Elasticity and applications. Elasticity. Price elasticity of demand. Two demand curves

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1 Elasticity Elasticity and applications Law of demand: The demand curve is downward-sloping. As price rises quantity demanded falls, [as price falls quantity demanded rises]. Two markets: public transportation vs movie theaters In 1984, the City of Chicago wanted to attract more transit riders with lower fares. J. L. Shofer, research director at Northwestern University s Transportation Center, wrote: Lower fares never make up for loss of revenues. Even when losing riders by increasing fares, revenue usually goes up. It s a law of economics. The law of demand is too general and not useful in analyzing the case above. We often need more (precise) information. P P 1 P 2 Two demand curves D b D a Q Q 1 Q 2 Q 3 As P decreases from P 1 to P 2, QD increases along both demand curves D a and D b. However, an equal decrease in price results in a smaller increase in QD in demand curve D a, in a larger increase in QD for demand curve D b. Curve D a is relatively less responsive to price changes whereas curve D b is relatively more responsive. elasticity of demand elasticity of demand is a measure of how much the quantity demanded of a good responds to a change in the price of that good. elasticity of demand is the percentage change in quantity demanded given a percent change in the price. If the amount of any good that people purchase changes a lot in response to a small price change, we say DEMAND IS ELASTIC If a large price change results in a small change in the amount that people purchase, we say DEMAND IS INELASTIC 1

2 elasticity of demand The determinants of the price elasticity of demand: Availability of Close Substitutes Necessities versus Luxuries Definition of the Market Time Horizon tends to be more elastic: If there are a large number of close substitutes. If the good is a luxury. If the market is more narrowly defined (food versus milk). If we consider a longer time period after the price change. How to compute the price elasticity of demand? The price elasticity of demand is computed as the percentage change in the quantity demanded divided by the percentage change in price. elasticity of demand (E ) P Percentage changeinquantity demand Percentage changeinprice 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. BUT, slope is not elasticity!! elasticity of demand: Examples % increase in the price of eggs leads to 5% reduction in the number of eggs sold. What is the price elasticity of demand? Answer: elasticity of demand for eggs is If the (price) elasticity of red apples is -0.8, then a one percent increase in the price of red apples will lead to a 0.8 percent decrease (or, 0.8 % decrease) in the quantity of red apples demanded. If the (price) elasticity of red apples is -0.8, then a 5 percent increase in the price of red apples, will lead to a 5 x 0.8 = 4 percent decrease in the quantity of red apples demanded. How to Calculate Percentage Changes in the Elasticity formula (the midpoint method)? The midpoint formula is preferable when calculating the price elasticity of demand because it gives the same answer regardless of the direction of the change. (Q 2 - Q 1 ) / [(Q 2 + Q 1 ) / 2] elasticity of demand (E P ) = (P 2 - P 1 ) / [(P 2 + P 1 ) / 2] elasticity of demand (E ) P Percentage changeinquantity demand Percentage changeinprice 2

3 Example using the Midpoint Method Point A: = $4 = 120 Point B: = $6 = 80 From Point A to Point B: rise = 50% and fall = 33% From Point B to Point A: fall = 33% and rise = 50% elasticity of demand (E P ) = Mid point method = -1 (80-120) / [( )/ 2] (6-4) / [(6 + 4)/ 2] Elastic versus inelastic demand curves Roughly, Inelastic demanded does not respond strongly to price changes. elasticity of demand is less than one. Elastic demanded responds strongly to changes in price. elasticity of demand is greater than one. Formally, If E P > 1, demand is (price) elastic. If E P < 1, demand is (price) inelastic. If E P = 1, demand is (price) unit elastic. A very important remark: Because price and quantity are negatively related along the (typical) demand curve, E P is (always) negative. Remark on elasticity calculation Elasticity calculation can be tricky, because there are many (simultaneous) influences on demand and supply. (See the example below.) Consider a demand curve drawn on the P vs. Q graph. E P is a measure that corresponds to movements up and down the demand curve. But changes in other variables (shown as shifts in the P vs. Q graph) also impact price and quantity. To calculate E P correctly, we have to make sure that all else is held constant. Remark on elasticity calculation The following data show the prices of X and Y, the annual income of the consumer, and the quantities of X consumed during the last 6 years. Year P X ($) Q X P Y ($) Income ($) , , , , , ,000 (a) Which pair of years would you use to calculate the price elasticity of demand for X? Why? (b) What is the price elasticity of demand for X? 3

4 Particular demand curves 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. Perfectly Inelastic 1. An increase in price E = leaves the quantity demanded unchanged. Inelastic Unit Elastic E < 1 E = 1 1. A 22% increase 1. A 22% increase Leads to a 11% decrease in quantity demanded Leads to a 22% decrease in quantity demanded. 4

