# Elasticity. Ratio of Percentage Changes. Elasticity and Its Application. Price Elasticity of Demand. Price Elasticity of Demand. Elasticity...

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1 Elasticity and Its Application Chapter 5 All rights reserved. Copyright 21 by Harcourt, Inc. Requests for permission to make copies of any part of the work should be mailed to: Permissions Department, Harcourt College Publishers, 6277 Sea Harbor Drive, Orlando, Florida Elasticity Ratio of Percentage Changes i.e. The percentage change in something over the percentage change in something. Elasticity... is a measure of how much buyers and sellers respond to changes in market conditions allows us to analyze supply and demand with greater precision. Elasticity of elasticity of demandis the percentage change in quantity demanded given a percent change in the price. It is a measure of how much the quantity demanded of a good responds to a change in the price of that good. Elasticity of for a good is said to be elastic if the quantity demanded responds substantially to a change in price. is said to be inelastic if the quantity demanded responds only slightly to changes in the price. Determinants of Elasticity of Necessities versus Luxuries Availability of Close Substitutes Definition of the Market Time Horizon 1

2 Necessities vs. Luxuries Necessities tend to have inelastic demands. Ex. Going to the doctor. Luxuries tend to have elastic demands. Ex. Buying a yacht. Availability of Close Substitutes Goods with close substitutes tend to have a more elastic demand because it is easier for consumers to switch from that good. Ex. Butter vs. Margarine. A small in the price of butter (assuming the price of margarine stays fixed) could cause a significant decline in the quantity of butter purchased. Definition of the Market The elasticity of demand depends on how we draw the boundaries of the market. Narrowly defined markets tend to be more elastic. Ex. The market for white Adidas running shoes. Broadly defined markets tend to be more inelastic. Ex. The market for shoes. Time Horizon Goods tend to have more elastic demand over longer time horizons. Ex. Gas prices rise. In the short run, people will probably buy somewhat less gas. However, in the long run, people may purchase more fuel efficient cars or move closer to work. Computing the Elasticity of The price elasticity of demand is computed as the percentage change in the quantity demanded divided by the percentage change in price. Percentage Change in ed Elasticity of = Percentage Change in Computing the Elasticity of elasticityof demand = Percentage change inquatity demanded Percentage change in price Example: If the price of an ice cream cone s from \$2. to \$2.2 and the amount you buy falls from 1 to 8 cones then your elasticity of demand would be calculated as: ( 1 8) percent = = 2 ( ) 1 percent

3 Computing the Elasticity of Using the Midpoint Formula The midpoint formula is preferable when calculating the price elasticity of demand because it gives the same answer regardless of the which point we start at. (Q2 Q1)/[(Q 2 + Q 1)/2] Elasticity of= (P P )/[(P + P )/2] Ranges of Elasticity Inelastic demanded does not respond strongly to price changes. elasticity of demand is less thanone. Elastic demanded responds strongly to changes in price. elasticity of demand is greater thanone. Computing the Elasticity of 5 1 E D (1-5) (1+ 5)/2 = (.-5.) (.+ 5.)/2 67percent = = -3-22percent is price elastic Elasticity Example Here are two points of a demand curve. Calculate the elasticity between these two points and determine if the elasticity is elastic, unit elastic, or inelastic. Pt A: P=5, Q=2 Pt B: P=2, Q= A Variety of Curves Because the price elasticity of demand measures how much quantity demanded responds to the price, it is closely related to the slope of the demand curve. Ranges of Elasticity Perfectly Inelastic demanded does not respond to price changes. Perfectly Elastic demanded changes infinitely with any change in price. Unit Elastic demanded changes by the same percentage as the price. 3

4 Perfectly Inelastic - Elasticity equals Inelastic - Elasticity is less than 1 1. An leaves the quantity demanded unchanged leads to a 11% decrease in quantity. Unit Elastic - Elasticity equals 1 Elastic - Elasticity is greater than leads to a 22% decrease in quantity leads to a 67% decrease in quantity. Perfectly Elastic - Elasticity equals infinity \$ 1. At any price above \$, quantity demanded is zero. 3. At a price below \$, quantity demanded is infinite. 2. At exactly \$, consumers will buy any quantity. Elasticity and Total Revenue Total revenue is the amount paid by buyers and received by sellers of a good. TR = * Another term that has a very similar meaning is total expenditures. Total revenue equals total expenditures. Revenue is the term used from the sellers perspective Expenditures is the term used from the buyers perspective.

