In this chapter, look for the answers to these questions: • What is elasticity? What kinds of issues can elasticity help us understand? • What is the price elasticity of demand? How is it related to the demand curve? How is it related to revenue & expenditure? • What is the price elasticity of supply? How is it related to the supply curve? • What are the income and cross-price elasticities of demand? © 2007 Thomson South-Western A scenario… You design websites for local businesses. You charge $200 per website, and currently sell 12 websites per month. Your costs are rising (including the opp. cost of your time), so you’re thinking of raising the price to $250. The law of demand says that you won’t sell as many websites if you raise your price. How many fewer websites? How much will your revenue fall, or might it increase? © 2007 Thomson South-Western Elasticity . . . • … allows us to analyze supply and demand with greater precision. • … is a measure of how much buyers and sellers respond to changes in market conditions • Elasticity is a numerical measure of the responsiveness of Qd or Qs to one of its determinants. © 2007 Thomson South-Western THE ELASTICITY OF DEMAND • The price 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. • When we talk about elasticity, that responsiveness is always measured in percentage terms. • Specifically, the price elasticity of demand is the percentage change in quantity demanded due to a percentage change in the price. © 2007 Thomson South-Western © 2007 Thomson South-Western The Price Elasticity of Demand and Its Determinants • • • • • Availability of Close Substitutes Necessities versus Luxuries Definition of the Market Time Horizon Demand tends to be more elastic: • • • • the larger the number of close substitutes. if the good is a luxury. the more narrowly defined the market. the longer the time period. © 2007 Thomson South-Western 1 What determines price elasticity? To learn the determinants of price elasticity, we look at a series of examples. Each compares two common goods. In each example: • Suppose the prices of both goods rise by 20%. • The good for which Qd falls the most (in percent) has the highest price elasticity of demand. Which good is it? Why? • What lesson does the example teach us about the determinants of the price elasticity of demand? EXAMPLE 1: Rice Krispies vs. Sunscreen • The prices of both of these goods rise by 20%. For which good does Qd drop the most? Why? • Rice Krispies has lots of close substitutes (e.g., Cap’n Crunch, Count Chocula), so buyers can easily switch if the price rises. • Sunscreen has no close substitutes, so consumers would probably not buy much less if its price rises. • Lesson: Price elasticity is higher when close substitutes are available. © 2007 Thomson South-Western © 2007 Thomson South-Western EXAMPLE 2: EXAMPLE 3: “Blue Jeans” vs. “Clothing” Insulin vs. Caribbean Cruises • The prices of both goods rise by 20%. For which good does Qd drop the most? Why? • For a narrowly defined good such as blue jeans, there are many substitutes (khakis, shorts, Speedos). • There are fewer substitutes available for broadly defined goods. (Can you think of a substitute for clothing, other than living in a nudist colony?) • Lesson: Price elasticity is higher for narrowly defined goods than broadly defined ones. • The prices of both of these goods rise by 20%. For which good does Qd drop the most? Why? • To millions of diabetics, insulin is a necessity. A rise in its price would cause little or no decrease in demand. • A cruise is a luxury. If the price rises, some people will forego it. • Lesson: Price elasticity is higher for luxuries than for necessities. © 2007 Thomson South-Western EXAMPLE 4: Gasoline in the Short Run vs. Gasoline in the Long Run • The price of gasoline rises 20%. Does Qd drop more in the short run or the long run? Why? • There’s not much people can do in the short run, other than ride the bus or carpool. • In the long run, people can buy smaller cars or live closer to where they work. • Lesson: Price elasticity is higher in the long run than the short run. © 2007 Thomson South-Western © 2007 Thomson South-Western Computing 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. Price elasticity of demand = Percentage change in quantity demanded Percentage change in price • Price elasticity of demand measures how much Qd responds to a change in P. • Loosely speaking, it measures the price-sensitivity of buyers’ demand. © 2007 Thomson South-Western 2 Computing the Price Elasticity of Demand • Example: If the price of an ice cream cone increases from $2.00 to $2.20 and the amount you buy falls from 10 to 8 cones, then your elasticity of demand would be calculated as: