1 Chapter 3 Applying the Supply-and- Demand Model Applying supply and demand model 1. shapes matter 2. sensitivity of quantity demanded to price 3. sensitivity of quantity supplied to price 4. sensitivity is different in long run than in the short run 5. effects of a sales tax Questions 1. condoms: how much of a subsidy is necessary to encourage French consumers to use 70% more condoms? 2. cigarettes taxes: how big a tax is needed to discourage a substantial number of people from smoking? 3. health care: if Congress passes a law forcing firms to provide health care, will firms pass on the full amount of these mandatory fees to consumers? What-if questions • how do equilibrium price and quantity change when an underlying factor changes? • use graphs to predict qualitative effects of changes: The direction of change • need to know shape of demand and supply curves to determine quantitative change: amount equilibrium quantity and price change Shapes of demand and supply curves matter • supply shock (25¢ increase in price of hogs) effect on Canadian processed pork depends on shape of demand curve • supply shock causes supply curve of pork to shift left from S 1 to S 2 p, $ per kg 215 2201760 Q, Million kg of pork per year 3.55 3.30 S 1 D 1 S 2 e 1 e 2 Pork demand and supply curves 2 If the demand curve is horizontal p, $ per kg 2202051760 Q, Million kg of pork per year 3.30 S 1 S 2 D 3 e 1 e 2 If the demand curve is vertical p, $ per kg 2201760 Q, Million kg of pork per year 3.675 3.30 S 1 S 2 D 2 e 1 e 2 -49.5-150Horizontal 82.5037.5Vertical 37.25-525Actual: Downward slope R, $million/ year Q, million kg/year p, cents/kg Demand Curve Elasticity of demand • summarize sensitivity of the quantity demanded to price in a single statistic: price elasticity of demand: % change in quantity demanded / %change in price / QQ p p ε ∆ == ∆ / / QQ Qp p ppQ ε ∆∆ == ∆∆ Linear demand curve • linear demand: Q = a – bp • elasticity of demand: • pork demand curve: Q = 286 – 20p Qp p b p QQ ε ∆ ==− ∆ 3.30 20 0.3 220 Qp p b pQ Q ε ∆ ==−=− =− ∆ Interpretation of pork demand elasticity • 1% increase in price of pork leads to an F% = -0.3% change in the quantity demanded • quantity falls less than in proportion to price • negative price elasticity, -0.3, is consistent with Law of Demand 3 Types of elasticities • elastic: the quantity demanded changes more than in proportion to a change in price • inelastic: the quantity demanded changes less than in proportion to a change in price • elasticity of demand varies along most linear demand curves Figure 3.2 Elasticity Along the Pork Demand Curve p, $ per kg a/2 = 143a/5 = 57.2 D a = 286220 Q, Million kg of pork per year 0 11.44 a/b = 14.30 3.30 a/(2b) = 7.15 Elastic: ε < –1 ε = –4 Unitary: ε = –1 ε = – 0.3 Inelastic: 0 > ε > –1 Perfectly inelastic Perfectly elastic Downward-sloping linear demand curve • perfectly elastic (F is -<) where demand curve hits vertical axis • unitary elasticity at midpoint: p = a/(2b) and Q = a/2 therefore, F = -bp/Q = -b(a/[2b])/(a/2) = -1 • perfectly inelastic (F = 0) where demand curve hits quantity axis ε = -bp/Q = -b0/Q = 0 Constant elasticity demand curves • elasticity same at every point along curve • smooth curves: • Q = Ap . , or, • vertical demand curve: perfectly inelastic (F = 0) everywhere: essential good • horizontal demand curve: perfectly elastic (-d): perfect substitutes Constant Elasticity Demand Curves Figure 3.3c Individual’s Demand for Insulin * p, Price of insulin dose * Q, Insulin doses per day p Q 4 Income elasticity of demand % change in quantity demanded % change in income / / QQ QY YY YQ ξ = ∆∆ == ∆∆ Pork income elasticity of demand pork demand function is Q = 171 – 20p + 20p b + 3p c + 2Y so pork income elasticity is at Q = 220 and Y = 12.5 Y = 2 x 12.5/220 = 0.114 2 QY Y YQ Q ξ ∆ == ∆ Cross-price elasticity of demand how quantity of one good