The Characteristics Approach to Consumer Theory

112 PART TWO Theory of Consumer Behavior and Demand (the dimensions of the box). Individual A is on indifference curve U\ and individual B is on indifference curve U\. Since at point C (where U\ and U\ intersect) the marginal rate of substitution ot good X for good Y (MRSxr) for individual A exceeds MRSxr for individual B, there is a basis lor mutually beneficial exchange between the two individuals. Starting at point C. individual A would be willing to give up 4 Y to get one additional unit of A- (and move to point D o n //,). On the other hand, individual B would be willing to give up IX for about 0.2 additional units of Y (and move to point H on U\). Because A is willing to give up more of Y than necessary to induce B to give up IX. there is a basis for trade in which individual A gives up some of Y in exchange for some of X from individual B. Whenever the MRSXy for the two individuals differs at the initial distribution of X and Y, either or both may gain from exchange. For example, starting from point C. if individual A exchanges 4 Y for IX with individual B. A would move from point C to point D along indifference curve U\, while B would move from point C on U\ to point D on U\. By moving from indifference curve U\ to indifference curve I/i, individual B receives all of the gains from the exchange while individual A gains or loses nothing (since A remains on U \). At point D, U i and U\ are tangent, and so their slopes (MRSxr) are equal. Thus, there is no basis for further exchange (at point D, the amount of Y that A is willing to give up for IX is exactly equal to what B requires to give up IX). Any further exchange would make either one or both individuals worse off than they are at point D. Alternatively, if individual A exchanged 1 / for 5X with individual B, individual A would move from point C on U\ to point F on C/3, while individual B would move from point C to point F along U{. In this case, A would reap all the benefits from exchange while B would neither gain nor lose. At point F, MRSxr for A equals MRSxr for B and there is no further basis for exchange. Finally, starting again from point C on U\ and U\. if A exchanges 3 Y for 3X with B and gets to point E, both individuals gain from the exchange since point E is on IA and I/i. Starting from any point within CDEF but not on curve DEF, both individuals can gain from exchange by moving to a point on curve DEF between points D and F. The closer individual A gets to point F (i.e.. the more shrewd A is as a bargainer), the greater is the proportion of the total gain from the exchange accruing to A and the less is left for B. The Edgeworth box is named after the English economist F. Y. Edgeworth, who in 1881 first outlined its construction. (We will return to exchange in greater detail in Chapter 17.) AT THE FRONTIER The Characteristics Approach to Consumer Theory T he characteristics approach to consumer theory, pioneered by Kelvin Lancaster, postulates that consumers demand a good because of the characteristics. properties, and attributes of the good, and it is these characteristics that

CHAPTER 4 Consumer Behavior and Individual Demand 1 1 3 give rise to utility.16 For example, a consumer does not demand beef, as such, but rather the characteristics of protein and calories, which are the direct source of utility. But protein and calories are also provided (though in different proportions) by pork and chicken. Thus, a good usually possesses more than one characteristic, and any given characteristic is present in more than one good. The characteristics approach to consumer theory can be shown graphically. In the top panel of Figure 4.9, the horizontal axis measures the characteristic of protein and the vertical axis measures calories. Suppose that the consumer s income is $10 and that $10 worth of pork provides the combination of protein and calories given by point A, while $ 10 worth of beef gives the combination at point B.17 The budget line is then AB. Area OAB is called the feasible region and budget line AB is the efficiency frontier. That is, the consumer can purchase any combination of protein and calories in area AOB, but he or she will maximize utility or satisfaction by choosing combinations on line AB. If U\ is a consumer s indifference curve in characteristics space (i.e., with characteristics protein and calories measured along the axes), the consumer maximizes utility at point C, where indifference curve U\ is tangent to budget line AB. The consumer reaches point C by obtaining OF characteristics from spending $5 on beef and FC characteristics from spending the remaining $5 on pork. OF = 1/2 OB and 0G = 1/2 