Chapter 3 Read this chapter together with unit 3 in the study guide. Applying the Supply-and- Demand Model

Transcription

1 Chapter 3 Read this chapter together with unit 3 in the study guide Applying the Supply-and- Demand Model

2 Topic How the shapes of demand and supply curves matter? Sensitivity of quantity demanded to price. Sensitivity of quantity supplied to price. Long run versus short run. Effects of a sales tax. 3-2

3 How Shapes of Demand and Supply Matter? The shapes of the demand and supply curves determine by how much a shock affects the equilibrium price and quantity. Example: processed pork (same as Chapter 2) Supply depends on the price of pork and the price of hogs. 3-3

4 Figure 3.1 How the Effect of a Supply Shock Depends on the Shape of the Demand Curve This shift of the supply curve causes a movement along the demand curve A $0.25 increase in the price of hogs causes the supply of pork to shift to the left (a) p, $ per kg D 1 A $0.25 increase in the price of hogs causes the supply of pork to shift to the left. (b) p, $ per kg D S 2 S 1 e 2 e 1 S 2 S 1 e 2 e Q, Million kg of pork per year and a reduction in quantity. Q, Million kg of pork per year But equilibrium quantity does not change since consumption is not sensitive to price 3-4

5 Figure 3.1 How the Effect of a Supply Shock Depends on the Shape of the Demand Curve (cont.) When demand is very sensitive to price a shift in the supply curve to S 2 (c) p, $ per kg has no effect on the equilibrium price and a substantial effect on the quantity 3.30 D 3 S 2 S 1 e 2 e Q, Million kg of pork per year 3-5

6 Sensitivity of Quantity Demanded to Price Elasticity the percentage change in a variable in response to a given percentage change in another variable. Price elasticity of demand (ε) the percentage change in the quantity demanded in response to a given percentage change in the price. 3-6

7 Sensitivity of Quantity Demanded to Price (cont.) Formally, % Q ε = % p = Q Q p p = Q p p Q where indicates change. Example If a 1% increase in price results in a 3% decrease in quantity demanded, the elasticity of demand is ε = -3%/1% =

8 Sensitivity of Quantity Demanded to Price (cont.) Along linear demand curve with a function of: Q = a bp Where -b is the slope or b = Q p the elasticity of demand is ε = Q p p Q = b p Q (3.3) 3-8

9 Sensitivity of Quantity Demanded to Price: Example The estimated linear demand function for pork is: Q = p where Q is the quantity of pork demanded in million kg per year and p is the price of pork in $ per year. At the equilibrium point of p = $3.30 and Q = 220 the elasticity of demand for pork is ε = b p Q 3.30 = 20 =

10 Elasticity: An Application and a Practice Problem Varian (2002) found that the price elasticity of demand for internet use was -2.0 for those who used a 128 Kbps service -2.9 for those who used a 64 Kbps service. Practice problem: A 1% increase in the price will result in a 2% reduction in the demand for high speed connection; and a 2.9% reduction in the demand for slower speed connection 3-10

11 Solved Problem 3.1 Calculate the elasticity of demand for the linear pork demand curve D in panel a of Figure 3.1 at the equilibrium e 1 where p=$3.30 and Q=220. The estimated linear demand function for pork, which holds constant other factors that influence demand besides price (Equation 2.3), is Q=286 20p, where Q is the quantity of pork demanded in million kg per year and p is the price of pork in dollars per kg. 3-11

12 Solved Problem 3.1: Answer Substitute the slope coefficient, the price, and the quantity values into Equation 3.3. By inspection, the slope coefficient for this demand equation is b = 20 (and a = 286). Substituting b = 20, p = $3.30, and Q = 220 into Equation 3.3, we find that the elasticity of demand at the equilibrium e 1 in panel a of Figure 3.1 is Comment: Thus, at the equilibrium, a 1% increase in the price of pork leads to a 0.3% fall in the quantity of pork demanded: A price increase causes a less than proportionate fall in the quantity of pork demanded. 3-12

13 Elasticity Along a Demand Curve The elasticity of demand varies along most demand curves. Along a downward-sloping linear demand curve the elasticity of demand is a more negative number the higher the price is. 3-13

14 Figure 3.2 Elasticity Along the Pork Demand Curve p, $ per kg a / b = Perfectly elastic Elastic ε < 1 ε = 4 ε = -b Q = p p Q = -20 x = -0.3 = D a /(2 b ) = 7.15 Unitary: ε = -1 Inelastic 0 > ε > ε = 0.3 Perfectly inelastic 0 a/5 = 57.2 a /2 = a = 286 Q, Million kg of pork per year 3-14

