Agri 2312 chapter  5 measurement and interpretation of elasticities 1
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Agri 2312 chapter 5 measurement and interpretation of elasticities 1 Presentation Transcript

  • 1. Measurement and Interpretation of Elasticities Chapter 5
  • 2. Discussion Topics
    • Own price elasticity of demand
    • Income elasticity of demand
    • Cross price elasticity of demand
    • Other general properties
    • Applicability of demand elasticities
  • 3. Key Concepts Covered…
    • Own price elasticity
    • Income elasticity
    • Cross price elasticity
    Pages 70-76
  • 4. What is Elasticity of Demand?
    • We define elasticity of demand as responsiveness of the quantity demanded to a change in the price.
      • Degree of responsiveness is measured by an elasticity coefficient — frequently called elasticities .
    • Invented by the British Economist Alfred Marshall
  • 5. Key Concepts Covered…
    • Own price elasticity =
      • %  Q beef for a given %  P beef
    • Income elasticity =
      • %  Q beef for a given %  Income
    • Cross price elasticity =
      • %  Q beef for a given %  P chicken
    Pages 70-76
  • 6. Key Concepts Covered…
    • Arc elasticity = range along the demand curve
    • Point elasticity = point on the demand curve
    Pages 70-76
  • 7. Key Concepts Covered…
    • Own price elasticity = %  Q beef for a given %  P beef
    • Income elasticity = %  Q beef for a given %  Income
    • Cross price elasticity = %  Q beef for a given %  P chicken
    • Arc elasticity = range along the demand curve
    • Point elasticity = point on the demand curve
    • Price flexibility = reciprocal of own price elasticity
    Pages 70-76
  • 8. Own Price Elasticity of Demand
  • 9. Own Price Elasticity of Demand Own price elasticity of demand Percentage change in quantity Percentage change in price = Point Elasticity Approach Pages 70-72
  • 10. Own Price Elasticity of Demand Point elasticity: = [  Q  P] × [P a  Q a ] Own price elasticity of demand Own price elasticity of demand Percentage change in quantity Percentage change in price =  Q = (Q a – Q b ); and  P = (P a – P b ) The subscript “a” here stands for “after” while “b” stands for “before” Pages 70-72
  • 11. Own Price Elasticity of Demand Point elasticity: = [  Q  P] × [P a  Q a ] Own price elasticity of demand Own price elasticity of demand Percentage change in quantity Percentage change in price =  Q = (Q a – Q b ); and  P = (P a – P b ) The subscript “a” here stands for “after” while “b” stands for “before” Single point on curve P a Q a Pages 70-72
  • 12. Own Price Elasticity of Demand Own price elasticity of demand Percentage change in quantity Percentage change in price = Page 72 Arc Elasticity Approach
  • 13. Own Price Elasticity of Demand Own price elasticity of demand Percentage change in quantity Percentage change in price = where: P = (P a + P b )  2; Q = (Q a + Q b )  2;  Q = (Q a – Q b ); and  P = (P a – P b ) Arc elasticity Own price elasticity of demand = [  Q  P] x [P  Q] The subscript “a” here again stands for “after” while “b” stands for “before” Equation 5.3 Page 72
  • 14. Own Price Elasticity of Demand Own price elasticity of demand Percentage change in quantity Percentage change in price = where: P = (P a + P b )  2; Q = (Q a + Q b )  2;  Q = (Q a – Q b ); and  P = (P a – P b ) Arc elasticity Own price elasticity of demand = [  Q  P] x [P  Q] The subscript “a” here again stands for “after” while “b” stands for “before” The “bar” over the P and Q variables indicates an average or mean. Page 72
  • 15. Own Price Elasticity of Demand Own price elasticity of demand Percentage change in quantity Percentage change in price = where: P = (P a + P b )  2; Q = (Q a + Q b )  2;  Q = (Q a – Q b ); and  P = (P a – P b ) Arc elasticity Own price elasticity of demand = [  Q  P] x [P  Q] The subscript “a” here again stands for “after” while “b” stands for “before” Specific range on curve P b P a Q b Q a Page 72
  • 16. Interpreting the Own Price Elasticity of Demand Page 72 If elasticity coefficient is: Demand is said to be: %  in quantity is: Greater than 1.0 Elastic Greater than %  in price Equal to 1.0 Unitary elastic Same as %  in price Less than 1.0 Inelastic Less than %  in price
  • 17. Demand Curves Come in a Variety of Shapes
  • 18. Demand Curves Come in a Variety of Shapes Perfectly inelastic Perfectly elastic Page 72
  • 19. Demand Curves Come in a Variety of Shapes Inelastic Elastic
  • 20. Demand Curves Come in a Variety of Shapes Inelastic where %  Q < %  P Elastic where %  Q > %  P Page 73 Unitary Elastic where %  Q = %  P
  • 21.
