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… 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 Percentage change in quantity = Percentage change in price Arc Elasticity Approach Page 71

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

Own Price Elasticity of Demand Percentage change in quantity = Percentage change in price Arc elasticity The “bar” over the P and Q variables indicates an average or midpoint. 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

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

Interpreting the Own Price Elasticity of Demand 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 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 Pb Cut in price Brings about a larger Pa increase in the quantity demanded Pa Qb Qa Quantity

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

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 Qb Qa Quantity

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 Qb Qa Quantity

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 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 Inelastic Page 81

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

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

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

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

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

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

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

Inelastic Demand Curve Price a Pb Consumer surplus increased by area PaPbab Pa b 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 Inelastic 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 Rice producer Revenue? Consumer surplus? 10% drop 1.467% increase 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: 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: 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: 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: 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.

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

Interpreting the Income Elasticity of Demand 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! Page 75

Some Examples Commodity Own Price elasticity Income elasticity Elastic 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 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. What impact would this tax cut have upon the demand for chicken? 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. 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. 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

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

Interpreting the Cross Price Elasticity of Demand If the cross price elasticity is equal to: The good is classified as: Positive Substitutes Negative Complements Zero Independent Page 76

Some Examples Item Prego Ragu Hunt’s -2.5502 .8103 .3918 .5100 -2.0610 .1381 1.0293 .5349 -2.7541 Values in red along the diagonal are own price elasticities… Page 80

Some Examples Item Prego Ragu Hunt’s -2.5502 .8103 .3918 .5100 -2.0610 .1381 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 -2.5502 .8103 .3918 .5100 -2.0610 .1381 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 -2.5502 .8103 .3918 .5100 -2.0610 .1381 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 -2.5502 .8103 .3918 .5100 -2.0610 .1381 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. 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?

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 = %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. 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?

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.

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?

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 = %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. 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 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!

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 Inelastic 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 a Pb 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. Pa b Increase in supply Qb Qa Quantity

Inelastic Demand Curve Price Price a a Pb Pb While subsidies increase the costs of government programs and hence budget deficits, remember consumers benefit from cheaper food costs. Pa Pa b b Qb Qa 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….