Daniel l. Rubinfeld

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86 Part 2 Producers, Consumers, and Competitive Markets 3 Consumer Behavior 87 Other Consumption (5) p Q Education (5) When given a college trust fund that must be spent on education, the student mO\'es from A to B, a comer solution. If, however, the trust fund could be spent on other as well as education, the shldent would be better off at C. The budget line that Jane faces before being awarded the trust is given by line PQ. The trust fund expands the budget line outward as long as the full amowlt of the hmd, shown by distance PB, is spent on education. By accepting the trust fund and going to college, Jane increases her satisfaction, moving from A on indifference CUlTe LI1 to B on indifference curve LI 2· Note that B represents a comer solution because Jane's marginal rate of substihltion of other consumption for education is lower than the relative price of other consumption. Jane would prefer to spend a portion of the trust fund on other goods in addition to education. Without resh'iction on the trust hmd, she would move to C on indifference cun'e LI}, decreasing her spending on education (perhaps going to a junior college rather than a four-year college) but increasing her spending on items that she enjoys more than education. Recipients usually prefer unrestricted to restricted trusts. Restricted trusts are popular, however, because they allmv parents to control children's expendihIres in 'ways that they belie\'e are in the children's long-nm best interests. In Section 3.1, we savv how an individual's preferences could be represented by a series of indifference curves. Then in Section 3.3, we saw how preferences, gi\'en budget constraints, determine choices. Can this process be reversed If we know the choices that a consumer has made, can we determine his or her preferences ¥M M _ H If an individual facing budget line 11 has chosen market basket A rather than market basket B, A is revealed to be preferred to B. Likewise, the individual facing budget line 12 chooses market basket B, which is then revealed to be preferred to market basket 0, Whereas A is preferred to all market baskets in the green-shaded area, all baskets in the pink-shaded area are preferred to A. We can if we have information about a sufficient number of choices that have been made when prices and income levels varied, The basic idea is simple, If a COIlSllJller chooses one market basket over allother, and if the chosen lIIarket basket is more expensive tlUlIl the a/temative, then the conSlllller IIllist prefer the chosen market basket. Suppose that an individual, facing the budget constraint given by line 11 in Figure 3.17, chooses market basket A Let's compare A to baskets Band D. Because the individual could have purchased basket B (and all baskets below line 11) and did not, we say that A is pr~felTed to B. It might seem at first glance that we cannot make a direct comparison behveen baskets A and 0 because 0 is not on 1 1 , But suppose the relative prices of food and clothing change, so that the new budget line is 12 and the individual then chooses market basket B. Because 0 lies on budget line 12 and was not chosen, B is preferred to 0 (and to all baskets below line 12)' Because A is preferred to Band B is preferred to 0, we conclude that A is preferred to D. Furthermore, note in Figure 3.17 that basket A is preferred to all of the baskets that appear in the green-shaded areas. However, because food and clothing are" goods" rather than "bads," all baskets that lie in the pink-shaded area in the rectangle above and to the right of A are preferred to A Thus, the indifference curve passing through A must lie in the unshaded area. Given more information about choices when prices and income levels vary, we can get a better fix on the shape of the indifference cun'e. Consider Figure 3.18. Suppose that facing line 13 (which was chosen to pass through A), the individual chooses market basket E Because E was chosen even though A was equally expensive (it lies on the same budget line), E is preferred to A, as are all points in the rectangle above and to the right of E. Now suppose that facing line 14 (which passes through A), the individual chooses market basket G. Because G was chosen and A was not, G is preferred to A, as are all market baskets above arId to the right of G.
88 Part 2 Producers, Consumers, and Competitive Markets Clothing 13 (units per month) - " Q, Other Recrea tional Activities (5) 80 &&b£i' e &5 Chapter :3 Consumer Behavior 89 60 40 20 o L-______ ~ ________ ~ ____ ~ __ L-___ 50 75 Amount of Exercise (hours) Food (muts per month) FacinO' budO'et line I, the individual chooses E, which is revealed to be preferred to A (beca~se A ~ould h~ve been chosen), Likewise, facing line I~, G is chosen, wl~ch is also revealed to be preferred to A Whereas A is to all market baskets m the all market baskets in the to A We can 0'0 further bv makina use of the assumption that preferences are com'ex, /:) ~ /:) 1 '1 f In that case, because E is preferred to A, all market baskets above and to t 1e ng 1t 0 line AE in Figure 3.18 must be preferred to A Otherwise, the indifference, curve passing through A would ha\'e to pass through a point ab~\,~ and to the nght of AE and then fall below the line at E-in which case the indltterence curve would not be com'ex, By a similar argument, all points on AG or above are also preferred to A Therefore, the indifference cun'e must lie ,-\'ithin the unshaded area. The revealed preference approach is \'aluable as a mean~ of checking vvhether individual choices are consistent with the assumptions ot consumer theory. As Example 35 shows, revealed preference analysis can help us understand the implications of choices that consumers must make in particular circumstances. A health club has been fferi~g the use of its,facilities to ~nyOl:~ who i: '~'ill~ ing to pay an hourly tee, Now the club deCldes to alter Its pncmg PO~ICY by charging both an annual membership fee and a lo::'er hourly f~~, Does Hus new financial arrangement make individuals better oft or 'worse ott than they were under the old arrangement The answer depends on people's prefereI~ces, Suppose that Roberta has 5100 of income available each week tor recreational activities, including exercise, movies, restaurant meals, and ,so. ~n, When the health club charged a fee of 54 per hour, Roberta used the taClhty 10 hours per \Neek. Under the new arrangement, she is required to pay 530 per week but can use the club for only 51 per hour. When facing budget line 1 1 , an individual chooses to use a health club for 10 hours per week at point A When the fees are altered, she faces budget line [2' She is then made better off because market basket A can still be purcl1ased, as can market basket B, which lies on a higher indifference curve. Is this change beneficial for Roberta Revealed preference analysis provides the answer, In Figure 3,19, line 11 represents the budget consh'aint that Roberta faced under the original pricing arrangement. In this case she maximized her satisfaction by choosing market basket A, with 10 hours of exercise and $60 of other recreational activities. Under the new arrangement, which shifts the budget line to 1 2 , she could still choose market basket A But because LI1 is clearly not tangent to 1 2 , Roberta will be better off choosing another basket, such as B, with 25 hours of exercise and $45 of other recreational activities, Because she would choose B when she could still choose A, she prefers B to A. The new pricing arrangement therefore makes Roberta better off. (Note that B is also preferred to C which represents the option of not using the health club at all.) We could also ask whether this ne\v pricing system-called a two-part tar~tf-will increase the club's profits, If all mernbers are like Roberta and more use generates more profit, then the answer is yes, In general, however, the answer depends on two factors: the preferences of all members and the costs of operating the facility We discuss the two-part tariff in detail in Chapter 11, where we study ways in which firms with market power set prices. In Section 3.3, vve showed graphically how a consumer can maximize his or her satisfaction given a budget constraint. We do this by finding the highest indifference curve that can be reached, given that budget constraint Because the highest
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Daniel l. Rubinfeld

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