(8th edition) (the pearson series in economics) robert pindyck, daniel rubinfeld microecon 128

CHAPTER • Consumer Behavior 103 This result holds generally Why? Because the Laspeyres price index assumes that consumers not alter their consumption patterns as prices change By changing consumption, however—increasing purchases of items that have become relatively cheaper and decreasing purchases of relatively more expensive items—consumers can achieve the same level of utility without having to consume the same bundle of goods that they did before the price change Paasche Index Another commonly used cost-of-living index is the Paasche index Unlike the Laspeyres index, which focuses on the cost of buying a base-year bundle, the Paasche index focuses on the cost of buying the current year’s bundle In particular, the Paasche index answers another question: What is the amount of money at current-year prices that an individual requires to purchase the current bundle of goods and services divided by the cost of purchasing the same bundle in the base year? • Paasche index Amount of money at current-year prices that an individual requires to purchase a current bundle of goods and services divided by the cost of purchasing the same bundle in a base year COMPARING THE LASPEYRES AND PAASCHE INDEXES It is helpful to compare the Laspeyres and the Paasche cost-of-living indexes • Laspeyres index: The amount of money at current-year prices that an individual requires to purchase the bundle of goods and services that was chosen in the base year divided by the cost of purchasing the same bundle at base-year prices • Paasche index: The amount of money at current-year prices that an individual requires to purchase the bundle of goods and services chosen in the current year divided by the cost of purchasing the same bundle in the base year Both the Laspeyres (LI) and Paasche (PI) indexes are fixed-weight indexes: The quantities of the various goods and services in each index remain unchanged For the Laspeyres index, however, the quantities remain unchanged at base-year levels; for the Paasche they remain unchanged at current-year levels Suppose generally that there are two goods, food (F) and clothing (C) Let: PFt and PCt be current-year prices PFb and PCb be base-year prices Ft and Ct be current-year quantities Fb and Cb be base-year quantities We can write the two indexes as: LI = PFtFb + PCtC b PFbFb + PCbC b PI = PFtFt + PCtC t PFbFt + PCbC t Just as the Laspeyres index will overstate the ideal cost of living, the Paasche will understate it because it assumes that the individual will buy the current-year bundle in the base period In actuality, facing base-year prices, consumers would have been able to achieve the same level of utility at a lower cost by changing their consumption bundles Because the Paasche index is a ratio of the cost of • fixed-weight index Cost-of-living index in which the quantities of goods and services remain unchanged