# Measurement and Interpretation of Elasticities

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Measurement and Interpretation of Elasticities
Chapter 5

Discussion Topics Own price elasticity of demand: A unit free measure of demand response to a good’s own-price change Cross price elasticity of demand: A unit free measure of demand response to other good’s price change Income elasticity of demand: A unit free measure of demand response to an income change Other general properties of demand curves How can we use these demand elasticities 2

Key Concepts Covered… Own price elasticity = % in Qi for a given % in Pi Represented as ηii i.e., the effect of a change in the price for hamburger on hamburger demand: ηHH = % in QH for a given % in PH Cross price elasticity = % in Qi for a given % in Pj Represented as ηij i.e., the effect of a change in the price of chicken on hamburger demand: ηHC = % in QH for a given % in PC Income elasticity = %Qi for a given %Income Represented as ηiY i.e., the effect of a change in income on hamburger demand: ηHY = %QH for a given %PY 3 Pages 70-76

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 % in Pi for a given % in Qi 4 Pages 70-76

Own Price Elasticity of Demand
5

Own Price Elasticity of Demand
Percentage change in quantity demanded (Q) ηii = Percentage change in its own price (P) \$ Point Elasticity Approach: Single point on curve Own price elasticity of demand Pa Pb % Δ in Q Q % Δ in P Qa Qb The subscript a stands for after price change b stands for before price change Q = (Qa – Qb) P = (Pa – Pb) 6 Pages 70-72

Own Price Elasticity of Demand
Percentage change in quantity Specific range on curve ηii = Percentage change in own price \$ Pa Arc Elasticity Approach: Pb Own price elasticity of demand Q Qa Qb where: P = (Pa + Pb) 2 Q = (Qa + Qb) 2 Q = (Qa – Qb) P = (Pa – Pb) Equation 5.3 Avg Price The subscript a stands for after price change b stands for before price change Avg Quantity 7 Page 72

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 Unitary Same as % in Price Greater than Inelastic Less than % in Price Note: The %Δ in Q is in terms of the absolute value of the change 8 Page 72

Own Price Elasticity of Demand
Snow Leopard was a previous version of Apple’s OS 9

Own Price Elasticity of Demand
What does a own-price elasticity of mean? For a 10% increase in price we get a 22.5% decrease in quantity purchase Example of an elastic demand with respect to own-price changes 10

Own Price Elasticity of Demand
ηii = -0.2 to -0.3 11

Own Price Elasticity of Demand
Why is ηii a unit free measure? Why do we get the same value regardless if the quantity is measured in tons versus pounds? Example of Soybean Meal Qb = 2.25 tons Pb = \$350/ton Qa = 2.50 tons Pa = \$300/ton 12

Own Price Elasticity of Demand
Lets recalculate the above elasticity but this time in terms of lbs. Qb = 4,500 lbs Pb = \$0.175/lb Qa = 5,000 lbs Pa = \$0.150/lb ←Same as previous value 13

Demand Curves Come in a Variety of Shapes
\$ Q 14

Demand Curves Come in a Variety of Shapes
\$ The two extremes Perfectly Inelastic ∆P Perfectly Inelastic: A price change does not change quantity purchased Can you think of a good that would have this characteristic? Perfectly Elastic Q 15 Page 72

Demand Curves Come in a Variety of Shapes
\$ Inelastic Demand ∆P ∆P Elastic Demand Q ∆Q ∆Q 16 Page 73

Demand Curves Come in a Variety of Shapes
\$ Elastic where (–%Q ) > % P Unitary Elastic where (–%Q) = % P Inelastic where (–%Q )< % P Q A single demand curve can exhibit various types of own-price elasticity 17 Page 73

Example of Arc Own-Price Elasticity of Demand
Unitary elasticity –% Change in Q = % Change in P ηii= –1.0 18 Page 73

Elastic demand Inelastic demand 19 Page 73

Elastic Demand Curve With the price decrease from Pb to Pa
\$ With the price decrease from Pb to Pa What happens to producer revenue (or consumer expenditures)? Pb Pa Q Qb Qa 20

Elastic Demand Curve \$ An elastic demand curve → a larger % ↑in quantity demanded than the absolute value of the % price change (a price decrease) Pb Cut in price Pa Q Qb Qa 21

Elastic Demand Curve Producer revenue (TR) = price x quantity
Revenue before the change (TRb) is Pb x Qb Represented by the area 0PbAQb Revenue after the change is (TRa) is Pa x Qa Represented by the area 0PaBQa \$ C A Pb B Pa Q Qa Qb 22