0,4. Note that FC equals 0G, both in length and direction.18 In the bottom panel, a new good is introduced, chicken, which has half as many calories per unit of protein as beef. If $10 worth of chicken provides the combination of protein and calories given by point //, the budget line or efficiency frontier becomes AH. The consumer now maximizes utility at point J, where indifference curve U2 is tangent to budget line AH. The consumer reaches point J by obtaining 0A" characteristics from spending $5 on chicken and KJ (equals 0G) characteristics from spending the remaining $5 on pork. No beef is now purchased. The reduction in the price of a good can be shown by a proportionate outward movement along the characteristics ray of the good, while an increase in income can be shown by a proportionate outward shift of the entire budget line. These shifts will allow the consumer to reach a higher indifference curve as in traditional consumer theory. The characteristics approach to consumer theory has several important advantages over traditional demand theory. First, substitution among goods can be easily explained in terms of some common characteristics of the goods. For example, according to this theory coffee and tea are substitutes because they both have the characteristic of being stimulants. Continued... 16 Kelvin Lancaster. Consumer Demand: A New Approach (New York: Columbia University Press. 1971). 1 Note that the characteristics ray for pork has a slope four times larger than the characteristics ray for beef. Thus, pork provides tour times as many calories per unit of protein as beef. Is FC and 0C are called vectors. Thus, the above is an example of vector analysis, whereby vector 0C (not shown in the top panel of Figure 4.9) is equal to the sum o f vectors OF and 0G.

C a lo rie s Pork P rotein P r o tein FIGURE 4.9 The Characteristics Approach to Consumer Demand Theory In the top panel, $10 worth of pork gives the combination of protein and calories Indicated by point A and $10 worth of beef gives the combination at point B Thus, AB is the budget line. The consumer maximizes utility at point C, where Ui is tangent to AB, by spending $5 on pork and $5 on beef, and receiving Of characteristics from beef and FC (equals OG) from pork. In the bottom panel, $10 worth of chicken gives point H, so that the budget line is AH. The consumer maximizes utility at point J on Ui by spending $5 on pork and $5 on chicken, and obtaining OK characteristics from chicken and KJ (equals OG) characteristics from pork, with no beef purchased. 1 1 4

CHAPTER 4 Consumer Behavior and Individual Demand 11 5 Second, the introduction of a new good can easily be taken care of by draw ing a new ray from the origin reflecting the combination of the two characteristics of the new good. This was shown by the introduction of chicken in the bottom panel of Figure 4.9. However, the new good will only be purchased if its price is sufficiently low (e.g., chicken in the bottom panel of Figure 4.9). Had $10 worth of chicken provided only the combination of protein and calories given by point K on the characteristics ray for chicken, the budget line would become ABK and the consumer would maximize utility by remaining at point C and purchasing no chicken. Third, a quality change can be shown by rotating the characteristics ray for the good. For example, the introduction of a new breed of leaner hogs resulting in pork with less calories per unit of protein can be shown by a clockwise rotation of the characteristics ray for pork. Finally, by comparing the price of two goods that are identical except for a particular characteristic, this approach permits the estimation of the implicit or hedonic price of the characteristic. For example, by comparing the price of houses that are otherwise identical except for some other characteristic, such as lower noise pollution, proximity to good schools, parks, and a good transportation network, we can estimate the implicit or hedonic price of each of these characteristics. Thus, if the price of a house that is near a park is $ 10,000 more than the price of another identical house that is not near a park, the characteristic of being closer to a park is worth $ 10,000. One disadvantage of the theory is that some characteristics, such as taste and style, are subjective and cannot be measured explicitly. The problem is even more serious in dealing with the characteristics of services. Nevertheless, the hedonic approach is very useful because it allows at least an implicit measure of the various characteristics of each good. SUMMARY 1. The income-consumption curve joins consumer optimum points resulting when only the consumer's income is varied. The Engel curve is derived from the income-consumption curve and shows the amount of a good that the consumer would purchase per unit of time at various income levels. A normal good is one of which the consumer purchases more with an increase in income. An inferior good is one of which the consumer purchases less with an increase in income. The income-consumption curve and the Engel curve are positively sloped for normal goods and negatively sloped for inferior goods. 