Abstract
When income elasticities of demand are all unity, every dollar being spent in the same proportions at all levels of income, a homogeneous-first-degree, concave utility function exists to serve as an unequivocal measure of real output. Dual to it, and with identical concavity and homogeneity properties, is the minimized-cost-per-unit-of-output, a function of prices. Distinct from this production dual is the indirect-utility dual, representing, except for algebraic sign, the maximized level of utility attainable as a function of prices relative to income. These basic alternative dualities are shown to be related by a unifying theorem: The logarithm of either of the pair of production-dual functions has for its indirect-utility dual the logarithm of the other function. What is shown to be the same thing, the indirect-utility dual of the output function is, except for sign, the reciprocal of the output's production-dual.
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