A Note on the Second-order Approximation of Hicksian Welfare Change Indicators

In 1930-1940, Hicks defined the welfare change indicators such as the equivalent variation and the compensating variation using the expenditure function and provided their approximation formular using the Taylor expansion. The famous Harberger's welfare indicator is a second order approximation of the Hicksian welfare change indicators. Weitzman(1988) showed that a refinement is needed for the Harberger's welfare indicator based on the modern microeconomic theory. Also Diewert(1992) extended Weitzman's result by providing two refined formular. This note claims that conventional second order Taylor approximation is not a good method in case of the expenditure function as seen from the standard numerical analysis theory. This note derives four kinds of welfare change indicators in succinct way using a variant of Taylor second order approximation. The two among the four are the same with Diewert's formulas