Elasticity: how much buyers respond to a price change
Grade 12 Social Studies Worksheet
Circle the best answer.
Read this first
A bridge toll over five years (example figures, made up for practice)
Time Toll Cars per hour Before $2 1,000 Year 1 $3 900 Year 5 $3 700 Percent change uses the midpoint method: the change divided by the average of the two values. Revenue per hour is the toll times the cars.
Pia measures elasticity from the Before row to Year 1, then from the Before row to Year 5. Which statement fits?
- Demand is elastic by year 5, since 300 fewer cars use the bridge, so revenue falls below its start.
- Demand is more elastic by year 5, about 0.88 against 0.26, so the revenue gain shrinks to $100 an hour.
- Demand is equally elastic in both years, because the toll stayed at $3 after the first year.
- Demand is less elastic by year 5, since the 700 drivers who remain have no choice but to pay the toll.
A councilor says the toll will keep raising $700 more an hour for years. How does Ari reply using the card?
- Doubtful: the card shows the gain shrinking to $100 an hour by year 5 as cars kept falling.
- Fair: the bridge has no substitutes, so cars will stay near 900 and the gain will hold at $700.
- Wrong: revenue already fell below $2,000 by year 5, so the toll has lost money for the council.
- Beside the point: forecasts of toll revenue depend on guesses, so any figure is as good as another.
Soda sales after a city tax (example figures, made up for practice)
Area Price change Units sold before Units sold after City stores +10% 10,000 8,200 Neighboring town stores 0% 6,000 6,420 Only the city taxed soda. The two areas share a border that shoppers can cross in a few minutes.
The city says its 18% fall in soda sales shows people drank 18% less soda. Bo tests the claim with the card. What is the best verdict?
- Understated: the neighboring town also saw a price rise, which pushed the total down further than 18%.
- Overstated: city stores lost 1,800 units, but neighboring stores gained 420, so the net drop is 1,380 units.
- Accurate: the tax cut city sales by 1,800 units, and what sold elsewhere has nothing to do with it.
- Overstated: the true drop is zero, because each unit lost in the city was bought in the town instead.
Esme asks why city demand looks elastic, at 1.8, when a region-wide response would be smaller. Which reason fits the card?
- City shoppers have a close substitute, the untaxed stores nearby, which makes city demand more elastic.
- City shoppers have no close substitute for their soda, which makes city demand more elastic than the region's.
- The tax rate was 10%, and a larger tax rate pushes elasticity above 1 for any good it covers.
- Soda is a luxury, and luxuries have an elasticity above 1 in any place where they are sold.
A $1 tax on two goods (example figures, made up for practice)
Good Buyers paid before Buyers pay after Sellers kept before Sellers keep after School shirts $20.00 $20.80 $20.00 $19.80 Souvenir mugs $5.00 $5.20 $5.00 $4.20 The tax of $1 per unit is collected from the sellers. Sellers keep the price buyers pay minus the tax.
Jun asks which good's buyers bear most of the $1 tax. What does that say about demand?
- Souvenir mugs: sellers keep $0.80 less per mug, so mug sellers pass most of the tax on to buyers.
- School shirts: buyers pay $0.80 more, so demand must be more elastic than supply in this market.
- School shirts: buyers pay $0.80 more, so demand is less elastic than supply.
- Souvenir mugs: buyers pay $0.20 more per mug, so mug demand is less elastic than mug supply.
The law collects the tax from sellers. Kira says sellers therefore bear all of it. What is the best verdict from the card?
- Wrong for both goods: buyers bear the whole tax once it is collected from the sellers by law.
- Wrong for shirts: sellers keep $0.20 less per shirt while buyers pay $0.80 more.
- Right for shirts: sellers write the check, so the whole $1 comes out of the sellers' own pockets.
- Right for mugs: sellers keep $0.80 less, and that makes the tax theirs in full for that good.
Luz infers elasticities from the school-shirt row. Which inference does the row support?
- Demand and supply are equally elastic, since the whole $1 tax came out of the shirt market.
- Supply is perfectly elastic, since sellers keep $19.80 a shirt after the tax is paid.
- Demand is less elastic than supply, since buyers could not avoid most of the tax.
- Demand is more elastic than supply, since buyers pay more after the tax than they paid before.
Club tickets at five prices (example figures, made up for practice)
Ticket price Tickets sold $4 600 $5 500 $6 400 $7 300 $8 200 Revenue is the price times the tickets sold. Percent change uses the midpoint method: the change divided by the average of the two values.
A club wants the most revenue from tickets priced $4 to $8. Noah uses the table. Which price and reason fit?
- $5: revenue peaks at $2,500, and above $5 sales fall by a larger percent than the price rises.
- $4: it fills the most seats, 600, and the club earns the most when its hall is as full as possible.
- $8: the highest price earns the most per ticket, and sales drop by just 100 for each $1 step up.
- $6: it sits in the middle of the range, where the price and quantity changes roughly balance out.
Raising the price $1 lifts revenue from $4 to $5 but lowers it from $5 to $6. How does Ren explain that?
- A straight demand line has the same elasticity at each point, so one of the revenue figures is off.
- The demand line bends at $5 and gets steeper above it, so buyers stop responding to the price.
- Elasticity changes along a straight demand line: about 0.8 from $4 to $5, but about 1.2 from $5 to $6.
- Tickets fall by 100 at each step, so revenue must change by the same amount at each step.
Card
a store's test (made up for practice). A store raised the price of one snack by 10% for one weekend. Sales fell 3%. The owner decides the snack's demand is inelastic and plans to raise the price 10% every month.
Tala reviews the owner's plan. What is the biggest weakness in the evidence on the card?
- Elasticity needs at least three goods to compare, so one snack cannot show it in a single test.
- One weekend shows the short run; over months shoppers find other snacks and respond more.
- A 3% fall is too small to measure, so no conclusion about elasticity can be drawn from it.
- A weekend is long enough, since shoppers react within days, so the 3% fall is the lasting response.