2. The price-consumption curve for a good joins consumer optimum points resulting w hen only the price of the good varies. This curve shows the amount of the good that the consumer w ould purchase per unit of time at various prices of the good while holding everything else constant. The individual consumer's demand curve for a good is negatively sloped, reflecting the law of demand. 3. When the price of a good falls, consumers substitute this good for other goods and their real income rises. If the good is normal, the income effect reinforces the substitution effect in increasing the quantity purchased of the good. If the good is inferior, the substitution effect tends to increase while the income effect tends to reduce the quantity demanded of the good. Because the former usually exceeds the latter, the quantity demanded of the good increases

1 1 6 PART TWO Theory of Consumer Behavior and Demand and the dem and curve is negatively sloped. O nly if the incom e effect overw helm s the op p osite substitution effect for an inferior good w ill the quantity dem anded o f the gtxxi d ecrease when its price falls, and the dem and curve w ill slop e upward. T his is called a Gift'en good, but it has never really been observed in the real world. 4. With the substitutability betw een dom estic and foreign goods and services having reached an all-tim e high in the w orld today, and with the expectation that it w ill rise even m ore in the future, the need to introduce an important international dim ension in the study o f m icroeconomics becomes even clearer. 5. A cash subsidy leads to an equal or greater increase in utility than a subsidy in kind (su ch as the food stamp program) that co sts the sam e. The consum er surplus is given by the differen ce betw een what the consum er is w illin g to pay for a good and what the consum er actual!) pays for it. Its value can be approxim ated by the area under the dem and curve and above the market price o f the good. An Edgeworth box diagram is constructed by rotating an individual's indifference map diagram by 180 degrees and superim posing it on another's, so that the dim ensions o f the box equal the com b ined initial distribution o f the tw o goods betw een the two individuals. The Edgeworth box diagram can be used to analyze voluntary exchange. The characteristics approach to consum er theory can be used to m easure the im plicit or hedonic price o f a particular characteristic o f a good or service. KEY TERMS In com e-consu m p tion curve Engel curve Normal good Inferior good Price-consum ption curve Individual s dem and curve Substitution effect Relative price Incom e effect G iffen good Food stam p program Consum er surplus W ater-diamond paradox Edgeworth box diagram Characteristics approach to consum er theory Incom e or expenditure index (E) L aspeyres price index (L) Paasche price index (P) REVIEW QUESTIONS 1. A consum er buys an O ldsm obile for $20,0 0 0 instead o f a Toyota for $ 2 2,000. D oes this mean that the consum er prefers the O ldsm obile to a Toyota? 2. H ow w ould indifference curves betw een m oney and autom ob iles differ b etw een tw o individuals with the sam e m oney incom e but with one having a stronger preference for au tom ob iles than the other? 3. W hy w ould the use o f gasolin e decline if its price rose as a result o f a gasolin e tax but the effect o f the price rise w as com p ensated by a tax rebate? 4. The incom e effect o f a 20% increase in housing rents is larger than the effect o f a 209c increase in the price o f salt. True or false? Explain. 5. A dem and curve sh ow ing only the substitution effect can never be p ositively slop ed, not even theoretically. True or false? Explain. 6. Is a dem and curve sh ow in g both the substitution and incom e effects flatter or steeper than the dem and curve sh ow in g only the substitution effect? Explain. 7. W ill a consum er purchase m ore or less o f an inferior good when its price declines? Explain. 8. Can all goods purchased by a consum er be inferior? 9. In 2003, the M en's Hair C om pany increased the price o f its sham poo and subsequently sold more sham poo than in 2002. Is the dem and curv e for this company's shampoo positively sloped? Explain.

