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The Empirical Implications of a Utility Tree

Robert H. Strotz

Abstract

The hypothesis considered is that the utility function can be written as $U = U[V^{A} (q_{\alpha 1}, \cdots, q_{\alpha}_{\alpha}), \cdots, V^{M} (q_{m 1}, \cdots, q_{m \mu})]$, where the V's are "branch" utility functions depending on quantities of different commodities assigned to different branches (e.g., food, clothing). This hypothesis implies certain empirically meaningful and interesting conditions on the price coefficients of the demand functions. These conditions are, however, not subjected here to statistical test. A price index formula is next developed for measuring branch prices (e.g., the price of food, the price of clothing) and with the use of these indices a rationale is found for the individual doing his budgeting by first deciding how to allocate expenditure among the several branches and then making independent decisions as to how best to spend each branch allocation on the commodities within the branch. That this budgeting practice is both familiar and consistent with the proposed hypothesis is taken as evidence in support of the hypothesis and, therefore, of the implications for the price coefficients in demand functions.