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

CHAPTER • Consumer Behavior 101 TABLE 3.3 IDEAL COST-OF-LIVING INDEX Price of books 2000 (SARAH ) 2010 (RACHEL) $20/book $100/book 15 $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 l1 l2 50 100 150 200 250 300 350 400 450 500 550 600 Food (lb per quarter)