Chapter Three Applying the Supply-and- Demand Model

© 2007 Pearson Addison-Wesley. All rights reserved.3–2 Applying the Supply-and-Demand Model In this chapter, we examine five main topics. –How 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

© 2007 Pearson Addison-Wesley. All rights reserved.3–3 How Shapes of Demand and Supply Curves Matter The shapes of the demand and supply curves determine by how much a shock affects the equilibrium price and quantity. A supply shock would have different effects if the demand curve had a different shape.

© 2007 Pearson Addison-Wesley. All rights reserved.3–4 Figure 3.1 How the Effect of a Supply Shock Depends on the Shape of the Demand Curve (a)(b)(c) Q, Million kg of pork per year S 1 D 1 S 2 e 1 e Q, Million kg of pork per year S 1 S 2 D 2 e 1 e Q, Million kg of pork per year 3.30 S 1 S 2 D 3 e 1 e 2

© 2007 Pearson Addison-Wesley. All rights reserved.3–5 Price Elasticity of Demand Elasticity –the percentage change in a variable in response to a given percentage change in another variable

© 2007 Pearson Addison-Wesley. All rights reserved.3–6 Price Elasticity of Demand The price elasticity of demand (or simply elasticity of demand) is the percentage change in the quantity demanded,, in response to a given percentage change in the price,, at a particular point on the demand curve. The price elasticity of demand (represented by ε, the Greek letter epsilon) is (3.1) where the symbol Δ (the Greek letter delta) indicates a change.

© 2007 Pearson Addison-Wesley. All rights reserved.3–7 Price Elasticity of Demand For a linear demand curve,, the elasticity of demand is (3.3)

© 2007 Pearson Addison-Wesley. All rights reserved.3–8 Elasticity along the Demand Curve The elasticity of demand varies along most demand curves. Downward-sloping linear demand curve –On strictly downward-sloping linear demand curves—those that are neither vertical nor horizontal—the elasticity of demand is a more negative number the higher the price is.

© 2007 Pearson Addison-Wesley. All rights reserved.3–9 Figure 3.2 Elasticity Along the Pork Demand Curve a /2 =143 a /5 = 57.2 D a = Q, Million kg of pork per year a / b = a /(2 b ) = 7.15 Elastic:  <–1  =–4 Unitary:  =–1  =–0.3 Inelastic: 0 >  >–1 Perfectly inelastic Perfectly elastic

© 2007 Pearson Addison-Wesley. All rights reserved.3–10 Horizontal Demand Curve –A small increase in price causes an infinite drop in quantity, so the demand curve is perfectly elastic. Vertical Demand Curve –The elasticity of demand is zero. –A demand curve is vertical for essential goods—goods that people feel they must have and will pay anything to get. Elasticity along the Demand Curve

© 2007 Pearson Addison-Wesley. All rights reserved.3–11 Figure 3.3 Vertical and Horizontal Demand Curves (a) Perfectly Elastic Demand Q, Units per time period p * (b) Perfectly Inelastic Demand Q * Q, Units per time period

© 2007 Pearson Addison-Wesley. All rights reserved.3–12 Figure 3.3 Vertical and Horizontal Demand Curves (cont’d) (c) Individual’s Demand for Insulin p * Q * Q, Insulin doses per day

© 2007 Pearson Addison-Wesley. All rights reserved.3–13 Other Demand Elasticities Income elasticity of demand (or income elasticity) –the percentage change in the quantity demanded in response to a given percentage change in income

© 2007 Pearson Addison-Wesley. All rights reserved.3–14 Other Demand Elasticities cross-price elasticity of demand –the percentage change in the quantity demanded in response to a given percentage change in price of another good

© 2007 Pearson Addison-Wesley. All rights reserved.3–15 Elasticity of Supply price elasticity of supply (or elasticity of supply, ) –the percentage change in the quantity supplied in response to a given percentage change in the price (3.5)

© 2007 Pearson Addison-Wesley. All rights reserved.3–16 The elasticity of supply may vary along the supply curve. The elasticity of supply varies along most linear supply curve. Only constant elasticity of supply curves have the same elasticity at every point along the curve. Elasticity along the Supply Curve

© 2007 Pearson Addison-Wesley. All rights reserved.3–17 Elasticity along the Supply Curve Two extreme examples of both constant elasticity of supply curves and linear supply curves are the vertical and horizontal supply curves. Constant elasticity of supply curves are one of the form, where B is a constant and is the constant elasticity of supply at every point along the curve.

© 2007 Pearson Addison-Wesley. All rights reserved.3–18 Derivation of Constant Elasticity of Supply

© 2007 Pearson Addison-Wesley. All rights reserved.3–19 Figure 3.4 Elasticity Along the Pork Supply Curve S  ≈ 0.71  ≈ 0.66  ≈ 0.6  ≈ Q, Million kg of pork per year

© 2007 Pearson Addison-Wesley. All rights reserved.3–20 Long Run Versus Short Run The shapes of demand and supply curves depend on the relevant time period. Short-run elasticities may differ substantially from long-run elasticities. Demand elasticities over time –Two factors that determine whether short- run demand elasticities are larger or smaller than long-run elasticities are ease of substitution and storage opportunities.

