Daniel l. Rubinfeld

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66 Part 2 Producers, Consumers, and Competitive Markets tells us that in moving from market basket A to market basket B, the consumer feels neither better nor worse off in giving up 10 Ul1its of food to obtain 20 additional units of clothing. Likewise, the consumer is indifferent behveen points A and 0: He or she will give up 10 units of clothing to obtain 20 units of food. On the other hand, the consumer prefers A to H, which lies below LI 1 . Note that the indifference curve in Figure 3.2 slopes downward from left to right. To tmderstand why this must be the case, suppose instead that it sloped upward from A to E. This would violate the assumption that more of any commodity is preferred to less. Because market basket E has more of both food and clothing than market basket A, it must be preferred to A and therefore cannot be on the same indifference curve as A. In fact, any market basket lying above alld to tile right of indifference curve LII in Figure 3.2 is preferred to any market basket all LI 1 • , f (units per week) LI: Chapter :3 Consumer Behavior 67 indifference map Graph containing a set of indifference curves showing the market baskets among which a consumer is indifferent Indifference Maps To describe a person's preferences for all combinations of food and clothing, \ve can graph a set of indifference curves called an indifference map. Each indifference curve in the map shows the market baskets among which the person is indifferent. Figure 3.3 shows three indifference curves that form part of an indifference map. Indifference curve LI3 generates the highest level of satisfaction, followed by indifference curves LI2 and LI 1 • Indiffer~nc:e curves cannot intersect. To see why, we will assume the contrary and see how the'iesurting graph-violates our assumptions about consumer behavior. Figure 3.4 shows hvo indifference curves, LII and LI 2 , that intersect at A. Because A and B are both on indifference curve LIlt the consumer must be indifferent behveen these hvo market baskets. Because both A and 0 lie on indifference curve LI 2 , the consumer must be indifferent behveen these market baskets. Consequently, the consumer must also be indifferent behveen Band D. But this conclusion can't be true: Market basket B must be preferred to 0 because it Clothing (units per week) Food (wlits per week) An indifference map is a set of indifference curves that describes a person's preferences. Any market basket on indifference curve U 3 , such as basket A, is preferred to any basket on curve LI2 (e.g., basket B), which in tum is preferred to any basket on such as D. Food (units per week) ~f in.difference curv:s U1 and. U 2 ~tersect, one of the assumptions of consumer theory IS VIOlated. Accordmg to this diagram, the consumer should be indifferent among market baskets A, B, and n Yet B should be preferred to 0 because B has more of both goods. contains more of both food and clothing. Thus, indifference curves that intersect contradicts our assumption that more is preferred to less. O~ course, there.are an infinite number of nonintersecting indifference curves, one tor every possIble level of satisfaction. In fact, every possible market basket (each corresponding to a point on the graph) has an indifference curve passina tlu'ough it. 0 The Shapes of Indifference Curves Recall tha~ indifference c\1rves are all downward sloping. In our example of food and clothmg, when the amount of food increases alona an indifference curve the amount of c.lothing. decreases. The fact that indiffere~ce curves slope down~ ward follows dIrectly trom our assumption that more of a aood is better than less. If an indifference curve sloped up"vard, a consumer w~uld be indifferent between two market baskets e\"en though one of them had more of both food and clothing. Th.e shape of an indifference curve describes ho'w a consumer is willing to SUbS~Ihl.te one good for another. As we saw in Chapter I, people face trade-offs. The IndIfference c~lrve in Figure 3.5 illustrates this principle. Starting at market basket A and movmg to basket B, we see that the consumer is willina to aive up 6 't f 1 l' '. 0 0 Ul1l ~ 0 ~ ~t ung t obtam 1 extra UIllt of food. However, in moving from B to D, he IS vnllmg to gIve up only 4 units of clothina to obtain an additional unit of ~OOd; in moving from 0 to E, he '\'ill give up onl)~ 2 units of clothing for Imut of ood .. n1~ more .clothing and the less food a person consumes, the more clothing he w1ll gl\'e up m order to o.btain m~re fod. Similarly, the more food that a person possesses, the less clotlung he WIll gIve up for more food.