CHAPTER 4 Consumer Behavior and Individual Demand 1 1 7 10. W hy is the gift o f any good likely to provide less satisfaction to the recipient than an equal cash gift? 11. W hen would the gift o f a good provide the recipient as m uch satisfaction as an equal cash gift? 12. H ow can a black market in food stam ps be explained? 13. What are the advantages and disadvantages o f the characteristics approach to consumer theory? PROBLEMS 1. a. Derive the income-consumption curve and Engel curve from the indifference curves o f Problem 2 in Chapter 3 and the budget lines from Problem 6(a) in Chapter 3. Is good X a normal or an inferior good? Why? b. D erive the E ngel curve for good Y. Is good Y a normal or an inferior good? Why? 2. a. For the budget lines o f Problem 6(a) in Chapter 3, draw indifference curves that show that good X is inferior; derive the incom e-consu m ption curve and the E ngel curve for good X. b. Draw the Engel curve for good Y. M ust good Y be normal? *3. a. Derive the price-consum ption curve and dem and curve for good X from the indifference curves o f Problem 2 in Chapter 3 and the budget lines from Problem 6(b) in Chapter 3 when the price o f X falls from Px = $2 to P x = $1 and then to Px = $0.50. b. U se the figure for your answ er to 3(a) to explain how you w ou ld derive the price-consum ption curve and dem and curve for good X when the price o f X rises from P x = $ 0.5 0 to P x = $1 and then to Px = $2. 4. U sing the indifference curves o f Problem 2 in Chapter 3 and the budget lines o f problem 6(b) in Chapter 3, separate the substitution effect from the incom e effect w h en the price o f X falls from P x = $2 to P x = $1 and then from P x = $1 to Px = $0.50. *5. Separate the substitution effect from the incom e effect for an in crea se in the price o f an inferior good. 6. Separate the substitution effect from the incom e effect for an increase in price o f a G iffen good. *7. It is som etim es asserted that rice in very poor Asian countries m ight be an inferior good. Even though there is no eviden ce that this is indeed the case, explain the reasoning behind this assertion. 8. The average number o f children per fam ily has declined in the face o f rapidly rising fam ily incomes, so children must be an inferior good. True or false? Explain. *9. U se indifference curve analysis to show that a poor fam ily can be m ade to reach a given higher indifference curve with a sm aller cash subsidy than with a subsidy in kind (such as, for exam p le, by the governm ent paying half o f the market price o f food for the fam ily). W hy m ight the governm ent still prefer a subsidy in kind? 10. W ith reference to Figure 4.7 in the text, indicate the size o f the consum er surplus when Px = $3 if a. good X can only be purchased in whole units. b. good X can be purchased in infinitesim ally small fractional units. 11. With reference to Figure 4.8 in the text, indicate how exchange could take place starting from the initial distribution o f good X and good Y betw een individual B given by the intersection o f U and U{- 12. Starting with the top panel o f Figure 4.9. show a. a 50% reduction in the price o f pork and its effect on consumer utility maximization. b. a 50% increase in the consum er's incom e and its effect on consum er utility m axim ization. = Answer provided at end o f book.

1 1 8 PART TWO Theory of Consumer Behavior and Demand A PP E N D IX In d e x N u m b e r s a n d C h a n g e s in C o n s u m e r W elfare In this appendix, we discuss index numbers and their use in measuring changes in standards of living or welfare, especially during inflationary periods. For example, workers and their unions are keen to know if money wages are keeping up with rising prices. Cost-of-living indices are often used for inflation adjustment in wage contracts, for pensions and welfare payments and, since 1984, even for tax payments. In this appendix, we will define three indices and, by comparing the values of these indices in two different time periods, determine if the standard of living has increased, decreased, or remained unchanged. For simplicity, we will assume that the consumer spends all income on only two commodities, X and Y. Expenditure, Laspeyres, and Paasche Indices To measure changes in the standard of living or welfare from one time period to another, we begin by defining three indices: the income or expenditure index, the Laspeyres price index, and the Paasche price index. The income or expenditure index ( ) is the ratio of period 1 to base period money income or expenditures. That is, E = x ' p; ' y ' p*' XaPxO + yopyo [4.i] where x and > refer to the quantities of commodities X and Y purchased, respectively; P refers to price, and the subscripts 1 and 0 refer to period 1 and the base period, respectively. Thus, the income and expenditure index is the sum of the product of period 1 quantities and their respective period 1 prices divided by the sum of the product of base period quantities and their respective base period prices. In short, E measures the ratio of the consumer's period 1 expenditures or income to the base period expenditures or income. If E is greater than 1, the individual's money income or expenditures have increased from the base period to period 1. However, since prices usually also rise, we cannot determine simply from the value of E whether the individual s real income or standard of living has also increased. To do that, we need to define the Laspeyres and the Paasche price indices and compare their values with that of the income or expenditure index. The Laspeyres price index (L) is the ratio of the cost of base period quantities at period 1 prices relative to base period prices. That is, L = XpPli + yppyt *0 PX0 + yopyo In the Laspeyres price index, we use the base period quantities as the weights and measure the cost of purchasing these base period quantities at period 1 prices relative to base period prices. The Paasche price index (P) is the ratio of the cost of period 1 quantities at period 1 prices relative to base period prices. That is.

