(8th edition) (the pearson series in economics) robert pindyck, daniel rubinfeld microecon 126

CHAPTER 3 • Consumer Behavior 101

TABLE 3.3

IDEAL COST-OF-LIVING INDEX

Price of books

2000 (SARAH )

2010 (RACHEL)

$20/book

$100/book

15

6

$2.00/lb.

$2.20/lb.

Number of books
Price of food
Pounds of food

100

300

Expenditure

$500

$1260

Ideal Cost-of-Living Index
Let’s look at two sisters, Rachel and Sarah, whose preferences are identical. When
Sarah began her college education in 2000, her parents gave her a “discretionary” budget of $500 per quarter. Sarah could spend the money on food, which
was available at a price of $2.00 per pound, and on books, which were available at a price of $20 each. Sarah bought 100 pounds of food (at a cost of $200)
and 15 books (at a cost of $300). Ten years later, in 2010, when Rachel (who had
worked during the interim) is about to start college, her parents promise her a
budget that is equivalent in buying power to the budget given to her older sister.
Unfortunately, prices in the college town have increased, with food now $2.20
per pound and books $100 each. By how much should the discretionary budget
be increased to make Rachel as well off in 2010 as her sister Sarah was in 2000?
Table 3.3 summarizes the relevant data and Figure 3.24 provides the answer.
The initial budget constraint facing Sarah in 2000 is given by line l1 in
Figure 3.24; her utility-maximizing combination of food and books is at point
A on indifference curve U1. We can check that the cost of achieving this level of
utility is $500, as stated in the table:
$500 = 100 lbs. of food * $2.00/lb. + 15 books * $20/book
As Figure 3.24 shows, to achieve the same level of utility as Sarah while facing the
new higher prices, Rachel requires a budget sufficient to purchase the food-book

Books
(per quarter)
U1
25

F IGURE 3.24

20

COST-OF-LIVING INDEXES

A
15
10
B

A price index, which represents the cost of
buying bundle A at current prices relative
to the cost of bundle A at base-year prices,
overstates the ideal cost-of-living index.

l3

5
l1

l2

0
50

100 150 200 250 300 350 400 450 500 550 600
Food (lb. per quarter)