1 Chapter 5 Applying Consumer Theory Key issues 1. deriving demand curves 2. income effect 3. effects of a price change 4. CPI bias 5. labor supply curve Questions 1.What would happen if a consumer behaved randomly? 2. Do we measure incomes in developing countries accurately? 3. What are the effects of overtime laws? 4. What are the effects on hours of work of tax cuts? 5. Can a flat tax be progressive? • trace out the demand curve by holding income and the price of wine constant, and varying the price of beer • example: estimated set of indifference curves for the typical American consumer are bowed away from origin, so beer and wine are imperfect substitutions Deriving Demand Curves Figure 5.1 Deriving an Individual’s Demand Curve 4.3 5.2 12.0 2.8 12.0 6.0 4.0 26.7 0 44.5 58.9 L 1 ( p b = $12) p b , $ per unit L 2 (p b = $6) L 3 (p b = $4) 26.70 44.5 58.9 e 3 e 2 e 1 E 3 E 2 E 1 I 1 I 2 I 3 Beer, Gallons per year Beer, Gallons per year D 1 , Demand for beer Price-consumption curve Wine, Gallons per year (a) Indifference Curves and Budget Constraints (b) Demand Curve Price-consumption curve shows how the optimal pairs of beer and wine vary as the relative price varies 2 How income changes shift demand curves • hold prices fixed and vary income • increase in income causes • shift of the demand curve • movement along income-consumption curve • movement along the Engel curve Figure 5.2 Effect of a Budget Increase on an Individual’s Demand Curve per year Income-consumption curve Engel curve for beer 0 2.8 4.8 7.1 49.138.226.7 Beer, Gallons per year 0 12 0 49.138.226.7 Beer, Gallons per year 49.138.226.7 Beer, Gallons per year I 2 I 3 I 1 (a) Indifference Curves and Budget Constraints Price of beer, $ per unit (b) Demand Curves Y, Budget (c) Engel Curve e 2 e 3 E 3 E 1 E 2 Y 1 = $419 Y 2 = $628 Y 3 = $837 L 3 L 2 L 1 e 1 D 1 D 2 D 3 E 1 * E 2 * E 3 * Wine, Gallons Income elasticities • income elasticity: • normal good: ξ >0 • inferior good: ξ≤0 p ercentage change in quantity demanded percentage change in income / / QQ YY ξ = ∆ = ∆ Mimi's income elasticities • beer: ξ b = 0.88 •wine: ξ w = 1.38 • both are normal goods Are children inferior? • mother with relative little education: ξ = -0.18 • mother relatively well educated: ξ = 0.044 Income-consumption curves and income elasticities • shape of income-consumption curve for 2 goods tells us sign of income elasticities • some goods must be normal: not all goods can be inferior 3 Figure 5.3 Income-Consumption Curves and Income Elasticities Housing, Square feet per year Food, Pounds per year Food normal, housing normal Food inferior, housing normal Food normal, housing inferior b c e a L 1 L 2 I ICC 2 ICC 1 ICC 3 Income elasticities may vary with income Gail may view hamburger as • a normal good at a low income • an inferior good at a high income Figure 5.4 A Good That Is Both Inferior and Normal Y 2 Y 1 Y 1 Y 2 Y 3 Y 3 L 1 Y, Income L 2 L 3 e 2 e 3 e 1 E 2 E 3 E 1 I 1 I 2 I 3 Hamburger per year Income-consumption curve Hamburger per year All other goods per year (a) Indifference Curves and Budget Constraints (b) Engel Curve Engel curve Quality and income elasticities • when their incomes rise, some people buy higher quality goods rather than more of what they’re currently buying •examples: • fancier cars • fancier foods • designer clothing Effects of a price change as price of one good goes up (all else the same), there are two effects: • a substitution effect • an income effect Substitution effect • consumers substitute other, now relatively cheaper, goods for the one whose price rose • direction of the effect is unambiguous 4 Income effect • price increase ⇒ consumers' buying power falls, reducing “income” (opportunity set) • so consumer buys less of at least some goods • direction of income effect depends on income elasticity of each good Income and substitution effects positivenegativeinferior good negativenegativenormal good income effectsubstitution effectprice rise Figure 5.5 Substitution and Income Effects with Normal Goods Wine, Gallons per year 12.0 5.5 0 58.926.7 30.6 Substitution effect Total effect Income effect Beer, Gallons per year I 2 I 1 L* L 2 L 1 e 2 e 1 e * Income and substitution effect with an inferior good • substitution effect: opposite of price movement • income effect: same direction as price movement • Giffen good: good for which a decrease in its price causes the quantity demanded to fall • potatoes in Ireland? • quinine water for lab rats Figure 5.6 Giffen Good Basketball, Tickets per year Movies, Tickets per year L 1 L* Total effect Income effect Substitution effect L 2 e 1 e 2 e* I 1 I 2 Solved problem • dinner plate manufacturer sells • first-quality (perfect) • second-quality (slight color defects) dinner plates • manufacturer has an outlet store located next to its manufacturing plant • [assume tastes same everywhere; cost of shipping each plate from factory to distant stores is s] 5 Solved problem (cont.) compared to sales at other stores, does the outlet store sell A. a relatively large share of seconds B. the same ratio of first and second quality plates C. a relatively small share of seconds? Answer • relative prices at outlet store: • relative prices elsewhere: • • relative price of seconds rises—causing substitution away from seconds • presumably the income effect is small / s f pp s f p s p s + + Shipping the Good Stuff Away • expect larger share of higher-quality goods shipped, greater per-unit shipping fee • Hummels and Skiba (2002) examined shipments between 6,000 country pairs for more than 5,000 goods Results • doubling per unit shipping costs results in a 70 to 143% increase in average price (excluding cost of shipping) — larger share of top-quality products shipped • farther apart are trading countries, greater the cost of shipping—may explain relatively high-quality of Japanese goods Results (cont.) • ad valorem tariff raises relative price of higher- quality goods (given that there is also a per unit shipping fee) • doubling ad valorem tariff decreases average price three to four fold, as average quality falls • thus, using an ad valorem rather than a specific (per unit) tariff reduces quality of imported goods Inflation • because of inflation, prices today are not directly comparable to past prices • inflation harms people on fixed incomes, net lenders, and others 6 Cost-of-living adjustments many long-term contracts include cost-of- living adjustments (COLAs): • general business contracts •rental • alimony payments • salaries • pensions Consumer Price Index (CPI) • many governments report a cost-of-living measure: CPI • measure of inflation: overall rise in prices over time • CPI overestimates how true cost-of-living changes over time • overestimate hurts you if your landlord increases rent on your apartment using CPI Real vs. nominal prices • nominal price = “current dollars” price • real price = “constant dollar” price (adjusted for inflation) • • real price = nominal price divided by CPI CPI for 2000 168.7 price of a burger = 15¢ 94¢ CPI for 1955 26.8 ××= Government collects prices on 364 individual goods and services, such as: • housing • dental services • watch and jewelry repairs • college tuition fees •taxi fares • women's hair pieces and wigs • hearing aids • slip covers and decorative pillows • bananas • funeral expenses Summary statistics • if government reports all price increases separately, information is overwhelming • instead use a single summary statistic, CPI: how prices rose on average Averaging • one way to average price increases: weight the good equally • but do we really want to weight price increase of skateboards as much as that of automobiles? 7 CPI approach • give a larger weight to price change of a good, the larger its budget share • example: suppose CPI consists of only clothing (C) and food (F) Price of bundles • CPI in Year 1: • cost of buying first year’s bundle in second year is: • how much income would have to rise to buy first year’s bundle in second year: 11 111CF YpCpF = + 22 211CF YpCpF = + 22 211 11 111 CF CF YpCpF YpCpF + = + Calculate rate of inflation Y 2 /Y 1 shows average price rise 21 21 1 21 11 11 1 2 2 11 CC FF CF C F CF CF ppC YppF YpY pY p p pp θθ   =+       =+     CPI adjustment • we assume price of clothing rose more rapidly than that of food • CPI overcompensates (upward bias) • utility rises because consumer substitutes toward the relatively cheaper good Figure 5.7 The Consumer Price Index C 2 C 1 C, Units of clothing per year e 2 e 1 I 1 L 1 e* L* L 2 I 2 F , Units of food per year Y 2 */p 2 F Y 1 /p 1 F Y 1 /p 1 C Y */p 2 C F 2 F 1 Y 2 /p 2 F Y 2 /p 2 C Source of Bias • CPI calculates price increase as Y 2 /Y 1 . We can