Week3: Elasticity and Its Applications. 17 th March 2014

Transcription

1 Week3: Elasticity and Its Applications 17 th March 2014

2 In this week, 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?

3 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 opportunity cost of your time), so you consider 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?

4 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

5 Elasticity! Basic idea: Elasticity measures how much one variable responds to changes in another variable.! One type of elasticity measures how much demand for your websites will fall if you raise your price.! Definition: Elasticity is a numerical measure of the responsiveness of Q d or Q s to one of its determinants.

6 Price Elasticity of Demand Price elasticity of demand = Percentage change in Q d Percentage change in P! Price elasticity of demand measures how much Q d responds to a change in P.! Price elasticity of demand is the percentage change in quantity demanded given a percent change in the price.!! Loosely speaking, it measures the price-sensitivity of buyers demand.

7 Calculating Percentage Changes $250 $200 P Demand for your websites 8 B 12 A D Q Standard method of computing the percentage (%) change: end value start value start value x 100% Going from A to B, the % change in P equals ($250 $200)/$200 = 25%

8 Calculating Percentage Changes $250 $200 P Demand for your websites 8 B 12 A D Q 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 From B to A, P falls 20%, Q rises 50%, elasticity = 50/20 = 2.50

9 Calculating Percentage Changes! So, we instead use the midpoint method: end value start value midpoint x 100%!! 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.!! The midpoint is the number halfway between the start and end values, the average of those values.!! It doesn t matter which value you use as the start and which as the end you get the same answer either way!

10 Calculating Percentage Changes! Using the midpoint method, the % change in P equals $250 $200 $225 x 100% = 22.2%!! The % change in Q equals x 100% = 40.0%!! The price elasticity of demand equals 40/22.2 = 1.8

11 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 Q d 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?

12 EXAMPLE 1: Breakfast Cereal vs. Sunscreen! The prices of both of these goods rise by 20%. For which good does Q d drop the most? Why?! Breakfast cereal has close substitutes (e.g., pancakes, Eggo waffles, leftover pizza), 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.

13 EXAMPLE 2: Blue Jeans vs. Clothing! The prices of both goods rise by 20%. For which good does Q d 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. (There aren t too many substitutes for clothing, other than living in a nudist colony.)! Lesson: Price elasticity is higher for narrowly defined goods than for broadly defined ones.

14 EXAMPLE 3: Insulin vs. Caribbean Cruises! The prices of both of these goods rise by 20%. For which good does Q d 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.

15 EXAMPLE 4: Gasoline in the Short Run vs. Gasoline in the Long Run! The price of gasoline rises 20%. Does Q d 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.

16 The Determinants of Price Elasticity: A Summary The price elasticity of demand depends on:! the extent to which close substitutes are available! whether the good is a necessity or a luxury! how broadly or narrowly the good is defined! the time horizon elasticity is higher in the long run than the short run

17 The Variety of Demand Curves! 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.! Five different classifications of D curves.

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

19 Inelastic demand Pricee lasticity of demand D curve: relatively steep = % change in Q % change in P = P < 10% 10% < 1 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

20 Unit elastic demand Pricee lasticity 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%

21 Elastic demand Pricee lasticity of demand D curve: relatively flat = % change in Q % change in P = P > 10% 10% > 1 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

22 Perfectly elastic demand (the other extreme) Pricee lasticity 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

23 A few elasticities from the real world Eggs 0.1 Healthcare 0.2 Rice 0.5 Housing 0.7 Beef 1.6 Restaurant meals 2.3 Mountain Dew 4.4 Inelastic demand Inelastic demand Inelastic demand Inelastic demand Elastic demand Elastic demand Elastic demand

24 Price Elasticity and Total Revenue! 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.! Which of these two effects is bigger? It depends on the price elasticity of demand.

25 Price Elasticity and Total Revenue Price elasticity of demand = Percentage change in Q Percentage change in P Revenue = P x Q! If demand is elastic, then price elast. of demand > 1 % 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.

26 Price Elasticity and Total Revenue Elastic demand (elasticity = 1.8) If P = $200, Q = 12 and revenue = $2400. If P = $250, Q = 8 and revenue = $2000. When D is elastic, a price increase causes revenue to fall. $250 $200 P increased Demand for revenue due your websites lost to higher P revenue due to lower Q 8 12 D Q

27 Price Elasticity and Total Revenue Price elasticity of demand = Percentage change in Q Percentage change in P! 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. Revenue = P x Q! In our example, suppose that Q only falls to 10 (instead of 8) when you raise your price to $250.

