Chapter Three. Topics To Be Covered


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1 Chater Three Alying the SulyandDemand Model Toics To Be Covered How the shaes of demand and suly curves matter? Sensitivity of quantity demanded to rice. Sensitivity of quantity sulied to rice. Long run versus short run Effects of a sales tax Pearson AddisonWesley. All rights reserved. 32 How shaes of demand and suly matter? The shaes of the demand and suly curves determine by how much a shock affects the equilibrium rice and quantity. Examle: rocessed ork (same as Chater 2) Suly deends on the rice of ork and the rice of hogs Pearson AddisonWesley. All rights reserved
2 Figure 3.1 How the Effect of a Suly Shock Deends on the Shae of the Demand Curve This shift of the suly curve causes a movement along the demand curve (a), $ er kg D S 2 S 1 A $0.25 increase in the rice of ork causes the suly of ork to shift to the left. e 2 e 1 (b), $ er kg A $0.25 increase in the rice of ork causes the suly of ork to shift to the left S 2 S 1 e 2 D 2 e , Million kg of ork er year, Million kg of ork er year and a reduction in quantity. But equilibrium quantity does not change since consumtion is not sensitive to rice 2009 Pearson AddisonWesley. All rights reserved. 34 Figure 3.1 How the Effect of a Suly Shock Deends on the Shae of the Demand Curve (cont d) When demand is very sensitive to rice a shift in the suly curve to S 2 has no effect on the equilibrium rice and a substantial effect on the quantity (c), $ er kg 3.30 D 3 S 2 S 1 e 2 e , Million kg of ork er year 2009 Pearson AddisonWesley. All rights reserved. 35 Sensitivity of quantity demanded to rice. Elasticity the ercentage change in a variable in resonse to a given ercentage change in another variable. Price elasticity of demand (ε) the ercentage change in the quantity demanded in resonse to a given ercentage change in the rice Pearson AddisonWesley. All rights reserved
3 Sensitivity of quantity demanded to rice (cont). Formally, Δ %Δ Δ ε = = = % where Δ indicates change. Examle If a 1% increase in rice results in a 3% decrease in quantity demanded, the elasticity of demand is ε =  3%/1% = Pearson AddisonWesley. All rights reserved. 37 Sensitivity of quantity demanded to rice (cont). Along linear demand curve with a function of: Where b is the sloe or = a b Δ b = the elasticity of demand is ε = Δ = b (3.3) 2009 Pearson AddisonWesley. All rights reserved. 38 Sensitivity of quantity demanded to rice: Examle. The estimated linear demand function for ork is: = where is the quantity of ork demanded in million kg er year and is the rice of ork in $ er year. At the equilibrium oint of = $3.30 and = 220 the elasticity of demand for ork is ε = b 3.30 = 20 = Pearson AddisonWesley. All rights reserved
4 Elasticity: An Alication and a ractice roblem Varian (2002) found that the rice elasticity of demand for internet use was 2.0 for those who used a 128 Kbs service 2.9 for those who used a 64 Kbs service. Practice roblem: A 1% increase in the rice er minute reduced the connection time by for those with high seed access, and by for those with slow hone line access Pearson AddisonWesley. All rights reserved Elasticity Along a Demand Curve The elasticity of demand varies along most demand curves. Along a downwardsloing linear demand curve the elasticity of demand is a more negative number the higher the rice is Pearson AddisonWesley. All rights reserved Figure 3.2 Elasticity Along the Pork Demand Curve, $ er kg a/b = Perfectly elastic Elastic ε < 1 ε = 4 ε = b = = 20 x = 57.2 = D a/(2b) = 7.15 Unitary: ε = 1 Inelastic 0 > ε > ε = 0.3 Perfectly inelastic 0 a/5 = 57.2 a/2 = a = 286, Million kg of ork er year 2009 Pearson AddisonWesley. All rights reserved
5 Elasticity Along The Demand Curve: Practice Problem According to AgcaoliSombilla (1991), the elasticity of demand for rice is in Austria; 0.8 in Bangladesh, China, India, Indonesia, and Thailand; in Jaan; in the EU and the US; and in Vietnam. In which countries is the demand for rice inelastic? In all the countries, since in all cases ε > 1. In which country is the least elastic? In Vietnam, where ε = Pearson AddisonWesley. All rights reserved Figure 3.3 Vertical and Horizontal Demand Curves (a) Perfectly Elastic Demand (b) Perfectly Inelastic Demand (c) Individual s Demand for Insulin, Price er unit *, Price er unit, Price of insulin dose *, Units er time eriod *, Units er time eriod *, Insulin doses er day 2009 Pearson AddisonWesley. All rights reserved Sensitivity of quantity demanded to income. Formally, Δ %Δ Δ ξ = = = % ΔY ΔY ΔY Y Y where Y stands for income. Examle If a 1% increase in income results in a 3% decrease in quantity demanded, the income elasticity of demand is ξ = 3%/1% = Pearson AddisonWesley. All rights reserved
6 Sensitivity of quantity demanded to rice: Examle. The estimated demand function for ork is: = b + 3 c + 2Y where is the rice of ork, b is the rice of beef, c is the rice of chicken and Y is the income (in thousands of dollars). uestion: what would be the income elasticity of demand for Pork if = 220 and Y = 12.5 Answer: Since Δ = 2, then ΔY Δ Y Y 12.5 ξ = = 2 = ΔY Pearson AddisonWesley. All rights reserved Sensitivity of quantity demanded to the rice of a related good. Formally, Δ % Δ Δ = = % o o o o where P o stands for rice of another good. Examle If a 1% increase in the rice of a related good results in a 3% decrease in quantity demanded, the crossrice elasticity of demand is = 3%/1% = 3. o 2009 Pearson AddisonWesley. All rights reserved Sensitivity of quantity demanded to the rice of a related good. If the crossrice elasticity is ositive, the goods are substitutes. uestion: can you think of any examles of two goods that are substitutes? Roses and carnations. If the crossrice elasticity is negative, the goods are comlements uestion: can you think of any examles of two goods that are comlements? Peanut butter and jelly 2009 Pearson AddisonWesley. All rights reserved
