Unit 2 · Topic 2.3

Price Elasticity of Demand

Price elasticity of demand measures how strongly the quantity demanded responds to a price change: the percent change in quantity over the percent change in price, read as an absolute value.

Practice 3: Manipulation

Part 1 · Hook

Why this matters

Two stores raise prices by 10% on the same day. The gas station on the highway barely notices: drivers still fill up. The sparkling water brand at the supermarket loses a third of its sales overnight, because five other brands sit on the same shelf. How strongly buyers respond to a price is a number you can calculate.

Part 2 · Before you start

What this builds on

Part 3 · Prerequisite check

Quick check before you start

1. By the law of demand, when a good's price rises the quantity demanded

  1. falls
  2. rises
  3. stays the same
  4. shifts the curve right
Show the answer

Price and quantity demanded move in opposite directions.

  • Correct: falls:
  • rises:
  • stays the same:
  • shifts the curve right:

2. Goods used in place of each other, such as two brands of water, are

  1. substitutes
  2. complements
  3. inferior goods
  4. factors of production
Show the answer

Substitutes can replace each other.

  • Correct: substitutes:
  • complements:
  • inferior goods:
  • factors of production:

3. The slope of a straight line is

  1. the rise over the run, the same at each point
  2. largest at its middle
  3. the area under the line
  4. the point where it meets an axis
Show the answer

A straight line has one constant slope.

  • Correct: the rise over the run, the same at each point:
  • largest at its middle:
  • the area under the line:
  • the point where it meets an axis:

Part 4 · See it

See it first

A straight-line demand curve for phone cases is elastic above its midpoint, unit elastic at $5 and 50 cases, and inelastic below it. Total revenue rises to its largest value, $250, at the midpoint and then falls.
Demand is elastic above the midpoint and inelastic below it, and total revenue peaks where demand is unit elastic. Invented data for practice. LevlPrep original diagram.

Part 5 · Step by step

How it works, step by step

  1. A good has many close substitutesbuyers switch away when its price rises
  2. Buyers switch awaythe quantity demanded falls by a larger percent than the price rose: demand is elastic
  3. Demand is elasticthe lost sales outweigh the higher price, so total revenue falls

Part 6 · Key ideas

Key ideas

  • Price elasticity of demand = percent change in quantity demanded divided by percent change in price. Read the absolute value.
  • Greater than 1: elastic. Less than 1: inelastic. Exactly 1: unit elastic. Zero: perfectly inelastic (vertical). Infinite: perfectly elastic (horizontal).
  • Total revenue test: elastic demand, price and TR move opposite; inelastic demand, they move together; unit elastic, TR does not change.
  • Along a straight-line demand curve the slope is constant but elasticity is not: elastic at the top, unit elastic at the midpoint, inelastic at the bottom.
  • Demand is more elastic with close substitutes, a large budget share, a narrowly defined good and more time to adjust.

Part 7 · Misconception

A common mistake

The wrong idea: An elasticity of −0.4-0.4 is negative, so demand is elastic; a steeper curve is always the less elastic one.

What actually happens: Judge elasticity by the absolute value: 0.4 is less than 1, so demand is inelastic. And slope is not elasticity: one straight-line demand curve has the same slope everywhere but is elastic at high prices and inelastic at low ones.

Part 8 · Check yourself

Check yourself

Exam-style questions. Anything you miss goes into your review queue.

Data

A demand schedule for phone cases at Juno Cases

Phone cases demanded per week at Juno Cases at each price (invented data for practice)
PriceQuantity demanded
$820
$640
$550
$460
$280

1. Using the starting values, calculate the price elasticity of demand for phone cases when the price falls from $8 to $6. Give the absolute value.

Type a number. A four-function calculator is allowed, as on the exam.

Show the answer

Percent change in quantity: 40−2020×100=100%\frac{40 - 20}{20} \times 100 = 100\%. Percent change in price: 6−88×100=−25%\frac{6 - 8}{8} \times 100 = -25\%. Elasticity: |100÷(−25)|=4|100 \div (-25)| = 4, so demand is elastic in this range.

  • Answer: 4

2. By how many dollars does Juno's weekly total revenue change when it cuts the price from $8 to $6?

Type a number. A four-function calculator is allowed, as on the exam.

Show the answer

Total revenue is price times quantity. At $8: 8×20=1608 \times 20 = 160. At $6: 6×40=2406 \times 40 = 240. The change is 240−160=80240 - 160 = 80 dollars, a rise, as the total revenue test predicts for elastic demand.

  • Answer: 80

Scenario

Three goods at an island general store

The only store on Tallis Island, an invented place reached by a weekly ferry, sells three goods among many others:

  • Insulin, which some islanders need every day and which has no substitute on the island.
  • Fizzle, one of six brands of sparkling water on the shelf, all of which taste much the same.
  • Table salt, which costs about $1 a box and lasts a family a month.

The store manager raises the price of Fizzle by 10% and sees the quantity of Fizzle sold fall by 30%.

3. Which good in the store most likely has the most elastic demand?

  1. Insulin
  2. Table salt
  3. They are equally elastic
  4. Fizzle sparkling water
Show the answer

Fizzle has close substitutes on the same shelf, so buyers switch brands when its price rises. Many close substitutes make demand elastic.

  • Insulin: Insulin is a necessity with no substitute, so demand is very inelastic.
  • Table salt: Salt is a tiny share of a budget, so buyers barely react to its price.
  • They are equally elastic: Substitutes, necessity and budget share differ across the three.
  • Correct: Fizzle sparkling water: Right: five other brands are close substitutes.

4. Calculate the price elasticity of demand for Fizzle from the manager's results. Give the absolute value.

Type a number. A four-function calculator is allowed, as on the exam.

Show the answer

Elasticity is the percent change in quantity demanded over the percent change in price: |−30%÷10%|=3|-30\% \div 10\%| = 3. Demand for Fizzle is elastic.

  • Answer: 3

5. Demand for a concert band's T-shirts is elastic at the current price. The band wants to raise its total revenue from shirts. What should it do to the price, according to the total revenue test?

  1. Lower the price
  2. Raise the price
  3. Keep the price, since revenue will not change
  4. Raise the price until demand turns elastic
Show the answer

With elastic demand, price and total revenue move in opposite directions, so a lower price raises total revenue: the quantity rises by a larger percent than the price falls.

  • Correct: Lower the price: Right: with elastic demand, a price cut raises total revenue.
  • Raise the price: With elastic demand, a price rise loses more sales than it gains per shirt.
  • Keep the price, since revenue will not change: Revenue changes with price unless demand is unit elastic.
  • Raise the price until demand turns elastic: Demand is already elastic; higher prices make it more so.

Part 9 · Summary

Summary

Price elasticity of demand measures how strongly the quantity demanded responds to a price change: the percent change in quantity over the percent change in price, read as an absolute value. Above 1 demand is elastic, below 1 inelastic, at 1 unit elastic. The total revenue test follows: with elastic demand a price rise lowers total revenue, with inelastic demand it raises it. Close substitutes, a large budget share and more time to adjust make demand more elastic.

Part 10 · Up next

What comes next

Part 11 · Connections

Connections

Question set for this topic