Demand Elasticity Lecture Notes

DEMAND ELASTICITY

Introduction to Elasticity Concept

• Definition: Elasticity measures the responsiveness of one variable to changes in another variable.

• Graphical Representation: Elasticity describes the steepness or flatness of curves or functions in economics.

Types of Elasticities

• Price elasticity of demand

• Income elasticity of demand

• Cross price elasticity of demand

• Price elasticity of supply

PRICE ELASTICITY OF DEMAND

Definition of Price Elasticity of Demand

• Meaning: Measures the responsiveness of quantity demanded to changes in a good’s own price.

• Formula: Price elasticity of demand is defined as the percentage change in quantity demanded divided by the percentage change in price that caused the change in quantity demanded.

Elasticity Formula

• The price elasticity of demand is mathematically expressed as:
  ext{Price elasticity of demand} = \frac{% \text{ change in } Q_d}{% \text{ change in } P}

Example of Price Elasticity of Demand

• Calculation:

  • Given: Price rises by 10% and quantity falls by 15%.

  • Calculation:
    ext{Price elasticity of demand} = \frac{-15\%}{10\%} = -1.5

Elasticity and Slope

• Key Point: Elasticity is not the same as slope.

  • For a linear demand function (straight line), the slope remains constant.

  • In contrast, elasticity (Ed) changes along the demand curve.

Calculating Price Elasticity of Demand (Step-by-Step)

1. Identify Two Points on the Demand Curve:

   • Point A: Price = $12, Quantity demanded = 50 units

   • Point B: Price = $10, Quantity demanded = 100 units

2. Calculating Elasticity at Point A (moving to B):
   ext{%} \Delta Q / %\Delta P = \frac{50/50}{-2/12} = \frac{100\%}{-17\%} = -5.88

3. Calculating Elasticity at Point B (moving to A):
   ext{%} \Delta Q / %\Delta P = \frac{-50/100}{2/10} = \frac{-50\%}{20\%} = -2.5

Elasticity Terms

• Elastic Demand: Demand is elastic when the absolute value of elasticity is greater than 1.

• Inelastic Demand: Demand is inelastic when the absolute value of elasticity is less than 1.

• Unit Elastic Demand: Demand is unit elastic when the absolute value of elasticity equals 1.

Relative Elasticity of Demand Curves

• Demand curves exhibit different elasticity characteristics based on the prices and quantities at a certain point:

  • More elastic damage at a specific price (p), comparatively more inelastic at the same price.*

Graphical Representations of Demand Elasticity

Perfectly Elastic Demand

• A small change in price leads to an extremely large change in quantity demanded (from buying all to buying none).

Perfectly Price Inelastic Demand

• The quantity demanded does not change regardless of the price changes.

• Defined graphically as a vertical line.

Price Unitary Elastic Demand

• The percentage change in quantity demanded is equal to the percentage change in price.

• Graphically, these are 45-degree lines from the origin, indicating proportional changes in both quantity and price.

DETERMINANTS OF DEMAND ELASTICITY

Key Determinants

• Availability of Substitutes: The more substitutes available, the more elastic the demand tends to be.

• Time Period: The longer the time period involved, the more elastic the demand is.

• Fraction of Income: The larger the fraction of income spent on the good, the more elastic the demand tends to be.

Examples Illustrating Determinants

Example 1: Breakfast Cereal vs. Sunscreen

• Price increase: 20% for both.

• Result: Quantity demanded drops more for breakfast cereal (due to close substitutes - pancakes, waffles, etc.) vs. sunscreen (fewer substitutes).

• Lesson: Price elasticity of demand is higher when close substitutes are available.

Example 2: Blue Jeans vs. Clothing

• Price increase: 20% for both.

• Result: Qd drops more for blue jeans due to numerous substitutes compared to clothing.

• Lesson: Price elasticity tends to be higher for narrowly defined goods.

Example 3: Insulin vs. Caribbean Cruises

• Price increase: 20% for both.

• Insulin, a necessity for diabetics, sees minimal decrease in demand, whereas luxury cruise demand decreases.

• Lesson: Price elasticity is higher for luxuries compared to necessities.

Example 4: Gasoline Short Run vs. Long Run

• Price rise: 20%. In the short run, demand drops minimally due to limited options; in the long run, more elastic demand as people adjust.

• Lesson: Price elasticity is higher in the long run than the short run.

Example 5: Apartment Rent vs. Box of Matches

• Price rise: 20% for both.

• Rent will lead to noticeable Qd changes, while matches will hardly affect behavior.

• Lesson: Price elasticity is higher for goods comprising a larger fraction of income.

Real-World Demand Elasticities

• Practical Data:

  • Eggs: ε = -0.1 (inelastic)

  • Healthcare: ε = -0.2 (inelastic)

  • Rice: ε = -0.5 (inelastic)

  • Housing: ε = -0.7 (inelastic)

  • Beef: ε = -1.6 (elastic)

  • Restaurant meals: ε = -2.3 (elastic)

PRICE GOUGING

Case Study: Martin Shkreli

• Background: Founder and CEO of Turing Pharmaceuticals; bought rights to Daraprim in Fall 2015.