rewrite this expression as • Y*/Y 1 = increase in true cost of living • Y 2 /Y* = substitution bias in CPI (> 1 because Y 2 > Y*) * 22 * 11 YY Y YYY = 8 Total CPI bias CPI Commission concluded that CPI has a total upward bias of about 1.1 percentage points per year: • substitution bias: 0.4 percentage points per year • failure to take proper account of spread of discount stores: 0.1 percentage point • failure to account fully for quality improvements and new products (drugs, computers): 0.6 percentage point USPS • in 2002, a typical union employee earned $59,900 (including benefits) • Substitution bias of 0.5% a year costs USPS $300 extra per employee • multiplied by 860,000 employees: substitution bias costs USPS over $257 million per year (and benefits its employees by same amount) Federal Government • CPI Commission concluded CPI is fourth largest "federal program" after Social Security, health care, defense • $634 billion of national debt would be eliminated in 5 years if CPI rose 1% less rapidly per year • gain to government would largely be at expense of Social Security recipients How rich are developing countries? • commonly used measure of income understates third-world country incomes relative to those of industrial nations • problem: ignores substitution effects (as with CPI) International Monetary Fund • IMF used to report country’s income by converting native currency into dollars at market exchange rate • IMF switched to using purchasing-power parities (PPP), which take account of international differences in prices • used to report how much Chinese could buy at high US prices, now use lower Chinese prices Result IMF now reports that third world's share of world's income went from • 18% to 34% for developing countries • 9% to 11% for Eastern Europe and the former Soviet Union • 7% to 18% for Asia • 73% to 54% for industrialized countries 9 More plausible • old system: China's total income < Canada's; its income per person only slightly > India • improbable • China has a high daily food consumption • 70% of Chinese urban households have color TVs • 81% have washing machines • new Chinese av. income is $1,950 • China's share of the world income rose from 2% to 6%, making it third-biggest economy behind U.S. (22.5%) and Japan (7.6%) 0.0 0.2 0.4 0.6 0.8 1.0 012345 income density 1999 U.S. income distribution (solid) 2001 China income distribution (dashes) Deriving labor supply curves • use consumer-theory model to derive supply curve of labor by deriving demand curve for time spent not working • time constraint: H = 24 - N • H = hours of work in a day • N = hours of leisure or nonwork in a day Price of leisure foregone earnings are greater for a lawyer who earns $250 an hour than for someone who works for minimum wage Utility • Jackie's utility, U(Y, N) • depends on • goods she consumes, represented by her income, Y • number of hours of leisure, N Budget constraint • her total income is: Y = wH + Y* • where • w = her wage • H = hours she works • wH = her earned income • Y* = unearned income (if any) 10 Time constraint  can’t increase hours in a day  vertical constraint at 24 hours of leisure Figure 5.8 Demand for Leisure Y, Goods per day Time constraint H 2 = 12 H 1 = 824 0 N 2 = 12 N 1 = 16024 H, Work hours per day N, Leisure hours per day H 2 = 12 H 1 = 8 N 2 = 12 N 1 = 160 H, Work hours per day N, Leisure hours per day Demand for leisure I 2 I 1 1 –w 2 L 1 L 2 (a) Indifference Curves and Constraints w, Wage per hour (b) Demand Curve –w 1 1 e 2 Y 2 Y 1 w 1 w 2 e 1 E 2 E 1 Supply curve of labor • her supply curve of hours worked (labor) is “mirror image” of demand curve for leisure: H = 24 - N • for every extra hour of leisure she consumes, she works one fewer hour Figure 5.9 Supply Curve of Labor w, Wage per hour (a) Leisure Demand Demand for leisure w 1 w 2 16120 N, Leisure hours per day E 1 E 2 w, Wage per hour (b) Labor Supply Supply of work hours w 1 w 2 8120 H, Work hours per day e 2 e 1 Solved problem • Mark’s utility function is • his budget constraint is: • How many hours a day does he chose to work if the wage is w? (, )UUYN YN== YwH= Answer • substitute Mark’s budget constraint and his hours constraint, H = 24 – N, into his utility function: • he maximizes his utility by differentiating U with respect to N and setting the derivative equal to 0: •or N = 12 2 () ([24 ]) (24 ) 24 UYN wHN w NN wwNN wN wN = ==− =− = − 24 2 0wwN − = [...]