Chapter Five Applying Consumer Theory

© 2007 Pearson Addison-Wesley. All rights reserved.5–2 Applying Consumer Theory In this chapter, we examine five main topics. –Deriving demand curves –How changes in income shift demand curves –Effects of a price change –Cost-of-living adjustments –Deriving labor supply curves

© 2007 Pearson Addison-Wesley. All rights reserved.5–3 Deriving Demand Curves An individual chooses an optimal bundle of goods by picking the point on the highest indifference curve that touches the budget line (Chapter 4). When a price changes, the budget constraint the consumer faces shifts, so the consumer choose a new optimal bundle.

© 2007 Pearson Addison-Wesley. All rights reserved.5–4 By varying one price and holding other prices and income constant, we can determine how the quantity demanded changes as the price changes, which is the information we need to draw the demand curve. Deriving Demand Curves

© 2007 Pearson Addison-Wesley. All rights reserved.5–5 We derive a demand curve using the information about tastes from indifference curves. These indifference curves are convex to the origin: Mimi views beer and wine as imperfect substitutes (Chapter 4). We can construct Mimi’s demand curve for beer by holding her budget, her tastes, and the price of wine constant at their initial levels and varying the price of beer. Deriving Demand Curves

© 2007 Pearson Addison-Wesley. All rights reserved.5–6 Figure 5.1 Deriving an Individual’s Demand Curve L 1 ( p b = $12) L 2 ( p b = $6) L 3 ( p b = $4) e 3 e 2 e 1 E 3 E 2 E 1 I 1 I 2 I 3 Beer, Gallons per year D 1, Demand for beer Price-consumption curve (a) Indifference Curves and Budget Constraints (b) Demand Curve

© 2007 Pearson Addison-Wesley. All rights reserved.5–7 Deriving Demand Curves Price-consumption curve, is the line through the equilibrium bundles, such as,, and, that Mimi would consume at each price of beer, when the price of wine and Mimi’s budget are held constant.

© 2007 Pearson Addison-Wesley. All rights reserved.5–8 How Changes in Income Shift Demand Curves Effects of a rise in income –We illustrate the relationship between the quantity demanded and income by examining how Mimi’s behavior changes when her income rises, while the prices of beer and wine remain constant.

© 2007 Pearson Addison-Wesley. All rights reserved. Figure 5.2 Effect of a Budget Increase on an Individual’s Demand Curve Income-consumption curve Engel curve for beer Beer, Gallons per year Beer, Gallons per year Beer, Gallons per year I 2 I 3 I 1 (a) Indifference Curves and Budget Constraints (b) Demand Curves (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 *

© 2007 Pearson Addison-Wesley. All rights reserved.5–10 The income-consumption curve through bundles,, and in panel a shows how Mimi’s consumption of beer and wine increases as her income rises. As Mimi’s income goes up, her consumption of both wine and beer increases. How Changes in Income Shift Demand Curve

© 2007 Pearson Addison-Wesley. All rights reserved.5–11 Engel curve –the relationship between the quantity demanded of a single good and income, holding prices constant How Changes in Income Shift Demand Curve

© 2007 Pearson Addison-Wesley. All rights reserved.5–12 Page 112 Solved Problem 5.1 Y 2 / p * Y 1 / p * Y 1 = pq 1 Y 2 = 2 q 1 = Y 1 / pq 2 = Y 2 / p e 2 e 1 E 2 E 1 p 1 q, Cans of Cragmont per week q 1 q 2 q, Cans of Cragmont per week (a) Indifference Curves and Budget Constraints (b) Engel Curve Cragmont Engel curve L 1 L 2 I 1 I 2

© 2007 Pearson Addison-Wesley. All rights reserved.5–13 Consumer Theory and Income Elasticities Income elasticities tell us how much the quantity demanded changes as income increases. We can use income elasticities to summarize the shape of the Engel curve, the shape of the income-consumption curve, or the movement of the demand curves when income increases.

