Hicks 소비자잉여와 계산 알고리즘 = Hicksian Consumer’s Surplus and Computational Algorithms

국문 초록 (Abstract)

Hicks 소비자잉여는 보상소득함수에 의해서 정의된다. 문헌에서 보상소득함수는 Hurwicz and Uzawa(1971)에서는 편미분방정식, Hausman(1981), Vartia(1983)에서는 상미분방정식으로 정의되고 있다. 먼저 본고는 추정된 시장수요함수로부터 보상소득함수를 복구할 수 있는 적분가능성(integrability) 조건 하에서 두 개의 미분방정식은 유일하고 동일한 해를 갖는다는 것을 보였다. 두 형태의 미분방정식 중에서 보상소득을 구하는 목적에는 Hausman-Vartia의 상미분방정식이 보다 유용할 것이다. McKenzie and Pearce(1976), Vartia (1983), Breslaw and Smith(1995), Hausman and Newey(1995) 등의 연구는 Hausman-Vartia 상미분방정식에 수치적 알고리즘을 적용하였다. 그러나 이들 연구에서 사용된 계산 알고리즘들은 일반적으로 추천되는 것들과는 거리가 있다. 본 연구에서는 상미분방정식의 대표적 계산 알고리즘들이 보상소득함수의 계산에 용이하게 적용될 수 있음을 보이고 있다. 본고에서 제안되는 계산 알고리즘은 적분가능성 제약 하에 추정된 시장수요함수로부터 소비자잉여는 물론이고 생계비지수, 사중손실(deadweight loss)의 추정에 사용될 수 있다.

다국어 초록 (Multilingual Abstract)

The Hicksian consumer’s surplus is defined by the income consumption function (Hurwicz and Uzawa, 1971, p.116) or the moneymetric utility (Varian, 1992, pp.108-113). In the literature it is defined by differential equations; the partial differential equation in Hurwicz and Uzawa (1971) and the ordinary differential equation in Hausman (1981) and Vartia (1983). It is natural that the ordinary differential equation is the preferred one among the two differential equations for computating the money metric utility from the system of estimated market demand function with the integrability condition. McKenzie and Pearce (1976), Vartia (1983), Breslaw and Smith (1995), Hausman and Newey (1995) considered various numerical methods for the computaion of money metric utility. This paper compares and evaluates those algorithms in the economics literature with an algorithm more popular in the mathematics literature by the theoretical approximation orders and numerical relative errors from the exact solution. The algorithm suggested in this paper can be used for the computation of consumer’s surplus as well as the cost-of-living index and dead weight loss.

목차 (Table of Contents)

• Ⅰ. 서론
• Ⅱ. Hicks 소비자잉여의 정의
• Ⅲ. 보상소득함수의 미분방정식
• Ⅳ. 계산 알고리즘
• Ⅴ. 요약 및 향후 연구방향
• [참고문헌]
• 〈부록〉 GAUSS 프로그램(Runge-Kutta Method order 4, Runge-Kutta Method order 2, Vartia algorithm)
• [Abstract]

참고문헌 (Reference)

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