Cost-of-living index

A cost-of-living index is a theoretical price index that measures relative cost of living over time or regions. It is an index that measures differences in the price of goods and services, and allows for substitutions with other items as prices vary. There are many different methodologies that have been developed to approximate cost-of-living indexes. A Konüs index is a type of cost-of-living index that uses an expenditure function such as one used in assessing expected compensating variation. The expected indirect utility is equated in both periods. The United States Consumer Price Index (CPI) is a price index that is based on the idea of a cost-of-living index. The U.S. Department of Labor's Bureau of Labor Statistics (BLS) explains the differences: The basis for the theory behind the cost-of-living index is attributed to Russian economist A. A. Konüs. The theory assumes that consumers are optimizers and get as much utility as possible from the money that they have to spend. These assumptions can be shown to lead to a 'consumer's cost function', C(u,p), the cost of achieving utility level u given a set of prices p. Assuming that the cost function holds across time (i.e., people get the same amount of utility from one set of purchases in year as they would have buying the same set in a different year) leads to a 'true cost of living index'. The general form for Konüs's true cost-of-living index compares the consumer's cost function given the prices in one year with the consumer's cost function given the prices in a different year: Since u can be defined as the utility received from a set of goods measured in quantity, q, u can be replaced with f(q) to produce a version of the true cost of living index that is based on price and quantities like most other price indices: