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• #### Index 319-332

current (or comparison) period. The ratio of these two costs is a basket price index or cost-of-goods index. If the basket is the list of goods actually purchased in the base period, this is a Laspeyres price index. If the current basket is used as the base and the price index is the ratio of the current to reference period costs of the current period basket, the result is a Paasche price index. Because the ratio of prices in the comparison to reference period differs from one good to another and because the baskets purchased in the two periods are generally different, the Laspeyres and the Paasche indexes are generally not the same. In principle, one could calculate a price index from any basket—for example, one at any point between the current and the base baskets. The relationship between various indexes cannot be known without information about how the baskets are generated and how quantity is related to price. In particular, it is not true, although it is often so claimed, that the Laspeyres must necessarily be greater than the Paasche, though this is usually the case in practice.

As we have noted, the Laspeyres index has an important practical advantage: once base quantities have been set, a Laspeyres index can be produced on the same schedule as prices are collected. The idea of continuously repricing a fixed basket is easily explained even to nonspecialists and corresponds well to what most people think of as a price index. The Laspeyres price index is the concept that is most frequently used by statistical offices around the world.

When the Laspeyres index is used to calculate a national CPI, the basket to be repriced is usually the total purchases of each good by all consumers in the country during the base period. But it is also possible to think about baskets purchased by various subsets of the population. Groups might be defined by region, to derive a regional price index; by age, to look at a price index for the elderly; or by income levels, to construct separate price indexes for the rich and the poor. Indeed, there is nothing in principle to stop us from thinking about a Laspeyres index for each individual in the economy. Different people spend their money in different ways, so that each is affected differently by changes in prices. For example, those who commute long distances to work are seriously affected by an increase in energy prices, while those who walk are not; smokers are affected by an increase in the price of cigarettes; nonsmokers are not.

Two important issues are raised by thinking about price indexes for groups or for individuals. First, not only do different people buy different baskets of goods, but different people often pay different prices for the same goods. Second, if one constructs (say) a national Laspeyres index and an individual Laspeyres index for each person in the country, how does one relate to the other? In particular, is the national price index an average of the individual price indexes? Both of these issues arise repeatedly throughout the report, so it is useful to discuss both at the outset.

The second issue, the aggregation of individual price indexes to get a national price index, is more easily dealt with if one assumes away the first issue and pretends that everyone in the economy pays the same price for everything. In

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