# Chapter 3. Applying the Supply-and- Demand Model

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1 Chapter 3 Applying the Supply-and- Demand Model

2 Reading Assignment for Week: Finish Chapter 3 Chapter 9 (sections 9.2, 9.3, 9.4) Chapter 13 (first few pages through section 13.1) 3-2

3 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. 3-3

4 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. 3-4

5 p, \$ per kg p, \$ per kg 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 pork causes the supply of pork to shift to the left (a) D 1 A \$0.25 increase in the price of pork causes the supply of pork to shift to the left. (b) D S 2 S 1 e 2 e S 2 S 1 e 2 e Q, Million kg of pork per year Q, Million kg of pork per year and a reduction in quantity. But equilibrium quantity does not change since consumption is not sensitive to price 3-5

6 p, \$ per kg 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 (c) a shift in the supply curve to S 2 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 3-6

7 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 (e) the percentage change in the quantity demanded in response to a given percentage change in the price. 3-7

8 Sensitivity of Quantity Demanded to Price (cont.) Formally, ε = % change in quantity demanded % change in price = dq dp p Q = Q/Q p/p where D indicates change, Q is quantity demanded, and p is price Example If a 1% increase in price results in a 3% decrease in quantity demanded, the elasticity of demand is e = -3%/1% = -3. NOTE: elasticity is unitless 3-8

9 Sensitivity of Quantity Demanded to Price (cont.) Along linear demand curve with a function of: Q a bp Where -b is the slope or the elasticity of demand is ε = dq dp b = dq dp = Q p p Q = b p Q (3.3) 3-9

10 Elasticity of demand answers the question How much does quantity demanded fall in response to a 1% increase in price? 3-10

11 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 e b p Q

12 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 per minute reduced the connection time by for those with high speed access, and by for those with slow phone line access. 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. 3-15

14 p, \$ per kg Figure 3.2 Elasticity Along the Pork Demand Curve a/b = Perfectly elastic Elastic e < 1 e = 4 e = -b Q = p p Q = -20 x = 57.2 = D a/(2b) = 7.15 Unitary: e = -1 Inelastic 0 > e > e = 0.3 Perfectly inelastic 0 a/5 = 57.2 a/2 = a = 286 Q, Million kg of pork per year 3-16

15 Demand Elasticity Nomenclature ε = 0 perfectly inelastic 1 < ε < 0 inelastic ε = 1 unit elastic < ε < 1 elastic As ε approaches( ) perfectly elastic 3-17

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 3-19

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 pe riod Q* Q, Units per time pe riod Q* Q, Insulin doses per d ay 3-20

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 3-21

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 3-22

20 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 (e.g., gasoline) For most goods elasticities tend to be larger (i.e., more elastic) in the long-run 3-26

21 Income Elasticity of Demand Formally, ξ = where Y stands for income. Example % change in quantity demanded % change in income = dq dy Y Q = Q/Q Y/Y If a 1% increase in income results in a 3% increase in quantity demanded, the income elasticity of demand is x = 3%/1% =

22 Cross-Price Elasticity of Demand Formally, Cross-price elasticity= % change in quantity demanded % change in price of another good where P o stands for price of another good. Example = dq dp 0 p 0 Q = Q/Q p 0 /p 0 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% =

23 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 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 3-30

24 Sensitivity of Quantity Supplied to Price Formally, % change in quantity supplied η = % change in price = dq dp p Q = Q/Q p/p where Q indicates quantity supplied. If supply is upward sloping, the supply elasticity is positive: η > 0 If supply slopes downward, the supply elasticity is negative: η < 0 Example If a 1% increase in price results in a 3% increase in quantity supplied, the elasticity of supply is h = 3%/1% =

25 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: h DQ Dp P Q

26 Sensitivity of Quantity Supplied to Price (cont.) Along linear supply curve with a function of: Q g hp Where h is the slope or h = dq dp the elasticity of supply is η = dq dp p Q = h p Q 3-34

27 Figure 3.5 Elasticity Along the Pork Supply Curve 3-35

28 Supply Elasticity Nomenclature η = 0 perfectly inelastic 0 < η < 1 inelastic η = 1 unit elastic η > 1 elastic As η approaches perfectly elastic 3-36

29 Different Supply Elasticities Supply elasticities may differ in the shortrun and the long-run So-called constant elasticity of supply curves can exist (e.g., vertical and horizontal supply curves) Vertical supply curve is perfectly inelastic Horizontal supply curve is perfectly elastic 3-37

30 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? 3-40

31 Two Types of Sales Taxes Ad valorem tax (Sales tax) - for every dollar the consumer spends, the government keeps a fraction, α, which is the ad valorem tax rate Specific tax (Unit tax) - where a specified dollar amount, t, is collected per unit of output 3-41

32 p, \$ per kg Figure 3.6 Effect of a \$1.05 Specific Tax on the Pork Market Collected from Producers p 2 = 4.00 p 3 = 3.30 p 2 t = e 2 T = \$216.3 million e 1 Q 2 = 206 Q 1 = 220 S 2 t = \$1.05 S 1 D Q, Million kg of pork per year A tax on producers shifts the supply curve upward by the amount of the tax (t = \$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. 3-42

33 How Specific Tax Effects Depend on Elasticities The government raises the tax from zero to t, so the change in the tax is Dt =t 0 = t. The price buyers pay increases by: Effect of a unit tax h Dp Dt h e If e = -0.3 and h = 0.6, a change of a tax of Dt = \$1.05 causes the price buyers pay to rise by Dp h Dt h e 0.6 \$ [ 0.3] \$

34 p, \$ per kg Figure 3.7 Effect of a \$1.05 Specific Tax on Pork Collected from Consumers but the new equilibrium is the same as when the tax is applied to suppliers p = 4.00 e 2 Wedge, t = \$1.05 S p = 3.30 p 2 t = 2.95 T = \$216.3 million e 2 t = \$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 3-46

35 Affect of Tax on Equilibrium Depends on Elasticity For a given supply elasticity, the more elastic demand is, the less the equilibrium price rises when a tax is imposed. For a given demand elasticity, the greater the supply elasticity (i.e., supply is more elastic), the larger the increase in the equilibrium price consumers pay when a tax is imposed. 3-47

36 Tax Incidence of a Unit Tax The incidence of a tax on consumers is the share of the tax that falls on consumers. Defined as, = p τ Example: the unit tax increases by \$1.05 and consumers pay 70 cents more (in equilibrium). What is the tax incidence? 3-49

37 Tax Incidence Depends on Elasticities Downward sloping demand and upward sloping supply both consumers and producers pay portion of tax Firms can pass along all the tax only under extreme cases: 1. ε 0 (inelastic/vertical demand) 2. η (elastic/horizontal supply) For this class, equilibrium and incidence are same regardless of whether tax is levied on consumers or producers 3-50

38 Ad Valorem (Sales Tax) This is a tax on goods and services. Specifically, it is a tax on the price that consumers pay. Typically, it is expressed as a percentage, α (e.g., α =25%, 30%, etc.). 3-51

39 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? 3-52

40 Solved Problem

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