Elasticity Notes

Chapter 6: Elasticity: The Responsiveness of Demand and Supply

6.1 The Price Elasticity of Demand and Its Measurement

• Definition: Elasticity measures how one economic variable responds to changes in another.
• Price Elasticity of Demand: Measures the responsiveness of quantity demanded to a change in price.
  • Calculated by dividing the percentage change in quantity demanded by the percentage change in price.
    *Slope vs. Elasticity: Slope is sensitive to units, making elasticity a better measure.

A. Measuring the Price Elasticity of Demand

• The price elasticity of demand is always negative, but we often compare absolute values.

B. Elastic Demand and Inelastic Demand

• Elastic Demand: Percentage change in quantity demanded > percentage change in price (elasticity > 1).
• Inelastic Demand: Percentage change in quantity demanded < percentage change in price (elasticity < 1).
• Unit-Elastic Demand: Percentage change in quantity demanded = percentage change in price (elasticity = 1).

C. Computing Price Elasticities

• Calculating elasticity between two points yields different values for price increases vs. decreases.

D. The Midpoint Formula

• Midpoint Formula: Used to ensure a single elasticity value between two points.
  • Uses the average of initial and final quantities and prices.
  • Formula: Price\ Elasticity\ of\ Demand = \frac{\frac{Q2 - Q1}{(Q2 + Q1)/2}}{\frac{P2 - P1}{(P2 + P1)/2}}
    • Where Q1 and P1 are the initial quantity and price, and Q2 and P2 are the final quantity and price.

E. When Demand Curves Intersect

• The flatter curve is more elastic (smaller slope in absolute value).
• The steeper curve is less elastic (larger slope in absolute value).

F. Polar Cases of Perfectly Inelastic and Perfectly Elastic Demand

• Perfectly Inelastic Demand: Quantity demanded is completely unresponsive to price (elasticity = 0).
  • Vertical demand curve.
• Perfectly Elastic Demand: Quantity demanded is infinitely responsive to price (elasticity = ∞).
  • Horizontal demand curve.

G. The Many Uses of Elasticity: An Example from Law Enforcement Policy in Denmark

• Efficient allocation of resources requires policies that provide the most deterrence per dollar cost.
• Expansion of DNA database in Denmark:
  • A 1 percent higher detection probability reduces crime by 2 percent.

6.2 The Determinants of the Price Elasticity of Demand

• Five key determinants:

A. Availability of Close Substitutes

• Most important determinant.
• More substitutes → more elastic demand.
• Fewer substitutes → less elastic demand.

B. Passage of Time

• The more time passes, the more elastic the demand becomes.

C. Luxuries versus Necessities

• Demand for a luxury is more elastic than for a necessity.

D. Definition of the Market

• The more narrowly defined the market, the more elastic the demand.

E. Share of a Good in a Consumer’s Budget

• The larger the share, the more elastic the demand.

F. Some Estimated Price Elasticities of Demand

• Estimates vary depending on data and time period.

6.3 The Relationship between Price Elasticity of Demand and Total Revenue

• Total Revenue: Total amount received from selling a good or service (price * quantity).
• Inelastic Demand: Price and total revenue move in the same direction.
  • Price increases, total revenue increases.
  • Price decreases, total revenue decreases.
• Elastic Demand: Price and total revenue move in opposite directions.
  • Price increases, total revenue decreases.
  • Price decreases, total revenue increases.
• Unit Elastic Demand: Change in price is offset by a proportional change in quantity, leaving revenue unaffected.

A. Elasticity and Revenue with a Linear Demand Curve

• Elasticity is not constant along most demand curves.
• At high prices and low quantities, demand is elastic.
• At low prices and high quantities, demand is inelastic.

6.4 Other Demand Elasticities

• Two other important demand elasticities:
  • Cross-price elasticity of demand.
  • Income elasticity of demand.

A. Cross-Price Elasticity of Demand

• Measures the responsiveness of the quantity demanded of one good to a change in the price of another good.
• Formula:
  • Cross-Price\ Elasticity\ of\ Demand = \frac{\%\ Change\ in\ Quantity\ Demanded\ of\ Good\ A}{\%\ Change\ in\ Price\ of\ Good\ B}
• Substitutes: Positive cross-price elasticity (price of one good increases, demand for the other increases).
• Complements: Negative cross-price elasticity (price of one good increases, demand for the other decreases).

B. Income Elasticity of Demand

• Measures the responsiveness of the quantity demanded to changes in income.
• Formula:
  • Income\ Elasticity\ of\ Demand = \frac{\%\ Change\ in\ Quantity\ Demanded}{\%\ Change\ in\ Income}
• Normal Good: Quantity demanded increases as income increases.
  • Necessity: Income elasticity is positive but less than 1.
  • Luxury: Income elasticity is greater than 1.
• Inferior Good: Quantity demanded decreases as income increases.

6.5 Using Elasticity to Analyze the Disappearing Family Farm

• From 1950 to 2022, the number of farms decreased significantly.
• Rapid growth in farm output and low price and income elasticities made family farming difficult.
• Increased wheat production led to a substantial decline in prices because:
  • Demand for wheat is price inelastic.
  • Income elasticity of demand for wheat is low.

6.6 The Price Elasticity of Supply and Its Measurement

• Measures how much quantity supplied increases when price increases.

A. Measuring the Price Elasticity of Supply

• The responsiveness of the quantity supplied to a change in price.
• Formula:
  • Price\ Elasticity\ of\ Supply = \frac{\%\ Change\ in\ Quantity\ Supplied}{\%\ Change\ in\ Price}
• Due to the law of supply, price elasticity of supply is positive.
• Inelastic Supply: Elasticity < 1
• Elastic Supply: Elasticity > 1
• Unit Elastic Supply: Elasticity = 1

B. Determinants of the Price Elasticity of Supply

• Depends on firms' ability and willingness to alter production with price changes.
• Supply is inelastic in the short term, more elastic in the long term.

C. Polar Cases of Perfectly Elastic and Perfectly Inelastic Supply

• Perfectly Inelastic Supply: Vertical supply curve.
• Perfectly Elastic Supply: Horizontal supply curve.

D. Using Price Elasticity of Supply to Predict Changes in Price

• When demand increases, the amount that price increases depends on the price elasticity of supply.
• Inelastic supply leads to a larger price increase than elastic supply.