These are original Marlbridge practice questions, not past exam questions. The mark points are a suggested Marlbridge rubric to help you check your work; they are not an official scoring guideline. All businesses and data are fictional. Only addition, subtraction, multiplication and division are needed, so a four-function calculator is enough. Give elasticities to 2 decimal places unless they are exact.
Questions 1, 4, 5 and 7 use the daily demand for smoothies at Mira’s Smoothie Stall, a fictional market stall. The demand curve is a straight line.
| Price ($ per smoothie) | 3 | 5 | 7 | 8 | 10 | 12 |
|---|---|---|---|---|---|---|
| Quantity demanded (smoothies per day) | 72 | 60 | 48 | 42 | 30 | 18 |
Question 1 (multiple choice · foundation)
Mira raises her price from $10 to $12. Using the midpoint method, what is the magnitude of the price elasticity of demand?
- (A) 0.36
- (B) 2.00
- (C) 2.75
- (D) 6.00
Answer and explanation
Answer: (C). % change in Q = (18 − 30) ÷ 24 × 100 = −50%. % change in P = (12 − 10) ÷ 11 × 100 = 18.18%. |PED| = 50 ÷ 18.18 = 2.75.
- (A) divides the wrong way round: 18.18 ÷ 50 = 0.36. PED puts the quantity change on top.
- (B) uses the starting values instead of the averages: (−12 ÷ 30) ÷ (2 ÷ 10) = −40% ÷ 20% = −2. Without the midpoint method, the answer would change if the price fell from $12 to $10.
- (D) divides the raw change in quantity by the raw change in price: 12 ÷ 2 = 6. That is a slope-type ratio, not an elasticity.
Question 2 (multiple choice · core)
For which good is the price elasticity of demand likely to be largest in magnitude?
- (A) Insulin for people with diabetes
- (B) Table salt
- (C) One brand of bottled water in a supermarket that stocks many similar brands
- (D) Petrol for commuters over the next week
Answer and explanation
Answer: (C). A single brand in a narrowly defined market has many close substitutes. If its price rises, shoppers can easily pick another brand, so quantity demanded falls by a large percentage.
- (A) is a necessity with no close substitute, so demand is very inelastic.
- (B) takes a tiny share of income and has few substitutes, so demand is inelastic.
- (D) gives buyers very little time to adjust (to change jobs, cars or travel habits), so demand is inelastic in the short run.
Question 3 (multiple choice · core)
A city museum cuts the price of an adult ticket. Its total revenue from adult tickets falls. Over this price range, demand for adult tickets must be:
- (A) elastic
- (B) inelastic
- (C) unit elastic
- (D) perfectly elastic
Answer and explanation
Answer: (B). Price fell and total revenue fell: they moved in the same direction, which is the sign of inelastic demand. The percentage rise in visitors was smaller than the percentage cut in price.
- (A) would make a price cut raise total revenue.
- (C) would leave total revenue unchanged.
- (D) is the extreme case of elastic demand, where a price cut would raise revenue, not lower it.
Question 4 (calculation · core)
Use the table for Mira’s Smoothie Stall.
(a) Calculate |PED| when the price rises from $3 to $5, and when it rises from $7 to $8. Use the midpoint method. (b) Classify demand in each range. (c) Calculate total revenue at $3, $5, $7 and $8, and show that your answers to (b) agree with the total revenue test.
Worked solution
(a) $3 → $5: % change in Q = (60 − 72) ÷ 66 × 100 = −18.18%. % change in P = 2 ÷ 4 × 100 = 50%. |PED| = 18.18 ÷ 50 = 0.36.
$7 → $8: % change in Q = (42 − 48) ÷ 45 × 100 = −13.33%. % change in P = 1 ÷ 7.5 × 100 = 13.33%. |PED| = 1 (exactly).
(b) $3 to $5: 0.36 < 1, inelastic. $7 to $8: unit elastic.
(c) TR at $3 = 3 × 72 = $216; at $5 = 5 × 60 = $300; at $7 = 7 × 48 = $336; at $8 = 8 × 42 = $336.
- $3 → $5: inelastic, price rises, TR rises ($216 → $300). Agrees.
- $7 → $8: unit elastic, TR unchanged ($336 → $336). Agrees.
Suggested mark points (4): 1 for 0.36 with both percentages shown; 1 for exactly 1; 1 for both classifications; 1 for the four TR values linked correctly to the test.
Common error: dividing the percentage change in price by the percentage change in quantity. Check: quantity always goes on top of the fraction.
Question 5 (graph · core)
Use the table for Mira’s Smoothie Stall. The demand curve continues in a straight line to both axes: it meets the price axis at $15 and the quantity axis at 90 smoothies.
(a) Draw a correctly labelled demand curve. (b) Mark the point where demand is unit elastic, giving its price and quantity. Label the elastic and inelastic sections. (c) Shade the area that shows total revenue at a price of $10 and state its value. (d) Explain why the slope of this curve is the same everywhere but its elasticity is not.
Model answer and suggested Marlbridge rubric
(a) Vertical axis: “Price ($ per smoothie)”. Horizontal axis: “Quantity of smoothies (per day)”. A straight, downward-sloping line from $15 on the price axis to 90 on the quantity axis, labelled D, passing through the table points.