    • Demand curves often exhibit all three ranges of elasticity in a single curve.
      • Always true when a demand curve is a straight line.
    Straight line demand curves are elastic with respect to price at relatively high prices, and inelastic at relatively low prices.
  • 22. Page 73 Example of arc own-price elasticity of demand Unitary elasticity…a one for one exchange
  • 23. Page 73 Inelastic demand Elastic demand
  • 24. P b P a Q b Q a Price Quantity Elastic Demand Curve 0 Cut in price Brings about a larger increase in the quantity demanded c
  • 25. P b P a Q b Q a Price Quantity Elastic Demand Curve What happened to producer revenue? What happened to consumer surplus? 0 c
  • 26. P b P a Q b Q a Price Quantity Elastic Demand Curve Producer revenue increases since %  P is less that %  Q. Revenue before the change was 0P b aQ b . Revenue after the change was 0P a bQ a . a b 0 c
  • 27. P b P a Q b Q a Price Quantity Elastic Demand Curve Producer revenue increases since %  P is less that %  Q. Revenue before the change was 0P b aQ b . Revenue after the change was 0P a bQ a . a b 0 c
  • 28. P b P a Q b Q a Price Quantity Elastic Demand Curve Producer revenue increases since %  P is less that %  Q. Revenue before the change was 0P b aQ b . Revenue after the change was 0P a bQ a . a b 0 c
  • 29. Revenue Implications Page 81 Own-price elasticity is: Cutting the price will: Increasing the price will: Elastic Increase revenue Decrease revenue Unitary elastic Not change revenue Not change revenue Inelastic Decrease revenue Increase revenue
  • 30. P b P a Q b Q a Price Quantity Elastic Demand Curve Consumer surplus before the price cut was area P b ca. a b 0 c
  • 31. P b P a Q b Q a Price Quantity Elastic Demand Curve Consumer surplus after the price cut is Area P a cb. a b 0 c
  • 32. P b P a Q b Q a Price Quantity Elastic Demand Curve So the gain in consumer surplus after the price cut is area P a P b ab. a b 0 c
  • 33. P b P a Q b Q a Price Quantity Inelastic Demand Curve Cut in price Brings about a smaller increase in the quantity demanded
  • 34. P b P a Q b Q a Price Quantity Inelastic Demand Curve What happened to producer revenue? What happened to consumer surplus?
  • 35. P b P a Q b Q a Price Quantity Inelastic Demand Curve Producer revenue falls since %  P is greater than %  Q. Revenue before the change was 0P b aQ b . Revenue after the change was 0P a bQ a . a b 0
  • 36. P b P a Q b Q a Price Quantity Inelastic Demand Curve Producer revenue falls since %  P is greater than %  Q. Revenue before the change was 0P b aQ b . Revenue after the change was 0P a bQ a . a b 0
  • 37. P b P a Q b Q a Price Quantity Inelastic Demand Curve Consumer surplus increased by area P a P b ab a b 0
  • 38. Revenue Implications Characteristic of agriculture Page 81 Own-price elasticity is: Cutting the price will: Increasing the price will: Elastic Increase revenue Decrease revenue Unitary elastic Not change revenue Not change revenue Inelastic Decrease revenue Increase revenue
  • 39. Retail Own Price Elasticities
    • Beef and veal= .6166
    • Milk = .2588
    • Wheat = .1092
    • Rice = .1467
    • Carrots = .0388
    • Non food = .9875
    Page 79
  • 40. Interpretation Let’s take rice as an example, which has an own price elasticity of - 0.1467. This suggests that if the price of rice drops by 10%, for example, the quantity of rice demanded will only increase by 1.467%. P Q 10% drop 1.467% increase Rice producer Revenue? Consumer surplus?
