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Measurement and Interpretation of Elasticities

Measurement and Interpretation of Elasticities. Chapter 5. Discussion Topics. Own price elasticity of demand Income elasticity of demand Cross price elasticity of demand Other general properties Applicability of demand elasticities. Key Concepts Covered….

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Measurement and Interpretation of Elasticities

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  1. Measurementand Interpretationof 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 = %Qbeeffor a given%Pbeef • Incomeelasticity = %Qbeeffor a given%Income • Cross priceelasticity = %Qbeeffor a given%Pchicken • Arc elasticity = range along the demand curve • Point elasticity = point on the demand curve • Price flexibility = reciprocal of own price elasticity

  4. Own Price Elasticityof Demand

  5. Own Price Elasticity of Demand Own price elasticity of demand Percentage change in quantity = Percentage change in price Arc Elasticity Approach Page 71

  6. Own Price Elasticity of Demand Own price elasticity of demand Percentage change in quantity = Percentage change in price Arc elasticity Own price elasticity of demand Equation 5.3 = [QP] x [PQ] where: P= (Pa + Pb) 2; Q= (Qa + Qb) 2; Q = (Qa – Qb); and P = (Pa – Pb) The subscript “a” here again stands for “after” while “b” stands for “before” Page 71

  7. Own Price Elasticity of Demand Own price elasticity of demand Percentage change in quantity = Percentage change in price The “bar” over the P and Q variables indicates an average or midpoint. Arc elasticity Own price elasticity of demand = [QP] x [PQ] where: P= (Pa + Pb) 2; Q= (Qa + Qb) 2; Q = (Qa – Qb); and P = (Pa – Pb) The subscript “a” here again stands for “after” while “b” stands for “before” Page 71

  8. Own Price Elasticity of Demand Own price elasticity of demand Percentage change in quantity = Percentage change in price Specific range on curve Arc elasticity Pb Own price elasticity of demand Pa = [QP] x [PQ] Qb Qa where: P= (Pa + Pb) 2; Q= (Qa + Qb) 2; Q = (Qa – Qb); and P = (Pa – Pb) The subscript “a” here again stands for “after” while “b” stands for “before” Page 71

  9. Interpreting the Own Price Elasticity of Demand Page 72

  10. Demand Curves Come in a Variety of Shapes

  11. Demand Curves Come in a Variety of Shapes Perfectly inelastic Perfectly elastic Page 72

  12. Demand Curves Come in a Variety of Shapes Inelastic Elastic

  13. Demand Curves Come in a Variety of Shapes Elastic where %Q > % P Unitary Elastic where %Q = % P Inelastic where %Q < % P Page 73

  14. Example of arc own-price elasticity of demand Unitary elasticity…a one for one exchange Page 73

  15. Elastic demand Inelastic demand Page 73

  16. Elastic Demand Curve Price c Pb Cut in price Brings about a larger increase in the quantity demanded Pa 0 Qb Qa Quantity

  17. Elastic Demand Curve Price What happened to producer revenue? What happened to consumer surplus? c Pb Pa 0 Qb Qa Quantity

  18. Elastic Demand Curve Price Producer revenue increases since %P is less that %Q. Revenue before the change was 0PbaQb. Revenue after the change was 0PabQa. c a Pb b Pa 0 Qb Qa Quantity

  19. Elastic Demand Curve Price Producer revenue increases since %P is less that %Q. Revenue before the change was 0PbaQb. Revenue after the change was 0PabQa. c a Pb b Pa 0 Qb Qa Quantity

  20. Elastic Demand Curve Price Producer revenue increases since %P is less that %Q. Revenue before the change was 0PbaQb. Revenue after the change was 0PabQa. c a Pb b Pa 0 Qb Qa Quantity

  21. Revenue Implications Page 81

  22. Elastic Demand Curve Price Consumer surplus before the price cut was area Pbca. c a Pb b Pa 0 Qb Qa Quantity

  23. Elastic Demand Curve Price Consumer surplus after the price cut is Area Pacb. c a Pb b Pa 0 Qb Qa Quantity

  24. Elastic Demand Curve Price So the gain in consumer surplus after the price cut is area PaPbab. c a Pb b Pa 0 Qb Qa Quantity

