Unconditional Elasticities in Two‐Stage Demand Systems: An Approximate Solution

Two‐stage budgeting postulates that the consumer's utility maximization decision can be decomposed into two steps. In the first stage, total expenditure is allocated over broad groups of goods. In the second stage, group expenditures are allocated over elementary commodities. In this article, we assume that the current weighted true cost‐of‐living price indices defined for each broad group of elementary commodities vary only very slightly with sub‐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. Relationships between conditional and unconditional expenditure and price elasticities are derived within this context.