Price elasticity of demand = Percentage change in quantity demanded Percentage change in price (10 − 8) × 100 20% 10 = =2 (2.20 − 2.00) × 100 10% 2.00 Calculating Percentage Changes Standard method of computing the percentage (%) change: Demand for your websites end value – start value x 100% start value P $250 B Going from A to B, the % change in P equals A $200 D 8 12 ($250–$200)/$200 = 25% Q © 2007 Thomson South-Western Calculating Percentage Changes Demand for your websites P $250 B A $200 D 8 12 Q © 2007 Thomson South-Western Calculating Percentage Changes Problem: The standard method gives different answers depending on where you start. From A to B, P rises 25%, Q falls 33%, elasticity = 33/25 = 1.33 • So, we instead use the midpoint method: From B to A, P falls 20%, Q rises 50%, elasticity = 50/20 = 2.50 • It doesn’t matter which value you use as the “start” and which as the “end” – you get the same answer either way! end value – start value x 100% midpoint • The midpoint is the number halfway between the start & end values, also the average of those values. © 2007 Thomson South-Western © 2007 Thomson South-Western The Midpoint Method: A Better Way to Calculate Percentage Changes and Elasticities The Midpoint Method: A Better Way to Calculate Percentage Changes and Elasticities • The midpoint formula is preferable when calculating the price elasticity of demand because it gives the same answer regardless of the direction of the price change. • Example: If the price of an ice cream cone increases from $2.00 to $2.20 and the amount you buy falls from 10 to 8 cones, then your elasticity of demand, using the midpoint formula, would be calculated as: (Q − Q1 ) /[(Q2 + Q1 ) / 2] Price elasticity of demand = 2 ( P2 − P1 ) /[( P2 + P1 ) / 2] © 2007 Thomson South-Western (8 − 10) − 2 2 2 10 = 10 = − × = −2 (2.20 − 2.00) 0.2 10 0.2 2.00 2.00 © 2007 Thomson South-Western 3 Calculate an elasticity The Variety of Demand Curves Use the following information to calculate the price elasticity of demand for hotel rooms: • Inelastic Demand • Quantity demanded does not respond strongly to price changes. • Price elasticity of demand is less than one. if P = $70, Qd = 5000 if P = $90, Qd = 3000 • Elastic Demand Use midpoint method to calculate % change in Qd (3000 – 5000)/4000 = -50% • Quantity demanded responds strongly to changes in price. • Price elasticity of demand is greater than one. % change in P ($90 – $70)/$80 = 25% The price elasticity of demand equals -50%/25% = -2 18 © 2007 Thomson South-Western The Variety of Demand Curves Computing the Price Elasticity of Demand (100 − 50) ED = Price (100 + 50)/2 (4.00− 5.00) (4.00+ 5.00)/2 Demand = • Perfectly Inelastic • Quantity demanded does not respond to price changes. • Perfectly Elastic $5 4 © 2007 Thomson South-Western 67 percent = −3 − 22 percent • Quantity demanded changes infinitely with any change in price. • Unit Elastic 0 50 100 Quantity Demand is price elastic. • Quantity demanded changes by the same percentage as the price. © 2007 Thomson South-Western © 2007 Thomson South-Western The Variety of Demand Curves Figure 1 The Price Elasticity of Demand • 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 it is not the same thing as the slope! (a) Perfectly Inelastic Demand: Elasticity Equals 0 Price Demand $5 4 1. An increase in price . . . 0 100 Quantity 2. . . . leaves the quantity demanded unchanged. © 2007 Thomson South-Western © 2007 Thomson South-Western 4 Figure 1 The Price Elasticity of Demand Figure 1 The Price Elasticity of Demand (c) Unit Elastic Demand: Elasticity Equals 1 (b) Inelastic Demand: Elasticity Is Less Than 1 Price Price $5 $5 4 4 1. A 22% increase in price . . . 1. A 22% increase in price . . . Demand 0 90 0 Quantity 100 Demand 80 Quantity 100 2. . . . leads to a 22% decrease in quantity demanded. 2. . . . leads to an 11% decrease in quantity demanded. © 2007 Thomson South-Western Figure 1 The Price Elasticity of Demand © 2007 Thomson South-Western Figure 1 The Price Elasticity of Demand (d) Elastic Demand: Elasticity Is Greater Than 1 (e) Perfectly Elastic Demand: Elasticity Equals Infinity Price Price 1. At any price above $4, quantity demanded is zero. $5 4 Demand $4 Demand 1. A 22% increase in price . . . 2. At exactly $4, consumers will buy any quantity. 0 50 100 Quantity 2. . . . leads to a 67% decrease in quantity demanded. Quantity 0 3. At a price below $4, quantity demanded is infinite. © 2007 Thomson South-Western Total Revenue and the Price Elasticity of Demand • Total revenue is the amount paid by buyers and received by sellers of a good. • Continuing our scenario, if you raise your price from $200 to $250, would your revenue rise or fall? Revenue = P x Q • A price increase has two effects on revenue: • Higher P means more revenue on each unit you sell. • But you sell fewer units (lower Q), due to Law of Demand. © 2007 Thomson South-Western Figure 2 Total Revenue Price When the price is $4, consumers will demand 100 units, and spend $400 on this good. $4 P × Q = $400 (revenue) P Demand • Which of these two effects is bigger? It depends on the price elasticity of demand. 