5 Elastic Perfectly Elastic E > 1 E = 1. At any price above $4, quantity demanded is zero. 1. A 22% increase 2. At exactly $4, consumers will buy any quantity. 3. At any price below $4, quantity demanded is infinite Leads to a 67% decrease in quantity demanded. 0 Total Revenue and the price elasticity of demand Remember the quotation: In 1984, the City of Chicago wanted to attract more transit riders with lower fares. J. L. Shofer, research director at Northwestern University s Transportation Center, wrote: Lower fares never make up for loss of revenues. Even when losing riders by increasing fares, revenue usually goes up. It s a law of economics. Total revenue is the amount paid by buyers and received by sellers of a good and computed as the price of the good times the quantity sold. TR = P x Q $3.00 $1.00 Inelastic : How does total revenue change when prices change? With an inelastic demand curve, an increase in the price leads to a decrease in quantity demanded that is proportionately smaller. Thus, total revenue increases when price increases. P x Q = $240 (revenue) P x Q = $100 (revenue)

6 Elastic : How does total revenue change when prices change? With an elastic demand curve, an increase in the price leads to a decrease in quantity demanded that is proportionately larger. Thus, total revenue decreases when price increases. Elasticity along a linear demand curve Elasticity is larger than Elasticity is smaller than 1. Revenue = $ Revenue = $ Elasticity and Total Revenue along a Linear Curve Income elasticity of demand Income elasticity of demand measures 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. Percentage change in quantity demanded Income elasticity of demand = Percentage change in income 6

7 Income elasticity of demand Income elasticity of demand measures 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. Percentage change in quantity demanded Income elasticity of demand = Percentage change in income Income elasticity of demand 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. Higher income raises the quantity demanded for normal goods but lowers the quantity demanded for inferior goods. Thus, income elasticity of demand is positive for normal goods and negative for inferior goods. Cross price elasticity of demand Cross- elasticity of demand measures how much the quantity demanded of a good responds to a change in the price of another good. It is computed as the percentage change in the quantity demanded divided by the percentage change in the price of the other good. The cross elasticity of the demand for good X with respect to the price of good Y is defined as: Cross price elasticity of demand = Percentage change in quantity demanded of good X Percentage change in the price of good Y Cross price elasticity of demand Cross- elasticity of demand measures how much the quantity demanded of a good responds to a change in the price of another good. It is computed as the percentage change in the quantity demanded divided by the percentage change in the price of the other good. The cross elasticity of the demand for good X with respect to the price of good Y is defined as: Cross price elasticity of demand = Percentage change in quantity demanded of good X Percentage change in the price of good Y Cross elasticity is positive if X and Y are substitutes, and it is negative if X and Y are complements. (Why?) 7

8 elasticity of supply The price elasticity of supply is a measure of how much the quantity supplied of a good responds to a change in the price of that good. The price elasticity of supply is computed as the percentage change in the quantity supplied divided by the percentage change in price. Ability of sellers to change the amount of the good they produce. Beach-front land is inelastic. Books, cars, or manufactured goods are elastic. Supply is more elastic in the long run. elasticity of supply: an example Suppose an increase in the price of milk from $1.90 to $2.10 per liter raises the amount that dairy farmers produce from 9000 to liters (per month) using the midpoint method, we calculate the percent change in the price as ( ) / 2.00 x 100 = 10% Similarly, we calculate the percent change in the quantity supplied as (11,000 9,000) / 10,000 x 100 = 20% 20% elasticity of supply = 10% = 2.0 Percentage change in quantity supplied elasticity of supply = Percentage change in price Perfectly Inelastic Supply Inelastic Supply Supply E = 0 Supply E < 0 1. An increase in price 1. A 22% increase leaves the quantity supplied unchanged leads to a 10% increase in quantity supplied. 8

9 Unit Elastic Supply Elastic Supply E = 1 E > 1 Supply Supply 1. A 22% increase 1. A 22% increase leads to a 22% increase in quantity supplied leads to a 67% increase in quantity supplied. Perfectly Elastic Supply How the price elasticity of supply can vary? E = $15 Elasticity is less than 1 $12 1. At any price above $4, quantity supplied is infinite. Supply 2. At exactly $4, producers will supply any quantity. 3. At any price below $4, quantity supplied is zero. $4 $3 Elasticity is greater than

10 Elasticity of supply: examples When the price of DaVinci paintings increases by 1% the quantity supplied doesn't change at all, so the quantity supplied of DaVinci paintings is completely insensitive to the price. elasticity of supply is 0. When the price of beef increases by 1% the quantity supplied increases by 5%, so beef supply is very price sensitive. elasticity of supply is 5. Three applications of supply, demand, and elasticity Good news vs bad news for farmers OPEC Drugs and crime Teen smokers Gasoline tax decreases accidents. Application 1: Good news vs bad news for the farmers Application 2: OECD of Wheat 1. When demand is inelastic, an increase in supply Increase in Supply of Oil (a) Oil Market in the Short Run 1. In the short run, when supply and demand are inelastic, a shift in supply of Oil (b) Oil Market in the Long Run S 2 S 2 1. In the long run, when supply and demand are elastic, a shift in supply S 2 $3 $2 P 2 P 2 P 1 2. leads to a fall in price of Wheat P 1 2. leads to a large increase 2. leads to a small increase in price 3. and a proportionately smaller increase in quantity sold. As a result revenue falls from $300 to $220. of Oil of Oil 10

