Chapter 5 Elasticity and Taxation Slides created by

Chapter 5 Elasticity and Taxation Slides created by Dr. Amy Scott © 2010 Worth Publishers

More Precious than a Flu Shot q. The U. S. supply of the flu vaccine for the 2004– 2005 flu season was suddenly cut in half q. As news of it spread, there was a rush to get the shots. q. Some pharmaceutical distributers detected a profit - making opportunity in the frenzy. q. Consumers of the vaccine were relatively unresponsive to price; Ø that is, the large increase in the price of the vaccine left the quantity demanded by consumers relatively unchanged. q. In this chapter we will show the price elasticity of demand is calculated and why it is the best measure of how the quantity demanded responds to changes in price.

Chapter Objectives 1. What is elasticity? A. B. C. D. Price elasticity of demand Cross-price elasticity of demand Income elasticity of demand Price elasticity of supply 2. The effects of taxes on supply and demand 3. What determines who bears the burden of a tax 4. The costs and benefits of taxes, and why taxes impose a cost that is larger than the tax revenue they raise

Defining and Measuring Elasticity Ø The price elasticity of demand is the ratio of the percent change in the quantity demanded to the percent change in the price as we move along the demand curve %∆Q %∆P Ø Drop the minus sign - Price elasticity of demand is always negative because of the inverse relationship between price and quantity demandedso drop the minus sign and use Absolute Value

Demand for Vaccinations Price of vaccination $21 20 When price rises to $21 per barrel, world demand falls to 9. 9 million barrels per day (point B). B A D 0 9. 9 10. 0 Quantity of vaccinations (millions)

The Price Elasticity of Demand

Calculating the Price Elasticity of Demand 1) 2) 3)

The Midpoint Method ØPercentage change can vary depending on which variables are used to measure. To alleviate this problem: Ø The midpoint method is a technique for calculating the percent change using averages of starting and final values (midpoints).

Midpoint Method

Using the Midpoint Method

The price of strawberries falls from $1. 50 to $1. 00 per carton and the quantity demanded goes from 100, 000 to 200, 000 cartons. Using the midpoint method, the price elasticity of demand is: 1. 2. 3. 4. 1. 7. 0. 6. 67. 40.

Interpreting Price Elasticity of Demand Extreme Cases of Price Elasticity of Demand: o Demand is perfectly inelastic when the quantity demanded does not respond at all to changes in the price n o demand curve is a vertical line. Demand is perfectly elastic when any price increase will cause the quantity demanded to drop to zero. n demand curve is a horizontal line.

Two Extreme Cases of Price Elasticity of Demand Perfectly Inelastic Demand: Price Elasticity of Demand = 0 Price of shoelaces (per pair) An increase in price… D 1 $3 $2 … leaves the quantity demanded unchanged. 0 1 Quantity of shoelaces (billions of pairs per year)

Two Extreme Cases of Price Elasticity of Demand Price Elastic Demand: Price Elasticity of Demand = ∞ Price of pink tennis balls (per dozen) At any price above $5, quantity demanded is zero $5 At exactly $5, consumers will buy any quantity D 2 At any price below $5, quantity demanded is infinite 0 Quantity of tennis balls (dozens per year)

Interpreting Price Elasticity of Demand (continued) Ø Demand is elastic if the price elasticity of demand is greater than 1 Ø Price Elasticity of Demand > 1 Ø Demand is inelastic if the price elasticity of demand is less than 1 Ø Price Elasticity of Demand < 1 Ø Demand is unit-elastic if the price elasticity of demand is exactly 1 Ø Price Elasticity of Demand = 1

Some Estimated Price Elasticities of Demand Good Inelastic demand o o Eggs Beef Stationery Gasoline Elastic demand o o Housing Restaurant meals Airline travel Foreign travel Price elasticity 0. 1 0. 4 0. 5 1. 2 2. 3 2. 4 4. 1 Price elasticity of demand<1 Price elasticity of demand>1

Unit-Elastic Demand, Inelastic Demand, and Elastic Demand is unit-elastic if the price elasticity of demand is exactly 1 Price of crossing Unit-Elastic Demand: Price Elasticity of Demand = 1 B A 20% increase in the price. . . $1. 10 A 0. 90 D 0 900 1, 100 . . . generates a 20% decrease in the quantity of crossings demanded. 1 Quantity of crossings (per day)