7 Sensitivity of quantity demanded to rice: Examle. Again, the estimated demand function for ork is: = b + 3 c + 2Y uestion: what would be the crossrice elasticity between the rice of beef and the quantity of ork if = 220 and b = $4? Answer: Since Δ = 20, then Δ Δ b b 4 = 20 = b b 2009 Pearson AddisonWesley. All rights reserved Sensitivity of quantity sulied to rice. Formally, Δ %Δ Δ η = = = % where indicates quantity sulied. Examle If a 1% increase in rice results in a 3% decrease in quantity demanded, the elasticity of sulied is η = 3%/1% = Pearson AddisonWesley. All rights reserved Sensitivity of quantity demanded to rice: Examle. The estimated linear suly function for ork is: = where is the quantity of ork sulied in million kg er year and is the rice of ork in $ er year. At the equilibrium, where = $3.30 and = 220, the elasticity of sulied is: Δ η = P 3.30 = 40 = Pearson AddisonWesley. All rights reserved
8 Sensitivity of quantity sulied to rice (cont). Along linear suly curve with a function of: Where b is the sloe or = g h Δ h = the elasticity of demand is η = Δ = h 2009 Pearson AddisonWesley. All rights reserved Figure 3.4 Elasticity Along the Pork Suly Curve 2009 Pearson AddisonWesley. All rights reserved Demand Elasticities Over Time Elasticities tend to be larger in the longrun. Can you think why? In the case of demand: Substitution and storage oortunities. In the case of suly: Converting fixed inuts into variable inuts Pearson AddisonWesley. All rights reserved
9 Solved Problem 3.1 What would be the effect of ANWR roduction on the world rice of oil given that ε = 0.4,η = 0.3, the reanwr daily world roduction of oil is 1 = 82 million barrels er day, the re ANWR world rice is 1 = $100 er barrel, and daily ANWR roduction would be 0.8 million barrels er day? For simlicity, assume that the suly and demand curves are linear and that the introduction of ANWR oil would cause a arallel shift in the world suly curve to the right by 0.8 million barrels er day Pearson AddisonWesley. All rights reserved Solved Problem Pearson AddisonWesley. All rights reserved Effects of a Sales Tax 1. What effect does a sales tax have on equilibrium rices and quantity? 2. Is it true, as many eole claim, that taxes assessed on roducers are assed along to consumers? 3. Do the equilibrium rice and quantity deend on whether the tax is assessed on consumers or on roducers? 2009 Pearson AddisonWesley. All rights reserved
10 Two Tyes of Sales Taxes Ad valorem tax  for every dollar the consumer sends, the government kees a fraction, α, which is the ad valorem tax rate. Unit tax  where a secified dollar amount, τ, is collected er unit of outut Pearson AddisonWesley. All rights reserved Figure 3.5 Effect of a $1.05 Secific Tax on the Pork Market Collected from Producers, $ er kg 2 = = τ = e 2 T = $216.3 million e 1 2 = = 220 S 2 τ = $1.05 S 1, Million kg of ork er year A tax on roducers shifts the suly curve downward by the amount of the tax (τ = $1.05). which causes the market rice to increase After the tax, buyers are worse off by $0.70 ($ $3.30) D sellers are worse off by $0.35 ($ $2.95) and the government collects $216.3 in revenue Pearson AddisonWesley. All rights reserved How Secific Tax Effects Deend on Elasticities. The government raises the tax from zero to τ, so the change in the tax is Δτ =τ 0 = τ. The rice buyers ay increases by: η = Δτ η ε If ε = 0.3 and η = 0.6, a change of a tax of Δτ = $1.05 causes the rice buyers ay to rise by η 0.6 = Δτ = $1.05 = $0.70 η ε 0.6 [ 0.3] 2009 Pearson AddisonWesley. All rights reserved
11 Solved Problem 3.2 If the suly curve is erfectly elastic and demand is linear and downward sloing, what is the effect of a $1 secific tax collected from roducers on equilibrium rice and quantity, and what is the incidence on consumers? Why? 2009 Pearson AddisonWesley. All rights reserved Solved Problem Pearson AddisonWesley. All rights reserved Figure 3.6 Effect of a $1.05 Secific Tax on Pork Collected from Consumers, $ er kg = 4.00 but the new equilibrium is the same as when the tax is alied to suliers e 2 Wedge, τ = $1.05 S = 3.30 T = $216.3 million 2 τ = 2.95 e 2 τ = $1.05 The tax shifts the demand curve down by τ = $1.05 D 1 D = = 220, Million kg of ork er year 2009 Pearson AddisonWesley. All rights reserved
12 Figure 3.7 Comarison of an Ad Valorem and a Secific Tax on Pork 2009 Pearson AddisonWesley. All rights reserved Solved Problem 3.3 If the shortrun suly curve for fresh fruit is erfectly inelastic and the demand curve is a downwardsloing straight line, what is the effect of an ad valorem tax on equilibrium rice and quantity, and what is the incidence on consumers? Why? 2009 Pearson AddisonWesley. All rights reserved Solved Problem Pearson AddisonWesley. All rights reserved
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