效用函数的存在性

The Existence of Utility Function

运用Riemann几何的一些基本知识证明效用函数的存在性,用数学式表示了效用函数的2个特征:效用是随着单个商品数量递增而增长的,且单个商品的边际效用是递减的同时,得出了对于效用函数,商品组合X和商品组合Y产生的效用之和大于商品组合X+Y产生的效用.

The existence of utility function is proved by using the basic knowledge of Riemannian geometry,the two characteristics of utility function are expressed by mathematical formulas, the characteristics are that, the utiltity is rising with the rising quantity of the single commodity, and the boundary utility of single commodity is reducing. Then, the result is got, for the utility function, the sum utility of the combination of commdity X and the combimation of commodity Y is more than the combination of commodity X and Y.