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 = %  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

Own Price Elasticity of Demand

Own price elasticity of demand Percentage change in quantity Percentage change in price = Page 71 Arc Elasticity Approach

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] Page 71 The subscript “a” here again stands for “after” while “b” stands for “before” The subscript “a” here again stands for “after” while “b” stands for “before” Equation 5.3

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 = [  Q  P] x [P  Q] Page 71 The subscript “a” here again stands for “after” while “b” stands for “before” 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 midpoint. The “bar” over the P and Q variables indicates an average or midpoint. 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 ) = [  Q  P] x [P  Q] Page 71 The subscript “a” here again stands for “after” while “b” stands for “before” The subscript “a” here again stands for “after” while “b” stands for “before” Specific range on curve Specific range on curve PbPb PaPa QbQb QaQa Arc elasticity Own price elasticity of demand

Interpreting the Own Price Elasticity of Demand If elasticity coefficient is: Demand is said to be: %  in quantity is: Greater than 1.0Elastic Greater than %  in price Equal to 1.0Unitary elastic Same as %  in price Less than 1.0Inelastic Less than %  in price Page 72

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 Inelastic where %  Q < %  P Elastic where %  Q > %  P Page 73 Unitary Elastic where %  Q = %  P

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

Page 73 Inelastic demand Elastic demand

PbPb PaPa Q b Q a Price Quantity Elastic Demand Curve 0 Cut in price Cut in price Brings about a larger increase in the quantity demanded Brings about a larger increase in the quantity demanded c

PbPb PaPa Q b Q a Price Quantity What happened to producer revenue? What happened to consumer surplus? What happened to producer revenue? What happened to consumer surplus? 0 c Elastic Demand Curve

PbPb PaPa Q b Q a Price Quantity 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. 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 Elastic Demand Curve

PbPb PaPa Q b Q a Price Quantity 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. 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 Elastic Demand Curve

PbPb PaPa Q b Q a Price Quantity 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. 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 Elastic Demand Curve

Revenue Implications Own-price elasticity is: Cutting the price will: Increasing the price will: ElasticIncrease revenue Decrease revenue Unitary elastic Not change revenue InelasticDecrease revenue Increase revenue Page 81

PbPb PaPa Q b Q a Price Quantity Consumer surplus before the price cut was area P b ca. Consumer surplus before the price cut was area P b ca. a b 0 c Elastic Demand Curve

PbPb PaPa Q b Q a Price Quantity Consumer surplus after the price cut is Area P a cb. Consumer surplus after the price cut is Area P a cb. a b 0 c Elastic Demand Curve

PbPb PaPa Q b Q a Price Quantity So the gain in consumer surplus after the price cut is area P a P b ab. So the gain in consumer surplus after the price cut is area P a P b ab. a b 0 c Elastic Demand Curve

PbPb PaPa Q b Q a Price Quantity Cut in price Cut in price Brings about a smaller increase in the quantity demanded Brings about a smaller increase in the quantity demanded Elastic Demand Curve

PbPb PaPa Q b Q a Price Quantity What happened to producer revenue? What happened to consumer surplus? What happened to producer revenue? What happened to consumer surplus? Elastic Demand Curve

PbPb PaPa Q b Q a Price Quantity 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. 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 Elastic Demand Curve

PbPb PaPa Q b Q a Price Quantity 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. 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 Elastic Demand Curve

PbPb PaPa Q b Q a Price Quantity Consumer surplus increased by area P a P b ab Consumer surplus increased by area P a P b ab a b 0 Elastic Demand Curve

Revenue Implications Own-price elasticity is: Cutting the price will: Increasing the price will: ElasticIncrease revenue Decrease revenue Unitary elasticNot change revenue InelasticDecrease revenue Increase revenue Characteristic of agriculture Page 81

Retail Own Price Elasticities Beef = Cheese = Bananas = Milk = Carrots = Page 79

Interpretation Let’s take rice as an example, which has an own price elasticity of 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?

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: = %  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 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 Indicates potential changes or shifts in the demand curve as consumer income (I) changes…. Indicates potential changes or shifts in the demand curve as consumer income (I) changes….

Interpreting the Income Elasticity of Demand If the income elasticity is equal to: The good is classified as: Greater than 1.0A luxury and a normal good Less than 1.0 but greater than 0.0 A necessity and a normal good Less than 0.0An inferior good! Page 75

Some Examples Commodity Own Price elasticity Income elasticity Beef and veal Chicken Cheese Rice Lettuce Tomatoes Fruit juice Grapes Nonfood items Elastic Page 99

Some Examples Commodity Own Price elasticity Income elasticity Beef Chicken Cheese Rice Lettuce Tomatoes Fruit juice Grapes Nonfood items Inferior good Elastic Page 99

Some Examples Commodity Own Price elasticity Income elasticity Beef Chicken Cheese Rice Lettuce Tomatoes Fruit juice Grapes Nonfood items Inferior good Luxury good Elastic Page 79

Example Assume the government cuts taxes, thereby increasing disposable income by 5%. The income elasticity for chicken is 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 a.What impact would this tax cut have upon the demand for chicken? Solution:.3645 = %  Q Chicken  %  I.3654 = %  Q Chicken  5 %  Q Chicken =.3645  5 = %

The Answer 1.Assume the government cuts taxes, thereby increasing disposable income by 5%. The income elasticity for chicken is a.What impact would this tax cut have upon the demand for chicken? _____ %___ 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 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… Indicates potential changes or shifts in the demand curve as the price of other goods change…

Interpreting the Cross Price Elasticity of Demand If the cross price elasticity is equal to: The good is classified as: PositiveSubstitutes NegativeComplements ZeroIndependent Page 76

Some Examples ItemPregoRaguHunt’s Prego Ragu Hunt’s Values in red along the diagonal are own price elasticities… Values in red along the diagonal are own price elasticities… Page 80

Some Examples ItemPregoRaguHunt’s Prego Ragu Hunt’s Values off the diagonal are all positive, indicating these products are substitutes as prices change… Page 80

Some Examples ItemPregoRaguHunt’s Prego Ragu Hunt’s Page 80 An increase in the price of Ragu Spaghetti Sauce has a bigger impact on Hunt’s Spaghetti Sauce than vice versa. An increase in the price of Ragu Spaghetti Sauce has a bigger impact on Hunt’s Spaghetti Sauce than vice versa.

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

Some Examples ItemPregoRaguHunt’s Prego Ragu Hunt’s 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%….. But…a 10% increase in the price of Hunt’s Spaghetti Sauce increases the demand for Ragu Spaghetti Sauce by only 1.381%…..

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 = %  Q H  %  P HB -.60 = %  Q H  3 %  Q H = 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 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 a.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  5 %  QPepsi=5*.7=3.5% New quantity sold = 1,000  = 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 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 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 , then the flexibility would be

Price Flexibility We earlier said that the price flexibility is the reciprocal of the own-price elasticity. If the calculated elasticty is , then the flexibility would be 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 = x %  Quantity = x (+2%) = - 8% If supply increases by 2%, price would fall by 8%!

We earlier said that the price flexibility is the reciprocal of the own-price elasticity. If the calculated elasticty is , then the flexibility would be 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 = x %  Quantity = 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. Price Flexibility

Revenue Implications Own-price elasticity is: Increase in supply will: Decrease in supply will: ElasticIncrease revenue Decrease revenue Unitary elasticNot change revenue InelasticDecrease revenue Increase revenue Characteristic of agriculture Page 81

Short run effectsLong run effects Over time, consumers respond in greater numbers. This is referred to as a recognition lag… Over time, consumers respond in greater numbers. This is referred to as a recognition lag… Page 77 Changing Price Response Over Time

PbPb PaPa 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 situation explains why major program crops receive subsidies from the federal government. A small increase in supply will cause the price of Ag products to fall sharply. This situation explains why major program crops receive subsidies from the federal government. a b 0 Increase in supply Increase in supply

PbPb PaPa Q b Q a Price Quantity Inelastic Demand Curve While subsidies increase the costs of government programs and hence budget deficits, remember consumers benefit from cheaper food costs. While subsidies increase the costs of government programs and hence budget deficits, remember consumers benefit from cheaper food costs. a b 0 PbPb PaPa Q b Q a Price a b 0

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….