Chapter 19: Demand and Supply Elasticity

Economics Today Chapter 19: Demand and Supply Elasticity

Introduction

  • Various taxes imposed on air travel add approximately 10% to the price of a typical airline ticket for U.S. airlines.
  • Higher ticket prices lead to a reduction in the quantity of airline tickets demanded, according to the law of demand.
  • The chapter discusses price elasticity of demand, which measures the proportionate change in quantity demanded in response to a proportionate change in price.

Learning Objectives

19.1 Calculate Price Elasticity of Demand

19.2 Explain the Relationship Between Price Elasticity of Demand and Total Revenues

19.3 Describe the Factors that Determine Price Elasticity of Demand

19.4 Explain Cross Price Elasticity of Demand and Income Elasticity of Demand

19.5 Classify Supply Elasticities and Explain How the Length of Time for Adjustment Affects Price Elasticity of Supply

Chapter Outline

  • 19.1 Price Elasticity
  • 19.2 Elasticity and Total Revenues
  • 19.3 Determinants of Price Elasticity of Demand
  • 19.4 The Cross Price and Income Elasticities of Demand
  • 19.5 Price Elasticity of Supply

Did You Know That…

  • During a recent holiday season, ride-sharing prices from services like Uber and Lyft decreased by 10-50%, leading to substantial increases in ride demand and overall total revenues for these companies.
  • Understanding such events involves the concept of quantity responsiveness, or elasticity.

19.1 Price Elasticity

  • Definition: Price elasticity of demand measures the responsiveness of the quantity demanded of a commodity to changes in its price. It is defined mathematically as:
    • E_d = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in price}}

Example 1

  • If the price of oil increases by 10% and the quantity demanded decreases by 2%, then:
    • E_d = \frac{-2\%}{10\%} = -0.2 (elasticity is typically presented as positive)

Example: Price Elasticity of Demand for Freshman Enrollments at Private Colleges

  • Average inflation-adjusted tuition rates increase by 1.5%, leading to a decrease in freshman enrollments by 1.9%.
  • Price Elasticity of Demand Calculation:
    • E_d = \frac{-1.9\%}{1.5\%} = -1.267

Interpretation of Elasticity

  • Elasticity of -0.1: A 10% increase in price results in a 1% decrease in quantity demanded.
  • Elasticities are generally negative because price increases lead to decreased quantity demanded (ceteris paribus), but the sign is often ignored in reporting.

Calculating Elasticity

  • The elasticity formula can be expressed as:
    • E_d = \frac{\Delta Q}{Q}/\frac{\Delta P}{P} or simplistically as above.

International Example: Price Elasticity of Demand for Tesla Vehicles in Hong Kong

  • Price of Tesla increases from $75,000 to $130,000, while quantity demanded decreases from 500 to 30.
  • Elasticity Calculation:
    • E_d = \frac{(30-500)/500}{(130,000-75,000)/75,000} = -2.8
    • A 1% increase in price results in a 2.8% decrease in quantity demanded.

Types of Demand Elasticity

  • Elastic Demand: Quantity demanded changes more than price change (Price elasticity of demand > 1).
  • Unit Elastic Demand: Quantity demanded changes equal to price change (Price elasticity of demand = 1).
  • Inelastic Demand: Quantity demanded changes less than price change (Price elasticity of demand < 1).

Extreme Elasticities

  • Perfectly Inelastic Demand: Demand curve is vertical; quantity demanded remains constant regardless of price changes.
  • Perfectly Elastic Demand: Demand curve is horizontal; any increase in price will reduce quantity demanded to zero.

Impacts of Government Taxation on Demand

  • A per-unit tax on a good with highly elastic demand shifts the market supply curve up and to the left, resulting in a small increase in market-clearing price and a larger cost burden on producers due to lower demand.

19.2 Elasticity and Total Revenues

  • When demand is elastic:
    • A negative relationship exists between price changes and total revenues (if prices go up, total revenues go down).
  • When demand is unit-elastic:
    • Price changes do not affect total revenues.
  • When demand is inelastic:
    • A positive relationship exists between price changes and total revenues (if prices go up, total revenues go up).

Total Revenues Explained

  • Total revenues are calculated as the product of price and quantity sold:
    • TR = P \times Q
  • The law of demand states that along any demand curve, price and quantity move in opposite directions.

Elasticity-Revenue Relationship Table

Price Elasticity of Demand ($E_p$)Effect of Price Change on Total Revenues (TR)Price DecreasePrice Increase
Inelastic ($E_p < 1$)TR downTR up
Unit-elastic ($E_p = 1$)No change in TRNo change in TR
Elastic ($E_p > 1$)TR upTR down

Price Optimization

  • The inverse U-shaped relationship between price elasticity and total revenues allows firms to optimize prices using AI-guided data analytics techniques.

