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 How can we use these demand elasticities 2

Key Concepts Covered… Own price elasticity = %  Q i for a given %  P i, η ii  i.e., the effect of a change in the price for hamburger on hamburger demand: η HH = %  Q H for a given %  P H Cross price elasticity = %  Q i for a given %  P j, η ij  i.e., the effect of a change in the price of chicken on hamburger demand: η HC = %  Q H for a given %  P C Income elasticity = %  Q i for a given %  Income, η iY  i.e., the effect of a change in income on hamburger demand: η HY = %  Q H for a given %  P Y Pages

Key Concepts Covered… Arc elasticity = elasticity estimated over a range of prices and quantities along a demand curve Point elasticity = elasticity estimated at a point on the demand curve Price flexibility = reciprocal (the inverse) of the own price elasticity  %  P i for a given %  Q i Pages

Own Price Elasticity of Demand 5

Point Elasticity Approach: Own price elasticity of demand  Q = (Q a – Q b )  P = (P a – P b ) Pages Single point on curve Single point on curve PaPa QaQa The subscript a stands for after price change b stands for before price change The subscript a stands for after price change b stands for before price change $ Q PbPb QbQb Own price elasticity of demand Percentage change in quantity demanded (Q) Percentage change in own price (P) η ii = 6

Own Price Elasticity of Demand Percentage change in quantity Percentage change in own price η ii = where: P = (P a + P b )  2 Q = (Q a + Q b )  2  Q = (Q a – Q b )  P = (P a – P b ) Arc Elasticity Approach: Own price elasticity of demand Page 72 The subscript a stands for after price change b stands for before price change The subscript a stands for after price change b stands for before price change Avg Price Avg Quantity Equation 5.3 PaPa PbPb QaQa QbQb Specific range on curve Specific range on curve $ Q Own price elasticity of demand 7

Interpreting the Own Price Elasticity of Demand If Elasticity Measure is: Demand is said to be: %  in Quantity is: Less than –1.0 Elastic Greater than %  in Price Equal to –1.0 Unitary Elastic Same as %  in Price Greater than –1.0 Inelastic Less than %  in Price Page 72 8 Note: The %Δ in Q is in terms of the absolute value of the change

Demand Curves Come in a Variety of Shapes $ Q 9

Page 72 $ Q Perfectly Elastic Perfectly Inelastic Perfectly Inelastic: A price change does not change quantity purchased ∆P 10

Demand Curves Come in a Variety of Shapes Inelastic Demand Elastic Demand ∆P ∆Q ∆P ∆Q $ Q 11 Page 73

Demand Curves Come in a Variety of Shapes Inelastic where –%  Q < %  P Elastic where –%  Q > %  P Page 73 Unitary Elastic where –%  Q = %  P $ Q 12

Page 73 Example of Arc Own-Price Elasticity of Demand Unitary elasticity  –% Change in Q = % Change in P  η ii = –1.0 Unitary elasticity  –% Change in Q = % Change in P  η ii = –1.0 13

Page 73 Inelastic demand Elastic demand 14

PbPb PaPa QbQb $ Q Elastic Demand Curve With the price decrease from P b to P a  What happens to producer revenue? 0 QaQa 15

PbPb PaPa Q b Q a $ Q Elastic Demand Curve 0 Cut in price Cut in price Results in a larger % increase in quantity demanded Results in a larger % increase in quantity demanded 16

PbPb PaPa QbQb Q Elastic Demand Curve Producer revenue (TR) = price x quantity Revenue before the change (TR b ) is P b x Q b  Represented by the area 0P b AQ b Revenue after the change is (TR a ) is P a x Q a  Represented by the area 0P a BQ a Producer revenue (TR) = price x quantity Revenue before the change (TR b ) is P b x Q b  Represented by the area 0P b AQ b Revenue after the change is (TR a ) is P a x Q a  Represented by the area 0P a BQ a A B 0 C $ QaQa 17

PbPb PaPa QbQb Q Elastic Demand Curve Change in revenue (∆TR) is TR a – TR b  → ∆TR = 0P a BQ a – 0P b AQ b  → ∆TR = Q b DBQ a – P a P b AD  →TR ↑  %Q ↑ is greater than %P ↓ A B 0 C $ QaQa D Red Box Purple Box When you have elastic demand  ↑ in price → ↓ total revenue  ↓ in price → ↑ total revenue 18

