# ELASTICITY AND ITS APPLICATION. J. Mao

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1 ELASTICITY AND ITS APPLICATION J. Mao

2 Elasticity Until now, we ve been talking about the direction in which quantities change. A downward-sloping demand: price é è quantity demanded ê In real life it is quite important to know the intensity of the change (how much) By how much will the demand for my product decrease if I increase the price by 10%?

3 Elasticity Elasticity: a measure of the responsiveness of quantity demanded or quantity supplied to a change in one of their determinants Price elasticity of demand measures how much quantity demanded changes in response to a change in price.

4 Price elasticity of demand Price elasticity of demand = Percentage change in Q d Percentage change in P

5 Price elasticity of demand Price elasticity of demand = Percentage change in Q d Percentage change in P Example: P Price elasticity of demand equals P rises by 10% P 2 P 1 D 15% 10% = 1.5 Q falls by 15% Q 2 Q 1 Q 5

6 Price Elasticity of Demand Elasticity is unit free: Allows comparison of price sensitivity across markets. Car market and T-shirt market Xiamen market and China market

7 Price elasticity of demand Formally, Price elasticity of demand d,p = dq/q dp/p = dq/q dp/p (Q 2 Q 1 )/ 1 2 (Q 1+Q 2 ) (P 2 P 1 )/ 1 2 (P 1+P 2 )

8 Prof Jonathan Wolff ( Department PrinciplesofofEconomics Micro Economics University of Notre Dame) September 10th, 2012

9 Elasticity Prof Jonathan Wolff ( Department PrinciplesofofEconomics Micro Economics University of Notre Dame) September 10th, /

10 Price Elasticity of Demand The price elasticity of demand is closely related to the slope of the demand curve. Rule of thumb: The flatter the curve, the bigger the elasticity. The steeper the curve, the smaller the elasticity.

11 Perfectly inelastic demand (one extreme case) Price elasticity of demand = % change in Q % change in P = 0% 10% = 0 D curve: vertical P D Consumers price sensitivity: none P 1 P 2 Elasticity: 0 P falls by 10% Q 1 Q changes by 0% Q 20

12 Inelastic demand Price elasticity of demand = % change in Q % change in P = < 10% 10% < 1 D curve: relatively steep P Consumers price sensitivity: relatively low P 1 P 2 D Elasticity: < 1 P falls by 10% Q 1 Q 2 Q rises less than 10% Q 21

13 Unit elastic demand Price elasticity of demand = % change in Q % change in P = 10% 10% = 1 D curve: intermediate slope P Consumers price sensitivity: intermediate P 1 P 2 D Elasticity: 1 P falls by 10% Q 1 Q 2 Q Q rises by 10%

14 Elastic demand Price elasticity of demand = % change in Q % change in P = > 10% 10% > 1 D curve: relatively flat P Consumers price sensitivity: relatively high P 1 P 2 D Elasticity: > 1 P falls by 10% Q 1 Q 2 Q rises more than 10% Q 23

15 Perfectly elastic demand (the other extreme) Price elasticity of demand = % change in Q % change in P = any % 0% = infinity D curve: horizontal Consumers price sensitivity: extreme P 2 = P 1 P D Elasticity: infinity P changes by 0% Q 1 Q 2 Q changes by any % Q 24

16 Price elasticity of demand > 1 < 1 =1 =0!1 Elastic Inelastic Unit Elastic Perfectly inelastic Perfectly elastic

17 Price Elasticity of Demand When two demand curves cross 12 P/Q is the same for both curves (1/slope) is smaller for the steeper curve At the common point demand is less price elastic for the steeper curve Price 6 4 D 1 Less Elastic More Elastic D Quantity

18 Price Elasticity along a Linear Demand Curve At the midpoint, demand is unit elastic At high P and low Q, demand is elastic At low P and high Q, P/Q is small a 1 1 Price a/2 1 b/2 Quantity b

19 What determines Price Elasticity?

20 Availability of Close Substitutes McDonalds Cheeseburgers vs. Hubble Telescopes Price elasticity is higher when there exist close substitutes

21 Necessities vs Luxuries Insulin" vs. Caribbean Cruise" Necessities are more price inelastic Luxuries are more price elastic

22 Definition of the market Macbook Air" vs. Laptop Computers Price elasticity is higher for narrowly defined goods than more broadly defined ones

23 Time horizon Gasoline in the Short Run" vs Gasoline in the Long Run" Price elasticity is higher in the long run than in the short run.

24 Price Elasticity and Total Revenue Total Revenue/Expenditure = P x Q If you raise your price from \$2,000 to \$2,500, would your revenue rise or fall? A price increase has two effects on revenue: Higher P means more revenue on each unit But you sell fewer units (lower Q), due to law of demand Which of these two effects is bigger? It depends on the price elasticity of demand.

