Principles of Microeconomics – Chapter 4 : Elasticity

Price Elasticity of Demand

• Price elasticity of demand: Measures how much the quantity demanded of a product changes due to a change in its price.

• Coefficient of elasticity: Denoted by epsilon (\varepsilon) . It's an absolute number, so the sign is ignored.

  • Formula: \varepsilon_p = \frac{\% \Delta \text{ quantity demanded}}{\% \Delta \text{ price}}

Types of Demand

• Inelastic Demand: Quantity demanded is not very responsive to price changes.

  • |\varepsilon| < 1

• Elastic Demand: Quantity demanded is very responsive to price changes.

  • |\varepsilon| > 1

• Unitary Demand: Percentage change in quantity demanded equals the percentage change in price.

  • |\varepsilon| = 1

Elasticity Coefficient

• Measures the responsiveness of quantity demanded to price changes.

  • If |\varepsilon| > 1, demand is elastic.

  • If |\varepsilon| < 1, demand is inelastic.

  • If |\varepsilon| = 1, demand is unitary.

Determinants of Price Elasticity

• Number of available substitutes.

• Percentage of household income spent on the product.

• Time period involved.

Examples of Elasticities

• Elastic Demands

  • Fresh Tomatoes (4.60)

  • Movies (3.41)

  • Lamb (2.65)

  • Restaurant Meals (1.63)

  • China and Tableware (1.54)

  • Automobiles (1.14)

• Inelastic Demands

  • Household Electricity (0.13)

  • Eggs (0.32)

  • Car Repairs (0.36)

  • Food (0.58)

  • Household Appliances (0.63)

  • Tobacco (0.86)

Examples of Elastic/Inelastic Demand

• Sugar: Inelastic (\varepsilon < 1)

• Gasoline: Inelastic (\varepsilon < 1)

• Ocean Cruises: Elastic (\varepsilon > 1)

• Restaurant Meals: Elastic (\varepsilon > 1)

• Women's Hats: Elastic (\varepsilon > 1)

• Alcohol: Inelastic (\varepsilon < 1)

Measuring Price Elasticity

• Formula: \varepsilon_p = \frac{\% \Delta \text{ quantity demanded}}{\% \Delta \text{ price}}

• Expanded Formula: \varepsilonp = \frac{\frac{\Delta Qd}{\text{average } Q_d} \times 100}{\frac{\Delta P}{\text{average } P} \times 100}

Example Calculations

• Vancouver to Edmonton

  • Price decreases from $650 to $550, quantity of tickets increases from 1000 to 1100.

  • \% \Delta Q_d = \frac{100}{1050} \times 100 = 9.5\%

  • \% \Delta P = \frac{-100}{600} \times 100 = -16.7\%

  • \varepsilon_p = \frac{9.5\%}{16.7\%} = 0.57

  • Demand is inelastic because \varepsilon_p < 1

• Vancouver to Calgary

  • Price decreases from $650 to $550, quantity of tickets increases from 1000 to 1250.

  • \% \Delta Q_d = \frac{250}{1125} \times 100 = 22.2\%

  • \% \Delta P = \frac{-100}{600} \times 100 = -16.7\%

  • \varepsilon_p = \frac{22.2\%}{16.7\%} = 1.33

  • Demand is elastic because \varepsilon_p > 1

Understanding Elasticity Coefficients

• Set I: Price changes from $9 to $8, quantity changes from 1 to 2.

  • \varepsilon = \frac{(2-1)/1.5}{(9-8)/8.5} = \frac{66.66\%}{11.76\%} = 5.67

• Set II: Price changes from $2 to $1, quantity changes from 8 to 9.

  • \varepsilon = \frac{(9-8)/8.5}{(2-1)/1.5} = \frac{11.76\%}{66.66\%} = 0.18

• The coefficients are different because the same $1 change in price represents a small percentage change in Set I but a large percentage change in Set II. Similarly, the change of 1 unit in quantity represents a large percentage change in Set I, but a small percentage change in Set II.

Elasticity and Total Revenue

• If demand is elastic, an increase in price will decrease revenue.

• If demand is inelastic, an increase in price will increase revenue.

Impact on Total Revenue

• If demand is inelastic (\varepsilon < 1):

  • Price falls, Total Revenue falls.

  • Price rises, Total Revenue rises.

• If demand is elastic (\varepsilon > 1):

  • Price falls, Total Revenue rises.

  • Price rises, Total Revenue falls.

• If demand is unitary elastic (\varepsilon = 1):

  • Price falls, Total Revenue stays the same.

