Objectives Express and calculate price elasticity of demand Understand the relationship between the price elasticity of demand and total revenues Discuss the factors that determine the price elasticity of demand

Objectives Describe the cross price elasticity of demand and how it may be used to indicate whether two goods are substitutes or complements Explain the income elasticity of demand Classify supply elasticities and explain how the length of time for adjustment affects the price elasticity of supply 2

Price Elasticity Price Elasticity of Demand (Ep) The responsiveness of quantity demanded of a commodity to changes in its price

Price Elasticity Price Elasticity of Demand (Ep) percentage change in quantity demanded percentage change in price Ep = %ΔQd %ΔP

Calculating Elasticity % change in Qd = change in Qd original Qd % change in price = change in price original price

Calculating Elasticity Adjusting for the percent change bias change in Q sum of quantities/2 Ep = change in P or change in Q (Q1 + Q2)/2 Ep = change in P (P1 + P2)/2 Δ Q Avg. Q Ep = Δ P Avg. P or

Price Elasticity Relative quantities only Always negative Elasticity is measuring the change in quantity relative to the change in price Always negative An increase in price decreases the quantity demanded, ceteris paribus

Relationship Between Price Elasticity of Demand and Total Revenues Price Elasticity Effect of Price Change of Demand on Total Revenues (TR) Price Price Decrease Increase Inelastic (Ep < 1) TR TR Unit-elastic (Ep = 1) No change in TR No change in TR Elastic (Ep > 1) TR TR

Price Elasticity Example Price of oil increases 10 percent Quantity demanded decreases 1 percent Ep = -1% +10% = -.1

Price Elasticity Question Answer How would you interpret an elasticity of -0.1? Answer A one percent increase in the price of oil will lead to a one percent decrease in quantity demanded

Calculating Elasticity Example If the price increases from 1 to 2: 1 3/2 %ΔP = = .67

Calculating Elasticity Example If the price decreases from 2 to 1: 1 3/2 %ΔP = = .67

International Example: Price Elasticity of Demand for World’s Fair Tickets Price of admission to World’s Fair in Hannover, Germany was lowered from $12 to $5. Daily attendance rose from 60,000 to 100,000.

International Example: Price Elasticity of Demand for World’s Fair Tickets Δ Q (Q1 + Q2)/2 Ep = Δ P (P1 + P2)/2 Ep = 100,000 - 60,000 (100,000 + 60,000)/2 12 - 5 (12 + 5)/2

International Example: Price Elasticity of Demand for World’s Fair Tickets 40,000 80,000 Ep = 7.0 8.5 = .61 Interpretation A 1 percent decrease in price would increase quantity demanded by .61 percent.

Price Elasticity Ranges Elastic Demand Percentage change in quantity demanded is larger than the percentage change in price Ep > 1

Price Elasticity Ranges Unit Elasticity of Demand Percentage change in quantity demanded is equal to the percentage change in price Ep = 1

Price Elasticity Ranges Inelastic Demand Percentage change in quantity demanded is smaller than the percentage change in price Ep < 1

Price Elasticity Ranges Extreme elasticities Perfectly Inelastic Demand A demand curve that is a vertical line It has only one quantity demanded for each price No matter what the price, quantity demanded does not change

Extreme Price Elasticities Quantity Demanded per Year (millions of units)

Extreme Price Elasticities D Perfect inelasticity, or zero elasticity Price 8 Quantity Demanded per Year (millions of units)

Extreme Price Elasticities D P1 Price Perfect inelasticity, or zero elasticity P0 8 Quantity Demanded per Year (millions of units)

Price Elasticity Ranges Extreme elasticities Perfectly Elastic Demand A demand curve that is a horizontal line It has only one price for every quantity The slightest increase in price leads to zero quantity demanded

Extreme Price Elasticities Price (cents) Quantity Demanded per Year (millions of units)

Extreme Price Elasticities 30 D Price (cents) Perfect elasticity, or infinite elasticity Quantity Demanded per Year (millions of units)

Extreme Price Elasticities P1 never touches the demand curve P1 30 D Price (cents) Perfect elasticity, or infinite elasticity Quantity Demanded per Year (millions of units)

Quantity per period (billions of minutes) The Relationship Between Price Elasticity of Demand and Total Revenues for Cell Phone Service 1.10 1.00 .90 .80 .70 Price per Minute ($) .60 .50 .40 .30 .20 .10 10 20 30 40 50 60 70 80 90 100 110 Quantity per period (billions of minutes)

