1. Price Elasticity of Demand Overheads

2. A Little Photo Retrospective Malcolm X Paul McCartney

3. Sidney Poitier Howard Cossel

4. Bill Cosby Joe Frazier

5. Joe Lewis Jackson 5

6. Nelson Mandela

7. How much would your roommate pay to watch a live fight? How does Showtime decide how much to charge for a live fight?

9. What about Hank and Son’s Concrete? How much should they charge per square foot? Can ISU raise parking revenue by raising parking fees? Or will the increase in price drive demand down so far that revenue falls?

10. All of these pricing issues revolve around the issue of how responsive the quantity demanded is to price. Elasticity is a measure of how responsive one variable is to changes in another variable?

11. The Law of Demand The law of demand states that when the price of a good rises, and everything else remains the same, the quantity of the good demanded will fall. The real issue is how far it will fall.

12. The demand function is given by Q D = quantity demanded P = price of the good Z D = other factors that affect demand

13. The inverse demand function is given by To obtain the inverse demand function we just solve the demand function for P as a function of Q

14. Examples Q D = 20 - 2P 2P + Q D = 20 2P = 20 - Q D P = 10 - 1/2 Q D Slope = - 1/2

15. Examples Q D = 60 - 3P 3P + Q D = 60 3P = 60 - Q D P = 20 - 1/3 Q D Slope = - 1/3

16. The slope of a demand curve is given by the change in Q divided by the change in P One measure of responsiveness is slope For demand

17. The slope of an inverse demand curve is given by the change in P divided by the change in Q For inverse demand

18. Q D = 60 - 3P Examples Slope = - 1/3 Slope = - 3 P = 20 - 1/3 Q D

19. Q D = 20 - 2P Examples Slope = - 1/2 Slope = - 2 P = 10 - 1/2 Q D

20. We can also find slope from tabular data QP 010 29 48 67 86 105 QQ PP 

21. QP 010 19.5 29 38.5 48 57.5 67 76.5 86 95.5 105 114.5 124 133.5 143 152.5 162 171.5 181 190.5 200 Demand for Handballs

22. QP 010 19.5 29 38.5 48 57.5 67 76.5 86 95.5 105 114.5 124 133.5 143 152.5 162 171.5 181 190.5 200 Demand for Handballs 0 1 2 3 4 5 6 7 8 9 10 11 0246810121416182022 Quantity Price P

23. QP 010 19.5 29 38.5 48 57.5 67 76.5 86 95.5 105 114.5 124 133.5 143 152.5 162 171.5 181 190.5 200 Demand for Handballs 0 1 2 3 4 5 6 7 8 9 10 11 0246810121416182022 Quantity Price  QQ  PP  Q = 2 - 4 = -2  P = 9 - 8 = 1

24. Problems with slope as a measure of responsiveness Slope depends on the units of measurement The same slope can be associated with very different percentage changes

25. Examples Q D = 200 - 2P 2P + Q D = 200 2P = 200 - Q D P = 100 - 1/2 Q D

26. QP 0100 199.5 299 398.5 498 597.5 697 796.5 896 995.5 1095 1194.5 1294 1393.5 1493 Consider data on racquets Let P change from 95 to 96  P = 96 - 95 = 1  Q = 8 - 10 = -2  QQ PP  A $1.00 price change when P = $95.00 is tiny

27. Graphically for racquets Demand for Racquets 88 90 92 94 96 98 100 102 024681012141618 Quantity Price Large % change in Q Small % change in P Slope = - 1/2

28. Graphically for hand balls Large % change in QLarge % change in P Slope = - 1/2 Demand for Handballs 0 1 2 3 4 5 6 7 8 9 10 11 0246810121416182022 Quantity Price P  P = 7 - 6 = 1  Q = 6 - 8 = -2

29. So slope is not such a good measure of responsiveness Instead of slope we use percentage changes The ratio of the percentage change in one variable to the percentage change in another variable elasticity is called elasticity