15 Elasticity Along The Demand Curve: Practice Problem According to Agcaoli-Sombilla (1991), the elasticity of demand for rice is in Austria; -0.8 in Bangladesh, China, India, Indonesia, and Thailand; in Japan; 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 =

16 Elasticity Along the Demand Curve (cont.) Along a horizontal demand curve, elasticity is infinite perfectly elastic demand a increase in price causes an infinite change in quantity demanded Along a vertical demand curve, elasticity is zero perfectly inelastic demand A change in the price does not cause a change in the quantity demanded 3-16

17 Figure 3.3 Vertical and Horizontal Demand Curves (a) Perfectly Elastic Demand (b) Perfectly Inelastic Demand (c) Individual s Demand for Insulin p, Price per unit p* p, Price per unit p, Price of insulin dose p* Q, Units per time period Q* Q, Units per time period Q* Q, Insulin doses per day 3-17

18 Demand Elasticity and Revenue Any shock that changes the equilibrium price will affect an industry s revenue Whether revenue increases or decreases when the equilibrium price changes depends on elasticity With elastic demand, a higher price reduces revenue With inelastic demand, a higher price increases revenue 3-18

19 Figure 3.4 Effect of a Price Change on Revenue Revenue decreases by B, but increases by C, resulting in revenue of A+C An increase in price to p2 reduces quantity Revenue = A + B 3-19

20 Solved Problem 3.2 Does revenue increase or decrease if the demand curve is inelastic at the initial price? How does it change if the demand curve is elastic? Answer Consider the extreme case where the demand curve is perfectly inelastic and then generalize to the inelastic case. Show that if the demand curve is elastic at the initial price, then area C is relatively small. 3-20

21 HIV HIGH AMONG TERTIARY STUDENTS JOURNAL OF INTERNATIONAL AIDS SOCIETY : many are unaware of their HIV status 44% said HIV is only spread through deep kissing >25% said HIV is spread through witchcraft 15% believed they can pass or contract HIV by shaking hands Out of 3608 repondents, 103 (2.8%) who participated in the screening were positive, with prevalence rates of 3.5% among female students and 1.8% among males Among part-time students, its 5.4% (6% among females, 4.8% among Males Its estimated 6.3% of all students at Poly are HIV positive 3-21

22 Solved Problem 3.2: Answer 3-22

23 Solved Problem 3.2 Does revenue increase or decrease if the demand curve is inelastic at the initial price? How does it change if the demand curve is elastic? 3-23

24 Effect of elasticity on revenue: Price Elastic demand Price Inelastic demand C B A C B A 0 0 Quantity, Q, units per year Quantity, Q, units per year 3-24

25 Demand Elasticities Over Time Demand elasticities may be different in the short-run and the long-run The difference depends on substitution and storage opportunities For most goods elasticities tend to be larger in the long-run For easily storable or durable goods, the reverse is true 3-25

26 Sensitivity of Quantity Demanded to Income Formally, where Y stands for income. Example % Q ξ = % Y = Q Q Y Y Q Y If a 1% increase in income results in a 3% increase in quantity demanded, the income elasticity of demand is ξ = 3%/1% = 3. = Y Q 3-26

27 Sensitivity of Quantity Demanded to Income: Example The estimated demand function for pork is: Q = p + 20p b + 3p c + 2Y where p is the price of pork, p b is the price of beef, p c is the price of chicken and Y is the income (in thousands of dollars). Question: what would be the income elasticity of demand for Pork if Q = 220 and Y = 12.5 Answer: Q Since = 2, then Y Q Y Y 12.5 ξ = = 2 = Y Q Q

28 Sensitivity of Quantity Demanded to the Price of a Related Good Formally, % Q % p o = Q Q po p o = Q p o p Q o where P o stands for price of another good. Example If a 1% increase in the price of a related good results in a 3% decrease in quantity demanded, the cross-price elasticity of demand is = -3%/1% =

29 Sensitivity of Quantity Demanded to the Price of a Related Good If the cross-price elasticity is positive, the goods are substitutes Question: can you think of any examples of two goods that are substitutes? Roses and carnations; tea and coffee If the cross-price elasticity is negative, the goods are complements Question: can you think of any examples of two goods that are complements? Peanut butter and jelly; cheese and wine 3-29

