Demand and Elasticity

4 Demand and Elasticity Outline ● Elasticity: Measure of Responsiveness ● Price Elasticity of Demand: Its Effect on Total Revenue ● What Determines Demand Elasticity? ● Elasticity as a General Concept ● Real-World Application: Polaroid versus Kodak Elasticity: Measure of Responsiveness ● Elasticity = measure of the responsiveness of one variable to changes in another variable % ∆ Qd ● Price elasticity of demand = %∆P Real-World Application: Polaroid versus Kodak ● In 1989, Polaroid sued Kodak –copyright infringement of its instant-photography patents. ● Court case would determine how much Kodak should pay in compensation to Polaroid. ♦ Polaroid: could have charged ↑P film without illegal competition from Kodak ♦ Kodak: ↑P film → ↓Qd film Real-World Application: Polaroid versus Kodak ● Relevant Question: How would ↑P film affect Polaroid’s TR? ♦ Depends on how responsive Qd is to P, which depends on the shape of the D curve for film ● Court’s decision would be based on the responsiveness of Qd to P. 1(a). Hypothetical Demand Curves for Film FIGURE Kodak’s claim Price per Package $20 Df D is relatively responsive to P. b TRa = $10 x 4 = $40 TRb = $20 x 1.5 = $30 a 10 Df 0 1.5 4 Quantity Demanded in millions Here P doubles and TR falls by 25%. 1(b). Hypothetical Demand Curves for Film FIGURE Polaroid’s claim DS Price per Package $20 D is relatively unresponsive to P. B TRa = $10 x 4 = $40 TRb = $20 x 3 = $60 A 10 DS 0 3 4 Quantity Demanded in millions Here P doubles and TR rises by 50%. Elasticity: Measure of Responsiveness ● Governments, courts, and businesses need to understand the relationship between Qd and P ● If consumers respond sharply to ∆P →D is elastic ♦ E.g., graph (a) above ● If consumers are unresponsive to ∆P →D is inelastic ♦ E.g., graph (b) above Calculation of Elasticity of D ● Price Elasticity of Demand: ♦ % ∆ Qd ÷ % ∆ P ● Units problems: cannot judge elasticity by looking at a graph and its slope ♦ ∆ in units of measurement make graphs appear steeper or flatter when they convey the same info. 2(a). Sensitivity of Slope to Units of Measurement Price per Pizza FIGURE $18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 ↓P by $4 →↑Qd by 80. D A B D 280 500 360 1,000 1,500 2,000 Pizzas per Week (a) 2,500 3,000 2(b). Sensitivity of Slope to Units of Measurement Price per Pizza FIGURE $18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 D 1 pizza = 8 slices ↓P by $4 →↑Qd by 640. A B D 500 1,000 1,500 2,000 2,500 3,000 2,240 2,880 Slices of Pizza per Week (b) Calculation of Elasticity of D ● Slope of a curve changes whenever units of measurement changes. ● ↓P by $4 → (a) ↑Qd by 80 → (b) ↑Qd by 640 ● Same info is portrayed but slope is flatter (and looks more elastic) when measured in slices. ● Need % ∆ not absolute ∆ (slope) to measure elasticity. ♦ E.g., if defense budget doubles, it goes up by 100% whether it is measured in millions or billions of dollars. Calculation of Elasticity of D ● Percentage problems: ♦ Fig. 1(b). Pa = $10 and Qa = 4; Pb = $20 and Qb = 3. ∆Qd = 1, so should we take 1 as a % of 3? → 33.3% or 1 as a % of 4? → 25.0% ● No right answer, so compromise by using the average Qs ● Average of 3 & 4 = 3.5 →%∆Qd = 1/3.5 = 28.6% ● Same is done with price: %∆P = $10/$15 = 66.7% Calculation of Elasticity of D ● Drop (-) sign and use absolute values: ♦ P and Qd have a (-) relationship ε = (∆Qd / average of 2 Q’s) ÷ (∆P /average of 2 P’s) ● Polaroid example: ♦ Fig. 1(a): ε = (2.5/2.75) ÷ (10/15) = 1.4 ♦ Fig. 1(b): ε = (1/3.5) ÷ (10/15) = 0.43 3(a). Perfectly Inelastic Demand FIGURE Qd is 90 no matter the P. Elasticity = 0 P %∆Qd = 0 D Consumer purchases do not respond to ∆P. E.g., goods with very low prices that are used with something else –salt or shoelaces. Or an essential medicine. 0 90 QD 3(b). Perfectly Elastic Demand FIGURE P Slight ↑P → ↓Qd to 0. Elasticity = ∞ $5 %∆Qd = infinitely large D 0 QD Consumer are completely responsive to ∆P. E.g., Demand for a firm that produces an undifferentiated product. 3(c). Straight-line Demand FIGURE Slope remains constant but ε is changing. P ε (a-b) = (2/3) ÷ (2/5) = 1.67 6 a ε (c-d) = (2/6) ÷ (2/2) = 0.33 b 4 3 c Moving down the D curve ε is getting smaller because average Q is rising while average P is falling. d 1 2 4 5 7 D QD FIGURE 3(d). Unit-elastic Demand Slope is changing but ε is constant and equal to 1. P ε (e-f) = (7/10.5) ÷ (10/15) = 1.0 Note: if ε = 1 → D is “unit elastic” 20 if ε > 1 → D is “elastic” e 10 if ε < 1 → D is “inelastic” f D 7 14 QD Elasticity of Demand and Total Revenue ● Firms want to know whether an ↑P will raise or lower their sales revenues. ♦ If D is elastic: ↑P → ↓TR ♦ If D is unit elastic: ↑P → TR constant ♦ If D is inelastic: ↑P → ↑TR ■Recall: TR = TE = P x Qd Elasticity of Demand and Total Revenue ● Further examples: ♦ If P↓ by 10% and ↑Qd by 10% → D is unit elastic and TR are constant. ♦ If P↓ by 10% and ↑Qd by 15% → D is elastic and ↑TR. ♦ If P↓ by 10% and ↑Qd by 5% → D is inelastic and ↓TR. FIGURE Curve 4. An Elastic Demand $6 Price 5 D R Pt. S: TR = $24 = area of 0RST S W V 4 D is elastic as ↓P → ↑TR. 3 2 1 T 0 Pt. V: TR = $60 D = area of 0WVU 4 U 12 Quantity Demanded 1. Estimates of Price Elasticities TABLE What Determines Demand Elasticity? 1. Nature of the good: ♦ Necessities have very inelastic demands, while luxuries have elastic demands. ♦ E.g., ε potatoes = 0.3 and the ε restaurant meals = 1.6. What do these numbers mean? ● 10%↑ in P of potatoes → ↓sales of potatoes by 3%. And 10%↑ in P of restaurant meals → ↓restaurant dining by 16%. ♦ Comes from the elasticity formula: %∆P * ε = %∆Qd What Determines Demand Elasticity? 2. Availability of a close substitute: ♦ If consumers can buy a good substitute for a product whose ↑P, they will readily switch. ■ E.g., D for gas is inelastic because you can’t run a car without it. But D for Chevron gas is elastic because Mobile or Shell gas work just as well. What Determines Demand Elasticity? 3. Fraction of Income Absorbed: ♦ Very inexpensive items have an inelastic demand. Who will use more salt if the price falls? ♦ Very expensive items have elastic demands. Families will buy fewer homes if housing prices increase. What Determines Demand Elasticity? 4. Passage of Time: ● D for products is more elastic in LR than SR because consumers have more time to adjust their purchases. ♦ E.g., suppose recent ↑P gas continues. In SR, consumers may take fewer summer road trips to ↓Qd gas. But in LR, consumers can buy more fuel efficient cars to further ↓Qd gas. Elasticity as a General Concept ● Elasticity can be used to measure the responsiveness of anything to anything else. ● Income Elasticity: ♦ Income elasticity of D = % ∆ Qd ÷ % ∆Y ● Price Elasticity of Supply: ♦ Price elasticity of S = % ∆ Qs ÷ % ∆ P Cross Elasticity of Demand ● Cross εd is used to determine whether two goods are compliments or substitutes. It is calculated as: εcross = (%∆Qd good X) ÷ (%∆P good Y) Cross Elasticity of Demand ● Two goods are compliments if an ↑Qd for one good → ↑Qd of the other good. ♦ E.g, ketchup and french fries or coffee and cream. ■ If ↓P of coffee → ↑purchases of coffee and cream. Cross elasticity for compliments is (-). As ↓P of coffee falls → ↑Qd of cream. Cross Elasticity of Demand ● Two goods are substitutes if an ↑Qd for one good → ↓Qd of the other good. ♦ E.g., ice cream and frozen yogurt or cans of salmon and cans of tuna. ■ If ↑P of ice cream → ↓purchases of ice cream and ↑purchases of frozen yogurt. Cross elasticity for substitutes is (+). As ↑P of ice cream → ↑Qd of frozen yogurt. ● Cross elasticity is often used in “anti-trust” lawsuits. If firms face strong competition, it is difficult to overcharge customers. A very high and (+) cross elasticity indicates effective competition in a market. Real-World Application: Polaroid versus Kodak ● In 1989, Polaroid sued Kodak –copyright infringement ● How much could Polaroid’s TR have increased if Kodak did not infringe? ♦ Polaroid claimed lots! $9 billion or more –because D was inelastic ♦ Kodak claimed neighborhood of $450 million – because D was elastic -(very close to judge’s verdict) Real-World Application: Polaroid versus Kodak ● Some complications involving Cross εd ♦ During 1980s, period of Kodak’s infringement, ↓P of 35-mm cameras, film, and processing→ ↑Qd 35-mm cameras, film, and processing and ↓Qd instant cameras and film (substitutes). ♦ So Kodak’s infringement need not be the only reason for reduced sales of Polaroid’s instant film. ♦ If cross εd was (+) and low → Kodak owes more ♦ If cross εd was (+) and high → Kodak owes less