0 100 Q Quantity © 2007 Thomson South-Western © 2007 Thomson South-Western 5 Elasticity and Total Revenue along a Linear Demand Curve • With an inelastic demand curve, an increase in price leads to a decrease in quantity that is proportionately smaller. Thus, total revenue increases. • Total revenue = P x Q • If demand is inelastic, then price elast. of demand < 1 % change in Q < % change in P • The fall in revenue from lower Q is smaller than the increase in revenue from higher P, so revenue rises. Figure 3 How Total Revenue Changes When Price Changes: Inelastic Demand Price Price An Increase in price from $1 to $3 … … leads to an Increase in total revenue from $100 to $240 $3 Revenue = $240 $1 Demand Revenue = $100 Demand Quantity 100 0 Quantity 80 0 © 2007 Thomson South-Western © 2007 Thomson South-Western Elasticity and Total Revenue along a Linear Demand Curve • 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. • Total Revenue = P x Q • If demand is elastic, then price elast. of demand > 1 Figure 3 How Total Revenue Changes When Price Changes: Elastic Demand Price Price An Increase in price from $4 to $5 … … leads to an decrease in total revenue from $200 to $100 $5 $4 Demand Demand Revenue = $200 Revenue = $100 % change in Q > % change in P • The fall in revenue from lower Q is greater than the increase in revenue from higher P, so revenue falls. Quantity 50 0 0 Quantity 20 Note that with each price increase, the Law of Demand still holds – an increase in price leads to a decrease in the quantity demanded. It is the change in TR that varies! © 2007 Thomson South-Western © 2007 Thomson South-Western Elasticity of a Linear Demand Curve Figure 4 Elasticity of a Linear Demand Curve Demand is elastic; demand is responsive to changes in price. Price $7 When price increases from $4 to $5, TR declines from $24 to $20. Elasticity is > 1 in this range. 6 5 Elasticity is < 1 in this range. 4 Demand is inelastic; demand is not very responsive to changes in price. When price increases from $2 to $3, TR increases from $20 to $24. 3 2 1 0 © 2007 Thomson South-Western 2 4 6 8 10 12 14 Quantity © 2007 Thomson South-Western 6 Elasticity and expenditure/revenue A. B. Other Demand Elasticities Pharmacies raise the price of insulin by 10%. Does total expenditure on insulin rise or fall? Expenditure = P x Q Since demand is inelastic, Q will fall less than 10%, so expenditure rises. As a result of a fare war, the price of a luxury cruise falls 20%. Does luxury cruise companies’ total revenue rise or fall? Revenue = P x Q The fall in P reduces revenue, but Q increases, which increases revenue. Which effect is bigger? Since demand is elastic, Q will increase more than 20%, so revenue rises. • 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. 36 © 2007 Thomson South-Western © 2007 Thomson South-Western Other Demand Elasticities Other Demand Elasticities • Income Elasticity • Types of Goods • Normal Goods • Inferior Goods • Computing Income Elasticity • Recall from chap.4: An increase in income causes an increase in demand for a normal good. • Hence, for normal goods, income elasticity > 0. • For inferior goods, income elasticity < 0. • Higher income raises the quantity demanded for normal goods but lowers the quantity demanded for inferior goods. Remember, all elasticities are measured by dividing one percentage change by another • 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. © 2007 Thomson South-Western © 2007 Thomson South-Western Other Demand Elasticities • Cross-price elasticity of demand A measure of how much the quantity demanded of one good responds to a change in the price of another good, • Cross Price Elasticity= % change in quantity demanded of Good Y • of Demand % change in price of Good X Substitutes have positive cross-price elasticities, while complements have negative cross-price elasticities. The price of apples rises from $1.00 per pound to $1.50 per pound. As a result, the quantity of oranges demanded rises from 8,000 per week to 9,500. % change in quantity of oranges demanded = (9,500-8,000)/8,750 = .1714 = 17.14% % change in price of apples = (1.50-1.00)/1.25 = .40 = 40% cross-price elasticity = 17.14% / 40% = 0.43 Because the cross-price elasticity is positive, the two goods are substitutes. © 2007 Thomson South-Western THE ELASTICITY OF SUPPLY • 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. • Price elasticity of supply is the percentage change in quantity supplied resulting from a percentage change in price. © 2007 Thomson South-Western 7 Figure 5 The Price Elasticity of Supply Figure 5 The Price Elasticity of Supply (a) Perfectly Inelastic Supply: Elasticity Equals 0 (b) Inelastic Supply: Elasticity Is Less Than 1 Price Price Supply Supply $5 $5 4 4 1. An increase in price . . . 