68 Part 2 Producers, Consumers, and Competitive Markets Chapter 3 Consumer Behavior 69 M= 16 Clothing (units per week) 1-b 12 10 8 -6 Thus the MRS at any point is equal in magnitude to the slope of the indifference curve. In Figure 3.5, for example, the MRS between points A and B is 6: The consumer is willing to give up 6 units of clothing to obtain 1 additional unit of food, Between points Band 0, however, the MRS is 4: With these quantities of food and clothing, the consumer is willing to give up only 4 units of clothina to obtain 1 additional unit of food. 0 Also observe in Figure 3.5 that the MRS falls as we move down the indifference curve. This is not a coincidence. This decline in the MRS reflects an important characteristic of consumer preferences. To understand this, we will add an additional assumption regarding consumer preferences to the three that we discussed earlier in the chapter: 6 -b 2 2 3 G 5 Food (units per week) 4. Diminishing. Illargil1.c3,Lra le_oLsubstituti on: Indifference curves are convex or bowed inward. The term cOllve .... means that the slope of the indifferen~~ curve ill creases (i.e., becomes less negative) as we move down along the curve. In other words, Illl illdifferellce curve is call vex if the MRS dimillishes Il/ollg the clirve. The indifference curve in Figure 3.5 is convex. As we have seen, starting with market basket A in Figure 3.5 and moving to basket B, the MRS of food F for clothing C is ~C/.lF = - (- 6)/1 = 6, However, when we start at basket B and move from B to 0, the MRS falls to 4, If we start at basket D and move to E, the MRS is 2. Starting at E and moving to G, we get an MRS of 1. As food consumption increases, the slope of the indifference curve falls in magnitude. Thus the MRS also falls. 2 marginal rate of substitution (MRS) Amount of a good that a consumer is willing to give up in order to obtain one additional unit of another good. 111e slope of an indifference curve measures the consumer's marginal rate of substitution (MRS) between two goods. In this figure, the MRS behveen clothing (C) and food (F) falls from 6 (between A and B) to 4 (between B and D) to 2 (behveen D and E) to 1 (beh\'een E and G). When the MRS diminishes along an indifference curve, the curve is convex. Marginal To quantify the amount of one good that a consumer will give up to obtain more of another, we use a measure called the marginal rate of substitution (MRS). The MRS off'ood F f'or clothing C is the 1lll101lIZt of clothing tllllt II person is willillg to giue lip to obtllin one Ildditiollill lInit off'ood. Suppose, for example, the MRS is 3. This means that the consumer will give up 3 units of clothing to obtain 1 additional unit of food. If the MRS is 1/2, the consumer is willing to give up only 1/2 unit of clothing. Thus, the MRS measures the mille that the individuill pillces Oil 1 extm lInit of one good in terms of another. Look again at Figure 3S Note that clothing appears on the vertical axis and food on the horizontal axis. When vve describe the MRS, we must be clear about which good we are giving up and which we are getting more of. To be consistent throughout the book, we will define the MRS in terms of the alllolillt of the good 011 the uerticiliaxis that the COll51l11ler is willing to give lip to Obtllill 1 extm lInit of the good on the llOri20lltlllaxis. Thus in Figure 3.5, the MRS refers to the amount of clothing that the consumer is willing to give up to obtain an additional unit of food. If we denote the cJzllIzge in clothing by .lC and the change in food by .IF, the MRS can be written as - .lC/.lF. We add the negative sign to make the marginal rate of substitution a positive number (remember that ~C is always negative; the con SUlT1.er gives lip clothing to obtain additional food). Is it reasonable to expect indifference curves to be convex Yes. As more and more of one good is consumed, we can expect that a conSUIl1er will prefer to aive up fewer and fewer muts of a second good to get additionallmits of the fil'st ~ne. As we move down the indifference curve in Figure 3.5 and consumption of food increases, the additional satisfaction that a consumer gets from still more food will dimirush. Thus, he will give up less and less clothing to obtain additional food. Another way of describir1g this prir1ciple is to say that conSUIl1ers generally prefer balanced market baskets to market baskets that contain all of one aood and none of another. Note from Figure 3.5 that a relatively balanced market basket contairung 3 uruts of food and 6 ruuts of clothir1a (basket D) aenerates as much satisfaction as another market basket containino tmut of fool and 16 muts of clothin~ (bas~et A). It follows that a balanced malket basket containing (for example) 6 lUutS of tood and 8 m1its of clothing will generate a higher level of satisfaction. Perfect Substitutes and! Perfect Complements The shape of an indifference curve describes the willinaness of a consumer to ~ubs~itute one good for another. An indifference curve °with a different shape unphes a different willingness to substitute. To see this principle, look at the two polar cases illustrated in Figure 3.6. Figure 3.6(a) shows Bob's preferences for apple juice and orange juice. 111ese two goods are perfect substitutes for Bob because he is entirely indifferent between having a glass of one or the other. In Hus case, the MRS of apple juice for orange juice is 1: Bob is always willir1g to h'ade 1 glass of one for 1 glass of the 2 With noncom' ex preferences, the MRS increases as the amount of the (Tood measured on the hori ~ontal axis increases along any indifference curve .. This unlikely possibility might arise if one or both "oods are addICtIve. For e~ample, the wIllmgness to substitute an addictive drug for other goods mIght mcrease as the use ot the addIctl\"e drug mcreased In §2 .. 1, ,ve explain that goods are substitlltes when an increase in the price of one leads to an increase in the quantity demanded of the other.
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Daniel l. Rubinfeld

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