  • Price rises, Total Revenue stays the same.

• Revenue is not the same as profit.

Examples

• \varepsilon > 1 and price falls: Total Revenue rises.

• \varepsilon < 1 and price rises: Total Revenue rises.

• \varepsilon < 1 and price falls: Total Revenue falls.

• \varepsilon > 1 and price rises: Total Revenue falls.

• \varepsilon = 1 and price rises: No change in Total Revenue.

Quantity Change and Total Revenue Effect

• Product A: \varepsilon = 2, price increases by 5%.

  • \% \Delta Q = -10\%, Total Revenue decreases.

• Product B: \varepsilon = 0.4, price increases by 10%.

  • \% \Delta Q = -4\%, Total Revenue increases.

• Product C: \varepsilon = 0.2, price decreases by 20%.

  • \% \Delta Q = 4\%, Total Revenue decreases.

• Product D: \varepsilon = 1, price increases by 7%.

  • \% \Delta Q = -7\%, Total Revenue shows no change.

• Product E: \varepsilon = 3, price decreases by 2%.

  • \% \Delta Q = 6\%, Total Revenue increases.

Price Elasticity Graphically

• Slope is rise over run.

• A straight-line demand curve has a constant slope.

• Elasticity is percentage change in quantity over percentage change in price.

• A straight-line demand curve's elasticity varies from point to point.

• The upper half of any straight-line demand curve is elastic, and the lower half is inelastic.

• A relatively steep demand curve is mostly inelastic.

• A relatively shallow demand curve is mostly elastic.

Types of Elasticity

• Inelastic demand: A percentage change in price causes a smaller percentage change in quantity.

• Unit elastic demand: A percentage change in price causes the same percentage change in quantity.

• Elastic demand: A percentage change in price causes a larger percentage change in quantity.

Elasticity and Total Revenue

• As price drops from $10 to $5, demand is elastic, and total revenue increases.

• At $5, demand is unitary, and total revenue is at its maximum.

• Below $5, upon a drop in price, demand is inelastic, and total revenue is falling.

Range of Elasticities

• Perfectly inelastic: \varepsilon = 0

• Inelastic: 0 < |\varepsilon| < 1

• Unitary elastic: |\varepsilon| = 1

• Elastic: |\varepsilon| > 1

• Perfectly elastic: \varepsilon = \infty

Loss and Gain in Total Revenue

• With inelastic demand, the gain in total revenue from increased purchasing is less than the loss from a drop in price (but an increase in price will increase total revenue).

• With unit elastic demand, the gain in total revenue from increased purchasing is equal to the loss from a drop in price.

• With elastic demand, the gain in total revenue from increased purchasing is greater than the loss from a drop in price (but an increase in price will decrease total revenue).

Example

• Demand Schedule

  • Price Quantity

  • 1 18

  • 2 16

  • 3 14

  • 4 12

  • 5 10

  • 6 8

  • 7 6

  • 8 4

  • 9 2

• The slope of this demand curve is \frac{\Delta P}{\Delta Q} = \frac{1}{-2} = -0.5

• The elasticity coefficient for a price change from, say, 4 to 5 is 0.82, which is quite different from the slope of –0.5. The elasticity varies along any curve where the slope is constant.

Applications of Price Elasticity

• Sales tax.

• Excise tax on products such as cigarettes.

• Crackdown on illegal drugs.

• A good harvest is not always good news for farmers.

Impact of Taxes

• The more inelastic the demand for a product, the larger is the percentage of a sales (or excise) tax the consumer will pay.

Excise Tax

• A sales tax imposed on a particular product.

• They are an “easy” form of tax revenue for governments.

• Taxes are usually imposed on products with inelastic demands (gasoline, cigarettes, alcohol) where the resulting increase in price is bigger than the drop in quantity.

  • The result: greater tax revenue for governments.

Sin Taxes

The Effect of a $1 Increase in the Tax on Salt and Tomatoes

• Salt (inelastic demand)

  • TAX REVENUES BEFORE TAX INCREASE: 10m.units @ $2 = $20m

  • TAX REVENUES AFTER $1 TAX INCREASE: 9m.units @ $3 = $27m

• Tomatoes (elastic demand)

  • TAX REVENUES BEFORE TAX INCREASE: 10m.units @ $2 = $20m

  • TAX REVENUES AFTER $1 TAX INCREASE: 6m.units @ $3 = $18m

War on Drugs

• With an inelastic demand, a campaign against the drug trade will reduce the supply causing a great increase in the price, thus increasing the amount paid by drug users.