  25. Inelastic Demand Curve Price Pb Cut in price Pa Brings about a smaller increase in the quantity demanded Qb Qa Quantity

  26. Inelastic Demand Curve Price What happened to producer revenue? What happened to consumer surplus? Pb Pa Qb Qa Quantity

  27. Inelastic Demand Curve Price a Producer revenue falls since %P is greater than %Q. Revenue before the change was 0PbaQb. Revenue after the change was 0PabQa. Pb b Pa 0 Qb Qa Quantity

  28. Inelastic Demand Curve Price a Producer revenue falls since %P is greater than %Q. Revenue before the change was 0PbaQb. Revenue after the change was 0PabQa. Pb b Pa 0 Qb Qa Quantity

  29. Inelastic Demand Curve Price a Consumer surplus increased by area PaPbab Pb b Pa 0 Qb Qa Quantity

  30. Revenue Implications Page 81 Characteristic of agriculture

  31. Retail Own Price Elasticities • Beef = -.6166 • Cheese = -.3319 • Bananas = -.4002 • Milk = -.2588 • Carrots = -.0388 Page 79

  32. 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 Rice producer Revenue? Consumer surplus? 10% drop 1.467% increase Q

  33. Example • 1. The Dixie Chicken sells 1,500 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 70 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.

  34. The answer… • 1. The Dixie Chicken sells 1,500 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 70 cents: • How many platters will the chicken sell?__1,110____ • Solution: • -1.30 = %Q%P • -1.30= %Q[20%] • %Q=(-1.30 × 20) = –26% • So the new quantity of burger platters is 1,110, or • (1-.26) ×1,500, or .74 ×1,500

  35. The answer… • 1. The Dixie Chicken sells 1,500 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 70 cents: • How many platters will the chicken sell?__1,110____ • b. The Chicken’s revenue will change by $__-$588___ • Solution: • Current revenue = 1,500 × $3.50 = $5,250 per month • New revenue = 1,110 × $4.20 = $4,662 per month • So revenue decreases by $588 per month, or $4,662 • minus $5,250

  36. The answer… • 1. The Dixie Chicken sells 1,500 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 70 cents: • How many platters will the chicken sell?__1,110____ • b. The Chicken’s revenue will change by $__-$588___ • Consumers will be __worse___ off as a result of this price change. • Why? Because price increased.

  37. Income Elasticityof Demand

  38. Income Elasticity of Demand Income elasticity of demand Percentage change in quantity = Percentage change in income = [QI] x [IQ] where: I= (Ia + Ib) 2 Q= (Qa + Qb) 2 Q = (Qa – Qb) I = (Ia – Ib) Indicates potential changes or shifts in the demand curve as consumer income (I) changes…. Page 74

  39. Interpreting the Income Elasticity of Demand Page 75

  40. Some Examples Luxury good Elastic Inferior good Page 79

  41. 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?

  42. 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 = %QChicken  % I • .3654 = %QChicken  5 • %QChicken = .3645 5 = + 1.8225%

  43. 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? _____+ 1.8225%___ • 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

  44. Cross Price Elasticityof Demand

  45. Cross Price Elasticity of Demand Cross Price elasticity of demand Percentage change in quantity = Percentage change in another price = [QHPT] × [PTQH] where: PT= (PTa + PTb) 2 QH= (QHa + QHb) 2 QH = (QHa – QHb) PT = (PTa – PTb) Indicates potential changes or shifts in the demand curve as the price of other goods change… Page 75

  46. Interpreting the Cross Price Elasticity of Demand Page 76

  47. Some Examples Values in red along the diagonal are own price elasticities… Page 80

  48. Some Examples Values off the diagonal are all positive, indicating these products are substitutes as prices change… Page 80

  49. 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

  50. Some Examples A 10% increase in the price of Ragu Spaghetti Sauce increases the demand for Hunt’s Spaghetti Sauce by 5.349%….. Page 80

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