Economics - Elasticity and Its Applications

Elasticity and Its Applications

Key Questions

  • What is elasticity?
  • What issues can elasticity help understand?
  • What is the price elasticity of demand?
    • How is it related to the demand curve?
    • How is it related to revenue and expenditure?
  • What is the price elasticity of supply?
    • How is it related to the supply curve?

Scenario: Website Design

  • You design websites for local businesses.
  • Price: 200perwebsite</li><li>Currentsales:12websitespermonth</li><li>Costsarerising,consideringapriceincreaseto200 per website</li> <li>Current sales: 12 websites per month</li> <li>Costs are rising, considering a price increase to250.
  • Law of demand: Higher price means fewer websites sold.
  • Questions:
    • How many fewer websites will be sold?
    • How much will revenue fall, or might it increase?

I. Elasticity

  • Definition: Elasticity measures how much one variable responds to changes in another variable.
    • Example: How much demand for websites will fall if the price is raised.
  • Elasticity: A numerical measure of the responsiveness of quantity demanded (QD) or quantity supplied (QS) to one of its determinants.

II. Elasticity of Demand

  • There is an inverse relationship between price and quantity demanded.
  • Elastic: A demand curve is elastic when an increase in price reduces the quantity demanded a lot (and vice versa).
  • Inelastic: A demand curve is inelastic when the same increase in price reduces quantity demanded just a little.
  • The more responsive quantity demanded is to a change in price, the more elastic is the demand curve.

III. Elasticity Rule

  • Elasticity ≠ Slope, but:
  • If two linear demand (or supply) curves run through a common point, then at any given quantity the curve that is Flatter is More Elastic.

IV. Determinants of the Elasticity of Demand

  1. Availability of Substitutes

    • Fewer substitutes: demand is inelastic.

    • Many substitutes: demand is elastic.

    • Example 1: Patent expires on a brand-name drug, and 5 generic drugs come on the market.

      • Elasticity of demand rises.

    • Example 2: Breakfast Cereal vs. Sunscreen

      • Breakfast cereal has close substitutes, so demand is more elastic.
      • Sunscreen has no close substitutes, so demand is more inelastic.
      • Lesson: Price elasticity is higher when close substitutes are available.

  2. Time Horizon

    • Less time to adjust means lower elasticity.
    • Over time, consumers can adjust their behavior, making demand more elastic.
    • Example 3: Gasoline in the Short Run vs. Gasoline in the Long Run
      • Short run: Demand is inelastic.
      • Long run: Demand is more elastic.
      • Lesson: Price elasticity is higher in the long run than in the short run.

  3. Category of Product (Narrow vs. Broad)

    • Less specific classification: demand is inelastic.
    • More specific classification: demand is elastic.
    • Example 4: Blue Jeans vs. Clothing
      • Blue jeans (narrowly defined): demand is more elastic.
      • Clothing (broadly defined): demand is more inelastic.
      • Lesson: Price elasticity is higher for narrowly defined goods than for broadly defined ones.

  4. Necessities vs. Luxuries

    • Necessities: demand is inelastic.
    • Luxuries: demand is elastic.
    • Example 5: Insulin vs. Caribbean Cruises
      • Insulin (necessity): demand is inelastic.
      • Caribbean cruise (luxury): demand is elastic.
      • Lesson: Price elasticity is higher for luxuries than for necessities.

  5. Purchase Size

    • Small purchase size: demand is inelastic.
    • Large purchase size: demand is elastic.

V. Price Elasticity of Demand

  • Definition: Price Elasticity of Demand (ED) measures how much quantity demanded (QD) responds to a change in price (P).
    • Measures the price-sensitivity of buyers’ demand.
  • Formula: ED=Percentage change in quantity demandedPercentage change in priceED = \frac{Percentage \ change \ in \ quantity \ demanded}{Percentage \ change \ in \ price}
  • Example: If the price of oil increases by 10%, and the quantity demanded falls by 5%:
    • ED=−5%10%=−0.5ED = \frac{-5\%}{10\%} = -0.5
  • Along a demand curve, price and quantity move in opposite directions, making price elasticity negative.
  • Typically, the negative sign is dropped, and absolute value is used.
    • If |ED| < 1, the demand curve is inelastic.
    • If |ED| > 1, the demand curve is elastic.
    • If ∣ED∣=1|ED| = 1, the demand curve is unit elastic.
Calculating Percentage Changes
  • Problem: The standard method gives different answers depending on where you start.
  • Solution: Use the Midpoint Method.
  • Formula: end value–start valuemidpoint×100%\frac{end \ value – start \ value}{midpoint} \times 100\%
  • The midpoint is the number halfway between the start and end values.
  • It doesn’t matter which value you use as the start and which as the end—you get the same answer either way!
Example
  • Price increases from 200 to $250, and quantity demanded falls from 12 to 8.
  • Percentage change in price: \frac{$250 – $200}{$225} \times 100\% = 22.2\%</li><li>Percentagechangeinquantity:</li> <li>Percentage change in quantity: \frac{12 – 8}{10} \times 100\% = 40.0\%</li><li>Priceelasticityofdemand:</li> <li>Price elasticity of demand:40 / 22.2 = 1.8

VI. Variety of Demand Curves

  • The price elasticity of demand is closely related to the slope of the demand curve.
  • Rule of thumb:
    • Flatter curve: bigger elasticity.
    • Steeper curve: smaller elasticity.
Perfectly Inelastic Demand
  • Vertical demand curve.
  • Elasticity = 0.
Inelastic Demand
  • Relatively steep demand curve.
  • Elasticity < 1.
Unit Elastic Demand
  • Intermediate slope.
  • Elasticity = 1.
Elastic Demand
  • Relatively flat demand curve.
  • Elasticity > 1.
Perfectly Elastic Demand
  • Horizontal demand curve.
  • Elasticity = infinity.