  • 41. Example
    • 1. The Dixie Chicken sells 1,500 Freddie Burger platters per month at $3.50 each. The own price elasticity for this platter is estimated to be –0.30. If the Chicken increases the price of the platter by 50 cents:
    • How many platters will the chicken sell?__________
    • b. The Chicken’s revenue will change by $__________
    • c. Consumers will be ____________ off as a result of this price change.
  • 42. The answer…
    • 1. The Dixie Chicken sells 1,500 Freddie Burger platters per month at $3.50 each. The own price elasticity for this platter is estimated to be –0.30 . If the Chicken increases the price of the platter by 50 cents :
    • How many platters will the chicken sell?__ 1,440 ____
    • Solution:
    • -0.30 = %  Q  %  P
    • -0.30= %  Q  [($4.00-$3.50)  (($4.00+$3.50)  2)]
    • -0.30= %  Q  [$0.50  $3.75]
    • -0.30= %  Q  0.1333
    • %  Q=(-0.30 × 0.1333) = -0.04 or –4%
    • So new quantity is 1,440, or (1-.04) ×1,500,
    • or .96 ×1,500
  • 43. The answer…
    • 1. The Dixie Chicken sells 1,500 Freddie Burger platters per month at $3.50 each. The own price elasticity for this platter is estimated to be –0.30 . If the Chicken increases the price of the platter by 50 cents :
    • How many platters will the chicken sell?__ 1,440 ____
    • b. The Chicken’s revenue will change by $__ +$510 ___
    • Solution:
    • Current revenue = 1,500 × $3.50 = $5,250 per month
    • New revenue = 1,440 × $4.00 = $5,760 per month
    • So revenue increases by $510 per month, or $5,760
    • minus $5,250
  • 44. The answer…
    • 1. The Dixie Chicken sells 1,500 Freddie Burger platters per month at $3.50 each. The own price elasticity for this platter is estimated to be –0.30. If the Chicken increases the price of the platter by 50 cents :
    • How many platters will the chicken sell?__ 1,440 ____
    • b. The Chicken’s revenue will change by $__ +$510 ___
    • Consumers will be __ worse ___ off as a result of this price change.
    • Why? Because price increased.
  • 45. Another Example
    • 1. The Dixie Chicken sells 1,500 Freddie Burger platters per month at $3.50 each. The own price elasticity for this platter is estimated to be –1.30 . If the Chicken increases the price of the platter by 50 cents :
    • How many platters will the chicken sell?__________
    • b. The Chicken’s revenue will change by $__________
    • c. Consumers will be ____________ off as a result of this price change.
  • 46. The answer…
    • 1. The Dixie Chicken sells 1,500 Freddie Burger platters per month at $3.50 each. The own price elasticity for this platter is estimated to be –1.30 . If the Chicken increases the price of the platter by 50 cents :
    • How many platters will the chicken sell?__ 1,240 ____
    • Solution:
    • -1.30 = %  Q  %  P
    • -1.30= %  Q  [($4.00-$3.50)  (($4.00+$3.50)  2)]
    • -1.30= %  Q  [$0.50  $3.75]
    • -1.30= %  Q  0.1333
    • %  Q=(-1.30 × 0.1333) = -0.1733 or –17.33%
    • So new quantity is 1,240, or (1-.1733) ×1,500,
    • or .8267 ×1,500
  • 47. The answer…
    • 1. The Dixie Chicken sells 1,500 Freddie Burger platters per month at $3.50 each. The own price elasticity for this platter is estimated to be –1.30 . If the Chicken increases the price of the platter by 50 cents :
    • How many platters will the chicken sell?__ 1,240 ____
    • b. The Chicken’s revenue will change by $__ - $290 ___
    • Solution:
    • Current revenue = 1,500 × $3.50 = $5,250 per month
    • New revenue = 1,240 × $4.00 = $4,960 per month
    • So revenue decreases by $290 per month,
    • or $4,960 minus $5,250
  • 48. The answer…
    • 1. The Dixie Chicken sells 1,500 Freddie Burger platters per month at $3.50 each. The own price elasticity for this platter is estimated to be –1.30. If the Chicken increases the price of the platter by 50 cents :
    • How many platters will the chicken sell?__ 1,240 ____
    • b. The Chicken’s revenue will change by $__ - $290 ___
    • Consumers will be __ worse ___ off as a result of this price change.
