other. Its sign decides the relationship: negative means complements. The new quantity has to follow from the bundle given in (ii).
Common mistakes
From what the exam readers reported seeing in 2019 students' answers, in our words:
- Finding the total benefit of the water alone, or of good X alone, when the question asks for both together.
- Multiplying $18 by 2 for two bottles of water, or counting only the second bottle's $18, instead of adding $24 and $18.
- Multiplying 3 by $5 and then subtracting the third unit's $12, instead of subtracting the price from each unit's marginal benefit.
- Giving the total cost of the three units of good X instead of the consumer surplus.
- Treating the table as a straight demand curve and working out the area of a triangle for consumer surplus.
- Comparing the marginal benefit of water with that of good X without dividing each by its price.
- Explaining why Dana is not maximizing by working out the optimal bundle instead of comparing benefit per dollar at the bundle she chose.
- Leaving the $30 budget out when choosing the optimal bundle.
- Writing the cross-price elasticity with quantities instead of percentage changes, or with the price change on top and the quantity change underneath.
Question, scoring guidelines and Chief Reader report: College Board, from the Internet Archive. The title, summary and worked answer are ours.