Unconditional elasticities in two-stage demand systems: An approximate solution

Two-stage budgeting postulates that the consumer's utility maximization dec ision can be decomposed into two steps. In the first stage, total expenditu re is allocated over broad groups of goods. In the second stage, group expe nditures are allocated over elementary commodities. In this article, we ass ume that the current weighted true cost-of-living price indices defined for each broad group of elementary commodities vary only very slightly with su b-utility levels. Hence, it is possible to approximate the first stage of a two-stage budgeting structure by a maximization problem involving a single price index and a single quantity index for each of the broad groups. Rela tionships between conditional and unconditional expenditure and price elast icities are derived within this context.