    • Why? Because the price increased.
  • 49. Income Elasticity of Demand
  • 50. Income Elasticity of Demand Income elasticity of demand Percentage change in quantity Percentage change in income = where: I = (I a + I b )  2 Q = (Q a + Q b )  2  Q = (Q a – Q b )  I = (I a – I b ) = [  Q   I] x [I  Q] Page 74-75 Indicates potential changes or shifts in the demand curve as consumer income (I) changes….
  • 51. Interpreting the Income Elasticity of Demand Page 75 If the income elasticity is equal to: The good is classified as: Greater than 1.0 A luxury and a normal good Less than 1.0 but greater than 0.0 A necessity and a normal good Less than 0.0 An inferior good!
  • 52. Some Examples Elastic Page 79 Commodity Own Price elasticity Income elasticity Beef and veal -0.6166 0.4549 Chicken -0.5308 .3645 Cheese -0.3319 0.5927 Rice -0.1467 -0.3664 Lettuce -0.1371 0.2344 Tomatoes -0.5584 0.4619 Fruit juice -0.5612 1.1254 Grapes -1.3780 0.4407 Nonfood items -0.9875 1.1773
  • 53. Some Examples Inferior good Elastic Page 79 Commodity Own Price elasticity Income elasticity Beef -0.6166 0.4549 Chicken -0.5308 .3645 Cheese -0.3319 0.5927 Rice -0.1467 -0.3664 Lettuce -0.1371 0.2344 Tomatoes -0.5584 0.4619 Fruit juice -0.5612 1.1254 Grapes -1.3780 0.4407 Nonfood items -0.9875 1.1773
  • 54. Some Examples Inferior good Luxury good Elastic Page 79 Commodity Own Price elasticity Income elasticity Beef -0.6166 0.4549 Chicken -0.5308 .3645 Cheese -0.3319 0.5927 Rice -0.1467 -0.3664 Lettuce -0.1371 0.2344 Tomatoes -0.5584 0.4619 Fruit juice -0.5612 1.1254 Grapes -1.3780 0.4407 Nonfood items -0.9875 1.1773
  • 55. Example
    • Assume the government cuts taxes, thereby increasing disposable income by 5%. The income elasticity for chicken is .3645.
    • What impact would this tax cut have upon the demand for chicken?
    • Is chicken a normal good or an inferior good? Why?
  • 56. The Answer
    • 1. Assume the government cuts taxes, thereby increasing disposable income (I) by 5%. The income elasticity for chicken is .3645 .
    • What impact would this tax cut have upon the demand for chicken?
    • Solution:
    • .3645 = %  Q Chicken  %  I
    • .3654 = %  Q Chicken  .05
    • %  Q Chicken = .3645  .05 = .018 or + 1.8%
  • 57. The Answer
    • 1. Assume the government cuts taxes, thereby increasing disposable income by 5%. The income elasticity for chicken is .3645.
    • What impact would this tax cut have upon the demand for chicken? _____ + 1.8% ___
    • Is chicken a normal good or an inferior good? Why?
