[Joseph_E._Stiglitz,_Carl_E._Walsh]_Economics(Bookos.org) (1)

is 30, and that of the last pizza is also 30. At this point, she will not want to switch
anymore. If she buys another sweatshirt, she gains 28, but the last pizza, her 3rd,
which she will have to give up, has a marginal utility of 30; she loses more than she
gains. If she buys another pizza, she gains 28, but the last sweatshirt (her 17th) gave
her a marginal utility of 30; again, she loses in net. We can thus see that with her
budget, she is best off when the marginal utility of the two goods is the same.
The same general principle applies when the prices of two goods differ. Assume
that a sweatshirt costs twice as much as a pizza. So long as the marginal utility of
sweatshirts is more than twice that of pizzas, it still pays for Mary to switch to sweatshirts.
To get one more sweatshirt, she has to give up two pizzas, and we reason, as
before, that she will adjust her consumption until she gets to the point where the
marginal utilities of the two goods, per dollar spent, are equal. This is a general rule:
in choosing between two goods, consumers adjust choices to the point at which the
marginal utilities are proportional to the prices. Thus, the last unit purchased of a
good that costs twice as much as another must generate twice the marginal utility
as the last unit purchased of the other good; the last unit purchased of a good that
costs three times as much must generate three times the marginal utility as the last
unit purchased of the other good; and so on.
Table 5.1
UTILITY AND MARGINAL UTILITY
Mary’s
Mary’s
Number of willingness to Marginal Number of willingness to Marginal
sweatshirts pay (utility) utility pizzas pay (utility) utility
0 0 100 0 0 36
1 100 90 1 36 32
2 190 80 2 64 30
3 270 70 3 98 28
4 340 60 4 126 26
5 400 56 5 152 24
6 456 52 6 176 22
7 508 48 7 198 20
8 556 46 8 218 18
9 602 44 9 236 16
10 646 42 10 252 14
11 688 40 11 266 12
12 728 38 12 272 10
13 766 36 13 288 8
14 802 34 14 296
15 836 32
16 868 30
17 898 28
18 926 26
19 952 24
20 976
UTILITY AND THE DESCRIPTION OF PREFERENCES ∂ 115