Unit-Elastic Demand, Inelastic Demand, and Elastic Demand is inelastic if the price elasticity of demand is less than 1 Price of crossing A 20% increase in the price. . . Inelastic Demand: Price Elasticity of Demand = 0. 5 B $1. 10 A 0. 90 D 0 950 1, 050 . . . generates a 10% decrease in the quantity of crossings demanded. 2 Quantity of crossings (per day)

Unit-Elastic Demand, Inelastic Demand, and Elastic Demand is elastic if the price elasticity of demand is greater than 1 Elastic Demand: Price Elasticity of Demand = 2 Price of crossing B $1. 10 A 20% increase in the price. . . A 0. 90 D 0 800 1, 200 … generates a 40% decrease in the quantity of crossings demanded. 3 Quantity of crossings (per day)

Why Does It Matter Whether Demand is Unit. Elastic, Inelastic, or Elastic? Ø Ø Ø Because this predicts how changes in the price of a good will affect the total revenue earned by producers from the sale of that good. The total revenue is defined as the total value of sales of a good or service, i. e. Total Revenue = Price × Quantity Sold

Total Revenue by Area Total Revenue = Price × Quantity Sold Price of crossing $0. 90 Total revenue = price x quantity = $990 0 D 1, 100 Quantity of crossings (per day)

Elasticity and Total Revenue Ø When a seller raises the price of a good, there are two effects in action (except in the rare case of a good with perfectly elastic or perfectly inelastic demand): Ø A price effect: After a price increase, each unit sold sells at a higher price, which tends to raise revenue. Ø A quantity effect: After a price increase, fewer units are sold, which tends to lower revenue.

Figure 5. 4 b Effect of a Price Increase on Total Revenue Price of crossing $1. 10 Price effect of price increase: higher price for each unit sold Quantity effect of price increase: fewer units sold C 0. 90 B 0 A 900 D 1, 100 Quantity of crossings (per day)

Elasticity and Total Revenue demand for a good is elastic (the price elasticity of demand > 1), an increase in price reduces total revenue. Ø The quantity effect is stronger than the price effect. Ø If Price TR Ø If demand for a good is inelastic (the price elasticity of demand < 1), a higher price increases total revenue. Ø The price effect is stronger than the quantity effect. Price TR Ø If demand for a good is unit-elastic (the price elasticity of demand = 1), an increase in price does not change total revenue. Ø The sales effect and price effect exactly offset each other.

Price Elasticity of Demand Total Revenue

Demand Schedule and Total Revenue Price Elastic $10 9 8 7 6 5 4 3 2 1 Unit-elastic Inelastic D 0 1 2 3 4 5 6 7 8 9 10 Quantity Total revenue $25 24 21 16 9 0 0 1 2 3 Demand is elastic: a higher reduces total revenue 4 5 6 7 8 9 10 Quantity Demand is inelastic: a higher price increase total revenue Demand Schedule and Total Revenue for a Linear Demand Curve Quantity Total Price demanded Revenue $0 10 $0 1 9 9 2 8 16 3 7 21 4 6 24 5 5 25 6 4 24 7 3 21 8 2 16 9 10 0 0 The price elasticity of demand changes along the demand curve

What Factors Determine the Price Elasticity of Demand? Price Elasticity of Demand is determined by: Ø Whether Close Substitutes Are Available Ø Whether the Good Is a Necessity or a Luxury Ø Share of Income Spent on the Good Ø Time

How Mad?

Responding to your tuition bill § § For years tuition has been rising faster than the overall cost of living, but does rising tuition keep people from going to college? A 1988 study found that a 3% increase in tuition led to an approximately 2% fall in the number of students enrolled at four-year institutions, giving a price elasticity of demand of 0. 67 (2%/3%) and 0. 9 for two-year institutions. Enrollment decision for students at two-year colleges was significantly more responsive to price than for students at four-year colleges. The result: students at two-year colleges are more likely to forgo getting a degree because of tuition costs than students at four year colleges. A 1999 study confirmed this pattern.