28 Price Elasticity and Total Revenue Now, demand is inelastic: elasticity = 0.82 If P = $200, Q = 12 and revenue = $2400. If P = $250, Q = 10 and revenue = $2500. When D is inelastic, a price increase causes revenue to rise. $250 $200 P increased Demand for revenue your due websites to higher P lost revenue due to lower Q D Q

29 APPLICATION: 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 drugrelated crime.! For simplicity, we assume the total dollar value of drug-related crime equals total expenditure on drugs.! Demand for illegal drugs is inelastic, due to addiction issues.

30 Policy 1: Interdiction Interdiction reduces the supply of drugs. Price of Drugs Since demand for drugs is inelastic, P rises propor -tionally more than Q falls. Result: an increase in total spending on drugs, and in drug-related crime P 2 P 1 new value of drug -related crime D 1 Q 2 Q 1 S 2 S 1 initial value of drug -related crime Quantity of Drugs

31 Policy 2: Education Education reduces the demand for drugs. Price of Drugs new value of drug -related crime D 2 D 1 S P and Q fall. Result: A decrease in total spending on drugs, and in drug-related crime. P 1 P 2 Q 2 Q 1 initial value of drug -related crime Quantity of Drugs

32 Price Elasticity of Supply Price elasticity of supply = Percentage change in Q s Percentage change in P! Price elasticity of supply measures how much Q s responds to a change in P.!! Loosely speaking, it measures sellers price-sensitivity.!! Again, use the midpoint method to compute the percentage changes.

33 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

34 The Variety of Supply Curves! The slope of the supply curve is closely related to price elasticity of supply.! Rule of thumb: The flatter the curve, the bigger the elasticity. The steeper the curve, the smaller the elasticity.! Five different classifications

35 Perfectly inelastic (one extreme) Pricee lasticity of supply = % change in Q % change in P = 0% 10% = 0 S curve: vertical P S Sellers price sensitivity: none P 2 P 1 Elasticity: 0 P rises by 10% Q 1 Q changes by 0% Q

36 Inelastic Pricee lasticity of supply = % change in Q % change in P = < 10% 10% < 1 S curve: relatively steep P S Sellers price sensitivity: relatively low P 2 P 1 Elasticity: < 1 P rises by 10% Q 1 Q 2 Q rises less than 10% Q

37 Unit elastic Pricee lasticity of supply = % change in Q % change in P = 10% 10% = 1 S curve: intermediate slope P S Sellers price sensitivity: intermediate P 2 P 1 Elasticity: = 1 P rises by 10% Q 1 Q 2 Q rises by 10% Q

38 Elastic Pricee lasticity of supply = % change in Q % change in P = > 10% 10% > 1 S curve: relatively flat P S Sellers price sensitivity: relatively high P 2 P 1 Elasticity: > 1 P rises by 10% Q 1 Q 2 Q rises more than 10% Q

39 Perfectly elastic (the other extreme) Pricee lasticity of supply = % change in Q % change in P = any % 0% = infinity S curve: horizontal Sellers price sensitivity: extreme P 2 = P 1 P S Elasticity: infinity P changes by 0% Q 1 Q 2 Q changes by any % Q

40 The Determinants of Supply Elasticity! The more easily sellers can change the quantity they produce, the greater the price elasticity of supply.! Example: Supply of beachfront 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, because firms can build new factories, or new firms may be able to enter the market.

41 How the Price Elasticity of Supply Can Vary P $ elasticity > 1 elasticity < 1 S Supply often becomes less elastic as Q rises, due to capacity limits. $ Q

42 Other Elasticities! Income elasticity of demand: measures the response of Q d to a change in consumer income Income elasticity of demand = Percent change in Q d Percent change in income!! Recall from Chapter 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.

