Measurement and Interpretation of Elasticities
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MEASUREMENT AND INTERPRETATION OF ELASTICITIES 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… Own price elasticity = %Qbeef for a given %Pbeef Income elasticity = %Qbeef for a given %Income Cross price elasticity = %Qbeef for a given %Pchicken Arc elasticity = range along the demand curve Point elasticity = point on the demand curve Price flexibility = reciprocal of own price elasticity Own Price Elasticity of Demand Own Price Elasticity of Demand Own = price elasticity of demand Percentage change in quantity Percentage change in price Arc Elasticity Approach Page 71 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 = [QP] x [PQ] where: P = (Pa + Pb) 2; Q = (Qa + Qb) 2; Q = (Qa – Qb); and P = (Pa – Pb) Equation 5.3 The subscript “a” here again stands for “after” while “b” stands for “before” Page 71 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 = [QP] x [PQ] 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 Own Price Elasticity of Demand Own price elasticity = of demand Percentage change in quantity Percentage change in price Specific range on curve Arc elasticity Own price elasticity of demand = [QP] x [PQ] where: P = (Pa + Pb) 2; Q = (Qa + Qb) 2; Q = (Qa – Qb); and P = (Pa – Pb) Pb Pa Qb Qa The subscript “a” here again stands for “after” while “b” stands for “before” Page 71 Interpreting the Own Price Elasticity of Demand If elasticity coefficient is: Greater than 1.0 Equal to 1.0 Less than 1.0 Demand is said to be: % in quantity is: Elastic Greater than % in price Unitary elastic Same as % in price Inelastic Less than % in price Page 72 Demand Curves Come in a Variety of Shapes Demand Curves Come in a Variety of Shapes Perfectly inelastic Perfectly elastic Page 72 Demand Curves Come in a Variety of Shapes Inelastic Elastic Demand Curves Come in a Variety of Shapes Elastic where %Q > % P Unitary Elastic where %Q = % P Inelastic where %Q < % P Page 73 Example of arc own-price elasticity of demand Unitary elasticity…a one for one exchange Page 73 Elastic demand Inelastic demand Page 73 Elastic Demand Curve Price c Cut in price Pb Brings about a larger increase in the quantity demanded Pa 0 Qb Qa Quantity Elastic Demand Curve Price What happened to producer revenue? c What happened to consumer surplus? Pb Pa 0 Qb Qa Quantity Elastic Demand Curve Price Producer revenue increases since %P is less that %Q. c Pb a b Pa Revenue before the change was 0PbaQb. Revenue after the change was 0PabQa. 0 Qb Qa Quantity Elastic Demand Curve Price Producer revenue increases since %P is less that %Q. c Pb a b Pa Revenue before the change was 0PbaQb. Revenue after the change was 0PabQa. 0 Qb Qa Quantity Elastic Demand Curve Price Producer revenue increases since %P is less that %Q. c Pb a b Pa Revenue before the change was 0PbaQb. Revenue after the change was 0PabQa. 0 Qb Qa Quantity Revenue Implications Own-price elasticity is: Elastic Cutting the price will: Decrease Increase revenue revenue Not change Unitary elastic revenue Inelastic Increasing the price will: Not change revenue Increase Decrease revenue revenue Page 81 Elastic Demand Curve Price Consumer surplus before the price cut was area Pbca. c Pb a b Pa 0 Qb Qa Quantity Elastic Demand Curve Price Consumer surplus after the price cut is Area Pacb. c Pb a b Pa 0 Qb Qa Quantity Elastic Demand Curve Price So the gain in consumer surplus after the price cut is area PaPbab. c Pb a b Pa 0 Qb Qa Quantity Elastic Demand Curve Price Pb Cut in price Pa Brings about a smaller increase in the quantity demanded Qb Qa Quantity Elastic Demand Curve Price Pb What happened to producer revenue? Pa What happened to consumer surplus? Qb Qa Quantity Elastic Demand Curve Price Pb Pa a Producer revenue falls since %P is greater than %Q. b Revenue before the change was 0PbaQb. Revenue after the change was 0PabQa. 0 Qb Qa Quantity Elastic Demand Curve Price Pb Pa a Producer revenue falls since %P is greater than %Q. b Revenue before the change was 0PbaQb. Revenue after the change was 0PabQa. 0 Qb Qa Quantity Elastic Demand Curve Price Pb Pa a Consumer surplus increased by area PaPbab b 0 Qb Qa Quantity Revenue Implications 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 Increase revenue Decrease revenue Characteristic of agriculture Page 81 Retail Own Price Elasticities • Beef = -.6166 • Cheese = -.3319 • Bananas = -.4002 • Milk = -.2588 • Carrots = -.0388 Page 79 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 10% drop 1.467% increase Rice producer Revenue? Consumer surplus? Q 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: a. 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. 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: a. 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 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: a. 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 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: a. How many platters will the chicken sell?