Benefit

Bruce C. Dieffenbach ()
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Bruce C. Dieffenbach: Independent author

Chapter 47 in Conjugate Duality in Economic Analysis, 2026, pp 357-362 from Springer

Abstract: Abstract Luenberger introduces and applies “benefit” for a consumer, as a novel alternative to utility. For a classical consumer having consumption x and consumption price x*, we define and analyze benefit and relate it to compensated demand. Let C denote the upper contour set for a particular indifference curve. Benefit is the maximum amount that can be subtracted without falling below the indifference curve: $$b\left ( \boldsymbol {x}\right ) :=\sup _{y}\left [ y^{\ast }y-\delta _{C}\left ( \boldsymbol {x}-\mathbf {1}y\right ) \right ] \!.$$ Here 1 denotes consumption of one unit of each good. Here y*=1 is the dual perturbation. The compensated demand is the set of cost-minimizing x for price x*. Because benefit is a dollar value, it is meaningful to consider benefit minus cost. Consider a price x*: If x maximizes benefit minus cost and benefit is zero, then x is the compensated demand for price x*; Conversely, the compensated demand x maximizes benefit minus cost, and benefit is zero.

Date: 2026
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DOI: 10.1007/978-3-032-21396-9_47

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