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28 How Total Revenue is affected by a change in price d (Total Revenue) dp = d (QP ) dp = dq dp P + Q Therefore, d (Total Revenue) dp d (Total Revenue) dp > 0, dq dp < 0, dq dp P Q > 1, d,p < 1 P Q < 1, d,p > 1

29 How Total Revenue is affected by a change in price

30 Price Elasticity and Total Revenue Movie ticket price increases from \$2 to \$4 A and B are both below the midpoint of the curve Inelastic portion of the demand curve Total revenue increases when price increases Price (\$/ticket) 12 2 D Expenditure = \$1,000/day A Price (\$/ticket) 12 4 D Expenditure = \$1,600/day B 5 6 Quantity (00s of tickets/day) Quantity (00s of tickets/day) 4 6

31 Price Elasticity and Total Revenue Movie ticket price increases from \$8 to \$10 Prices are both above the midpoint of the curve Elastic portion of the demand curve Total revenue decreases when price increases Price (\$/ticket) 12 8 Y Expenditure = \$1,600/day D Price (\$/ticket) Z Expenditure = \$1,000/day D 2 6 Quantity (00s of tickets/day) 1 6 Quantity (00s of tickets/day)

32 Total Revenue along a Linear Demand Curve Price \$12 \$10 \$8 \$6 \$4 \$2 \$0 Quantity 0 1,000 2,000 3,000 4,000 5,000 6,000 Expenditure \$0 \$1,000 \$1,600 \$1,800 \$1,600 \$1,000 \$0 Price (\$/ticket) Total expenditure (\$/day) 1,800 1,600 1, Quantity (00s of tickets/day) Price (\$/ticket)

33 Estimating Elasticities When estimating demand elasticity, need to hold fixed other determinants of demand isolate impact of change in price.

34 Gasoline Market in the US June 2007 and June 2008 Time Period Per Capita Daily Consumption of Motor Gasoline Average Price Per Gallon in Dollars June June Average of Both Years %.05.28

35 Estimating Elasticities ε d,p of US gas demand? Elastic or inelastic? As prices go up, total spending should increase or decrease? Is this short-run elasticity or long-run elasticity?

36 Estimating Elasticities Is the price change due to supply shift or demand shift or both? To estimate price elasticity of demand, you want the demand curve stay constant while the supply curve shifts Consumer tastes Tastes for driving higher in summer than winter. So comparing June to June Number of buyers Population grows about 1% a year Not significant. Also comparing per capita Income Income in June 2007 and June 2008 about the same (financial crisis led to income decrease after summer 2008) Prices of substitutes and complements Didn t change much over the one year period Expectations?

37 Estimating long-run Elasticities One way to estimate long-run elasticity is to compare cases where prices have been different a long time. Fuel Consumption in Europe and the U.S. Europe has long taxed gasoline. If taxes on gasoline are high for a long time, like in Europe, consumers will shift to fuel-efficient cars. People will move closer to where they work, etc. All these adjustments take time.

38 Country Average Price \$US per Gallon United States Selected Countries in Europe Norway 7.00 *.30 United Kingdom Germany France Spain Italy Consumption Per Capita Gallons Per Day Country United States 45.5 Selected Countries in Europe Norway 51.9 United Kingdom 35.7 Germany 34.3 France 32.7 Spain 31.6 Italy 30.4 Per Capita GDP (\$1,000) Some Other Countries Japan Mexico China Some Other Countries Japan 33.6 Mexico 14.0 China 5.3

39 Table 3: Price and Per Capita Quantit Consumed of Gasoline The United States and Norway in 200 Time Period Per Capita Daily Consumption of Motor Gasoline Average Price Per Gallon in Dollars United States Norway Average of Both Years %

40 Estimating long-run Elasticities Is the supply curve shifting between the two countries? Is demand curve staying fixed? Income Price of substitutes/complements n Can be a big problem. Public transit is much better in Norway than in the U.S. So there are really two main differences: (1) gas prices are higher and (2) public transit options are better. Both contribute to the lower consumption of gas in Norway Other factors n Population density impacts gasoline demand n Any other factors that make the demand curve in Norway and the U.S. different

41 Price Elasticity and Total Revenue The price of a pair of running shoes rises from \$100 to \$150, while the quantity demanded falls from 1200 to 900 Assumptions needed to calculate price elasticity of demand Calculate the price elasticity of demand Is demand elastic, unit elastic, or inelastic Calculate total revenue before and after the price increase By how much would the quantity demanded change if price rises another 5%? (and what further assumptions are needed to answer this question)

42 Price Elasticity of Supply Price elasticity of supply = Percentage change in Q s Percentage change in P Example: Price elasticity of supply equals 16% 8% = 2.0 P rises by 8% P 2 P 1 P Q rises by 16% Q 1 Q 2 S Q 43

43 Perfectly Inelastic Supply - Elasticity equals 0 Price Supply 1. An increase in price... \$ Quantity 2....leaves the quantity supplied unchanged.

