Benefit functions and duality.

*(English)*Zbl 0766.90011Summary: This paper studies a new representation of individual preferences termed the benefit function. The benefit function \(b(g;x,u)\) measures the amount that an individual is willing to trade, in terms of specific reference commodity bundle \(g\), for the opportunity to move from utility level \(u\) to a consumption bundle \(x\). The benefit function is therefore a generalization of the willingness-to-pay concept. This paper studies properties of this function, including its continuity and structural properties and its indirect relation to the underlying utility function. A very important property of the benefit function is that it is the natural precursor of the expenditure function, in the sense that the expenditure function is a (special) dual of the benefit function. This duality is shown to be complete by proving that when appropriate convexity properties hold, the (correspondingly special) dual of the expenditure function is, in fact, the benefit function. The duality makes the benefit function a powerful tool for analysis of welfare issues.

##### MSC:

91B16 | Utility theory |

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\textit{D. G. Luenberger}, J. Math. Econ. 21, No. 5, 461--481 (1992; Zbl 0766.90011)

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