    • Chicken is a normal good but not a luxury since the income elasticity is > 0 but < 1.0
  • 58. Cross Price Elasticity of Demand
  • 59. Cross Price Elasticity of Demand Cross Price elasticity of demand Percentage change in quantity Percentage change in another price = where: P T = (P Ta + P Tb )  2 Q H = (Q Ha + Q Hb )  2  Q H = (Q Ha – Q Hb )  P T = (P Ta – P Tb ) = [  Q H  P T ] × [P T  Q H ] Page 75 Indicates potential changes or shifts in the demand curve as the price of other goods change…
  • 60. Interpreting the Cross Price Elasticity of Demand Page 76 If the cross price elasticity is equal to: The good is classified as: Positive Substitutes Negative Complements Zero Independent
  • 61. Some Examples Values in red along the diagonal are own price elasticities… Page 80 Item Prego Ragu Hunt’s Prego -2.5502 .8103 .3918 Ragu .5100 -2.0610 .1381 Hunt’s 1.0293 .5349 -2.7541
  • 62. Some Examples Values off the diagonal are all positive , indicating these products are substitutes as prices change… Page 80 Item Prego Ragu Hunt’s Prego -2.5502 .8103 .3918 Ragu .5100 -2.0610 .1381 Hunt’s 1.0293 .5349 -2.7541
  • 63. Some Examples An increase in the price of Ragu Spaghetti Sauce has a bigger impact on Hunt’s Spaghetti Sauce than vice versa. Page 80 Item Prego Ragu Hunt’s Prego -2.5502 .8103 .3918 Ragu .5100 -2.0610 .1381 Hunt’s 1.0293 .5349 -2.7541
  • 64. Some Examples Page 80 A 10% increase in the price of Ragu Spaghetti Sauce increases the demand for Hunt’s Spaghetti Sauce by 5.349%….. Item Prego Ragu Hunt’s Prego -2.5502 .8103 .3918 Ragu .5100 -2.0610 .1381 Hunt’s 1.0293 .5349 -2.7541
  • 65. Some Examples Page 80 But…a 10% increase in the price of Hunt’s Spaghetti Sauce increases the demand for Ragu Spaghetti Sauce by only 1.381%….. Item Prego Ragu Hunt’s Prego -2.5502 .8103 .3918 Ragu .5100 -2.0610 .1381 Hunt’s 1.0293 .5349 -2.7541
  • 66. Example
    • 1. The cross price elasticity for hamburger demand with respect to the price of hamburger buns is equal to –0.60.
    • If the price of hamburger buns rises by 5 percent, what impact will that have on hamburger consumption?
    • What is the demand relationship between these products?
  • 67. The Answer
    • 1. The cross price elasticity for hamburger demand with respect to the price of hamburger buns is equal to –0.60.
    • If the price of hamburger buns rises by 5%, what impact will that have on hamburger consumption? ____ - 3% ______
    • Solution:
    • -.60 = %  Q H  %  P HB
    • -.60 = %  Q H  .05
    • %  Q H = .05  (-.60) = -.03 or – 3%
  • 68. The Answer
    • 1. The cross price elasticity for hamburger demand with respect to the price of hamburger buns is equal to –0.60.
    • If the price of hamburger buns rises by 5%, what impact will that have on hamburger consumption? ___ - 3% _____
    • What is the demand relationship between these products?
  • 69. The Answer
    • 1. The cross price elasticity for hamburger demand with respect to the price of hamburger buns is equal to –0.60.
    • If the price of hamburger buns rises by 5%, what impact will that have on hamburger consumption? ___ - 3% _____
    • What is the demand relationship between these products?
    • These two products are complements as evidenced by the negative sign on this cross price elasticity.
  • 70. Another Example
    • 2. Assume that a retailer sells 1,000 six-packs of Pepsi per day at a price of $3.00 per six-pack. Also assume the cross price elasticity for Pepsi with respect to the price of Coca Cola is 0.70.
    • If the price of Coca Cola rises by 5 percent, what impact will that have on Pepsi consumption?
    • b. What is the demand relationship between these products?
  • 71. The Answer
    • 2. Assume that a retailer sells 1,000 six-packs of Pepsi per day at a price of $3.00 per six-pack. Also assume the cross price elasticity for Pepsi with respect to the price of Coca Cola is 0.70.
    • If the price of Coca Cola rises by 5 percent, what impact will that have on Pepsi consumption?