30 Sensitivity of Quantity Demanded to the Price of a Related Good: Example Again, the estimated demand function for pork is: Q = p + 20p b + 3p c + 2Y Question: what would be the cross-price elasticity between the price of beef and the quantity of pork if Q = 220 and p b = $4? Answer: Q Since = 20, then p b Q p b pb Q = pb 4 20 = 20 Q

31 Sensitivity of Quantity Supplied to Price Formally, % Q η = % p = Q Q p p = Q p p Q where Q indicates quantity supplied. Example If a 1% increase in price results in a 3% increase in quantity supplied, the elasticity of supply is η = 3%/1% =

32 Sensitivity of Quantity Supplied to Price: Example The estimated linear supply function for pork is: Q = 88-40p where Q is the quantity of pork supplied in million kg per year and p is the price of pork in $ per year. At the equilibrium, where p = $3.30 and Q = 220, the elasticity of supply is: η = Q p P Q = =

33 Sensitivity of Quantity Supplied to Price (cont.) Along linear supply curve with a function of: Q = g + Where h is the slope or Q p the elasticity of supply is h = hp η = Q p = p Q h p Q 3-33

34 Figure 3.5 Elasticity Along the Pork Supply Curve 3-34

35 Supply Elasticities Over Time Supply elasticities may differ in the shortrun and the long-run The difference depends on the ability to convert fixed inputs into variable inputs 3-35

36 Solved Problem 3.3 What would be the effect of ANWR production on the world price of oil given that ε = 0.4,η = 0.3, the pre-anwr daily world production of oil is Q 1 = 84 million barrels per day, the pre- ANWR world price is p 1 = $70 per barrel, and daily ANWR production would be 0.8 million barrels per day? For simplicity, assume that the supply and demand curves are linear and that the introduction of ANWR oil would cause a parallel shift in the world supply curve to the right by 0.8 million barrels per day. 3-36

37 Solved Problem

38 Effects of a Sales Tax 1. What effect does a sales tax have on equilibrium prices and quantity? 2. Is it true, as many people claim, that taxes assessed on producers are passed along to consumers? 3. Do the equilibrium price and quantity depend on whether the tax is assessed on consumers or on producers? 3-38

39 Two Types of Sales Taxes Ad valorem tax - for every dollar the consumer spends, the government keeps a fraction, α, which is the ad valorem tax rate Specific tax - where a specified dollar amount, τ, is collected per unit of output 3-39

40 Figure 3.6 Effect of a $1.05 Specific Tax on the Pork Market Collected from Producers p, $ per kg p 2 = 4.00 p 3 = 3.30 p 2 τ = e 2 T = $216.3 million e 1 Q 2 = 206 Q 1 = 220 S 2 τ = $1.05 S 1 D Q, Million kg of pork per year A tax on producers shifts the supply curve downward by the amount of the tax (τ = $1.05). which causes the market price to increase After the tax, buyers pay an additional $.70 per unit ($ $3.30) sellers receive $0.35 less per unit ($ $2.95) and the government collects $216.3 in revenue. 3-40

41 How Specific Tax Effects Depend on Elasticities The government raises the tax from zero to τ, so the change in the tax is τ =τ 0 = τ. The price buyers pay increases by: η p = τ η ε If ε = -0.3 and η = 0.6, a change of a tax of τ = $1.05 causes the price buyers pay to rise by p = η τ = η ε 0.6 $ [ 0.3] = $

42 Solved Problem 3.4 If the supply curve is perfectly elastic and demand is linear and downward sloping, what is the effect of a $1 specific tax collected from producers on equilibrium price and quantity, and what is the incidence on consumers? Why? 3-42

43 Solved Problem

44 Figure 3.7 Effect of a $1.05 Specific Tax on Pork Collected from Consumers p, $ per kg but the new equilibrium is the same as when the tax is applied to suppliers p = 4.00 e 2 Wedge, τ = $1.05 S p = 3.30 p 2 τ = 2.95 T = $216.3 million e 2 τ = $1.05 The tax shifts the demand curve down by τ = $1.05 D 1 D Q 2 = 206 Q 1 = 220 Q, Million kg of pork per year 3-44

45 Figure 3.8 Comparison of an Ad Valorem and a Specific Tax on Pork 3-45

46 Solved Problem 3.5 If the short-run supply curve for fresh fruit is perfectly inelastic and the demand curve is a downward-sloping straight line, what is the effect of an ad valorem tax on equilibrium price and quantity, and what is the incidence on consumers? Why? 3-46

47 Solved Problem

48 Figure 3.9 Effect of a Specific Gasoline (Carbon) Tax in the Long Run and in the Short Run 3-48