CHAPTER 4 Consumer Behavior and Individual Demand 1 1 9 TABLE 4.2 Hypothetical Quantity Price Data in a Base Period and in Period 1 Period X P x y P y 0 (base) 4 $1 3 $2 1 3 2 6 1 In th e P a a sc h e p rice in d e x, w e u se p erio d 1 q u a n titie s as th e w e ig h ts and m ea su re the c o st o f p u r c h a sin g p erio d I q u a n titie s at p erio d 1 p r ice s r e la tiv e to b a se p erio d p r ices. T h u s, the d iffe r e n c e b e tw e e n th e L a sp e y r e s and th e P a a sch e p rice in d ic e s is that th e fo rm er u s e s the base period quantities as the w eigh ts w h ile the latter uses the period I quantities. For exam p le, using the hypothetical data in Table 4.2, w e can calculate E = x,pxl + y ia, = (3)($2) + (6)($1) = S12 =, 2 or {2Q% X()Px0 + y0py0 (4) ($ 1) + (3) ($2) $10, *0^1 +>d^vi (4)($2) + (3)($l) $11.. 11ft_ L = ----------------- = --------- --------------= - = 1.1 or 110% XoPxQ + yopyq $10 $10 p = + y. P J,1 = S12 = = 0.8 or 80% How Are Changes in Consumer Welfare Measured? Because some quantities and prices rise over time and others fall, it is often impossible to determine by simple inspection of the quantity-price data whether an individual's standard of living or welfare has increased, decreased, or remained unchanged from one time period to the next. To measure changes in the standard of living, we compare the value of the income or expenditure index to the values of the Laspeyres and the Paasche price indices. An individual's standard o f living is higher in period 1 than in the base period if E is greater than L. That is, the individual is better off in period 1 than in the base period if the increase in his or her money income (E) exceeds the increase in the cost of living using base-period quantities as weights (L ). For example, since we calculated from Table 4.2 that E = 1.2 or 120% while L = 1.1 or 110%, the individual's standard of living increased from the base period to period 1 because his or her income has risen more than his or her costs or prices. On the other hand, the individual's standard o f living is higher in the base period than in period I if E is smaller than P. That is, the individual is better off in the base period than in period 1 if the increase in his or her money income (E) is smaller than the increase in the cost of living using period I quantities as the weights (P). If E is not smaller than P. the individual's standard of living is not higher in the base period. For example, since E = 120% and P = 80% from Table 4.2. the individual is not better off in the base period than in period 1. Thus, with E greater than L and not smaller than P. the individual of the above numerical example is definitely better off in period 1 than in the base period.