30. Own Price Elasticity of Demand The Own Price Elasticity of Demand is given by There are a number of ways to compute percentage changes

31. Initial Initial point method for computing Own Price Elasticity of Demand The Own Price Elasticity of Demand

32. Price Elasticity of Demand (Initial Point Method) P Q 6 8 5.5 9 5 10 4.5 11 4 12 QQ   PP

33. Final Final point method for computing Own Price Elasticity of Demand The Own Price Elasticity of Demand

34. Price Elasticity of Demand (Final Point Method) P Q 6 8 5.5 9 5 10 4.5 11 4 12 QQ   PP

35. The answer is very different depending on the choice of the base point So we usually use The midpoint The midpoint method for computing Own Price Elasticity of Demand The Own Price Elasticity of Demand

36. Elasticity of Demand Using the Mid-Point For Q D we use the midpoint of the Q’s

37. Similarly for prices For P we use the midpoint of the P’s

39. Price Elasticity of Demand (Mid-Point Method) QP 86 95.5 105 114.5 124

40. Classification of the elasticity of demand Inelastic demand When the numerical value of the elasticity of demand inelastic is between 0 and -1.0, we say that demand is inelastic.

41. Classification of the elasticity of demand Elastic demand When the numerical value of the elasticity of demand elastic is less than -1.0, we say that demand is elastic.

42. Classification of the elasticity of demand Unitary elastic demand When the numerical value of the elasticity of demand unitary elastic is equal to -1.0, we say that demand is unitary elastic.

43. Classification of the elasticity of demand Perfectly elastic -  D = -  Perfectly inelastic -  D = 0 horizontal vertical

44. Elasticity of demand with linear demand Consider a linear inverse demand function The slope is (-B) for all values of P and Q For example, The slope is -0.5 = - 1/2

45. PQ 120 11.51 112 10.53 104 9.55 96 8.578 7.59 710 6.511 612 5.513 514 4.515 416 3.517 318 Demand for Diskettes 0 1 2 3 4 5 6 7 8 9 10 11 12 13 0246810121416182022 Quantity Price  PP QQ   PP QQ 

46. The slope is constant but the elasticity of demand will vary PQ 120 11.51 112 10.53 104 9.55 96 8.578 7.59 710 6.511 612 5.513 514 4.515 416 3.517 318  PP QQ 

47. The slope is constant but the elasticity of demand will vary PQ 120 11.51 112 10.53 104 9.55 96 8.578 7.59 710 6.511 612 5.513 514 4.515 416 3.517 318  PP QQ 

48. The slope is constant but the elasticity of demand will vary A linear demand curve becomes more inelastic as we lower price and increase quantity P smaller Q larger The elasticity gets closer to zero

49. QPElasticityExpenditure 0120 211-23.000022 410-7.000040 69-3.800054 88-2.428664 107-1.666770 126-1.181872 145-0.846270 164-0.600064 183-0.411854 202-0.263240 221-0.142922 240-0.04350 The slope is constant but the elasticity of demand will vary

50. QPElasticityExpenditure 0120 211-23.000022 410-7.000040 69-3.800054 88-2.428664 107-1.666770 126-1.181872 145-0.846270 164-0.600064 183-0.411854 202-0.263240 221-0.142922 240-0.04350 The slope is constant but the elasticity of demand will vary

51. Note We do not say that demand is elastic or inelastic ….. We say that demand is elastic or inelastic at a given point

52. Example Constant with linear demand

53. Own Price Elasticity of Demand The Own Price Elasticity of Demand Total Expenditure on an Item and Total Expenditure on an Item How do changes in an items price affect expenditure on the item? If I lower the price of a product, will the increased sales make up for the lower price per unit?

