Marshallian Surplus for Differentiable Preferences : Partial Equilibrium Approach

Modern mainstream economics, intermediate and advanced micro textbooks teach us after classical Marshall, Hicks, Samuelson etc. contributions that Marshallian surplus - area to the left from the textbook demand function - represents exact change in consumers' money metric utility only in special quasilinear case, when marginal utility of income is every time unity. In the general case, it is recommended therefore to use Hicksian equivalent or compensated variations as a measures of utility change, keeping in mind Marshallian surplus as a useful, but rather poor, approximation of true utility change. Our paper shows that in one-dimensional case when only price of the good changes, area to the left of Walrasian demand curve every time represents exact, not approximate, change in consumer' indirect money metric utility function, for rather general class of differentiable preferences