120 PART TWO Theory of Consumer Behavior and Demand Figure 4.10 presents a graphic interpretation of the numerical example of Table 4.2. In the figure, /o/o is the individual s budget line in the base period. That is, with X = 4, Px = $1, y = 3, and Py = $2, the individual s total income (I) and expenditure in the base period is $10 (obtained from 4X times $1 plus 3 V times $2). If the individual had spent the entire base-period income of $10 on commodity X, he or she could have purchased 10X If instead the individual had spent his or her entire base-period income of $10 on commodity Y, he or she could have purchased 5K. This defines /o/o as the individual's budget line in the base period. The individual s purchase of 4X and 3 Y in the base period (see the first row of Table 4.2) is indicated by point Bo on budget line lolo- We can similarly determine from the second row of Table 4.2 that in period 1 the individual s income is $12 (obtained from 3X times $2 plus 6Y times $1), so that his or her budget line is /(/). The individual's purchase of 3X and 6 Y in period 1 is indicated by point B\ on budget line / /. From Figure 4.10 we can conclude that since point Bo is below budget line / /, the individual must be better off in period 1 than in the base period. That is, since Bo was available to the individual in period 1 but was not chosen, the individual must be better off in period I. Specifically, in period I the individual could have purchased the base period bundle (So) at period 1 prices by spending only $11 (4X times $2 plus 3 / times $ 1) of his or her Quantity of X FIGURE 4.10 Changes in Consumer Welfare An individual is better off at B, in period 1 than at B0 in the base period because Bo was available in period 1 (i.e.. So is below period 1 budget line /1/1) but was not chosen. Had the individual been at point A in the base period, we would need the individual s indifference curves to determine if Si is superior inferior or equal to A

C H A P T E R 4 C o n s u m e r B e h a v i o r a n d I n d iv id u a l D e m a n d 121 period I income of $12. On the other hand, in the base period the indi\ idual could not ha\e purchased period 1 quantities at base period prices since that would have required an expenditure of $15 (3X times $1 plus 6V times $2). which would have exceeded his or her base period income of $10. Thus, the individual must be better off w ith Bi in period I than with Bo in the base period. Had the individual been at a point such as A rather than at point Bn on budget line ltjn in the base period (see Figure 4.10). we could no longer determine w ithout the individual's indifference curves whether the individual w as better off in period I. in the base period, or was equally well off in period I as in (he base period. This would depend on whether point B i was on a higher, lower, or (he same indifference curve as point /A. respectively. You should be able to calculale from comparing poinl A on l»lu in (he base period to point B on / 1/ in period I (hal E = 120%, L = 140%, and P = 80%. Since E is not larger than L (so that the individual is nol necessarily belter off in period 11 bul E is not smaller than P (so (hat the individual is nol necessarily better off in (he base period), we have conflicting results and we cannot tell whether the standard of living is higher, lower, or equal in period I as compared with the base period. This confirms (he inconclusive results of the graphic analysis (in the absence of the individual's indifference curves) in Figure 4.10. Because the Laspeyres price index (Z.) uses base period quantities as (he weights. L becomes available sooner than the Paasche price index (/>).l, The most common of the price indices is the Consumer Price Index (CPI), which has been published monthly by the Bureau of Labor Statistics for more than sixty years. The CPI is a Laspeyres index for a "typical" urban family of four. Il is the weighted average of the price of 400 goods and services purchased by consumers in the United States. The weights of the various commodities in the basket are periodically changed to reflect variations in consumption patterns. Other important (Laspeyres) price indices are the wholesale price index (WPI) and (he GNP deflator. The latter is used to calculate GNP in real terms. EXAMPLE 4-6 The Consumer Price Index, Inflation, and Changes in the Standard of Living One application of index numbers is in measuring changes in real earnings and standards of living over time. According to the Bureau of Labor Statistics, total private nonagricultural weekly money earnings in the United States was $345.35 in 1990 and $472.73 in 2000. The CPI rose from looin 1990to 131.8 in 2000. Dividing the weekly money earnings by the corresponding CPI. we find that weekly real earnings increased only slightly from $345.35 in 1990 to $358.67 in 2000. Since the CPI is known to have an upward bias, however, the true increase in real earnings may in fact have been somewhat greater. u The Laspeyres price index also uses period 1 prices. Houever, period 1 prices become u\ jilame much sooner than period I quantities.