43 Other Elasticities! Cross-price elasticity of demand: measures the response of demand for one good to changes in the price of another good Cross-pricee last. of demand = % change in Q d for good 1 % change in price of good 2!! For substitutes, cross-price elasticity > 0 (e.g., an increase in price of beef causes an increase in demand for chicken)!! For complements, cross-price elasticity < 0 (e.g., an increase in price of computers causes decrease in demand for software)

44 Cross-Price Elasticities in the News As Gas Costs Soar, Buyers Flock to Small Cars -New York Times, 5/2/2008 Gas Prices Drive Students to Online Courses -Chronicle of Higher Education, 7/8/2008 Gas prices knock bicycle sales, repairs into higher gear -Associated Press, 5/11/2008 Camel demand soars in India (as a substitute for gas-guzzling tractors ) -Financial Times, 5/2/2008 High gas prices drive farmer to switch to mules -Associated Press, 5/21/2008

45 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?

46 THREE APPLICATIONS OF SUPPLY, DEMAND, AND 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.

47 Figure 8 An Increase in Supply in the Market for Wheat Price of Wheat leads to a large fall in price When demand is inelastic, an increase in supply... S 1 S 2 $3 2 Demand Quantity of Wheat and a proportionately smaller increase in quantity sold. As a result, revenue falls from $300 to $220. Copyright 2003 Southwestern/Thomson Learning

48 Compute the Price Elasticity of Supply 100! 110 E D = ( ) / ! ( ) / 2 =! "! Supply is inelastic

49 Summary! Price elasticity of demand measures how much the quantity demanded responds to changes in the price.! 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.

50 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..

51 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.

52 Supply, Demand, and Government Policies

53 In this section, look for the answers to these questions:!what are price ceilings and price floors? What are some examples of each?!how do price ceilings and price floors affect market outcomes?!how do taxes affect market outcomes? How do the effects depend on whether the tax is imposed on buyers or sellers?!what is the incidence of a tax? What determines the incidence?

54 Government Policies That Alter the Private Market Outcome! Price controls! Price ceiling: a legal maximum on the price of a good or service Example: rent control! Price floor: a legal minimum on the price of a good or service Example: minimum wage! Taxes! The govt can make buyers or sellers pay a specific amount on each unit. We will use the supply/demand model to see how each policy affects the market outcome (the price buyers pay, the price sellers receive, and eq m quantity).

55 EXAMPLE 1: The Market for Apartments Rental price of apts P S Eq m w/o price controls $ D Quantity of apts Q

56 How Price Ceilings Affect Market Outcomes A price ceiling above the eq m price is not binding has no effect on the market outcome. $1000 $800 P S Price ceiling 300 D Q

57 How Price Ceilings Affect Market Outcomes The eq m price ($800) is above the ceiling and therefore illegal. P S The ceiling is a binding constraint on the price, causes a shortage. $800 $500 shortage D Price ceiling Q

58 How Price Ceilings Affect Market Outcomes In the long run, supply and demand are more price-elastic. $800 P S So, the shortage is larger. $500 Price ceiling 150 shortage 450 D Q

59 Shortages and Rationing! With a shortage, sellers must ration the goods among buyers.! Some rationing mechanisms: (1) Long lines (2) Discrimination according to sellers biases! These mechanisms are often unfair, and inefficient: the goods do not necessarily go to the buyers who value them most highly.! In contrast, when prices are not controlled, the rationing mechanism is efficient (the goods go to the buyers that value them most highly) and impersonal (and thus fair).

60 EXAMPLE 2: The Market for Unskilled Labor Wage paid to unskilled workers Eq m w/o price controls $6.00 W 500 S D Quantity of unskilled workers L

61 How Price Floors Affect Market Outcomes A price floor below the eq m price is not binding has no effect on the market outcome. $6.00 $5.00 W S Price floor 500 D L

62 How Price Floors Affect Market Outcomes The eq m wage ($6) is below the floor and W therefore illegal. $7.25 The floor is a binding constraint $6.00 on the wage, causes a surplus (i.e., unemployment). labor surplus S D Price floor L

63 The Minimum Wage Min wage laws do not affect highly skilled workers. $7.25 W unemp -loyment S Min. wage They do affect teen workers. $6.00 Studies: A 10% increase in the min wage raises teen unemployment by 1 3% D L

64 Evaluating Price Controls! Recall one of the Ten Principles from Chapter 1: Markets are usually a good way to organize economic activity.! Prices are the signals that guide the allocation of society s resources. This allocation is altered when policymakers restrict prices.! Price controls often intended to help the poor, but often hurt more than help.

65 Taxes! The govt levies taxes on many goods & services to raise revenue to pay for national defense, public schools, etc.! The govt can make buyers or sellers pay the tax.! The tax can be a % of the good s price, or a specific amount for each unit sold.! For simplicity, we analyze per-unit taxes only.