Elastic Demand Curve Change in revenue (∆TR) is TRa – TRb
→ ∆TR = 0PaBQa – 0PbAQb → ∆TR = QbDBQa – PaPbAD →TR ↑ %Q ↑ is greater than %P ↓ \$ Red Box Purple Box C A Pb D B Pa When you have elastic demand ↑ in price → ↓ total revenue (expenditures) ↓ in price → ↑ total revenue (expenditures) Q Qa Qb 23

Inelastic Demand Curve
\$ Pb Cut in price Pa Results in smaller % increase in quantity demanded Q Qb Qa 24

Inelastic Demand Curve
\$ With price decrease from Pb to Pa What happens to producer revenue or consumer expenditures)? Pb Pa Q Qb Qa 25

Inelastic Demand Curve
Producer revenue (TR) = price x quantity Revenue before the change (TRb) is Pb x Qb Represented by the area 0PbAQb Revenue after the change is (TRa) Pa x Qa Represented by the area 0PaBQa \$ A Pb Pa B Q 26 Qb Qa

Inelastic Demand Curve
Change in revenue (∆TR) is TRa – TRb ∆TR = 0PaBQa – 0PbAQb ∆TR = QbDBQa – PaPbAD →TR ↓ % Q increase is less than %P decrease \$ Red Box Purple Box A Pb Pa B When you have inelastic demand ↑ in price → ↑ total revenue ↓ in price → ↓ total revenue D Q Qb Qa 27

Revenue Implications Own-price Elasticity is: Cutting the Price Will:
Increasing the Price Will: Elastic (ηii< -1) Increase Total Revenue Decrease Total Revenue Unitary Elastic (ηii= -1) Not Change Revenue Inelastic (-1< ηii < 0) Typical of Agricultural Commodities 28 Page 81

Elastic Demand Curve Consumer surplus (CS)
\$ Consumer surplus (CS) Before price cut CS is area PbCA After the price cut CS is area PaCB C A Pb B Pa Q Qb Qa 29

Elastic Demand Curve \$ The gain in consumer surplus after the price cut is area PaPbAB = PaCB – PbCA C A Pb B Pa Q Qb Qa 30

Inelastic Demand Curve
\$ Inelastic demand and price decrease Consumer surplus increases by area PaPbAB A Pb Pa B Q Qb Qa 31

Retail Own Price Elasticities
Beef and veal= -0.62 Pork = -0.73 Fluid Milk = -0.26 Wheat = -0.11 Rice = -0.15 Carrots = -0.04 Non food = -0.99 Source: Huang, (1985) Page 79 32

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% \$ Demand Curve With a price drop What is the impact on rice producer revenues? What is the impact on consumer surplus from rice consumption? Pb A 10% drop B Pa 1.5% increase Q QB Qa 33

Own Price Elasticity Example
The local Kentucky Fried Chicken outlet typically sells 1,500 Crunchy Chicken platters per month at \$3.50 each The own price elasticity for the platter is estimated to be –0.30 If the KFC outlet increases the price of the platter to \$4.00: How many platters will the KFC outlet sell after the price change?__________ The KFC outlet’s revenue will change by \$__________ Will consumers be worse or better off as a result of this price change?_________ Inelastic demand 34

The answer… 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 – If the local KFC outlet increases the price of the platter by 50¢: 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 × ) = or –4% → New quantity = (1–0.04)×1,500 = 0.96×1,500 = 1,440 P Avg. Price %P 35

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 36

Another Example The local KFC outlet sells 1,500 crunchy chicken platters/month when their price was \$ The own price elasticity for this platter is estimated to be – If the KFC increases the platter price by 50¢: 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 37

The answer… The local KFC outlet sells 1,500 crunchy chicken platters/month when the price is \$ The own price elasticity for this platter is estimated to be – If the KFC increases the platter price by 50¢: How many platters will the KFC outlet 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 × ) = or –17.33% → New quantity = (1 ̶ )×1,500 = ×1,500 = 1,240 38

The answer… 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) Consumers will be worse off as a result of this price change Why? Because the price increased. 39

Income Elasticity of Demand
40

Income Elasticity of Demand
Percentage change in quantity demanded (Q) ηY = Percentage change in income (I) where: I = (Ia + Ib) 2 Q = (Qa + Qb) 2 Q = (Qa – Qb) I = (Ia – Ib) ηY : A quantitative measure of changes or shifts in quantity demanded (ΔQ) resulting from changes in consumer income (I) Page 74-75 41

Interpreting the Income Elasticity of Demand
When the income elasticity is: The good is classified as: Greater than 0.0 A 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 Page 75 42

Some Income Elasticity Examples
Commodity Income elasticity Beef and veal 0.455 Chicken 0.365 Cheese 0.594 Rice -0.366 Lettuce 0.234 Tomatoes 0.462 Fruit juice 1.125 Grapes 0.441 Nonfood items 1.177 Inferior good Luxury goods Source: Huang, 1985 Page 79 43

