Hicks 후생지표의 이차근사식에 관한 소고
A Note on the Second-order Approximation of Hicksian Welfare Change Indicators
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1930-40년대 Hicks는 동등변화(equivalent variation)와 보상변화(compensating variation)라는 지출함수에 기초한 후생지표를 정의하고 Taylor 전개에 의한 근사식들을 제시하였다. 유명한 Harberger 후생지표는 Hicks 후생지표의 Taylor 이차근사식이다. Weitzman(1988)은 현대 미시경제 이론에 기초하여 Harberger 후생지표에는 보정이 필요함을 보였다. 이어서 Diewert(1992)는 Weitzman의 결과를 확장하여 두 가지 보정된 이차근사식을 제시하였다. 본고는 수치해석의 표준적 방법론에 따르면 통상적인 Taylor 이차근사식이 지출함수의 경우에는 적절하지 않음을 지적하고 그 변형을 사용한 간명한 방법으로 모두 네 가지 형태의 후생지표를 유도한다. 그 중 두 가지는 Diewert의 결과와 동일하다.
Abstract
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.
참고문헌 (22)
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