A New Algorithm For Computing Compensated Income From Ordinary Demand Functions

This paper proposes a REversible Second-ORder Taylor (RESORT) expansion of the expenditure function to compute compensated income from ordinary demand functions as an alternative to the algorithm proposed by Vartia. These algorithms provide measures of Hicksian welfare changes and Konus-type cost of living indices. RESORT also validates the results by checking the matrix of compensated price effects. obtained through the Slutsky equation, for symmetry and negative semi-definiteness as required by expenditure minimization. In contrast, Vartia's algorithm provides no validation procedure. RESORT is similar to Vartia's algorithm in using price steps. It computes compensated income at each step "forward" from the initial to the terminal prices, and insures that the compensated income computed "backward" is equal to its value computed in the "forward" procedure. Thus, RESORT is "reversible" and guarantees unique values of compensated income for each set of prices and, as a result, also unique measures of welfare changes and cost of living indices. These unique results are not, however, guaranteed by the usual Taylor series expansion for computing compensated income.