© 2007 Pearson Addison-Wesley. All rights reserved.3–21 Supply elasticities over time –In the short run, how much a manufacturing firm can expand its output is limited by the fixed size of its manufacturing plant and the number of machines it has. –In the long run, however, the firm can build another plant and buy or build more equipment. Long Run Versus Short Run

© 2007 Pearson Addison-Wesley. All rights reserved.3–22 Page 59 Solved Problem 3.1 Q, Millions of barrels of oil per day S 1 S 2 e 1 e 2 D

© 2007 Pearson Addison-Wesley. All rights reserved.3–23 Effects of a Sales Tax What effect does a sales tax have on equilibrium prices and quantity? Is it true, as many people claim, that taxes assessed on producers are passed along to consumers? That is, do consumers pay for the entire tax? Do the equilibrium price and quantity depend on whether the tax is assessed on consumers or on producers?

© 2007 Pearson Addison-Wesley. All rights reserved.3–24 Two Types of Sales Taxes The most common sales tax is called an ad valorem tax ( 從價稅 ) by economists and the sales tax by real people. For every dollar the consumers spends, the government keeps a fraction, α, which is the ad valorem tax rate. The other type of sales tax is a specific or unit tax ( 從量稅 ), where a specified dollar amount, τ, is collected per unit of output.

© 2007 Pearson Addison-Wesley. All rights reserved.3–25 Figure 3.5 Effect of a $1.05 Specific Tax on the Pork Market Collected from Producers Q 2 = 206 Q 1 = T = $216.3 million Q, Million kg of pork per year 0 p 2 = 4.00 p 1 = 3.30 p 2 –  = 2.95  = $1.05 S 1 e 1 e 2 S 2 D

© 2007 Pearson Addison-Wesley. All rights reserved.3–26 Page 64 Solved Problem 3.2 Q, Quantity per time period Q 1 Q 2 p 1 p 2 = p S 1 S 2 e 1 e 2 D  = $1

© 2007 Pearson Addison-Wesley. All rights reserved.3–27 Figure 3.6 Effect of a $1.05 Specific Tax on Pork Collected from Consumers Q 2 = 206 Q 1 = T = $216.3 million Q, Million kg of pork per year0 p 2 = 4.00 p 1 = 3.30 p 2 –  = 2.95  = $1.05 Wedge,  = $1.05 D 1 D 2 e 1 e 2 S

© 2007 Pearson Addison-Wesley. All rights reserved.3–28 Specific Tax Effects in the Pork Market The specific tax causes the equilibrium price consumers pay to rise, the equilibrium quantity to fall, and tax revenue to rise.

© 2007 Pearson Addison-Wesley. All rights reserved.3–29 How Specific Tax Effects Demand on Elasticities The effects of the tax on the equilibrium prices and quantity depend on the elasticities of supply and demand. In response to this change in the tax, the price consumers pay increases by (3.6) where ε is the demand elasticity and is the supply elasticity at the equilibrium.

© 2007 Pearson Addison-Wesley. All rights reserved.3–30 Tax Incidence of a Specific Tax The incidence of a tax on consumers is the share of the tax that falls on consumers. The incidence of the tax that falls on consumers is, the amount by which the price to consumers rises as a fraction of the amount the tax increases.

© 2007 Pearson Addison-Wesley. All rights reserved.3–31 How Tax Incidence Depends on Elasticities To determine the conditions under which firms can pass along the full tax, we need to know how the incidence of the tax depends on the elasticities of demand and supply at the pretax equilibrium. By dividing both sides of Equation 3.6 by, we can write the incidence of the tax that falls on consumers as (3.7)

© 2007 Pearson Addison-Wesley. All rights reserved.3–32 The Same Equilibrium No Matter Who Is Taxed In the supply-and-demand model, the equilibrium and the incidence of the tax are the same regardless of whether the government collects the tax from consumers or producers.

© 2007 Pearson Addison-Wesley. All rights reserved.3–33 Figure 3.7 Comparison of an Ad Valorem and a Specific Tax on Pork Q 2 = 206 Q 1 = T = $216.3 million Q, Million kg of pork per year0 p 2 = 4.00 p 1 = 3.30 p 2 –  = 2.95 e 1 e 2 D a D s S D

© 2007 Pearson Addison-Wesley. All rights reserved.3–34 The Similar Effects of Ad Valorem Specific Taxes The specific tax shifts the pretax demand curve, D, down to D s, which is parallel to the original curve. The ad valorem tax shifts the demand curve to D a. The incidence of an ad valorem tax is generally shared between consumers and suppliers. Because the ad valorem tax of α = 26.25% has exactly the same impact on the equilibrium pork price and raises the same amount of tax per unit as the $1.05 specific tax, the incidence is the same for both types of taxes.

© 2007 Pearson Addison-Wesley. All rights reserved.3–35 Page 69 Solved Problem 3.3 Q * Q, Quantity per time period (1–  ) p * p *  p * D 1 e 1 e 2 D 2 S