44 Perfectly Inelastic Supply Example: land on Manhattan/HK island/xiamen Supply is completely fixed Any one-of-a-kind item has perfectly inelastic supply Work of art (Mona Lisa)

45 Inelastic Supply - Elasticity is less than 1 Price Supply 1. A 22% increase in price... \$ leads to a 10% increase in quantity. Quantity

46 Unit Elastic Supply - Elasticity equals 1 Price Supply 1. A 22% increase in price... \$ leads to a 22% increase in quantity. Quantity

47 Elastic Supply - Elasticity is greater than 1 Price Supply 1. A 22% increase in price... \$ leads to a 67% increase in quantity. Quantity

48 Perfectly Elastic Supply - Elasticity equals infinity Price 1. At any price above \$4, quantity supplied is infinite. \$4 Supply 2. At exactly \$4, producers will supply any quantity. 3. At a price below \$4, quantity supplied is zero. Quantity

49 Price Elasticity of Supply If the supply curve is linear and has a zero intercept, then ε s,p =1 If the supply curve is linear and has a positive intercept, then ε s,p >1 and Q é è ε s,p =1 ê

50 Price Elasticity of Supply In general, elasticity of can vary over the supply curve. Consider an industry in which firms have factories with a limited capacity for production. For low levels of quantity supplied, firms can use idle capacity to respond to changes in the price As the quantity supplied rises, firms begin to reach capacity. Once capacity is fully used, increasing production further requires the construction of new plants. To induce firms to incur this extra expense, the price must rise substantially

51 Price Elasticity of Supply

52 Determinants of Supply Elasticity The more easily sellers can change the quantity they produce, the greater the price elasticity of supply Example: Supply of beach front property is harder to vary and thus less elastic than supply of new cars For many goods, price elasticity of supply is greater in the long run than in the short run Firms can build factories new firms may enter the market

53 Supply Elasticity and Equilibrium Change The supply of beachfront property is inelastic. The supply of new cars is elastic. Suppose population growth causes demand for both goods to double For which product will P change the most? For which product will Q change the most?

54 Supply Elasticity and Equilibrium Change When supply is inelastic, an increase in demand has a bigger impact on price than on quantity. P 2 P D 1 Beachfront property (inelastic supply): D 2 S B P 1 A Q 1 Q 2 Q

55 Supply Elasticity and Equilibrium Change Answers When supply is elastic, an increase in demand has a bigger impact on quantity than on price. P 2 P 1 P D 1 D 2 New cars (elastic supply): A B S Q 1 Q 2 Q

56 Other Elasticities Income Elasticity of Demand d,i = Percentage change in quantity demanded Percentage change in income = dq/q di/i

57 Income Elasticity of Demand Normal goods ε d,i >0 Inferior goods ε d,i <0

58 Other Elasticities Cross-price Elasticity of Demand d,xy = Percentage change in quantity demanded of good x Percentage change in the price of good y = dq x/ Q x dp y / P y

59 Cross-price Elasticity of Demand Substitutes ε d,xy >0 Complements ε d,xy <0

60 Cross-price Elasticity of Demand Suppose the quantity demanded for good X decreased 25% while the price of good Y increased by 50% What is the cross-price elasticity of demand for X and Y? Are X and Y substitutes or complements? What assumptions do we need to answer these questions?

61 Cross-price Elasticity of Demand As Gas Costs Soar, Buyers Flock to Small Cars NYTimes, 5/2/2008 High Cost of Driving Ignites Online Classes Boom Chronicle of Higher Education, 7/11/2008 Gas prices knock bicycle sales, repairs into higher gear Associated Press, 5/11/2008 Camel demand soars in India (as oil price soars) Financial Times, 5/2/2008

62 Can Good News for Farming Be Bad News for Farmers? Scientific discovery of new wheat hybrid that can raise yield per acre by 20% Q é, P ê Change in total revenue depends on price elasticity of demand Demand for wheat is usually inelastic P ê -> total revenue ê (inelastic demand) If the new hybrid hurts farmers, why would they adopt it? In competitive markets, each farmer is a price taker: it s better for each to sell more given market price When all farmers do this, the supply of wheat increases, the price falls, and farmers are worse off.

63 Yacht Tax Proposal: luxury tax on yachts over \$100,000 will yield \$31 million in U.S. tax revenue Price elasticity of demand is high Outcome Tax took effect in Jan 1990 Actual tax revenue \$16.6 million People bought yachts outside US to avoid tax n 7,600 jobs in US boating industry lost Tax repealed after 2 years

64 The War on Drugs 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. One measure to stop drug-related violence: drug interdiction. i.e. stop the entry and supply of drugs What happens to drug use? What happens to the total revenue of drug sellers? Is demand for drugs elastic or inelastic? Short-run vs Long-run

65 The War on Drugs

66 The War on Drugs In the short run, increase in total revenue means Drug sellers have more incentive to engage in illicit drug trade, leading to more powerful drug cartels and organized crime in drug-producing countries Drug addicts have to spend more for drugs, which may lead to increase in drug-related crime in drugconsuming countries In the long run, this may encourage people to break their habit and discourage the number of new users.

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