© 2007 Pearson Addison-Wesley. All rights reserved.5–14 Income Elasticities We defined the income elasticities of demand in Chapter 3 as where is the Greek letter xi

© 2007 Pearson Addison-Wesley. All rights reserved.5–15 Consumer Theory And Income Elasticities normal good –a commodity of which as much or more is demanded as income rises inferior good –a commodity of which less is demanded as income rises

© 2007 Pearson Addison-Wesley. All rights reserved.5–16 Income-Consumption Curves and Income Elasticities The shape of the income-consumption curve for two goods tells us the sign of the income elasticities: whether the income elasticities for those goods are positive or negative.

© 2007 Pearson Addison-Wesley. All rights reserved.5–17 Some Goods Must Be Normal It is impossible for all goods to be inferior. If both goods were inferior, Peter would buy less of both goods as his income rises-which makes no sense.

© 2007 Pearson Addison-Wesley. All rights reserved.5–18 Figure 5.3 Income-Consumption Curves and Income Elasticities 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 1 3

© 2007 Pearson Addison-Wesley. All rights reserved.5–19 Income Elasticities May Vary with Income A good may be normal at some income levels and inferior at others.

© 2007 Pearson Addison-Wesley. All rights reserved. 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 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 (a) Indifference Curves and Budget Constraints (b) Engel Curve Engel curve

© 2007 Pearson Addison-Wesley. All rights reserved.5–21 Effects of a Price Change An increase in a price of a good, holding other prices and income constant, has two effects on an individual’s demand. One is the substitution effect: If utility is held constant, as the price of the good increases, consumers substitute other, now relatively cheaper goods for that one.

© 2007 Pearson Addison-Wesley. All rights reserved.5–22 The other is the income effect: An increase in price reduces a consumer’s buying power, effectively reducing the consumer’s income and causing the consumer to buy less of at least some goods. Effects of a Price Change

© 2007 Pearson Addison-Wesley. All rights reserved.5–23 Income and Substitution Effects with a Normal Good The substitution effect is the change in the quantity of a good that a consumer demands when the good’s price changes, holding other prices and the consumer’s utility constant The income effect is the change in the quantity of a good a consumer demands because of a change in income, holding prices constant.

© 2007 Pearson Addison-Wesley. All rights reserved.5–24 Income and Substitution Effects with a Normal Good The total effect from the price change is the sum of the substitution and income effects, as the arrows show. Mimi’s total effect (in gallons of beer per year) from a drop in the price of beer is

© 2007 Pearson Addison-Wesley. All rights reserved.5–25 Because indifference curves are convex to the origin, the substitution effect is unambiguous: More of a good is consumed when its price falls. A consumer always substitutes a less expensive good for a more expensive one, holding utility constant. Income and Substitution Effects with a Normal Good

© 2007 Pearson Addison-Wesley. All rights reserved.5–26 Income and Substitution Effects with a Normal Good The direction of the income effect depends on the income elasticity. Because beer is a normal good for Mimi, her income effect is positive. Thus both Mimi’s substitution effect and her income effect go in the same direction.

© 2007 Pearson Addison-Wesley. All rights reserved.5–27 Figure 5.5 Substitution and Income Effects with Normal Goods Substitution effect Total effect Income effect Beer, Gallons per year I 2 I 1 L * L 2 L 1 e 2 e 1 e *

© 2007 Pearson Addison-Wesley. All rights reserved.5–28 Income and Substitution Effects with an Inferior Good If a good is inferior, the income effect goes in the opposite direction from the substitution effect. For most inferior goods, the income effect is smaller than the substitution effect. As a result, the total effect moves in the same direction as the substitution effect, but the total effect is smaller.

© 2007 Pearson Addison-Wesley. All rights reserved.5–29 A good is called a Giffen good if a decrease in its price causes the quantity demanded to fall. The Law of Demand was an empirical regularity, not a theoretical necessity. Although it’s theoretically possible for a demand curve to slope upward, economists have found few, if any, real- world examples of Giffen goods. Income and Substitution Effects with an Inferior Good

© 2007 Pearson Addison-Wesley. All rights reserved.5–30 Figure 5.6 Giffen Good Movies, Tickets per year L 1 L * Total effect Income effect Substitution effect L 2 e 1 e 2 e * I 1 I 2

© 2007 Pearson Addison-Wesley. All rights reserved.5–31 Cost-of-Living Adjustments By knowing both the substitution and effects, we can answer questions that we could not if we knew only the total effect.