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? 44

The Answer 1. Assume the government cuts taxes, thereby increasing disposable income (I) by 5%. The income elasticity for chicken is What impact would this tax cut have upon the demand for chicken? Solution: = %QChicken  % I → = %QChicken  .05 →%QChicken = .05 = .018 or + 1.8% b. Chicken is a normal but not a luxury good since the income elasticity is > 0 and < 1.0 45

Cross Price Elasticity of Demand
46

Cross Price Elasticity of Demand
Percentage change in quantity demanded ηij = Percentage change in another good’s price i and j are goods (i.e., apples, oranges, peaches) where: Pj = (Pja + Pjb) 2 Qi = (Qia + Qib) 2 Qi = (Qia – Qib) Pj = (Pja – Pjb) ηij provides a quantitative measure of the impacts of changes or shifts in the demand curve as the price of other goods change Page 75 47

Cross Price Elasticity of Demand
If commodities i & j are substitutes (ηij > 0): Pi↑→Qi↓, Qj↑ i.e., strawberries vs. blueberries, peaches vs. oranges If commodities i & j are complements (ηij < 0): Pi↑→Qi↓, Qj↓ i.e., peanut butter and jelly, ground beef and hamburger buns If commodities i & j are independent (ηi j= 0): Pi↑→Qi↓, Qj is not impacted i.e., peanut butter and Miller Lite Page 75 48

Interpreting the Cross Price Elasticity of Demand
If the Cross-Price Elasticity is: The Good is Classified as a: Positive Substitute Negative Complement Zero Independent Page 76 49

Some Examples Quantity Changing Price That is Changing Prego Ragu
Hunt’s -2.550 0.810 0.392 0.510 -2.061 0.138 1.029 0.535 -2.754 Off diagonal values are all positive → These products are substitutes Values in red along the diagonal are own price elasticities Page 80 50

Some Examples Spaghetti Sauce Price Change Prego Ragu Hunt’s -2.550
0.810 0.392 0.510 -2.061 0.138 1.029 0.535 -2.754 Note: An increase in Ragu spaghetti sauce price has a bigger impact on Hunt’s spaghetti sauce demand (ηRH = 0.535) than an increase in Hunt’s spaghetti sauce price on Ragu demand (ηHR = 0.138) Page 80 51

Some Examples Spaghetti Sauce Price Change Prego Ragu Hunt’s -2.550
0.810 0.392 0.510 -2.061 0.138 1.029 0.535 -2.754 A 10% increase in Ragu spaghetti sauce price increases the demand for Hunt’s spaghetti sauce by 5.35% Page 80 52

Some Examples Spaghetti Sauce Price Change Prego Ragu Hunt’s -2.550
0.810 0.392 0.510 -2.061 0.138 1.029 0.535 -2.754 A 10% increase in Hunt’s spaghetti sauce price increases Ragu spaghetti sauce demand by 1.38% Page 80 53

Example 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? What is the demand relationship between these products? 54

The Answer 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? -3.0% Solution: -0.60 = %QH  %PHB -0.60 = %QH  .05 %QH = .05  (-.60) = -.03 or – 3.0% 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 55

Another Example Assume a retailer:
Sells 1,000 six-packs of Pepsi/day at a price of \$3.00 per six-pack The cross price elasticity for Pepsi with respect to Coca Cola price is 0.70 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? 56

The Answer If the price of Coca Cola rises by 5%, what impact will that have on Pepsi consumption? Solution: .70 = %QPepsi  %PCoke .70 = %QPepsi  .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 What is the demand relationship between these products? The products are substitutes as evidenced by the positive sign on this cross price elasticity 57

Price Flexibility of Demand
58

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) = - 4.0 Price Flexibility interpretation: %∆P ÷ %∆Q 59

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. 60

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 Characteristic of a large number of agricultural commodities Page 81 61

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 With increasing time, price elasticities tend to increase → flatter demand curve Page 77 62

Implications of Agriculture’s Inelastic Demand Curve
\$ Pb A Small ↑ in supply will cause agricultural product prices to ↓ sharply Explains why major program crops receive Federal government subsidies Pa Increase in supply Q Qb Qa 63

Inelastic Demand Curve
Price A Pb Pb While this ↑ the costs of government programs and hence budget deficits, remember consumers benefit from cheaper food costs. B Pa Pa Qb Qa Qb Qa Quantity 64

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? 65

The Market Demand Curve
Price What causes movement along a demand curve? Quantity 66

The Market Demand Curve
Price What causes the demand curve to shift? Quantity 67

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 68

Chapter 6 starts a series of chapters that culminates in a market supply curve for food and fiber products…. 69