PbPb PaPa Q b Q a $ Q Inelastic Demand Curve Cut in price Cut in price Results in smaller % increase in quantity demanded Results in smaller % increase in quantity demanded 19

PbPb PaPa Q b Q a $ Q Inelastic Demand Curve With price decrease from P b to P a  What happens to producer revenue? 20

PbPb PaPa Q b Q a $ Q Inelastic Demand Curve A B 0 Producer revenue (TR) = price x quantity  Revenue before the change (TR b ) is P b x Q b  Represented by the area 0P b AQ b  Revenue after the change is (TR a ) P a x Q a  Represented by the area 0P a BQ a 21

PbPb PaPa Q b Q a $ Q Inelastic Demand Curve A B 0 Change in revenue (∆TR) is TR a – TR b  ∆TR = 0P a BQ a – 0P b AQ b  ∆TR = Q b DBQ a – P a P b AD  →TR ↓  % Q increase is less than %P decrease D Red Box Purple Box When you have inelastic demand  ↑ in price → ↑ total revenue  ↓ in price → ↓ total revenue 22

Revenue Implications Own-price Elasticity is: Cutting the Price Will: Increasing the Price Will: Elastic (η ii < -1) Increase Total Revenue Decrease Total Revenue Unitary Elastic (η ii = -1) Not Change Revenue Inelastic (-1< η ii < 0) Decrease Total Revenue Increase Total Revenue Page 81 Typical of Agricultural Commodities 23

PbPb PaPa QbQb $ Q Elastic Demand Curve Consumer surplus (CS)  Before price cut CS is area P b CA  After the price cut CS is area P a CB A B 0 C QaQa 24

PbPb PaPa Q b Q a $ Q Elastic Demand Curve A B 0 C The gain in consumer surplus after the price cut is area P a P b AB = P a CB – P b CA 25

PbPb PaPa Q b Q a $ Q Inelastic Demand Curve A B 0 Inelastic demand and price decrease  Consumer surplus increases by area P a P b AB 26

Retail Own Price Elasticities Beef and veal= Pork = Fluid Milk = Wheat = Rice = Carrots = Non food = Page 79Source: Huang, (1985) 27

Interpretation Let’s use rice as an example  Previous Table: own price elasticity of –0.15  → If the price of rice drops by 10%, the quantity of rice demanded will increase by 1.5% $ Q 10% drop 1.5% increase With a price drop  What is the impact on rice producer revenues?  What is the impact on consumer surplus from rice consumption? Demand Curve PbPb PaPa A B 0 QBQB QaQa 28

Own Price Elasticity Example 1.The local Kentucky Fried Chicken outlet typically sells 1,500 Crunchy Chicken platters per month at $3.50 each 2.The own price elasticity for the platter is estimated to be – If the KFC outlet increases the price of the platter to $4.00: a.How many platters will the KFC outlet sell after the price change?__________ b.The KFC outlet’s revenue will change by $__________ c.Will consumers be worse or better off as a result of this price change?_________ Inelastic demand 29

The answer… 1.The local KFCsells 1,500 crunchy chicken platters per month at $3.50 each. The own price elasticity for this platter is estimated to be –0.30. If the local KFC outlet increases the price of the platter by 50¢: a.How many platters will the chicken sell? 1,440 Solution: = %  Q  %  P -0.30= %  Q  [($4.00-$3.50)  (($4.00+$3.50)  2)] -0.30= %  Q  [$0.50  $3.75] -0.30= %  Q  → %  Q=(-0.30 × ) = or –4% → New quantity = (1–0.04)×1,500 = 0.96×1,500 = 1,440 PP Avg. Price %P%P 30

The answer… b. The Chicken’s revenue will change by +$510 Solution: Current revenue = 1,500 × $3.50 = $5,250/month New revenue = 1,440 × $4.00 = $5,760/month →revenue increases by $510/month = $5,760 - $5,250 c.Consumers will be __worse___ off as a result of this price change Why? Because price has increased 31

