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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 Pages 91-95

  4. 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 Pages 91-95

  5. 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 Pages 91-95

  6. Own Price Elasticityof Demand

  7. Own Price Elasticity of Demand Own price elasticity of demand Percentage change in quantity = Percentage change in price Point Elasticity Approach Page 91

  8. Own Price Elasticity of Demand Own price elasticity of demand Percentage change in quantity = Percentage change in price Point elasticity: Own price elasticity of demand = [QP] × [PaQa] The subscript “a” here stands for “after” while “b” stands for “before” Q = (Qa – Qb); and P = (Pa – Pb) Page 91

  9. Own Price Elasticity of Demand Own price elasticity of demand Percentage change in quantity = Percentage change in price Single point on curve Point elasticity: Pa Own price elasticity of demand = [QP] × [PaQa] Qa The subscript “a” here stands for “after” while “b” stands for “before” Q = (Qa – Qb); and P = (Pa – Pb) Page 91

  10. Own Price Elasticity of Demand Own price elasticity of demand Percentage change in quantity = Percentage change in price Arc Elasticity Approach Page 91

  11. 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 91

  12. 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 mean. 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 91

  13. 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 91

  14. Interpreting the Own Price Elasticity of Demand Page 92

  15. Demand Curves Come in a Variety of Shapes

  16. Demand Curves Come in a Variety of Shapes Perfectly inelastic Perfectly elastic Page 92

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

  18. Demand Curves Come in a Variety of Shapes Elastic where %Q > % P Unitary Elastic where %Q = % P Inelastic where %Q < % P Page 93

  19. Example of arc own-price elasticity of demand Unitary elasticity…a one for one exchange Page 93

  20. Elastic demand Inelastic demand Page 93

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

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

  23. 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

  24. 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

  25. 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

  26. Revenue Implications Page 101

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

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

  29. 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

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

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

  32. 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

  33. 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

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

  35. Revenue Implications Page 101 Characteristic of agriculture

  36. Retail Own Price Elasticities • Beef and veal= .6166 • Milk = .2588 • Wheat = .1092 • Rice = .1467 • Carrots = .0388 • Non food = .9875 Page 99

  37. 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

  38. 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.

  39. 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

  40. 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

  41. 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.

  42. 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.

  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 –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

  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 –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

  45. 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 increasesthe 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.

  46. Income Elasticityof Demand

  47. 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 94

  48. Interpreting the Income Elasticity of Demand Page 95

  49. Some Examples Luxury good Elastic Inferior good Page 99

  50. 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?

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