__1,110____ b. The Chicken’s revenue will change by $__-$588___ c. Consumers will be __worse___ off as a result of this price change. Why? Because price increased. Income Elasticity of Demand Income Elasticity of Demand Income elasticity of demand Percentage change in quantity = = Percentage change in income [QI] x [IQ] 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 Interpreting the Income Elasticity of Demand If the income elasticity is equal to: Greater than 1.0 The good is classified as: 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! Page 75 Some Examples 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 Elastic Page 99 Some Examples 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 Commodity Elastic Inferior good Page 99 Some Examples 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 Commodity Elastic Inferior good Luxury good Page 79 Example Assume the government cuts taxes, thereby increasing disposable income by 5%. The income elasticity for chicken is .3645. a. What impact would this tax cut have upon the demand for chicken? b. Is chicken a normal good or an inferior good? Why? The Answer 1. Assume the government cuts taxes, thereby increasing disposable income (I) by 5%. The income elasticity for chicken is .3645. a. What impact would this tax cut have upon the demand for chicken? Solution: .3645 = %QChicken % I .3654 = %QChicken 5 %QChicken = .3645 5 = + 1.8225% The Answer 1. Assume the government cuts taxes, thereby increasing disposable income by 5%. The income elasticity for chicken is .3645. a. What impact would this tax cut have upon the demand for chicken? _____+ 1.8225%___ b. 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 Cross Price Elasticity of Demand Cross Price Elasticity of Demand Cross Price elasticity of demand Percentage change in quantity = Percentage change in another price = [QHPT] × [PTQH] 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 Interpreting the Cross Price Elasticity of Demand If the cross price elasticity is equal to: Positive The good is classified as: Substitutes Negative Complements Zero Independent Page 76 Some Examples Item Prego Ragu Hunt’s Prego -2.5502 .8103 .3918 Ragu .5100 -2.0610 .1381 Hunt’s 1.0293 .5349 -2.7541 Values in red along the diagonal are own price elasticities… Page 80 Some Examples Item Prego Ragu Hunt’s Prego -2.5502 .8103 .3918 Ragu .5100 -2.0610 .1381 Hunt’s 1.0293 .5349 -2.7541 Values off the diagonal are all positive, indicating these products are substitutes as prices change… Page 80 Some Examples Item Prego Ragu Hunt’s Prego -2.5502 .8103 .3918 Ragu .5100 -2.0610 .1381 Hunt’s 1.0293 .5349 -2.7541 An increase in the price of Ragu Spaghetti Sauce has a bigger impact on Hunt’s Spaghetti Sauce than vice versa. Page 80 Some Examples Item Prego Ragu Hunt’s Prego -2.5502 .8103 .3918 Ragu .5100 -2.0610 .1381 Hunt’s 1.0293 .5349 -2.7541 A 10% increase in the price of Ragu Spaghetti Sauce increases the demand for Hunt’s Spaghetti Sauce by 5.349%….. Page 80 Some Examples Item Prego Ragu Hunt’s Prego -2.5502 .8103 .3918 Ragu .5100 -2.0610 .1381 Hunt’s 1.0293 .5349 -2.7541 But…a 10% increase in the price of Hunt’s Spaghetti Sauce increases the demand for Ragu Spaghetti Sauce by only 1.381%….. Page 80 Example 1. The cross-price elasticity for hamburger demand with respect to the price of hamburger buns is equal to –0.60. a. If the price of hamburger buns rises by 5 percent, what impact will that have on hamburger consumption? b. What is the demand relationship between these products? The Answer 1. The cross-price elasticity for hamburger demand with respect to the price of hamburger buns is equal to –0.60. a. If the price of hamburger buns rises by 5%, what impact will that have on hamburger consumption? ____ - 3% ______ Solution: -.60 = %QH %PHB -.60 = %QH 3 %QH = 3 (-.60) = – 3% The Answer 1. The cross-price elasticity for hamburger demand with respect to the price of hamburger buns is equal to –0.60. a. If the price of hamburger buns rises by 5%, what impact will that have on hamburger consumption? ___ - 3% _____ b. What is the demand relationship between these products? The Answer 1. The cross-price elasticity for hamburger demand with respect to the price of hamburger buns is equal to –0.60. a. If the price of hamburger buns rises by 5%, what impact will that have on hamburger consumption? ___ - 3% _____ b. What is the demand relationship between these products? These two products are complements as evidenced by the negative sign on this cross-price elasticity. 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. a. 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? 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. a. If the price of Coca Cola rises by 5 percent, what impact will that have on Pepsi consumption? Solution: .70 = %QPepsi %PCoke .70 = %QPepsi 5 %QPepsi=5*.7=3.5% New quantity sold = 1,000 1.035 = 1,035 New value of sales = 1,035 $3.00 = $3,105 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. a. 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__ b. What is the demand relationship between these products? 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. a. 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__ b. What is the demand relationship between these products? The products are substitutes as evidenced by the positive sign on this cross-price elasticity! Price Flexibility of Demand 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. 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%! 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. Revenue Implications 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 Increase revenue Decrease revenue Characteristic of agriculture Page 81 Changing Price Response Over Time Short run effects Long run effects Over time, consumers respond in greater numbers. This is referred to as a recognition lag… Page 77 Ag’s Inelastic Demand Curve Price Pb Pa a A small increase in supply will cause the price of Ag products to fall sharply. b This situation explains why major program crops receive subsidies from the federal government. Increase in supply 0 Qb Qa Quantity Inelastic Demand Curve Price Pb Pa a b While subsidies increase the costs of government programs and hence budget deficits, remember consumers benefit from cheaper food costs. 0 Qb Qa Quantity 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 Chapter 6 starts a series of chapters that culminates in a market supply curve for food and fiber products….
