define an ‘‘economic good’’ as an item that yields positive benefits to people.1That is, more of a good is, by definition, better. Combinations of goods in the lightly shaded area of Figure 2.1 are definitely inferior toX*,Y* since they offer less of bothgoods.
These three assumptions about preferences are about enough to justify our use of the simple utility function that we introduced earlier. That is, if people obey these assumptions, they will make choices in a way consistent with using such a function. Notice that economists do not claim that people actually consult a utility function when deciding, say, what brand of toothpaste to buy. Instead, we assume that people have relatively well-defined preferences and make decisionsas ifthey consulted such a function. Remember Friedman’s pool player analogy from Chapter 1—the laws of physics can explain his or her shots even though the player knows nothing about physics. Similarly, the theory of utility can explain economic choices even though no one actually has a utility function embedded in his or her brain. Whether economists actually have to consider exactly what does go on in the brains of people has become a topic of some debate in recent years. In Application 2.2: Should Economists Care about How the Mind Works? we provide a first look at that debate.
VOLUNTARY TRADES AND
A P P L I C A T I O N 2 . 2 Should Economists Care about How the Mind Works?
The theory of utility is a pure invention of economists. When noneconomists think about the decisions of people to buy things or take jobs, they are very unlikely to describe these in utility-maximizing terms. Rather, noneconomists believe that peoples’ choices are influenced by a wide variety of social and psychological forces, and sometimes it may be simply impossible to explain certain decisions. Some scientists even believe that decisions are mainly influenced by chemical interactions in the brain and that these bear no particular relationship to economists’ models.
Arguments about Utility Are Long-Standing Economists have argued over the meaning of utility and utility maximization for over 100 years. For example, the the nineteenth-century economist F. Y. Edgeworth believed that eventually psychologists would develop a machine that could measure pleasure (he called the device a ‘‘hedoni- meter’’) and that the readings from this machine would provide a clear foundation for explaining choices. Other economists scoffed at the hedonimeter idea, stating that it was both impractical and unnecessary. For them, the utility model did a perfectly good job of predicting the economic behavior of people, and developing a more complete theory of the psychology underlying that behavior was totally un- necessary.1Building Edgeworth’s machine ultimately proved to be impossible, and the utility theorists seemed to have won out. But concerns that it might be important to understand a bit more about the psychology and neurology of economic behavior lingered on.
After many years of neglect, interest in studying the relationship between psychology and economic behavior has begun a return, primarily because economists have found it difficult to explain some types of behavior using simple utility models. In Chapter 17, we will study some of these challenges in detail. Here, we just look at two examples.
Self-Control and Gym Memberships
It seems that people pay far more than they need to for using the local gym. In a 2006 paper, DellaVigna and Malmendier2 look at the behavior of 7,000 health club members over a 3-year period. They conclude that most of those who buy
annual memberships would be much better off paying sepa- rately for each visit to the gym. Overall, people would save nearly 60 percent by opting for such a pay-as-you-go con- tract. Traditional theory would find it hard to explain why people choose a wasteful annual contract. Seemingly, only by introducing psychological ideas such as shortsightedness (perhaps people with annual memberships think they will go to the gym more often than they do) or the need for self- control (the annual membership may force people to go) can this type of behavior be explained. Adapting utility models to do this is an important area of current research.
Inattention to Full Prices
There is a lot of evidence that people don’t really pay much attention when they make some economic choices. Often, decisions must be made in a hurry, or a consumer’s thoughts may be focused on other things when he or she makes a purchase. For example, in an experimental study of pur- chases of CDs on eBay, Hossain and Morgan3found that buyers paid far less attention to shipping and handling costs than they did to the price of a good at auction, even when those other costs were a high fraction of a good’s overall price. A similar lack of attention to all aspects of the price of a good has been noted for such diverse goods as alcoholic beverages, hospital services, and vacation packages. Clear thinking about prices can sometimes be difficult for people—it may involve real costs in getting and assessing the relevant information. How utility models should be mod- ified to take such costs into account is a subject of increasing amounts of research.