    • Solution:
    • .70 = %  Q Pepsi  %  P Coke
    • .70 = %  Q Pepsi  .05 = .035 or 3.5%
    • New quantity sold = 1,000  1.035 = 1,035
    • New value of sales = 1,035  $3.00 = $3,105
  • 72. The Answer
    • 2. Assume that a retailer sells 1,000 six-packs of Pepsi per day at a price of $3.00 per six-pack. Also assume the cross price elasticity for Pepsi with respect to the price of Coca Cola is 0.70.
    • If the price of Coca Cola rises by 5 percent, what impact will that have on Pepsi consumption? __ 35 six-packs or $105 per day __
    • What is the demand relationship between these products?
  • 73. The Answer
    • 2. Assume that a retailer sells 1,000 six-packs of Pepsi per day at a price of $3.00 per six-pack. Also assume the cross price elasticity for Pepsi with respect to the price of Coca Cola is 0.70.
    • If the price of Coca Cola rises by 5 percent, what impact will that have on Pepsi consumption? __ 35 six-packs or $105 per day __
    • What is the demand relationship between these products?
    • The products are substitutes as evidenced by the positive sign on this cross price elasticity!
  • 74. Price Flexibility of Demand
  • 75. Price Flexibility We earlier said that the price flexibility is the reciprocal of the own-price elasticity. If the calculated elasticty is - 0.25, then the flexibility would be - 4.0 .
  • 76. Price Flexibility We earlier said that the price flexibility is the reciprocal of the own-price elasticity. If the calculated elasticty is - 0.25, then the flexibility would be - 4.0 . This is a useful concept to producers when forming expectations for the current year. If the USDA projects an additional 2% of supply will likely come on the market, then producers know the price will likely drop by 8%, or: %  Price = - 4.0 x %  Quantity = - 4.0 x (+2%) = - 8% If supply increases by 2%, price would fall by 8%!
  • 77. Price Flexibility We earlier said that the price flexibility is the reciprocal of the own-price elasticity. If the calculated elasticty is - 0.25, then the flexibility would be - 4.0 . This is a useful concept to producers when forming expectations for the current year. If the USDA projects an additional 2% of supply will likely come on the market, then producers know the price will likely drop by 8%, or: %  Price = - 4.0 x %  Quantity = - 4.0 x (+2%) = - 8% If supply increases by 2%, price would fall by 8%! Note : make sure you use the negative sign for both the elasticity and the flexibility.
  • 78. Revenue Implications Characteristic of agriculture Page 81 Own-price elasticity is: Increase in supply will: Decrease in supply will: Elastic Increase revenue Decrease revenue Unitary elastic Not change revenue Not change revenue Inelastic Decrease revenue Increase revenue
  • 79. Short run effects Long run effects Over time, consumers respond in greater numbers. This is referred to as a recognition lag… Page 77 Changing Price Response Over Time
  • 80. P b P a Q b Q a Price Quantity Ag’s Inelastic Demand Curve A small increase in supply will cause the price of Ag products to fall sharply. This explains why major program crops receive Subsidies from the federal government. a b 0 Increase in supply
  • 81. P b P a Q b Q a Price Quantity Inelastic Demand Curve While this increases the costs of government programs and hence budget deficits, remember consumers benefit from cheaper food costs. a b 0 P b P a Q b Q a Price a b 0
  • 82. Demand Characteristics
    • Which market is riskier for producers… elastic or inelastic demand?
    • Which market would you start a business in?
    • Which market is more apt to need government subsidies to stabilize producer incomes?
  • 83. The Market Demand Curve Price Quantity What causes movement along a demand curve?
  • 84. The Market Demand Curve Price Quantity What causes the demand curve to shift?
  • 85. In Summary…
    • Know how to interpret all three elasticities
    • Know how to interpret a price flexibility
    • Understand revenue implications for producers if prices are cut (raised)
    • Understand the welfare implications for consumers if prices are cut (raised)
    • Know what causes movement along versus shifts the demand curve
  • 86. Chapter 6 starts a series of chapters that culminates in a market supply curve for food and fiber products….