For each case that follows choose the condition that best characterizes demand: elastic demand, inelastic demand or unit-elastic demand Total revenue decreases when price increases. 1. 2. 3. elastic demand inelastic demand unit-elastic demand

For each case that follows choose the condition that best characterizes demand: elastic demand, inelastic demand or unit-elastic demand The additional revenue generated by an increase in quantity sold is exactly offset by revenue lost from the fall in price received per unit. 1. 2. 3. elastic demand inelastic demand unit-elastic demand

For each case that follows choose the condition that best characterizes demand: elastic demand, inelastic demand or unit-elastic demand Total revenue falls when output increases. 1. 2. 3. elastic demand inelastic demand unit-elastic demand

For each case that follows choose the condition that best characterizes demand: elastic demand, inelastic demand or unit-elastic demand Producers in an industry find they can increase their total revenues by working together to reduce industry output. 1. 2. 3. elastic demand inelastic demand unit-elastic demand

For each case that follows, would you expect demand to be elastic or inelastic? Demand by a snake-bite victim for an antidote elastic inelastic 1. 2. Demand by students for green erasers 1. 2. elastic inelastic

Cross-Price Elasticity The cross-price elasticity of demand between two goods measures the effect of the change in one good’s price on the quantity demanded of the other good. Equal to the percent change in the quantity demanded of one good divided by the percent change in the other good’s price. The Cross-Price Elasticity of Demand between Goods A and B

Cross-Price Elasticity Ø Ø Goods are substitutes when the crossprice elasticity of demand is positive. Goods are complements when the crossprice elasticity of demand is negative.

Income Elasticity of Demand ØThe income elasticity of demand is the percent change in the quantity of a good demanded when a consumer’s income changes divided by the percent change in the consumer’s income.

Normal Goods and Inferior Goods Ø When the income elasticity of demand is positive, the good is a normal good Ø that is, the quantity demanded at any given price increases as income increases. Ø When the income elasticity of demand is negative, the good is an inferior good Ø that is, the quantity demanded at any given price decreases as income increases.

Where Have All the Farmers Gone? Why do so few people now live and work on farms in the United States? § § The income elasticity of demand for food is much less than 1—it is income inelastic. As consumers grow richer, other things equal, spending on food rises less than income as the U. S. economy has grown, the share of income it spends on food—and therefore the share of total U. S. income earned by farmers—has fallen. Agriculture has been a technologically progressive sector for approximately 150 years in the U. S. , with steadily increasing yields over time. Competition among farmers means that technological progress leads to lower food prices. Meanwhile, the demand for food is price-inelastic, so falling prices of agricultural goods, other things equal, reduce the total revenue of farmers progress in farming has been good for consumers but bad for farmers.

Food’s Bite in World Budgets Spending on food (% of income) 80% Sri Lanka 60 40 Mexico United States Israel 20 0 20 40 60 80 100% Income (% of U. S. income per capital)

Spending It § § The Bureau of Labor Statistics captures data on spending. A classic result of their surveys is that the income elasticity of demand for ‘food eaten at home’ is considerably less than 1. As a family’s income rises, the share of income spent on food consumed at home falls, and vice a versa as family income falls. In 1950, 19% of U. S. income was spent on food consumed at home compared with 7% now. Over the same time period, the share of U. S. income spent on food away from home has stayed constant at 5%. An example of an inferior good is rental housing. As family income rises demand for rental housing decreases since higher income families are likely to own their homes.

After Chelsea’s income increased from $12, 000 to $18, 000 a year, her purchases of CDs increased from 10 to 40 CDs a year. Calculate Chelsea’s income elasticity of demand for CDs using the midpoint method. 1. 2. 3. 4. 3. 333 1 7

Price Elasticity of Supply The price elasticity of supply is a measure of the responsiveness of the quantity of a good supplied to the price of that good. It is the ratio of the percent change in the quantity supplied to the percent change in the price as we move along the supply curve.