11 of Drugs Application 3: Drugs and Crime (a) Drug Interdiction (b) Drug Education of 1. Drug interdiction reduces the supply Drugs of drugs 1. Drug education reduces the demand S 2 for drugs Application 3: Drugs and Crime How elasticity affects the market for illegal goods In an important new study, world-renowned economists argue that when demand for a good is inelastic, the cost of making consumption illegal exceeds the gain. Their forthcoming paper in the Journal of Political Economy is a definitive explanation of the economics of illegal goods and a thoughtful explication of the costs of enforcement. P 2 P 1 2. which raises the price Q 2 Q 1 P 1 P 2 2. which reduces the price of Drugs Q 2 Q 1 D 2 D 1 of Drugs The authors demonstrate how the elasticity of demand is crucial to understanding the effects of punishment on suppliers. Enforcement raises costs for suppliers, who must respond to the risk of imprisonment and other punishments. This cost is passed on to the consumer, which induces lower consumption when demand is relatively elastic. However, in the case of illegal goods like drugs--where demand seems inelastic--higher prices lead not to less use, but to an increase in total spending. In the case of drugs, then, the authors argue that excise taxes and persuasive techniques such as advertising-- are far more effective uses of enforcement expenditures. "This analysis helps us understand why the War on Drugs has been so difficult to win why efforts to reduce the supply of drugs leads to violence and greater power to street gangs and drug cartels," conclude the authors. "The answer lies in the basic theory of enforcement developed in this paper." 3. and reduces the quantity sold. 3. and reduces the quantity sold. Application 4: Teen smokers Elasticity of cigarettes U.S. has increased taxes on cigarettes dramatically in the past 5 years. A majority of adult smokers have sucked it up and continued smoking. Dr. Thomas R. Frieden, the commissioner of the city Department of Health and Mental Hygiene in New York has conducted several surveys among young adult and teen smokers. City and state tobacco taxes, which have been gradually rising in recent years and now add $3 to the price of each pack of cigarettes, for a total of $5.50 or more. Kids are most susceptible to price because they don t have a whole lot of disposable income, Dr. Frieden said. So when you increase the price of cigarettes, you drive smoking down generally among adults but especially for teens. Raising the taxes will have a much more noticeable effect short term users. The older (faithful users) they are less sensitive to price changes. Source: A. RAMIREZ, New York Times, Published: January 3, 2008 Teenagers in the City Smoke Less, Report Finds Application 5: Gasoline tax decreases accidents In a 1996 article in the Energy Journal, authors Jonathan Haughton and Soumodip Sarkar attempt to answer the question of what impact a $1 gasoline tax increase would have on driving and accidents. They submit that with a gas tax of $1, miles driven would decrease by up to 12% and fatalities by up to 18%. How do they get to these results? By estimating and using the own-price elasticity of gasoline to calculate the impact on gasoline consumption. The retail price of gasoline in 1991 was $1.13, of which 28% or $0.32 was tax. Assuming that the entire tax increase is applied to the price, this means a price increase of $0.68, or 46%. The long run own-price elasticity of demand for gasoline over a ten-year period was calculated to be in the range to Using this knowledge we can calculate the change in consumption: %ΔQ/46% = %ΔQ = * 46% = -10.6% %ΔQ/46% = %ΔQ = * 46% = -16.1% Without going into the effect on accidents, we can still determine that a gas tax of $1 would decrease gas consumption by between 10.6% and 16.1%. Source: Haughton, J. & Sarkar, S. (1996) Gasoline Tax as a Corrective Tax: Estimates for the United States, , Energy Journal vol 17 no 2 p

12 Why do economists use elasticity? Economists want to compare apples and oranges all the time. Is oil market demand more price sensitive than wheat demand? (no) Is the labor supply of women more wage sensitive than the labor supply of men? (yes) An elasticity is a unit-free measure. By comparing markets using elasticities, it does not matter how we measure the price or the quantity in the two markets. Elasticities allow economists to quantify the differences among markets without standardizing the units of measurement. Examples of unit-free comparisons Gasoline and jewelry It doesn't matter that gas is sold by the gallon for about $1.09 and gold is sold by the ounce for about $290. We compare the demand elasticities of -0.2 (gas) and -2.6 (gold jewelry). Gold jewelry demand is more price sensitive. Paintings and meat It doesn't matter that classical paintings are sold by the canvas for millions of dollars each while beef is sold by the pound for about $1.50. We compare the supply elasticities of 0 (classical paintings) and 5 (beef). Beef supply is more price sensitive. Summary elasticity of demand measures how much the quantity demanded responds to changes in the price. elasticity of demand is calculated as the percentage change in quantity demanded divided by the percentage change in 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 income elasticity of demand measures how much the quantity demanded responds to changes in consumers income. The cross-price elasticity of demand measures how much the quantity demanded of one good responds to the price of another good. The price elasticity of supply measures how much the quantity supplied responds to changes in the price. 12

13 Summary In most markets, supply is more elastic in the long run than in the short run. The price elasticity of supply is calculated as the percentage change in quantity supplied divided by the percentage change in price. The tools of supply and demand can be applied in many different types of markets. 13