5 \$ P Elasticity and Total Revenue P x Q = \$ (total revenue) Q 1 Elasticity and Total Revenue With an inelastic demand curve, an in price leads to a decrease in quantity that is proportionately smaller. Thus, total revenue s. Elasticity and Total Revenue: Inelastic Elasticity and Total Revenue \$1 Revenue = \$1 An in price from \$1 to \$ \$3 leads to an in total revenue from\$1 to \$2 Revenue = \$2 8 With an elastic demand curve, an in the price leads to a decrease in quantity demanded that is proportionately larger. Thus, total revenue decreases. \$ Elasticity and Total Revenue: Elastic An in price from \$ to... Revenue = \$2 leads to a decrease in total revenue from\$2 to \$1 Revenue = \$1 Elasticity and Total Revenue How Total Revenue is Affected by a Change in Elastic (ED,P > 1) Unit Elastic (ED,P = 1) Inelastic (ED,P < 1) fl No Change No Change fl 5 2 Ex. As price s for an elastic demand, total revenue decrease. 5

6 Computing the Elasticity of a Linear Curve Total Revenue ( x ) Percent Change in Elasticity Description Percent Change in \$ 1 \$ 2% 15%.1 Inelastic Inelastic Inelastic Unit elastic elastic elastic elastic 7 Class Example The price of a cd player rises from \$1 to \$15, while the quantity demanded falls from 12 to 9. Calculate the price elasticity of demand. Is demand elastic, unit elastic, or inelastic. Calculate total revenue before and after the price rise. Calculate the % change in quantity demanded if price rises another 5%. Remember: E D,P = %?Q / %?P Class Example - Solutions elasticity of demand =.71 is inelastic. TR when P = 1: \$12, TR when P = 15: \$135, If P rises by 5%, we would expect to see Q decrease by 3.55% Income Elasticity of Income elasticity of demandmeasures how much the quantity demanded of a good responds to a change in consumers income. It is computed as the percentage change in the quantity demanded divided by the percentage change in income. Computing Income Elasticity Income Elasticity of = Percentage Change in ed Percentage Change in Income Elasticity of demand with respect to income. Normal Goods Inferior Goods Income Elasticity - Types of Goods - Higher income raises the quantity demanded for normal goods but lowers the quantity demanded for inferior goods. E D,I 6

7 Income Elasticity Normal goods will have an income elasticity that is greater than zero. Why? Inferior goods will have an income elasticity that is less than zero. Why? Income Elasticity Example (Q A -Q B )(I A +I B ) / (Q A +Q B )(I A -I B ) When your income = \$1,, your demand for mac & cheese is 2. When your income = \$3,, your demand for mac & cheese is 15. Calculate the income elasticity and determine if mac & cheese is a normal or inferior good. Income Elasticity - Types of Goods - Goods consumers regard as necessities tend to be income inelastic Examples include food, fuel, clothing, utilities, and medical services. Goods consumers regard as luxuries tend to be income elastic. Examples include sports cars, furs, and expensive foods. Income Elasticity Necessities will have an income elasticity that is less than 1. Luxuries will have an income elasticity that is greater than 1. Income Elasticity Example When your income = \$1,, your quantity demanded for concerts is 1. When your income = \$3,, your quantity demanded for concerts is 12. Calculate income elasticity and determine if concert tickets are a necessity or luxury to you. Cross Elasticity This is a measure of how much the quantity demanded of one good responds to a change in the price of another good. Cross Elasticity is calculated as the percentage change in quantity demanded of the first good divided by the percentage change in the price of the second good. 7