... constraint LLS goes through e2,but family chooses e3 1 Deriving demand curves • individual demand curves derived using consumer' s indifference curve map • consumers' tastes (indifference curves) determine the shape of the demand curve (elasticity of demand) 16 2 Income effect • use indifference curve maps to show how entire demand curve shifts as a consumer' s income rises • relationship between income and... more than offsets substitution effect so that total effect > 0 (Giffen good) 4 CPI bias • Consumer Price Index, by ignoring the substitution effect, overestimates inflation • substitution bias is on average small, but may be substantial for particular individuals or firms 5 Labor supply curves • using consumer theory, we derive the demand curve for leisure • daily labor supply curve: 24 - demand curve... child-care program could provide an ad valorem or a specific subsidy (as many states currently do under PRWORA) • alternatively, government could provide an unrestricted lump-sum payment under the major welfare program that could be spent on day care or on all other goods such as food and housing • for a given government expenditure, does the price subsidy or the lump-sum subsidy provide greater benefit to... housing • for a given government expenditure, does the price subsidy or the lump-sum subsidy provide greater benefit to recipients? • which increases the demand for day care services by more? • which inflicts less cost on other consumers of day care? Solution e3 Y2 e2 e1 I3 I2 I1 Yo Lo 0 Q1 Q3 Q2 L LS LP S • on initial budget constraint is Lo, poor family chooses the bundle e1 • with a day-care price... who played the Massachusetts Megabucks lottery • prizes ranged from $22,000 to $9.7 million, with an average of $1.1 million (paid in yearly installments over two decades) Demographic differences • behavior same for: • men and women • big and very big prize winners • people of all education levels • differences by age of the winner and by income groups: • people 55 to 65 reduced their effort by about...Figure 5.10 Income and Substitution Effects of a Wage Change Income and substitution effects Y, Goods per day increase in wage causes both income and substitution effects that alter an individual's demand for leisure and supply of hours worked Time constraint I2 L2 I1 L* e2 e* L1 e1 0 N* N1 N 2 24 N, Leisure hours per day 24 H* H1 H 2 0 H, Work hours per day Substitution effect Total effect... adult pigeons - so far as I know, no one has ever seen a baby pigeon) Wages and income • wages could be altered by varying number of pecks required for a payoff from about 12 to 400 • income varied by providing free access for 3 seconds to food hopper at regular intervals • by varying both wage rate and income, experimenters could determined pure (compensated) substitution effect of a wage change and income... resulting top tax is 9.07%: a tax rate reduction of 0.23 percentage points • for everyone else, the tax cut is less • if you made $200,000, drop in your total tax is $460 • is that enough to change behavior? 14 State general fund revenues • share of total state general fund revenues (~$40 billion): personal income tax: 35% sales tax: 35.7% banking and corporations: 12.3% tobacco: 0.4% horse racing and... average winner received $55,200 in prize money per year and chose to work slightly fewer hours so that his or her labor earnings fell by $1,877 per year • thus, winners increased their consumption and savings but did not substantially decrease how much they worked • for every dollar of unearned income, winners reduced their work effort and hence their labor earnings by 11¢ on average Child-Care Subsidies . 1 Chapter 5 Applying Consumer Theory Key issues 1. deriving demand curves 2. income effect 3. effects of a price change 4. CPI bias 5. labor supply curve Questions 1.What would happen if a consumer. curves for the typical American consumer are bowed away from origin, so beer and wine are imperfect substitutions Deriving Demand Curves Figure 5.1 Deriving an Individual’s Demand Curve 4.3 5.2 12.0 2.8 12.0 6.0 4.0 26.7 0 44.5. price divided by CPI CPI for 2000 168.7 price of a burger = 15¢ 94¢ CPI for 1955 26.8 ××= Government collects prices on 364 individual goods and services, such as: • housing • dental services •