VII. Elasticity of a Linear Demand Curve

  • The slope of a linear demand curve is constant, but its elasticity is not.

VIII. Price Elasticity of Demand using the Midpoint Formula

  • Formula: ED = \frac{\%\Delta QD}{\%\Delta PD} = \frac{(Q{After} – Q{before})/[(Q{after} + Q{before})/2]}{(P{After} – P{before})/[(P{after} + P{before})/2]}
  • Example: At the initial price of $10, the quantity demanded is 100. When the price rises to $20, the quantity demanded is 90.

IX. Elasticity of Demand and Total Revenue

  • Revenue (R) = Price (P) x Quantity (Q)
  • The elasticity of demand directly influences revenues when the price of the good changes.

Price Increase Effects on Revenue

  • Higher P means more revenue on each unit sold.
  • Lower Q due to the law of demand.
  • Which effect is bigger depends on the price elasticity of demand.
Elastic Demand
  • Price elasticity of demand > 1
  • Percentage change in Q > Percentage change in P
  • The fall in revenue from lower Q is greater than the increase in revenue from higher P, so revenue falls.
Inelastic Demand
  • Price elasticity of demand < 1
  • Percentage change in Q < Percentage change in P
  • The fall in revenue from lower Q is smaller than the increase in revenue from higher P, so revenue rises.

Case Study: Does Drug Interdiction Increase or Decrease Drug-Related Crime?

  • Users often turn to crime to finance their habit.
  • Total dollar value of drug-related crime equals total expenditure on drugs.
  • Demand for illegal drugs is inelastic.
Policy 1: Interdiction
  • Interdiction reduces the supply of drugs.
  • Demand for drugs is inelastic, Price rises proportionally more than quantity falls.
  • Result: An increase in total spending on drugs and in drug-related crime.
Policy 2: Education
  • Education reduces the demand for drugs.
  • Price and Quantity fall.
  • Result: A decrease in total spending on drugs and in drug-related crime.

X. Elasticity of Supply

  • A supply curve is elastic when an increase in price increases the quantity supplied a lot (and vice versa).
  • A supply curve is inelastic when the same increase in price increases quantity supplied just a little.
  • Elasticity of Supply Captures the Sensitivity of Quantity Supplied to Changes in Price

XI. Determinants of the Elasticity of Supply

  1. Change in Per-Unit Costs with Increased Production
  2. Time Horizon
  3. Share of Market for Inputs
  4. Geographic Scope The more easily sellers can change the quantity they produce, the greater the price elasticity of supply.
    • Example: Supply of beachfront property is harder to vary and thus less elastic than supply of new cars.
  • For many goods, price elasticity of supply is greater in the long run than in the short run because firms can build new factories, or new firms may be able to enter the market.

XII. Price Elasticity of Supply using the Midpoint Formula

  • Formula: ES = \frac{\%\Delta QS}{\%\Delta PS} = \frac{(Q{After} – Q{before})/[(Q{after} + Q{before})/2]}{(P{After} – P{before})/[(P{after} + P{before})/2]}

XIII. Variety of Supply Curves

  • The slope of the supply curve is closely related to price elasticity of supply.
  • Rule of thumb:
    • The flatter the curve, the bigger the elasticity.
    • The steeper the curve, the smaller the elasticity.
Perfectly Inelastic Supply
  • Vertical supply curve.
  • Elasticity = 0.
Inelastic Supply
  • Relatively steep supply curve.
  • Elasticity < 1.
Unit Elastic Supply
  • Intermediate slope.
  • Elasticity = 1.
Elastic Supply
  • Relatively flat supply curve.
  • Elasticity > 1.
Perfectly Elastic Supply
  • Horizontal supply curve.
  • Elasticity = infinity.

XIV. How the Price Elasticity of Supply Can Vary

  • Supply often becomes less elastic as quantity rises due to capacity limits.

XV. Other Elasticities

Income Elasticity of Demand
  • Definition: Measures the response of quantity demanded (QD) to a change in consumer income
  • Formula: \frac{Percent \ change \ in \ QD}{Percent \ change \ in \ income}
  • For normal goods, income elasticity > 0.
  • For inferior goods, income elasticity < 0.
  • For luxury goods, Income Elasticity is greater than one.
Cross-Price Elasticity of Demand
  • Definition: Measures the response of demand for one good to changes in the price of another good.
  • Formula: \% \frac{change \ in \ QD \ for \ good \ 1}{\% \ change \ in \ price \ of \ good \ 2}$$
  • For substitutes, cross-price elasticity > 0 (e.g., an increase in price of beef causes an increase in demand for chicken).
  • For complements, cross-price elasticity < 0 (e.g., an increase in price of computers causes a decrease in demand for software).