• Price Increase: From $13.50 to $750 per pill (increase of 5500%).

• Political Response: Hillary Clinton's tweet aiming to drive down drug prices led to a $55 billion loss in US pharmaceutical stocks.

• Legal Outcomes: Shkreli convicted of securities fraud; sentenced to 7 years and a $7.4 million fine.

PRICE ELASTICITY AND SELLER'S TOTAL REVENUE

Total Revenue Definition

• Formula: Total Revenue (TR) is calculated as the price of a good multiplied by the quantity sold:
  TR = P * Q

Elastic Demand and Total Revenue

• Key Concept: If demand is elastic (Ed > 1), a price increase leads to lower revenue, while a price decrease increases revenue.

• Relationship: Price and total revenue are inversely related.

• Graphical Illustration: Price changes affect the total revenue rectangle sized based on price responses.

Inelastic Demand and Total Revenue

• Key Concept: If demand is inelastic (Ed < 1), a price increase leads to higher revenue, while a price decrease decreases revenue.

• Relationship: Price and total revenue are directly related.

• Graphical Illustration: Changes in price affect the size of the total revenue rectangle accordingly.

Price Elasticity of Demand Along a Straight-Line Demand Curve

• Elastic Range: Where elasticity (Ed) is greater than 1.

• Inelastic Range: Where elasticity (Ed) is less than 1.

• Midpoint: At the midpoint of the straight-line downward sloping demand curve, price elasticity of demand equals 1 (Ed = 1).

Total Revenue vs. Price Changes along the Demand Curve

• Elastic Range: Reducing prices increases total revenue.

• Inelastic Range: Reducing prices decreases total revenue.

• Peak Revenue: Total revenue peaks when price elasticity of demand equals 1.

COURSE REVIEW

Review Questions

• What is measured through demand elasticity?

• Which formula is used to calculate elasticity of demand?

• What does it mean for demand to be inelastic? Elastic?

• What factors determine the magnitude of demand elasticity?

• If demand is elastic, does a price increase lead to higher or lower revenues?

• As a manager of a theater club, should you increase or decrease ticket prices to raise revenues?

Exercise Question Example

• Analyze the case of decreased bus ridership after a 25 cent fare increase.

• Estimate price elasticity for bus rides and discuss revenue effects.

• Consider potential reliability issues of the elasticity estimate.

Multiple-Choice Questions for Review

• 1. What does price elasticity of demand measure?
  A. The relationship between price and supply.
  B. The responsiveness of quantity demanded to changes in price.
  C. The change in demand due to changes in consumer income.
  D. The total revenue earned by sellers at different prices.

• 2. When demand is price inelastic, how does a price increase affect total revenue?
  A. Total revenue increases.
  B. Total revenue decreases.
  C. Total revenue remains unchanged.
  D. Total revenue depends on elasticity of supply.

• 3. Which of the following is NOT a determinant of price elasticity of demand?
  A. Availability of substitutes.
  B. Proportion of income spent on the good.
  C. The cost of production.
  D. Time available to adjust to price changes.

• 4. In general, a flatter demand curve is more likely to be
  A. price elastic.
  B. unit price elastic.
  C. price inelastic.
  D. uniformed elastic.

• 5. If a good has many close substitutes, its demand is likely to be:
  A. Perfectly inelastic.
  B. Elastic.
  C. Unit elastic.
  D. Inelastic.

• 6. What happens to total revenue when the price of a product increases and the demand is elastic?
  A. Total revenue increases.
  B. Total revenue decreases.
  C. Total revenue remains constant.
  D. Total revenue doubles.

• 7. Which of the following goods is most likely to have inelastic demand?
  A. Luxury watches.
  B. Gasoline in the short term.
  C. Designer handbags.
  D. Soft drinks with many substitutes.

• 8. How does the price elasticity of demand affect seller revenue?
  A. Sellers always earn more revenue when they increase prices.
  B. Sellers earn more revenue when they decrease prices if demand is inelastic.
  C. Sellers earn more revenue when they increase prices if demand is inelastic.
  D. Sellers' revenue is unaffected by the elasticity of demand.

• 9. If the price of a necessity increases, demand for the good is likely to be:
  A. Elastic, because consumers can switch to substitutes.
  B. Inelastic, because consumers cannot easily reduce consumption.
  C. Perfectly elastic, because everyone must buy the good.
  D. Unit elastic, as the percentage change in demand matches the price change.

10. Which of the following statements is true about the relationship between demand elasticity and the demand curve?
    A. The demand elasticity is equal to the slope of the demand curve.
    B. Demand elasticity and the demand curve are two different and unrelated concepts.
    C. A straight-line demand curve does not have a demand elasticity.
    D. The demand elasticity varies along a straight-line demand curve.