© 2007 Pearson Addison-Wesley. All rights reserved.5–32 Inflation Indexes The price of most goods rise over time. We call the increase in the overall price level inflation.

© 2007 Pearson Addison-Wesley. All rights reserved.5–33 Real Versus Nominal Prices The actual price of a good is called the nominal price. The price adjusted for inflation is the real price.

© 2007 Pearson Addison-Wesley. All rights reserved.5–34 Calculating Inflation Indexes The CPI for the first year is the amount of income it takes to buy the market basket actually purchased that year: (5.1) The cost of buying the first year’s bundle in the second year is (5.2)

© 2007 Pearson Addison-Wesley. All rights reserved.5–35 To calculate the rate of inflation, we determine how much more income it would take to buy the first year’s bundle in the second year, which is the ratio of Equation 5.1 to Equation 5.2: Calculating Inflation Indexes

© 2007 Pearson Addison-Wesley. All rights reserved.5–36 Calculating Inflation Indexes The CPI is a weighted average of the price increase for each good, and, where the weights are each good’s budget share in the base year, and.

© 2007 Pearson Addison-Wesley. All rights reserved.5–37 CPI adjustment CPI adjustment to income does not keep an individual on his original indifference curve. Indeed, this person is better off in the second year than in the first. The CPI adjustment overcompensates for the change in inflation in the sense that his utility increases.

© 2007 Pearson Addison-Wesley. All rights reserved.5–38 Figure 5.7 The Consumer Price Index C 2 C 1 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

© 2007 Pearson Addison-Wesley. All rights reserved.5–39 True Cost-of-Living Adjustment How big an increase in Klaas’s salary would leave him exactly as well off in the second years as in the first? We can answer this question applying the same technique we use to identity the substitution and income effects.

© 2007 Pearson Addison-Wesley. All rights reserved.5–40 Table 5.1 Cost-of-Living Adjustments

© 2007 Pearson Addison-Wesley. All rights reserved.5–41 Deriving Labor Supply Curves Labor-Leisure Choice –People choose between working to earn money to buy goods and services and consuming leisure: all time spent not working. The number of hours worked per day, H, equals 24 minus the hours of leisure or nonwork, N, in a day: H=24 － N. –Using consumer theory, we can determine the demand curve for leisure once we know the price of leisure.

© 2007 Pearson Addison-Wesley. All rights reserved.5–42 Labor-Leisure Choice –We use an example to show how the number of hours of leisure and work depends on the wage, unearned income (such as inheritances and gifts from parents), and tastes. U ＝ U(Y, N). Deriving Labor Supply Curves

© 2007 Pearson Addison-Wesley. All rights reserved.5–43 Labor-Leisure Choice –Her total income, Y, is her earned income plus her unearned income, Y*: Y ＝ wH ＋ Y*. –The slope of her budget constraint is － w 1, because each extra hour of leisure she consumes costs her w 1 goods. –Her supply curve for hours worked is the mirror image of the demand curve for leisure: For every extra hour of leisure that Jackie consumes, she works on hour less. Deriving Labor Supply Curves

© 2007 Pearson Addison-Wesley. All rights reserved.5–44 Income and Substitution Effects An increase in the wage causes both income and substitution effects, which alter an individual’s demand for leisure and supply of hours worked. The substitution effect, the movement from to e*, must be negative: A compensated wage increase causes Jackie to consume fewer hours of leisure, N*, and work more hours, H*.

© 2007 Pearson Addison-Wesley. All rights reserved.5–45 Income and Substitution Effects The income effect is the movement from e* to. When leisure is a normal good, the substitution and income effects work in opposite direction, so whether leisure demand increases or not depends on which effect is larger. If leisure is an inferior good, both the substitution effect and the income effect work in the same direction, and hours of leisure definitely fall.