54. Expenditure for the consumer is equal to revenue for the firm Revenue = R = price x quantity = PQ Expenditure = E = price x quantity = PQ

55.  P = change in price Modeling changes in price and quantity  Q = change in quantity The Law of Demand says that as P increases Q will decrease P  Q 

56. P = initial price  P = change in price So P +  P = final price Q = initial quantity  Q = change in quantity Q +  Q = final quantity

57. Initial Revenue = PQ So P +  P = final price = P Q +  P Q + P  Q +  P  Q Q +  Q = final quantity Final Revenue = (P +  P) (Q +  Q)

58. Now find the change in revenue  R = final revenue - initial revenue = P Q +  P Q + P  Q +  P  Q - P Q =  P Q + P  Q +  P  Q %  R =  R / R =  R / P Q

59. We can rewrite this expression as follows

60. Classification of the elasticity of demand Inelastic demand %  Q and %  P are of opposite sign so %  R has the same sign as %  P + -

61. Classification of the elasticity of demand Inelastic demand %  Q and %  P are of opposite sign so %  R has the same sign as %  P - + Lower price  lower revenue Higher price  higher revenue

62. Classification of the elasticity of demand Elastic demand %  Q and %  P are of opposite sign so %  R has the opposite sign as %  P Higher price  lower revenue Lower price  higher revenue + -

63. Classification of the elasticity of demand Unitary elastic demand %  Q and %  P are of opposite sign so their effects will cancel out and %  R = 0. + -

64. QPElasticityRevenue 0120 211-23.000022 410-7.000040 69-3.800054 88-2.428664 107-1.666770 126-1.181872 145-0.846270 164-0.600064 183-0.411854 202-0.263240 221-0.142922 240-0.04350 Tabular data Elastic Revenue rises Inelastic Revenue falls Price falls

65. 0120 211-23.000022 410-7.000040 69-3.800054 88-2.428664 107-1.666770 126-1.181872 145-0.846270 164-0.600064 183-0.411854 202-0.263240 221-0.142922 240-0.04350 Graphical analysis QPElasticityRevenue Demand for Diskettes 0 1 2 3 4 5 6 7 8 9 10 11 12 13 0246810121416182022 Quantity Price Demand A B C P0, Q0 P1, Q1 Lose B, gain A, revenue rises

66. 0120 211-23.000022 410-7.000040 69-3.800054 88-2.428664 107-1.666770 126-1.181872 145-0.846270 164-0.600064 183-0.411854 202-0.263240 221-0.142922 240-0.04350 Graphical analysis QPElasticityRevenue Demand for Diskettes 0 1 2 3 4 5 6 7 8 9 10 11 12 13 0246810121416182022 Quantity Price Demand P1, Q1 Lose A, gain B, revenue falls P0, Q0 A B

67. Factors affecting the elasticity of demand Availability of substitutes Importance of item in the buyer’s budget

68. Availability of substitutes The easier it is to substitute for a good, the more elastic the demand With many substitutes, individuals will move away from a good whose price increases

69. Examples of goods with “easy “substitution Gasoline at different stores Soft drinks Detergent Airline tickets Local telephone service

70. Narrow definition of product The more narrowly we define an item, the more elastic the demand With a narrow definition, there will lots of substitutes

71. Examples of narrowly defined goods Lemon-lime drinks Corn at a specific farmer’s market Vanilla ice cream Food Transportation

72. “Necessities” tend to have inelastic demand Necessities tend to have few substitutes

73. Examples of necessities Salt Insulin Food Trips to Hawaii Sailboats

74. Demand is more elastic in the long-run There is more time to adjust in the long run

75. Examples of short and long run elasticity Postal rates Gasoline Sweeteners

76. Factors affecting the elasticity of demand Importance of item in the buyer’s budget The more of their total budget consumers spend on an item, the more elastic the demand for the good The elasticity is larger because the item has a large budget impact

77. “Big ticket” items and elasticity Housing Big summer vacations Table salt College tuition

78. The End