8 Cross Elasticity Whether cross price elasticity is positive or negative depends on whether the two goods are substitutes or complements. Substitutes will have a cross price elasticity that is greater than zero. Complements will have a cross price elasticity that is less than zero. Cross Elasticity Ex. Suppose the percentage change for the quantity demanded for good X decreased 25% while the percentage change in the price of good Y by 5% What is the cross price elasticity and are the goods substitutes or complements? Cross price elasticity = -.5 => Complements Elasticity of Supply elasticity of supply is the percentage change in quantity supplied resulting from a percent change in price. It is a measure of how much the quantity supplied of a good responds to a change in the price of that good. Determinants of Elasticity of Supply Ability of sellers to change the amount of the good they produce. Beach -front land is inelastic. Books, cars, or manufactured goods are elastic. Time period. Supply is more elastic in the long run. Computing the Elasticity of Supply The price elasticity of supply is computed as the percentage change in the quantity supplied divided by the percentage change in price. Elasticity of Supply = Percentage Change in Supplied Percentage Change in Ranges of Elasticity Perfectly Elastic E S = Relatively Elastic E S > 1 Unit Elastic E S = 1 8

9 Ranges of Elasticity Relatively Inelastic E S < 1 Perfectly Inelastic E S = Perfectly Inelastic Supply - Elasticity equals 1. An Supply leaves the quantity supplied unchanged. Inelastic Supply - Elasticity is less than 1 Unit Elastic Supply - Elasticity equals 1 Supply Supply leads to a 1% in quantity leads to a 22% in quantity. Elastic Supply - Elasticity is greater than 1 Supply Perfectly Elastic Supply - Elasticity equals infinity \$ 1. At any price above \$, quantity supplied is infinite. 2. At exactly \$, producers will supply any quantity. Supply leads to a 67% in quantity. 3. At a price below \$, quantity supplied is zero. 9

10 Application of Elasticity Can good news for farming be bad news for farmers? What happens to wheat farmers and the market for wheat when university agronomists discover a new wheat hybridthat is more productive than existing varieties? Application of Elasticity Examine whether the supply or demand curve shifts. Determine the direction of the shift of the curve. Use the supply-and-demand diagram to see how the market equilibrium changes. An Increase in Supply in the Market for Wheat of Wheat \$3 S 1 An Increase in Supply in the Market for Wheat of Wheat 2....leads to a large fall in price... \$ When demand is inelastic, an in supply... S 1 S 2 1 of Wheat 1 11 of Wheat 3....and a proportionately smaller in quantity sold. As a result, revenue falls from \$3 to \$22. Compute Elasticity 1-11 (1 + 11)/2 E D = ( )/ = -.2. Does Drug Interdiction Increase or Decrease Drug Related Crime? One adverse effect of drug use is that drug addicts often turn to robbery and other violent crimes to obtain the money needed to support their habit. The government spends billions of dollars each year to reduce the flow of drugs into this country. Let s see how this works. 1

11 Does Drug Interdiction Increase or Decrease Drug Related Crime? When the government stops some drugs from entering the country and arrests more smugglers, it raises the cost of selling drugs. How does this affect supply? Do you think that the demand for drugs is elastic or inelastic? Does Drug Interdiction Increase or Decrease Drug Related Crime? An in total expenditures means that the drug addicts now have to spend more for their drugs and this may lead to even more crime, when we the government was trying to reduce crime. In the long run, this may encourage people to break their habit and also discourage the number of new users. Compute Elasticity 1-11 (1 + 11)/2 E D = ( )/ = -.2. is inelastic Summary elasticity of demand measures how much the quantity demanded responds to changes in the price. If a demand curve is elastic, total revenue falls when the price rises. If it is inelastic, total revenue rises as the price rises. Summary The price elasticity of supply measures how much the quantity supplied responds to changes in the price. In most markets, supply is more elastic in the long run than in the short run. 11

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