1. A 22% increase in price . . . 100 0 Quantity 100 0 110 Quantity 2. . . . leads to a 10% increase in quantity supplied. 2. . . . leaves the quantity supplied unchanged. © 2007 Thomson South-Western Figure 5 The Price Elasticity of Supply © 2007 Thomson South-Western Figure 5 The Price Elasticity of Supply (c) Unit Elastic Supply: Elasticity Equals 1 (d) Elastic Supply: Elasticity Is Greater Than 1 Price Price Supply Supply $5 $5 (If SUPPLY is unit elastic and linear, it will begin at the origin.) 4 1. A 22% increase in price . . . 100 0 125 Quantity 2. . . . leads to a 22% increase in quantity supplied. 4 1. A 22% increase in price . . . 100 0 200 © 2007 Thomson South-Western • Ability of sellers to change the amount of the good they produce. (e) Perfectly Elastic Supply: Elasticity Equals Infinity Price 1. At any price above $4, quantity supplied is infinite. • Beach-front land is inelastic. • Books, cars, or manufactured goods are elastic. Supply • Time period 2. At exactly $4, producers will supply any quantity. 0 3. At a price below $4, quantity supplied is zero. © 2007 Thomson South-Western The Price Elasticity of Supply and Its Determinants Figure 5 The Price Elasticity of Supply $4 Quantity 2. . . . leads to a 67% increase in quantity supplied. • Supply is more elastic in the long run. Quantity © 2007 Thomson South-Western © 2007 Thomson South-Western 8 Computing the Price 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. Percentage change in quantity supplied Price elasticity of supply = Percentage change in price THREE APPLICATIONS OF SUPPLY, DEMAND, AND 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 hybrid that is more productive than existing varieties? © 2007 Thomson South-Western Can Good News for Farming Be Bad News for Farmers? • 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. © 2007 Thomson South-Western Figure 7 An Increase in Supply in the Market for Wheat Price of Wheat 2. . . . leads to a large fall in price . . . 1. When demand is inelastic, an increase in supply . . . S1 S2 $3 2 Demand 0 100 110 Quantity of Wheat 3. . . . and a proportionately smaller increase in quantity sold. As a result, revenue falls from $300 to $220. © 2007 Thomson South-Western © 2007 Thomson South-Western Compute the Price Elasticity of Demand When There Is a Change in Supply • Supply and Demand can behave differently in the short run and the long run 100 − 110 (100 + 110) / 2 ED = 3.00 − 2.00 (3.00 + 2.00) / 2 = Why Did OPEC Fail to Keep the Price of Oil High? • In the short run, both supply and demand for oil are relatively inelastic • But in the long run, both are elastic −0.095 ≈ −0.24 0.4 • Production outside of OPEC • More conservation by consumers Demand is inelastic. © 2007 Thomson South-Western © 2007 Thomson South-Western 9 Does Drug Interdiction Increase or Decrease Drug-Related Crime? • One side effect of illegal drug use is crime: Users often turn to crime to finance their habit. • We examine two policies designed to reduce illegal drug use and see what effects they have on drug-related crime. • For simplicity, we assume the total dollar value of drug-related crime equals total expenditure on drugs. Does Drug Interdiction Increase or Decrease Drug-Related Crime? • Drug interdiction impacts sellers rather than buyers. • Demand is unchanged. • Equilibrium price rises although quantity falls. • Drug education impacts the buyers rather than sellers. • Demand is shifted. • Equilibrium price and quantity are lowered. • Demand for illegal drugs is inelastic, due to addiction issues. © 2007 Thomson South-Western Policy 1: Interdiction Interdiction reduces Price of Drugs the supply of drugs. P2 Since demand for drugs is inelastic, P1 P rises proportionally more than Q falls. Result: an increase in total spending on drugs, and in drug-related crime © 2007 Thomson South-Western Policy 2: Education new value of drugrelated crime S2 D1 S1 initial value of drugrelated crime Q2 Q1 Quantity of Drugs © 2007 Thomson South-Western Education reduces the demand for drugs. Price of Drugs new value of drugrelated crime D2 D1 S P and Q fall. Result: A decrease in total spending on drugs, and in drug-related crime. initial value of drugrelated crime P1 P2 Q2 Q1 Quantity of Drugs © 2007 Thomson South-Western 10