TOTHINKABOUT
1. Positioning items on grocery store shelves is an impor- tant job for managers—they try to place profitable goods where they will draw attention. Doesn’t this seem to be a waste of time if people are true utility maximizers in their shopping behavior?
2. What kinds of ‘‘irrational’’ economic decisions do you make? Why do you make these decisions? Can you develop a ‘‘rational’’ explanation for them?
1For a discussion, see D. Colander ‘‘Edgeworth’s Hedonimeter and the Quest to Measure Utility’’Journal of Economic Perspectives, Spring 2007: 215–225.
2S. DellaVigna and U. Malmendier ‘‘Paying Not to Go to the Gym’’
American Economic Review, June 2006: 694–719.
3T. Hossain and J. Morgan ‘‘. . .Plus Shipping and Handling: Revenue (Non) Equivalence in Field Experiments on eBay’’Advances in Eco- nomic Analysis and Policy. 2006 (2): 1–27.
individual; that is, a person isindifferentabout which particular combination of goods on the curve he or she actually has. Figure 2.2 records the quantity of soft drinks consumed by a person in one week on the horizontal axis and the quantity of hamburgers consumed in the same week on the vertical axis. The curveU1in Figure 2.2 includes all those combinations of hamburgers and soft drinks with which this person is equally happy. For example, the curve shows that he or she would be just as happy with six hamburgers and two soft drinks per week (pointA) as with four hamburgers and three soft drinks (pointB) or with three hamburgers and four soft drinks (pointC). The points onU1all provide the same level of utility; therefore, he or she does not have any reason for preferring any point onU1to any other point.
The indifference curveU1is similar to a contour line on a map (as discussed in the Appendix to Chapter 1). It shows those combinations of hamburgers and soft drinks that provide an identical ‘‘altitude’’ (that is, amount) of utility. Points to the northeast ofU1promise a higher level of satisfaction and are preferred to points on U1. PointE(five soft drinks and four hamburgers) is preferred to pointCbecause it provides more of both goods. As in Figure 2.1, our definition of economic goods assures that combinationEis preferred to combinationC. Similarly, the assump- tion of transitivity assures that combinationEis also preferred to combinationsA, B, andDand to all other combinations onU1.
F I G U R E 2 . 2
I nd i f f e r e n c e Cu r v e Hamburgers
per week
6 A
B C
E
F D
U1 4
3 2
Soft drinks per week
2 3 4 5 6
0
The curveU1shows the combinations of hamburgers and soft drinks that provide the same level of utility to an individual. The slope of the curve shows the trades an individual will freely make. For example, in moving from pointAto pointB, the individual will give up two hamburgers to get one additional soft drink. In other words, the marginal rate of substitu- tion is approximately 2 in this range. Points belowU1(such asF) provide less utility than points onU1. Points aboveU1(such asE) provide more utility thanU1.
Combinations of hamburgers and soft drinks that lie belowU1, on the other hand, are less desirable because they offer less satisfaction. PointF offers less of both goods than does pointC. The fact that the indifference curveU1has a negative slope (that is, the curve runs from the upper left-portion of the figure to the lower- right portion) indicates that if a person gives up some hamburgers, he or she must receive additional soft drinks to remain equally well-off. This type of movement alongU1represents those trades that a person might freely make. Knowledge ofU1 therefore eliminates the ambiguity associated with the questionable areas we showed in Figure 2.1.
Indifference Curves and the Marginal Rate of Substitution
What happens when a person moves from pointA(six hamburgers and two soft drinks) to pointB(four hamburgers and three soft drinks)? This person remains equally well-off because the two commodity bundles lie on the same indifference curve. This person will voluntarily give up two of the hamburgers that were being consumed at pointAin exchange for one additional soft drink. The slope of the curve U1 between A and B is therefore approximately 2=1¼ 2. That is, Y (hamburgers) declines two units in response to a one-unit increase in X (soft drinks). We call the absolute value of this slope themarginal rate of substitution (MRS). Hence, we would say that the MRS (of soft drinks for hamburgers) between pointsAandBis 2: Given his or her current circumstances, this person is willing to give up two hamburgers in order to get one more soft drink. In making this trade, this person is substituting soft drinksforhamburgers in his or her consumption bundle. That is, by convention, we are looking at trades that involve more X and lessY.