changes as price of another good increases %change in quantity demanded %change in price of another good / / o oo o QQ Qp pp pQ ∆∆ == ∆∆ Negative cross-price elasticity • as the other good’s price increases, people buy less of this good • demand curve shifts to the left •examples • as price of cream rises, people consume less coffee (cross-price elasticity is negative) • Ford wants to know how much a change in the price of a Camry affects the demand for a Taurus Positive cross-price elasticity • as the price of the other good increases, people buy more of this good • demand curve shifts to the right • example: cross-price elasticity of pork with respect to the price of beef is positive Pork-beef example • pork demand function is Q = 171 – 20p + 20p b + 3p c + 2Y • so cross-price elasticity of demand for pork and the the price of beef is •at Q = 220 and p b = $4 per kg, cross-price elasticity is 20 x 4/220 = 0.364 20 ob o Qp p p QQ ∆ = ∆ 5 Price elasticity of supply / / %change in quantity supplied %change in price QQ Qp pp pQ η = ∆∆ == ∆∆ Sign of elasticity of supply • if supply curve slopes upward, %p/%Q > 0, then I > 0 • if supply curve slopes downward, %p/%Q > 0, then I < 0 • supply curve is elastic if I > 1 • supply curve is inelastic if 0 bI< 1 Pork supply elasticity • pork supply curve is Q = 88 + 40p • so pork supply elasticity is • as price of pork increases by 1%, the quantity supplied rises by nearly two-thirds of a percent 3.30 40 0.6 220 Qp pQ η ∆ == = ∆ Figure 3.4 Elasticity Varies Along Linear Pork Supply Curve p, $ per kg 220 260176 S η ≈ 0.71 η ≈ 0.66 η ≈ 0.6 η ≈ 0.5 300 Q, Million kg of pork per year 0 3.30 2.20 4.30 5.30 Constant Elasticity Supply Curves Long run versus short run • SR and LR elasticities may differ substantially • gasoline demand elasticities: • SR elasticity = -0.35 • 5-year intermediate-run elasticity = -0.7 • 10-year, LR elasticity = -0.8 • if a good can be easily stored, SR demand curve may be more elastic than LR curve 6 OPEC restricts output • according to news reports 1/17/01, OPEC may reduce quantity of oil by 5% • How does the price change in SR and LR? • %p/p = (%Q/Q)/F = -5%/(-0.35) = 14.3% (SR) = -5%/(-0.7) = 7.1% (intermediate run) = -5%/(-0.8) = 6.3% (LR) Predictions based on elasticities knowing only the elasticities of demand and supply, we can make accurate predictions about the effects of a new tax and determine how much of the tax falls on consumers Two types of sales taxes • ad valorem tax (the sales tax): for every dollar the consumer spends, the government keeps a fraction, B • specific (unit) tax: a specified amount, U, is collected per unit of output Tax on consumer pQ – UQT = UQspecific tax U (1 - B)pQT = BpQad valorem tax Bp Firms’ after-tax revenue Total tax revenue Per unit tax 4 Questions about sales taxes 1. What effect does a specific sales tax have on equilibrium prices and quantity? 2. Are sales taxes assessed on producers "passed along" to consumers? (do consumers pay entire tax?) 3. Do equilibrium price and quantity depend on whether the consumers or producers are taxed? 4. Do both types of sales taxes have the same effect on equilibrium? Specific tax • assume the specific tax is assessed on firms at the time of sale • consumer pays p • government takes U • seller receives p - U 7 Sin taxes • because output falls after tax, governments can use taxes to discourage "sin" activities • federal specific taxes have been used for: • cigarettes • alcohol • playing cards (in an earlier day) Price impact of tax • amount by which tax affects equilibrium price depends on elasticities of supply and demand • government raises tax by %U = U -0 = U • price consumers pay increases by p η ∆= ∆τ η −ε Pork example • Figure 3.5 shows %p = $4 - $3.30 = 70¢ • demand elasticity: F = -0.3 • supply elasticity, I = 0.6 • %U = U = $1.05 • therefore: 0.6 ($1.05) $0.70 0.6 ( 0.3) p η ∆= ∆τ= = η−ε − − Figure 3.5 Effect of a $1.05 Specific Tax on the Pork Market Collected from Producers p, $ per kg Q 2 = 206 Q 1 = 220176 T = $216.3 million Q, Million kg of pork per year 0 p 2 = 4.00 p 1 = 3.30 p 2 – τ = 2.95 τ = $1.05 S 1 e 1 e 2 S 2 D Question 2 • Who is hurt by the tax? • What is the incidence of the tax? Tax incidence incidence of a tax on consumers is share of tax that consumers pay p∆η = ∆τ η− ε 8 Incidence of a tax on pork • Figure 3.5 shows consumer incidence is %p/%7 = $0.70/$1.05 = 2/3 • using elasticities, consumer incidence is I/(I - F) = 0.6/(0.6 - [-0.3]) = 2/3 Restaurant tax incidence • estimated demand and supply for restaurant meals (Brown 1980): • constant elasticity demand curve: F = -0.188 • constant elasticity supply curve: I = 6.47 • original equilibrium: • Q 1 = 8.14 billion meals per year • p 1 = $10.47 per meal ($1992) Incidence specific gasoline taxes • specific taxes • federal range from nearly 11¢ and 20¢ per gallon • state from 7¢ to 36¢ per gallon • incidence: federal tax ³ 1¢ º • retail price ³ ½¢ • wholesale price m ½¢ • incidence: state tax ³ 1¢ º • retail price ³ 1¢ • no wholesale price effect Incidence ad valorem gas tax ad valorem gas tax • CA, Georgia, IL, Indiana, Louisiana, Michigan, Mississippi, NY • range up to 7% of retail price •tax rate ³ from 0 to 5% º • retail price ³ 3.6¢ • wholesale price m 1.8¢. Question 3 • does equilibrium depend on who is taxed? 9 Answer no: equilibrium is same whether government collects tax from firms or from consumers in a competitive market = $1.05 = 2.95 Figure 3.6 Effect of a $1.05 Specific Tax on Pork Collected from Consumers p , $ per kg Q 2 = 206 Q 1 = 220176 = $216.3 million Q, Million kg of pork per year0 p 2 = 4.00 p 1 = 3.30 p 2 – τ = $1.05 Wedge, τ D 1 D 2 e 1 e 2 S T τ Question 4 how can an ad valorem and specific tax have the same effect on equilibrium (in a competitive market)? Figure 3.7 A Comparison of an Ad Valorem and a Specific Tax on Pork p , $ per kg Q 2 = 206 Q 1 = 220176 T = $216.3 million Q , Million kg of pork per year0 p 2 = 4.00 p 1 = 3.30 p 2 – τ = 2.95 e 1 e 2 D a D s S D Luxury taxes • in 1990, an ad valorem tax was imposed on luxury goods • tax was 10% of the amount over • $100,000 paid for yachts • $250,000 for private planes • $10,000 for furs and jewels • $30,000 for cars • objective: raise tax revenues without harming the poor and middle class 1 Shapes of demand and supply curves matters shapes determine the size of the effect 10 2 Elasticity of demand • F = percentage change in quantity demanded due to an increase in price divided by percentage change in price • always negative due to the Law of Demand 3 Elasticity of supply • I = percentage change in the quantity supplied divided by the percentage change in price • may have any sign, but commonly positive (upward-sloping supply curve) 4 LR and SR elasticities frequently differ usually more adjustment is possible in the long run than in the short run 5 Sales taxes • common types of sales taxes: ad valorem and specific • both types of taxes usually raise equilibrium price and lower equilibrium quantity • tax incidence depends on demand and supply elasticities • in competitive markets, effect of a tax on equilibrium same whether collected from consumers or producers . 3 Applying the Supply-and- Demand Model Applying supply and demand model 1. shapes matter 2. sensitivity of quantity demanded to price 3. sensitivity of quantity supplied to price 4. sensitivity. increase in price divided by percentage change in price • always negative due to the Law of Demand 3 Elasticity of supply • I = percentage change in the quantity supplied divided by the percentage. $million/ year Q, million kg/year p, cents/kg Demand Curve Elasticity of demand • summarize sensitivity of the quantity demanded to price in a single statistic: price elasticity of demand: % change