Two Extreme Cases of Price Elasticity of Supply Perfectly Inelastic Supply: Price Elasticity of Supply = 0 Perfectly Elastic Supply: Price Elasticity of Supply = ∞ Price of cell phone frequency Price of pizza S 1 An increase in price… At any price above $12, quantity supplied is infinite. $3, 000 $12 2, 000 0 … leaves the quantity supplied unchanged 100 Quantity of cell phone frequencies At any price below $12, quantity supplied is zero. 0 At exactly $12, producers will produce any quantity S 2 Quantity of pizzas

Measuring the Price Elasticity of Supply o Supply is perfectly inelastic when the price elasticity of supply is zero. When changes in the price have no effect on the quantity supplied n o Supply curve is a vertical line Supply is perfectly elastic when price elasticity of supply is infinite. When any price change will lead to very large changes in the quantity supplied n Supply curve is a horizontal line

What Factors Determine Price Elasticity of Supply? Ø The Availability of Inputs: The price elasticity of supply tends to be large when inputs are readily available and can be shifted into and out of production at a relatively low cost. It tends to be small when inputs are difficult to obtain. Ø Time: The price elasticity of supply tends to grow larger as producers have more time to respond to a price change. This means that the long-run price elasticity of supply is often higher than the short-run elasticity.

European Farm Surpluses § § § Imposition of a price floors to support the incomes of farmers has created “butter mountains” and “wine lakes” in Europe. Were European politicians unaware that their price floors would create huge surpluses? They probably knew that surpluses would arise, but underestimated the price elasticity of agricultural supply. They thought big increases in production were unlikely since there was little new land available in Europe for cultivation. However, farm production could expand by adding other resources, especially fertilizer and pesticides, which were readily available So although farm acreage didn’t increase much, farm production did!

An Elasticity Menagerie

Using the midpoint method, calculate the elasticity of supply for webdesign services when the price per hour rises from $100 to $150 and the number of hours transacted increases from 300, 000 hours to 500, 000. Is supply elastic, inelastic, or unit-elastic? 1. 2. 3. 4. 1. 75, elastic 1 unit-elastic 0. 75, inelastic 1. 25 elastic

True or False? If the demand for milk were to rise, then, in the long run, milk-drinkers would be better off if supply were elastic rather than inelastic. 1. 2. True False

True or False? When supply is perfectly elastic, changes in demand have no effect on price 1. 2. True False

Table 5. 3 An Elasticity Menagerie (continued)

Tax Incidence – Putting It Together Ø When the price elasticity of demand is higher than the price elasticity of supply, an excise tax falls mainly on producers. Ø When the price elasticity of supply is higher than the price elasticity of demand, an excise tax falls mainly on consumers. Ø So elasticity—not who officially pays the tax— determines the incidence of an excise tax.

The Revenue from an Excise Tax The tax revenue collected is: Tax revenue = $40 per room × 5, 000 rooms = $200, 000 Price of hotel $140 room 120 A 100 Excise tax = $40 per room 80 D B The area of the shaded rectangle is: Area = Height × Width = $40 per room × 5, 000 rooms = $200, 000 40 20 0 E Area = tax revenue 60 S 6 5, 000 10, 000 15, 000 Quantity of hotel rooms

The Revenue from an Excise Tax The general principle is: The revenue collected by an excise tax is equal to the area of the rectangle(Area = Height x Width) whose height is the tax wedge between the supply and demand curves and whose width is the quantity transacted under the tax.

Tax Rates and Revenue Ø Ø Ø A tax rate is the amount of tax people are required to pay per unit of whatever is being taxed. In general, doubling the excise tax rate on a good or service won’t double the amount of revenue collected, because the tax increase will reduce the quantity of the good or service transacted. In some cases, raising the tax rate may actually reduce the amount of revenue the government collects.

Tax Rates and Revenue (a) An excise tax of $20 (b) An excise tax of $60 Price of $140 hotel room 120 Price of hotel room 120 90 80 70 E Area = tax revenue D Excise tax = $60 per room 80 50 40 40 20 20 0 6, 000 7, 500 10, 000 15, 000 Quantity of hotel rooms 0 Area = tax revenue 110 S Excise tax = $20 per room $140 2, 500 5, 000 S E D 10, 000 15, 000 Quantity of hotel rooms

The Laffer Curve § In 1974. during a conversation with WSJ writer, Jude Wanniski, and then Deputy White House chief of staff, Dick Cheney, economist Auther Laffer drew a diagram that was intended to explain how tax cuts could sometimes lead to higher tax revenues. § According to Laffer, raising tax rates initially increases revenue but beyond a certain level, revenue will fall as tax rates rise. § In 1981 Ronald Regan used Laffer Cure to argue that his proposed tax cuts would not reduce government tax revenues. § Is there a Laffer Curve? Yes, as a theoretical proposition but very few economists believe that there exists such a high tax rate that reducing it leads to an increase in revenue.