Quantity per period (billions of minutes) The Relationship Between Price Elasticity of Demand and Total Revenues for Cell Phone Service 1.10 Elastic (Ep >1) 1.00 Unit-Elastic (Ep =1) .90 Inelastic (Ep <1) .80 .70 Price per Minute ($) .60 .50 Demand, or average revenue curve .40 .30 .20 .10 D 10 20 30 40 50 60 70 80 90 100 110 Quantity per period (billions of minutes)

The Relationship Between Price Elasticity of Demand and Total Revenues for Cell Phone Service 3.0 2.5 2.0 Total Revenue ($ billions) 1.5 1.0 0.5 10 20 30 40 50 60 70 80 90 100 110 Quantity per period (billions of minutes)

The Relationship Between Price Elasticity of Demand and Total Revenues for Cell Phone Service 3.0 Elastic 2.5 Unit-Elastic Inelastic 2.0 Total Revenue ($ billions) 1.5 Total revenue curve 1.0 D 0.5 10 20 30 40 50 60 70 80 90 100 110 Quantity per period (billions of minutes)

Elasticity and Total Revenues Elastic Demand A negative relationship exists between small changes in price and changes in total revenue

Elasticity and Total Revenues Unit-Elastic Demand Changes in price do not change total revenue

Elasticity and Total Revenues Inelastic Demand A positive relationship exists between changes in price and total revenues

Relationship Between Price Elasticity of Demand and Total Revenues Price Elasticity Effect of Price Change of Demand on Total Revenues (TR) Price Price Decrease Increase Inelastic (Ep < 1) TR TR Unit-elastic (Ep = 1) No change in TR No change in TR Elastic (Ep > 1) TR TR

Determinants of Price Elasticity of Demand Existence of substitutes The closer the substitutes and the more substitutes there are, the more elastic is demand. Share of the budget The greater the share of the consumer’s total budget spent on a good, the greater is the price elasticity.

Determinants of Price Elasticity of Demand The length of time allowed for adjustment The longer any price change persists, the greater is the price elasticity of demand. Price elasticity is greater in the long-run than in the short-run.

Demand Elasticity for Selected Goods Estimated Elasticity Category Short Run Long Run Air travel (vacation) 1.1 2.7 Air travel (business) . 4 1.2 Beef .6 —— Cheese .3 —— Electricity .1 1.7 Fresh tomatoes 4.6 —— Gasoline . 2 .5 Hospital services .1 .7 Intercity bus service .6 2.2 Physician services .1 .6 Private education 1.1 1.9 Restaurant meals 2.3 —— Tires .9 1.2

Determinants of Price Elasticity of Demand How to define the short run and the long run The short run is a time period too short for consumers to fully adjust to a price change. The long run is a time period long enough for consumers to fully adjust to a change in price other things constant.

Policy Example: Making the Price of a “High” Higher Teenage cocaine abusers are three times as sensitive to price changes compared to adults. Legal crackdowns on cocaine dealers to decrease supply and raise prices may be an appropriate strategy in the war on drugs.

Short-Run and Long-Run Price Elasticity of Demand In the short run, quantity demanded falls slightly. However, with more time for adjustment the demand curve becomes more elastic and quantity demanded falls by a greater amount. P1 E Price per Unit Pe D2 D1 Q2 Q1 Qe Quantity Demanded per Period

Short-Run and Long-Run Price Elasticity of Demand In the short run, quantity demanded falls slightly. However, with more time for adjustment the demand curve becomes more elastic and quantity demanded falls by a greater amount. P1 E Price per Unit Pe D3 D2 D1 Q3 Q2 Q1 Qe Quantity Demanded per Period

Cross Price Elasticity of Demand Cross Price Elasticity of Demand (Exy) The percentage change in the demand for one good (holding its price constant) divided by the percentage change in the price of a related good The responsiveness of change in demand of one good to the change in prices of related goods

Cross Price Elasticity of Demand Formula for computing cross elasticity of demand %Δ in demand for good X %Δ in price of good Y Exy =

Cross Price Elasticity of Demand Substitutes Exy would be positive An increase in the price of X would increase the quantity of Y demanded at each price. Complements Exy would be negative An increase in the price of X would decrease the quantity of Y demanded at each price.

Issues and Applications: Taxation and Cigarette Smoking Would higher taxes on beer discourage cigarette smoking? Because the demand for cigarettes is relatively price inelastic, higher cigarette taxes do not appear to discourage smoking

Issues and Applications: Taxation and Cigarette Smoking If alcoholic beverages and cigarettes are complements, then taxes on alcohol could reduce the amount of smoking Estimates indicate that the cross-price elasticity of demand between beer and cigarettes is -.2 Therefore, a 10 percent increase in beer prices would reduce the number of cigarettes consumed by 2 percent.