19.3 Determinants of Price Elasticity of Demand

Major Determinants

  1. Existence of Substitutes: More and closer substitutes result in higher elasticity.
  2. Share of the Budget: Larger shares spent on a good correlate with higher elasticity.
  3. Length of Time for Adjustment: Longer adjustment periods yield greater elasticity; elasticity is greater in the long run compared to the short run.

Definitions of Short-Run vs. Long-Run

  • Short Run: A period too brief for consumers to fully adjust to a price change.
  • Long Run: A time long enough for consumers to adjust fully to price changes.

Price Elasticities for Selected Goods

GoodsShort RunLong Run
Air travel (business)0.41.2
Air travel (vacation)1.12.7
Beef0.6N.A.
Cheese0.3N.A.
Electricity0.11.7
Fresh tomatoes4.6N.A.
Gasoline0.20.5
Hospital services0.10.7
Intercity bus service0.62.2
Physician services0.10.6
Private education1.11.9
Restaurant meals2.3N.A.
Tires0.91.2

19.4 Cross Price and Income Elasticities of Demand

Cross Price Elasticity of Demand

  • Defined as the percentage change in demand for one good, holding its price constant, divided by the percentage change in the price of a related good.

Formula for Cross Price Elasticity

  • Between good X and good Y:
    • E{xy} = \frac{\Delta DY/DY}{\Delta PX/P_X}
  • Substitutes: Positive cross price elasticity; increase in price of X increases quantity demanded of Y.
  • Complements: Negative cross price elasticity; increase in price of X decreases quantity demanded of Y.

Income Elasticity of Demand

  • Defined as the percentage change in demand, holding price constant, divided by the percentage change in income.
  • It measures how responsive demand is to changes in income.

Formula for Income Elasticity of Demand

  • E_I = \frac{\Delta D/D}{\Delta I/I}
  • Income elasticity can be either positive or negative, indicating whether the good is a normal good (positive elasticity) or an inferior good (negative elasticity).

Example: Income Elasticity of Demand Calculation

  • Table 19-3 presents how the quantity of digital apps demanded varies with income, demonstrating how an increase in income from $4,000 to $6,000 increases demand from 6 to 8 apps monthly, leading to an elasticity calculation of:
    • E_I = \frac{2/6}{2000/4000} = 2

19.5 Price Elasticity of Supply

Price Elasticity of Supply Definition

  • Price elasticity of supply measures the responsiveness of the quantity supplied of a product to a change in its price defined as:
    • E_s = \frac{\% \text{ change in quantity supplied}}{\% \text{ change in price}}

Formula for Price Elasticity of Supply

  • Es = \frac{\Delta Qs/Q_s}{\Delta P/P}

Classifying Supply Elasticities

  1. Perfectly Elastic Supply:
    • Quantity supplied drops to zero if there is any decrease in price, represented by a horizontal supply curve.
  2. Perfectly Inelastic Supply:
    • Quantity supplied remains constant regardless of price changes, represented by a vertical supply curve.

Behavioral Example: Payment for Gym Workouts

  • A study with 690 participants showed that an additional payment of $30 increased the average number of workouts from 1.33 to 1.47 times per week, providing a price elasticity of supply of:
    • E_s = 0.15 (indicating 1% increase in payments results in a marginal increase in workouts).

Price Elasticity and Time for Adjustment

  • The length of time permitted for adjustment influences supply elasticity:
    • Longer adjustment times allow more resources to move into or out of an industry, impacting production levels.

Case Study: Philadelphia Soft Drinks Tax

  • A 1.5-cent-per-ounce tax on sugary drinks correlated with a 35% price increase and a 45% decrease in purchases, resulting in an elastic demand with price elasticity of demand of:
    • E_d = 1.3 = \frac{45\%}{35\%}.

Airline Ticket Price Elasticity and Revenues

  • A 1% increase in airline ticket prices due to taxes resulted in an 8% decrease in demand, leading to an elastic demand value of:
    • E_d = 8. Thus, predicting a decrease in revenues due to increased prices.

Summary of Learning Objectives

19.1 Calculate Price Elasticity of Demand

  • Percentage change in quantity demanded divided by percentage change in price.

19.2 Explain the Relationship Between Price Elasticity of Demand and Total Revenues

  • Elastic demand leads to inverse relationship with total revenues; inelastic demand leads to direct relationship.

19.3 Describe Determinants of Price Elasticity of Demand

  • Availability of substitutes, budget share, and adjustment time affect elasticity.

19.4 Explain Income and Cross Price Elasticities

  • Cross price elasticity measures responsiveness to price changes of related goods; income elasticity measures responsiveness to income changes.

19.5 Classify Supply Elasticities

  • Elastic supply, inelastic supply, and unit-elastic supply are defined by responsiveness to price changes with time impacting these classifications.