The Costs of Taxation Ø Ø A fall in the price of a good generates a gain in consumer surplus. Similarly, a rise in the price generates a loss in consumer surplus. Excise tax raises the price paid by consumers causing a loss. Meanwhile, the fall in the price received by producers leads to a fall in producer surplus. Thus a tax reduces both the CS and the PS.

A Tax Reduces Consumer and Producer Surplus Fall in consumer surplus due to tax iprice P C A Excise tax = T P B E E F C P S P Fall in producer surplus due to tax Q T Q E D Quantity

The Deadweight Loss of a Tax Consumers and producers are hurt by the tax, but the government gains revenue. Ø The revenue the government collects is equal to the tax per unit sold, T, multiplied by the quantity sold, QT. Ø Ø But a portion of the loss to producers and consumers from the tax is not offset by a gain to the government. The deadweight loss caused by the tax represents the total surplus lost to society because of the tax—that is, the amount of surplus that would have been generated by transactions that now do not take place because of the tax.

The Deadweight Loss of a Tax S Price Deadweight loss P Excise tax = T P P C E E P D Q T Q E Quantity

Cost of Collecting Taxes Ø Ø Ø The administrative costs of a tax are the resources used by government to collect the tax, and by taxpayers to pay it, over and above the amount of the tax, as well as to evade it. The total inefficiency caused by a tax is the sum of its deadweight loss and its administrative costs. The general rule for economic policy is that, other things equal, a tax system should be designed to minimize the total inefficiency it imposes on society.

Deadweight Loss and Elasticities (b) (a) Elastic Demand Price Inelastic Demand S S Deadweight loss is larger when demand is elastic P C P E P C Excise tax = T E Excise tax = T D P E P P E Deadweight loss is smaller when demand is inelastic P P D Q T Q E Quantity Q Q T E Quantity

Figure 5. 11 Deadweight Loss and Elasticities (d) Inelastic Supply (c) Elastic Supply Deadweight loss is larger when supply is elastic Price P C Price S Excise tax = T P E P P S E P C Excise tax = T P E E Deadweight loss is smaller when supply is inelastic P P D Q T Q E D Quantity Q Q T E Quantity

Deadweight Loss and Elasticities Ø To minimize the efficiency costs of taxation, one should choose to tax only those goods for which demand or supply, or both, is relatively inelastic. Ø For such goods, a tax has little effect on behavior because behavior is relatively unresponsive to changes in the price.

Deadweight Loss and Elasticities Ø Ø Ø When demand is perfectly inelastic (vertical demand curve), the quantity demanded is unchanged by the imposition of the tax. As a result, the tax imposes no deadweight loss. Similarly, if supply is perfectly inelastic (vertical supply curve), the quantity supplied is unchanged by the tax and there is no deadweight loss. If the goal is to minimize deadweight loss, then taxes should be imposed on goods and services that have the most inelastic response—goods and services for which consumers or producers will change their behavior the least in response to the tax.

Taxing the Marlboro Man One of the most important excise taxes in the United States is the tax on cigarettes. The table above shows the results of big increases in cigarette taxes. In each case, sales fell, just as our analysis predicts. The tax revenue rose in each case because cigarettes have a low price elasticity of demand.

The accompanying table shows five consumers’ willingness to pay for one can of diet soda as well as five producers’ cost of selling one can of diet soda. The government asks your advice about the effects of an excise tax of $0. 40 per can of soda. Assume there are no administrative costs from the tax.