Diminishing Marginal Rate of Substitution
The MRS varies along the curveU1. For points likeA, this person has quite a few hamburgers and is relatively willing to trade them away for soft drinks. On the other hand, for combinations such as those represented by pointD, this person has a lot of soft drinks and is reluctant to give up any more hamburgers to get more soft drinks. The increasing reluctance to trade away hamburgers reflects the notion that the consumption of any one good (here, soft drinks) can be pushed too far. This characteristic can be seen by considering the trades that take place in moving from pointAtoB, from pointBtoC, and from pointCtoD. In the first trade, two hamburgers are given up to get one more soft drink—the MRS is 2 (as we have already shown). The second trade involves giving up one hamburger to get one additional soft drink. In this trade, the MRS has declined to 1, reflecting an increased reluctance to give up hamburgers to get more soft drinks. Finally, for the third trade, from pointCtoD, this person is willing to give up a hamburger only if two soft drinks are received in return. In this final trade, the MRS is ½ (the individual is willing to give up one-half of a hamburger to get one more soft
Marginal rate of substitution (MRS) The rate at which an individual is willing to reduce consumption of one good when he or she gets one more unit of another good. The negative of the slope of an indifference curve.
drink), which is a further decline from the MRS of the previous trades. Hence, the MRS steadily declines as soft drinks (shown on theX-axis) increase.
Balance in Consumption
The conclusion of a diminishing MRS is based on the idea that people prefer balanced consumption bundles to unbalanced ones.2 This assumption is illustrated precisely in Figure 2.3, where the indif- ference curveU1from Figure 2.2 is redrawn. Our discussion here concerns the two extreme consump- tion optionsAandD. In consumingA, this person gets six hamburgers and two soft drinks; the same satisfaction could be received by consumingD(two hamburgers and six soft drinks). Now consider a bundle of commodities (say, G) ‘‘between’’ these extremes. WithG(four hamburgers and four soft drinks), this person obtains a higher level of satisfaction (pointGis northeast of the indifference curveU1) than with either of the extreme bundlesAorD.
The reason for this increased satisfaction should be geometrically obvious.
All of the points on the straight line joiningAandDlie aboveU1. PointGis one of these points (as the figure shows, there are many others). As long as the indifference curve obeys the assumption of a diminishing MRS, it will have the type of convex shape shown in Figure 2.3. Any consumption bundle that rep- resents an ‘‘average’’ between two equally attractive extremes will be preferred to those extremes. The assumption of a diminishing MRS (or convex indifference curves) reflects the notion that people prefer variety in their consumption choices.
2If we assume utility is measurable, we can provide an alternative analysis of a diminishing MRS. To do so, we introduce the concept of the marginal utility of a goodX(denoted byMUX). Marginal utility is defined as the extra utility obtained by consuming one more unit of goodX. The concept is meaningful only if utility can be measured and so is not as useful as the MRS. If the individual is asked to give up someY(DY) to get some additionalX(DX), the change in utility is given by
Change in utility ¼MUY·DYþMUX·DX fig
It is equal to the utility gained from the additional X less the utility lost from the reduction inY. Since utility does not change along an indifference curve, we can use Equation i to derive
DY DX ¼MUX
MUY
fiig
Along an indifference curve, the negative of its slope is given byMUX/MUY. That is, by definition, the MRS. Hence we have
MRS¼MUX=MUY fiiig
As a numerical illustration, suppose an extra hamburger yields two utils (units of utility;MUY¼2) and an extra soft drink yields four utils (MUX¼4). Now MRS¼2 because the individual will be willing to trade away two hamburgers to get an additional soft drink. If we can assume thatMUXfalls andMUYincreases asXis substituted forY, Equation iii shows that MRS will fall as we move counterclockwise alongU1.
M i c r o Q u i z 2 . 2
The slope of an indifference curve is negative.
1. Explain why the slope of an indifference curve would not be expected to be positive for economic ‘‘goods.’’
2. Explain why the MRS (which is the negative of the slope of an indifference curve) cannot be calculated for pointsEandFin Figure 2.2 without additional information.