Another Example 1.The local KFC outlet sells 1,500 crunchy chicken platters/month when their price was $3.50. The own price elasticity for this platter is estimated to be –1.30. If the KFC increases the platter price by 50¢: a.How many platters will the chicken sell?__________ b. The Chicken’s revenue will change by $__________ c. Will the consumers be worse or better off as a result of this price change? Elastic demand 32

The answer… 1.The local KFC outlet sells 1,500 crunchy chicken platters/month when the price is $3.50. The own price elasticity for this platter is estimated to be –1.30. If the KFC increases the platter price by 50¢: a.How many platters will the KFC outlet sell? 1,240 Solution: = %  Q  %  P -1.30= %  Q  [($4.00-$3.50)  (($4.00+$3.50)  2)] -1.30= %  Q  [$0.50  $3.75] -1.30= %  Q  %  Q=(-1.30 × ) = or –17.33% → New quantity = (1 ̶ )×1,500 = ×1,500 = 1,240 33

The answer… 1.b. The Chicken’s revenue will change by –$290 Solution: Current revenue = 1,500 × $3.50 = $5,250/mo New revenue = 1,240 × $4.00 = $4,960/mo →Revenue decreases by $290/mo = ($4,960 – $5,250) c.Consumers will be worse off as a result of this price change Why? Because the price increased. 34

Income Elasticity of Demand 35

Income Elasticity of Demand Income elasticity of demand Percentage change in quantity demanded (Q) Percentage change in income (I) η Y = where: I = (I a + I b )  2 Q = (Q a + Q b )  2  Q = (Q a – Q b )  I = (I a – I b ) Page η Y : A quantitative measure of changes or shifts in quantity demanded (ΔQ) resulting from changes in consumer income (I) 36

When the income elasticity is: The good is classified as: Greater than 0.0A normal good 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 Interpreting the Income Elasticity of Demand Page 75 37

Some Income Elasticity Examples Commodity Income elasticity Beef and veal0.455 Chicken0.365 Cheese0.594 Rice Lettuce0.234 Tomatoes0.462 Fruit juice1.125 Grapes0.441 Nonfood items1.177 Page 79 Source: Huang, 1985 Inferior good Luxury goods 38

Example Assume Federal income taxes are cut and disposable income (i.e., income fter taxes) is increased by 5% Assume the chicken income elasticity of demand is estimated to be What impact would this tax cut have upon the demand for chicken?  Is chicken a normal or an inferior good? Why? 39

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: = %  Q Chicken  %  I → = %  Q Chicken .05 →%  Q Chicken =.3645 .05 =.018 or + 1.8% b.Chicken is a normal but not a luxury good since the income elasticity is > 0 and <

Cross Price Elasticity of Demand 41

Cross Price Elasticity of Demand Cross Price elasticity of demand Percentage change in quantity demanded Percentage change in another good’s price η ij = where: P j = (P ja + P jb )  2 Q i = (Q ia + Q ib )  2  Q i = (Q ia – Q ib )  P j = (P ja – P jb ) Page 75 η ij provides a quantitative measure of the impacts of changes or shifts in the demand curve as the price of other goods change i and j are goods (i.e., apples, oranges, peaches) 42

Cross Price Elasticity of Demand Page 75 If commodities i & j are substitutes (η ij > 0):  P i ↑→Q i ↓, Q j ↑  i.e., strawberries vs. blueberries, peaches vs. oranges If commodities i & j are complements (η ij < 0):  P i ↑→Q i ↓, Q j ↓  i.e., peanut butter and jelly, ground beef and hamburger buns If commodities i & j are independent (η i j = 0):  P i ↑→Q i ↓, Q j is not impacted  i.e., peanut butter and Miller Lite 43

If the Cross-Price Elasticity is: The Good is Classified as a: PositiveSubstitute NegativeComplement ZeroIndependent Interpreting the Cross Price Elasticity of Demand Page 76 44

Some Examples Quantity Changing Price That is Changing PregoRaguHunt’s Prego Ragu Hunt’s Page 80 Off diagonal values are all positive → These products are substitutes Values in red along the diagonal are own price elasticities Values in red along the diagonal are own price elasticities 45

Spaghetti Sauce Price Change PregoRaguHunt’s Prego Ragu Hunt’s Some Examples Note: An increase in Ragu spaghetti sauce price has a bigger impact on Hunt’s spaghetti sauce demand (η RH = 0.535) than an increase in Hunt’s spaghetti sauce price on Ragu demand (η HR = 0.138) Page 80 46