© 2007 Pearson Addison-Wesley. All rights reserved.5–46 Figure 5.8 Demand for Leisure Time constraint H 2 =12 H 1 = 8240 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 (b) Demand Curve – w 1 1 e 2 Y 2 Y 1 w 1 w 2 e 1 E 2 E 1

© 2007 Pearson Addison-Wesley. All rights reserved.5–47 Figure 5.9 Supply Curve of Labor (a) Leisure Demand Demand for leisure w 1 w N, Leisure hours per day E 1 E 2 (b) Labor Supply Supply of work hours w 1 w H, Work hours per day e 2 e 1

© 2007 Pearson Addison-Wesley. All rights reserved.5–48 Figure 5.10 Income and Substitution Effects of a Wage Change Time constraint H 2 H * H N 2 N * N 1 0 Substitution effect Income effect Total effect H, Work hours per day N, Leisure hours per day I 2 I 1 L 2 L * L 1 e 2 e 1 e *

© 2007 Pearson Addison-Wesley. All rights reserved.5–49 Page 133 Solved Problem 5.3 (a) Leisure Normal Time constraint H 2 H 3 H H, Work hours per day L 2 I 2 I 1 L 1 Y * e 2 e 1 (b) Leisure Inferior Time constraint H H, Work hours per day L 2 I 1 L 1 Y * e 1 I 3 e 3

© 2007 Pearson Addison-Wesley. All rights reserved.5–50 Application (Page 134) Leisure- Income Choices of Textile Workers H, Work hours per week N, Leisure hours per week I 2 I 1 L 2 L * L e 1 e 2 e *

© 2007 Pearson Addison-Wesley. All rights reserved.5–51 Shape of the Labor Supply Curve Whether the labor supply curve slopes upward, bends backward, or has sections with both properties depends on the income elasticity of leisure. Do labor supply curves slope upward or backward? Economic theory alone cannot answer this question: Both forward-sloping and backward-bending supply curves are theoretically possible. Empirical research is necessary to resolve this question.

© 2007 Pearson Addison-Wesley. All rights reserved.5–52 Figure 5.11 Labor Supply Curve That Slopes Upward and Then Bends Backward (a) Labor-Leisure Choice Time constraint H 2 H 3 H H, Work hours per day E 1 E 3 E 2 L 2 I 2 I 3 I 1 L 3 L 1 e 2 e 1 e 3 (b) Supply Curve of Labor Supply curve of labor H 2 H 3 H H, Work hours per day

© 2007 Pearson Addison-Wesley. All rights reserved.5–53 Income Tax Rates and Labor Supply Why do we care about the shape of labor supply curves? One reason is that we can tell from the shape of the labor supply whether an increase in the income tax rate － a percent of earnings － will cause a substantial reduction in the hours of work.

© 2007 Pearson Addison-Wesley. All rights reserved.5–54 Taxes on earnings are an unattractive way of collecting money for the government if supply curves are upward sloping because the taxes cause people to work fewer hours, reducing the amount of goods society produces and raising less tax revenue than if the supply curve were vertical or backward bending. Income Tax Rates and Labor Supply

© 2007 Pearson Addison-Wesley. All rights reserved.5–55 On the other hand, if supply curves are backward bending, a small increase in the tax rate increases tax revenue and boots total production (but reduces leisure). Income Tax Rates and Labor Supply

© 2007 Pearson Addison-Wesley. All rights reserved.5–56 Income Tax Rates and Labor Supply The effect of a tax rate of ＝ 0.28 is to reduce the effective wage from w to (1 － )w ＝ 0.72w.

© 2007 Pearson Addison-Wesley. All rights reserved.5–57 Figure 5.12 Relationship of Tax Revenue to Tax Rates  *= , Marginal tax rate, % Tax revenue

© 2007 Pearson Addison-Wesley. All rights reserved.5–58 Cross Chapter Analysis Page 145 Q 2 Q 3 Q 1 0 Q, Hours of day care per day I 2 I 3 I 1 L PS L LS L o e 2 e 1 Y 2 Y o e 3

© 2007 Pearson Addison-Wesley. All rights reserved.5–59 台灣工資 ( 價格 ) 勞動供給彈性 年度 供給 彈性 台灣婦女工資 ( 價格 ) 供給彈性 資料來源 : 莊慧玲、林世昌 (2006) ，清華大學經濟系，「台灣婦女勞動供給實證研究之發展」，經濟論文叢刊