(b) The midpoint of the line is at $7.50 and 45 smoothies. Label it unit elastic. Label the section above it (higher prices) elastic and the section below it (lower prices) inelastic.
(c) Shade the rectangle from the origin to the point ($10, 30): width 30, height $10. TR = 10 × 30 = $300 per day.
(d) Every $1 rise in price lowers quantity by 6 smoothies, so the slope is constant. Elasticity uses percentage changes. Near the top of the curve, price is high and quantity is low, so a $1 change is a small percentage of the price while 6 smoothies is a large percentage of the quantity: demand is elastic. Near the bottom, the reverse is true: demand is inelastic.
| Point | What earns it |
|---|---|
| 1 | Both axes labelled with variable and unit; downward-sloping straight line labelled D |
| 1 | Unit-elastic point at $7.50 and 45, with elastic above and inelastic below |
| 1 | Correct rectangle shaded and $300 stated |
| 1 | Explanation contrasts constant raw changes with changing percentage changes |
Do not award the second point if the elastic and inelastic labels are swapped.
Question 6 (constructed response · core)
Harbour City’s bus company raises the standard fare from $2.00 to $2.50. Daily trips fall from 50,000 to 46,000.
(a) Calculate |PED| using the midpoint method. (b) Classify demand and calculate the change in the bus company’s daily fare revenue. (c) Give two reasons why demand for bus travel in the city might be in this range. (d) Explain how you would expect the elasticity to change if the higher fare stays in place for several years.
Model answer and suggested Marlbridge rubric
(a) % change in Q = (46,000 − 50,000) ÷ 48,000 × 100 = −8.33%. % change in P = 0.50 ÷ 2.25 × 100 = 22.22%. |PED| = 8.33 ÷ 22.22 = 0.375 (0.38 to 2 decimal places).
(b) 0.375 < 1, so demand is inelastic. Revenue before = $2.00 × 50,000 = $100,000. After = $2.50 × 46,000 = $115,000. Revenue rises by $15,000 per day, as the total revenue test predicts for a price rise with inelastic demand.
(c) Any two: few close substitutes for many riders (no car, too far to walk or cycle); travel to work or school is a necessity; the fare is a small share of most riders’ income; riders have had little time to adjust.
(d) Demand should become more elastic over time. Riders have time to find substitutes: buy bicycles or cars, share lifts, move closer to work or change jobs. So the long-run fall in trips is likely to be larger than 8.33%.
| Point | What earns it |
|---|---|
| 1 | Both midpoint percentages and |PED| ≈ 0.38 |
| 1 | Inelastic and revenue rises by $15,000, linked to the total revenue test |
| 1 | Two valid reasons for inelastic demand, in context |
| 1 | More elastic in the long run, with a reason about time to find substitutes |
Accept 0.37 or 0.38 for (a) if the working is shown.
Question 7 (explanation · stretch)
(a) A student says: “The demand curve for Mira’s smoothies is quite steep, so demand is inelastic.” Evaluate this claim using two of the prices in the table. (b) Mira currently charges $12. She wants the largest possible daily revenue. Should she raise or cut her price, and to what level? Explain using elasticity. (c) A remote region’s hospitals need exactly 400 doses of a snakebite antivenom each year, whatever the price. The supplier raises the price from $50 to $60 per dose. Describe the demand curve, give its PED and calculate the change in hospitals’ total expenditure.
Model answer and suggested Marlbridge rubric
(a) The claim is wrong, or at best incomplete. Elasticity depends on where you are on the curve, not on how steep it looks. Between $3 and $5, |PED| = 0.36 (inelastic). Between $10 and $12, |PED| = 2.75 (elastic). The same straight line is both, and its steepness also depends on the scale chosen for the axes.
(b) At $12, demand is elastic (|PED| = 2.75 between $10 and $12), so a price cut raises total revenue. Revenue keeps rising as she cuts the price until demand becomes unit elastic at the midpoint: $7.50, selling 45 smoothies, for TR = $337.50. Below $7.50, demand is inelastic and further cuts would lower revenue. (If she must charge whole dollars, $7 and $8 both give $336.)
(c) Demand is perfectly inelastic: a vertical line at 400 doses. PED = 0. Spending rises from 400 × $50 = $20,000 to 400 × $60 = $24,000, an increase of $4,000 (20%, the same as the price rise).
| Point | What earns it |
|---|---|
| 1 | Rejects the claim with two calculated elasticities from different ranges |
| 1 | Cut the price, because demand is elastic at $12 |
| 1 | Revenue is largest at the unit-elastic point, $7.50 and $337.50 |
| 1 | Vertical demand, PED = 0 and a $4,000 rise in expenditure |
How did you do?
- Q1 or Q4 wrong: re-read “The midpoint method” and Worked example 1 in the study guide. Convert both changes to percentages before dividing.
- Q2 or Q6(c)–(d) wrong: re-read “What makes demand more or less elastic”.
- Q3 or Q6(b) wrong: re-read “Elasticity and total revenue” and Figure 3.
- Q5 or Q7 marked down: re-read “Slope is not elasticity” and Figure 2.
Then tick off the topic checklist.