Income Elasticity of Demand Income Elasticity of Demand (Ei) The percentage change in demand for any good, holding its price constant, divided by the percentage change in income The responsiveness of demand to changes in income, holding the good’s relative price constant

Income Elasticity of Demand percentage change in demand percentage change in income Ei =

Income Elasticity of Demand Normal Exy would be positive Inferior Exy would be negative

Income Elasticity of Demand refers to a horizontal shift in the demand curve in response to changes in income Price elasticity of demand refers to a movement along the curve in response to price changes

How Income Affects Quantity of DVDs Demanded Number of CDs Period Demanded per Month Income per Month 1 6 $4,000 2 8 6,000

How Income Affects Quantity of DVDs Demanded Income increases from $400 to $600 per month (8 - 6)/6 (6000 - 4000)/4000 Ei = = 1/3 1/2 2 3 = .667

How Income Affects Quantity of DVDs Demanded Income decreases from $6000 to $4000 per month (6 - 8)/8 (4000 - 6000)/6000 Ei = = -1/4 -1/3 3 4 = .75

Income Elasticity of Demand Eliminating the bias of the base ΔQuantity sum of quantities/2 Ei = ΔIncome sum of income/2

Income Elasticity of Demand Demand and elasticities Accurate estimates of Ep and Ei can yield accurate forecasts of the demand for goods and services.

Elasticity of Supply Price Elasticity of Supply (Es) The responsiveness of the quantity supplied of a commodity to a change in its price The percentage change in quantity supplied divided by the percentage change in price

Elasticity of Supply Formula for computing price elasticity of supply percentage change in quantity supplied percentage change in price ES =

Elasticity of Supply Classifying supply elasticities Perfectly Elastic Supply Quantity supplied falls to zero when there is any decrease in price. The supply curve is horizontal at a given price.

Elasticity of Supply Classifying supply elasticities Perfectly Inelastic Supply Quantity supplied is constant no matter what happens to price. The supply curve is vertical at a given price.

The Extremes in Supply Curves Q1 S’ Perfect inelasticity Price per Unit Quantity Supplied per Period

The Extremes in Supply Curves Perfect inelasticity P1 S Price per Unit Perfect elasticity Q1 Quantity Supplied per Period

Elasticity of Supply Price elasticity of supply and length of time for adjustment The longer the time allowed for adjustment, the more elastic is supply. Firms can find ways to increase (or decrease) output. Resources can flow into (or out of) an industry through expansion (or contraction) of existing firms.

The Extremes in Supply Curves Price per Unit Quantity Supplied per Period

The Extremes in Supply Curves In the short run, the supply curve, S1, is vertical with price Pe and quantity supplied of Qe. Pe E Price per Unit Qe Quantity Supplied per Period

Short-Run and Long-Run Price Elasticity of Supply If price increases to P1 quantity stays unchanged P1 Pe Price per Unit E Qe Quantity Supplied per Period

Short-Run and Long-Run Price Elasticity of Supply Q1 As time passes the supply curve rotates from S1 to S2 and quantity supplied rises first to Q1. Pe Price per Unit E Qe Quantity Supplied per Period

Short-Run and Long-Run Price Elasticity of Supply Pe Price per Unit E As time passes the supply curve rotates to S2 then to S3 and quantity supplied rises first to Q1 and then to Q2. Qe Q1 Q2 Quantity Supplied per Period

Summary Expressing and calculating the price elasticity of demand Percentage change in quantity demanded divided by the percentage change in price

Summary The relationship between the price elasticity of demand and total revenues When demand is elastic, price and total revenue are inversely related When demand is inelastic, price and total revenue are positively related When demand is unit elastic, total revenue does not change when price changes

Summary Factors that determine price elasticity of demand Availability of substitutes Percentage of a person’s budget spent on the good The length of time allowed for adjustment to a price change

Summary The cross price elasticity of demand and using it to determine whether two goods are substitutes or complements Percentage change in the demand for one good divided by the percentage change in the price of another If cross elasticity is positive, the goods are substitutes If cross elasticity is negative, the goods are complements

Summary Income elasticity of demand Percentage change in the demand for a good divided by the percentage in income Defines Normal vs Inferior goods

Summary Classifying supply elasticities and how the length of time for adjustment affects price elasticity of supply Elastic supply: price elasticity of supply is > 1 Inelastic supply: price elasticity of supply is < 1 Unit-elastic supply: price elasticity of supply is = 1 The longer the time period for adjustment, the more elastic is supply