Spaghetti Sauce Price Change PregoRaguHunt’s Prego Ragu Hunt’s Some Examples Page 80 A 10% increase in Ragu spaghetti sauce price increases the demand for Hunt’s spaghetti sauce by 5.35% 47

Spaghetti Sauce Price Change PregoRaguHunt’s Prego Ragu Hunt’s Some Examples Page 80 A 10% increase in Hunt’s spaghetti sauce price increases Ragu spaghetti sauce demand by 1.38% 48

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%, what impact will that have on hamburger consumption? b.What is the demand relationship between these products? 49

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? -3.0% Solution: = %  Q H  %  P HB = %  Q H .05 %  Q H =.05  (-.60) = -.03 or – 3.0% b.What is the demand relationship between these products? These two products are complements as evidenced by the negative sign on the associated cross price elasticity 50

Another Example 2.Assume a retailer: i)Sells 1,000 six-packs of Pepsi/day at a price of $3.00 per six-pack ii)The cross price elasticity for Pepsi with respect to Coca Cola price is 0.70 a.If the price of Coca Cola rises by 5%, what impact will that have on Pepsi sales? b. What is the demand relationship between these products? 51

The Answer a.If the price of Coca Cola rises by 5%, what impact will that have on Pepsi consumption? Solution:.70 = %  Q Pepsi  %  P Coke.70 = %  Q Pepsi .05 =.035 or 3.5% New quantity of Pepsi sold = 1,000  = 1,035 six-packs, 35 additional six packs New value of sales = 1,035  $3.00 = $3,105 or $105/day extra b.What is the demand relationship between these products? The products are substitutes as evidenced by the positive sign on this cross price elasticity 52

Price Flexibility of Demand 53

Price Flexibility The price flexibility is the reciprocal (inverse) of the own-price elasticity If the calculated elasticty is , then the flexibility = 1/(-0.25) = Price Flexibility interpretation: %∆P ÷ %∆Q 54

Price Flexibility This is a useful concept to producers when forming expectations for the current year i.e., Assume USDA projects an additional 2% of supply will likely come on the market Given above price flexibility then producers know the price will likely drop by 8%, or: %  Price = x %  Quantity = x (+2%) = - 8% →If supply ↑ by 2%, price would ↓ by 8% Note: make sure you use the negative sign for both the elasticity and the flexibility. 55

Revenue Implications Own-Price Elasticity Resulting Price Flexibility Increase in Supply Will Decrease in Supply Will Elastic< -1.0 Increase Revenue Decrease Revenue Unitary elastic = -1.0 Not Change Revenue Not Change Rrevenue Inelastic Between 0 and -1.0 Decrease Revenue Increase Revenue Page 81 Characteristic of a large number of agricultural commodities 56

Short run effectsLong run effects Page 77 Changing Price Response Over Time Over time consumers respond in greater numbers  This is referred to as a recognition lag  With increasing time, price elasticities tend to increase → flatter demand curve Over time consumers respond in greater numbers  This is referred to as a recognition lag  With increasing time, price elasticities tend to increase → flatter demand curve 57

PbPb PaPa Q b Q a $ Q Implications of Agriculture’s Inelastic Demand Curve Implications of Agriculture’s Inelastic Demand Curve Small ↑ in supply will cause agricultural product prices to ↓ sharply  Explains why major program crops receive Federal government subsidies Small ↑ in supply will cause agricultural product prices to ↓ sharply  Explains why major program crops receive Federal government subsidies A 0 Increase in supply Increase in supply 58

PbPb PaPa Q b Q a Price Quantity Inelastic Demand Curve While this ↑ the costs of government programs and hence budget deficits, remember consumers benefit from cheaper food costs. A 0 PbPb PaPa Q b Q a B 0 59

Demand Characteristics Which market is riskier for producers…elastic or inelastic demand? Which market would you start a business in? Which market is more apt to need government subsidies to stabilize producer incomes? 60

The Market Demand Curve Price Quantity What causes movement along a demand curve? 61

The Market Demand Curve Price Quantity What causes the demand curve to shift? 62

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 63

Chapter 6 starts a series of chapters that culminates in a market supply curve for food and fiber products…. 64