66 EXAMPLE 3: The Market for Pizza Eq m w/o tax P S 1 $10.00 D Q

67 A Tax on Buyers The Hence, price a tax buyers on buyers pay is shifts now the $1.50 D curve higher down than by the market the amount price of P. the tax. P P would have to fall by $1.50 to make buyers willing $10.00 to buy same Q as before. $8.50 E.g., if P falls from $10.00 to $8.50, buyers still willing to purchase 500 pizzas. Effects of a $1.50 per unit tax on buyers 500 Tax D 2 S 1 D 1 Q

68 A Tax on Buyers New eq m: Q = 450 Sellers receive P S = $9.50 Buyers pay P B = $11.00 P B = $11.00 $10.00 P S = $9.50 Difference between them = $1.50 = tax 450 P Effects of a $1.50 per unit tax on buyers Tax 500 D 2 S 1 D 1 Q

69 The Incidence of a Tax: how the burden of a tax is shared among market participants In our example, buyers pay $1.00 more, sellers get $0.50 less. P B = $11.00 $10.00 P S = $9.50 P Tax S 1 D D 2 Q

70 A Tax on Sellers The tax effectively raises sellers costs by $1.50 per pizza. Sellers will supply 500 pizzas only if P rises to $11.50, to compensate for this cost increase. P $11.50 $10.00 Effects of a $1.50 per unit tax on sellers S 2 Tax S 1 D 1 Hence, a tax on sellers shifts the S curve up by the amount of the tax. 500 Q

71 A Tax on Sellers New eq m: Q = 450 Buyers pay P B = $11.00 Sellers receive P S = $9.50 P P B = $11.00 $10.00 P S = $9.50 Effects of a $1.50 per unit tax on sellers Tax S 2 S 1 Difference between them = $1.50 = tax D 1 Q

72 The Outcome Is the Same in Both Cases! The effects on P and Q, and the tax incidence are the same whether the tax is imposed on buyers or sellers! What matters is this: A tax drives a wedge between the price buyers pay and the price sellers receive. P B = $11.00 $10.00 P S = $9.50 P 450 Tax 500 S 1 D 1 Q

73 Elasticity and Tax Incidence CASE 1: Supply is more elastic than demand Buyers share of tax burden Price if no tax Sellers share of tax burden P B P S P Tax D S Q It s easier for sellers than buyers to leave the market. So buyers bear most of the burden of the tax.

74 Elasticity and Tax Incidence CASE 2: Demand is more elastic than supply Buyers share of tax burden Price if no tax Sellers share of tax burden P B P S P Tax S D It s easier for buyers than sellers to leave the market. Sellers bear most of the burden of the tax. Q

75 CASE STUDY: Who Pays the Luxury Tax?! 1990: Congress adopted a luxury tax on yachts, private airplanes, furs, expensive cars, etc.! Goal: raise revenue from those who could most easily afford to pay wealthy consumers.! But who really pays this tax?

76 CASE STUDY: Who Pays the Luxury Tax? The market for yachts Buyers share of tax burden P B P S Demand is price-elastic. In the short run, supply is inelastic. Sellers share of tax burden P S Tax D Q Hence, companies that build yachts pay most of the tax.

77 CONCLUSION: Government Policies and the Allocation of Resources! Each of the policies in this chapter affects the allocation of society s resources.! Example 1: A tax on pizza reduces eq m Q. With less production of pizza, resources (workers, ovens, cheese) will become available to other industries.! Example 2: A binding minimum wage causes a surplus of workers, a waste of resources.! So, it s important for policymakers to apply such policies very carefully.

78 SUMMARY! A price ceiling is a legal maximum on the price of a good. An example is rent control. If the price ceiling is below the eq m price, it is binding and causes a shortage.! A price floor is a legal minimum on the price of a good. An example is the minimum wage. If the price floor is above the eq m price, it is binding and causes a surplus. The labor surplus caused by the minimum wage is unemployment Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

79 SUMMARY! A tax on a good places a wedge between the price buyers pay and the price sellers receive, and causes the eq m quantity to fall, whether the tax is imposed on buyers or sellers.! The incidence of a tax is the division of the burden of the tax between buyers and sellers, and does not depend on whether the tax is imposed on buyers or sellers.! The incidence of the tax depends on the price elasticities of supply and demand Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.