Without the excise tax, what is the equilibrium price and quantity of soda transacted? 1. $0. 70, 2. $0. 50, 3. $0. 40, 4. $0. 30, 1 2 4 5

The excise tax raises the price paid by consumers to $0. 60 and lowers the price received by producers post-tax to $0. 20. With the tax, what is the quantity of soda transacted? 1. 1 2. 2 3. 4 4. 5

Without the excise tax, how much individual consumer surplus does each of the consumers gain? How much with the tax? How much total consumer surplus is lost as a result of the tax? 1. $1. 00, $. 20, $. 80 2. $. 60, $. 10, $0. 70 3. $. 60, $. 10, $0. 50 4. $0. 40, $. 20, $. 40

Without the excise tax, how much producer surplus does each of the producers gain? How much with the tax? How much total producer surplus is lost as a result of the tax? 1. $1. 00, $. 20, $. 30 2. $. 60, $. 10, $0. 70 3. $. 60, $. 10, $0. 50 4. $0. 40, $. 20, $. 40

How much government revenue does the excise tax create? 1. $1. 00 2. $0. 80 3. $0. 50 4. $0. 40

What is the deadweight loss from the imposition of this excise tax? 1. $0. 80 2. $0. 50 3. $0. 40 4. $0. 20

You would expect a tax on gasoline to have a ____ deadweight loss. 1. 2. Small Large

You would expect a tax on milk chocolate bars to have a ____ deadweight loss. 1. 2. Small Large

Summary 1. 2. 3. 1 of 5 Elasticity is a general measure of responsiveness The price elasticity of demand—the percent change in the quantity demanded divided by the percent change in the price (dropping the minus sign)—is a measure of the responsiveness of the quantity demanded to changes in the price. The responsiveness of the quantity demanded to price can range from perfectly inelastic demand, where the quantity demanded is unaffected by the price, to perfectly elastic demand, where there is a unique price at which consumers will buy as much or as little as they are offered. When demand is perfectly inelastic, the demand curve is a vertical line; when it is perfectly elastic, the demand curve is a horizontal line.

Summary 4. 5. 6. 2 of 5 The price elasticity of demand is classified according to whether it is more or less than 1. If it is greater than 1, demand is elastic; if it is less than 1, demand is inelastic; if it is exactly 1, demand is unit-elastic. This classification determines how total revenue, the total value of sales, changes when the price changes. The price elasticity of demand depends on whethere are close substitutes for the good, whether the good is a necessity or a luxury, the share of income spent on the good, and the length of time that has elapsed since the price change. The cross-price elasticity of demand measures the effect of a change in one good’s price on the quantity of another good demanded.

Summary 7. 8. 3 of 5 The income elasticity of demand is the percent change in the quantity of a good demanded when a consumer’s income changes divided by the percent change in income. If the income elasticity is greater than 1, a good is income elastic; if it is positive and less than 1, the good is income-inelastic. The price elasticity of supply is the percent change in the quantity of a good supplied divided by the percent change in the price. If the quantity supplied does not change at all, we have an instance of perfectly inelastic supply; the supply curve is a vertical line. If the quantity supplied is zero below some price but infinite above that price, we have an instance of perfectly elastic supply; the supply curve is a horizontal line.

Summary 9. 10. 11. 4 of 5 The price elasticity of supply depends on the availability of resources to expand production and ontime. It is higher when inputs are available at low cost and the longer the time since price change. “Excise taxes” (taxes on the purchase/sale of a good) raise the price paid by consumers and reduce the price received by producers, driving a wedge between the two. The incidence of the tax (how burden of tax is divided between consumers and producers) does not depend on who officially pays the tax. The incidence of an excise tax depends on the price elasticities of supply and demand. If the price elasticity of demand is higher than the price elasticity of supply, the tax falls mainly on producers; if the price elasticity of supply is higher than the price elasticity of demand, the tax falls mainly on consumers.

Summary 12. 13. 5 of 5 The tax revenue generated by a tax depends on the tax rate and on the number of units transacted with the tax. Excise taxes cause inefficiency in the form of deadweight loss because they discourage some mutually beneficial transactions. Taxes also impose administrative costs—resources used to collect the tax. An excise tax generates revenue for the government, but lowers total surplus. The loss in total surplus exceeds the tax revenue, resulting in a deadweight loss to society. This deadweight loss is represented by a triangle, the area of which equals the value of the transactions discouraged by the tax. The greater the elasticity of demand or supply, or both, the larger the deadweight loss from a tax. If either demand or supply is perfectly inelastic, there is no deadweight loss from a tax.

The End of Chapter 5 Coming attraction Chapter 6: Behind the Supply Curve: Inputs and Costs