Agricultural Products

• The demand for many agricultural products (including grain crops like rice and wheat) is inelastic.

• An increase in the supply causes a big drop in the price so that the total revenue of farmers decreases.

Other Elasticity Measures

Elasticity of Supply

• A measure of how much quantity supplied changes as a result of a change in price.

• \varepsilon_S = \frac{\% \Delta \text{ quantity supplied}}{\% \Delta \text{ price}}

• Expanded Formula: \varepsilonS = \frac{\frac{\Delta QS}{\text{average } Q_S} \times 100}{\frac{\Delta P}{\text{average } P} \times 100}

Example

• Price changes from $2 to $3, the quantity supplied rises from 400 to 500.

• \varepsilon_S = \frac{\frac{100}{450} \times 100}{\frac{1}{2.5} \times 100} = \frac{+0.22}{+0.4} = +0.55

Supply Elasticity in Three Periods

• In the market period, supply is perfectly inelastic.

• In the short run, supply is inelastic.

• In the long run, supply is elastic.

• Longer time frames have more elastic supply.

Perfectly Inelastic Supply

• Some products have perfectly inelastic supply.

• E.g., concert tickets for a single event.

• If demand is higher than the expected, there will be a shortage and ticket scalping.

• If demand is lower than expected, there will be unsold seats.

Income Elasticity

• The responsiveness of quantity demanded to a change in income.

• \varepsilonY = \frac{\% \Delta \text{ quantity demanded } (QD)}{\% \Delta \text{ income } (Y)}

• Expanded Formula: \varepsilonY = \frac{\frac{\Delta QD}{\text{average } Q_D} \times 100}{\frac{\Delta Y}{\text{average } Y} \times 100}

Types of Goods

• If |\varepsilon_Y| > 1 (positive number): Normal – Luxury good, Income elastic.

• If 0 < |\varepsilon_Y| < 1 (positive number): Normal – Necessity, Income inelastic.

• If |\varepsilon_Y| < 0 (negative number): Inferior good, Negative income elastic.

Example

• Income, Quantity Demanded of X, Quantity Demanded of Y

  • $10,000, 200, 50

  • $15,000, 350, 54

Calculations

• Product X:

  • \varepsilon = \frac{(350-200)/275}{(15000-10000)/12500} = \frac{+54.5\%}{+40\%} = +1.36

• Product Y:

  • \varepsilon = \frac{(54-50)/52}{(15000-10000)/12500} = \frac{+7.6\%}{+40\%} = +0.19

• Products X and Y are normal goods because both have a positive coefficient.

• X is a luxury (\varepsilon > 1).

• Y is a necessity (0 < \varepsilon < 1).

Cross-Elasticity of Demand

• Responsiveness of the change in Q_d of product A to a change in the price of product B.

• \varepsilon_{AB} = \frac{\% \Delta \text{ quantity demanded of product A}}{\% \Delta \text{ price of product B}}

• Expanded Formula: \varepsilon{AB} = \frac{\frac{\Delta Q{AD}}{\text{average } Q{AD}} \times 100}{\frac{\Delta PB}{\text{average } P_B} \times 100}

Example

Cross-Elasticity of Margarine and Butter

• Margarine, Butter Price, Quantity Demanded per Week (lb.), Price, Quantity Demanded per Week (lb.)

  • $1.50, 5000, $3.00, 1000

  • $2.10, 3200, $3.00, 2000

• \varepsilon_{AB} = \frac{\frac{1000}{1500} \times 100}{\frac{0.6}{1.8} \times 100} = +2

Types of Goods

• If coefficient is positive, goods are substitutes.

• If coefficient is negative, goods are complements.

Summary of Various Elasticities

• PRICE ELASTICITY OF DEMAND AND SUPPLY

  • Inelastic: 0 to 1

  • Unitary: 1

  • Elastic: 1 to \infty

• INCOME ELASTICITY

  • Inferior Goods: Negative Elasticity

  • Normal Goods

    • Necessities: Inelastic, 0 to 1

    • Luxuries: Elastic: 1 to \infty

• CROSS-ELASTICITY

  • Complements: Negative Elasticity

  • Substitutes: Positive Elasticity

Key Concepts to Remember

• Definition, calculation, and determinants of price elasticity of demand.

• Difference between slope and elasticity.

• Relationship between elasticity and total revenue.

• Real-world examples of elasticity.

• Elasticity of supply, income elasticity, and cross-elasticity of demand.