经济学中拟和生产函数的几何分类  

Geometric Classifications of Quasi-sum Production Functions in Economics

作　　者：骆艳茹 富宇[2] Yanru Luo;Yu Fu(School of Economics,Dongbei University of Finance and Economics,Dalian 116025,P.R.China;School of Data Science and Artificial Intelligence,Dongbei University of Finance and Economics,Dalian 116025,P.R.China)

机构地区：[1]东北财经大学经济学院,大连116025 [2]东北财经大学数据科学与人工智能学院,大连116025

出　　处：《数学学报(中文版)》2025年第1期81-98,共18页Acta Mathematica Sinica:Chinese Series

基　　金：辽宁省兴辽英才计划(XLYC2203194)。

摘　　要：生产函数是新古典经济学的核心概念之一,是经济学家进行经济分析的重要工具.本文从几何不变量的角度对拟和生产函数进行深入研究.通过探讨拟和生产函数对应曲面的常高斯曲率方程与常平均曲率方程,得到了一系列有意思的分类结果.本文的研究结果不仅对微分几何中曲面论的研究具有一定意义,而且为经济分析中的生产模型提供了更多可选择的类型,在一定程度上推动了生产函数理论的发展.Production function is one of the core concepts of neoclassical economics and an important tool for economic analysis.This paper studies quasi-sum production functions from the perspective of geometric invariants.By discussing the constant Gauss curvature equation and the constant mean curvature equation of the corresponding surfaces of quasi-sum production functions,a series of interesting classification results are obtained.The results of this paper not only have certain significance for the study of surface theory in differential geometry,but also provide more alternative types of production models in economic analysis,and promote the development of the theory of production function to a certain extent.

关 键 词：生产函数 曲面 高斯曲率 平均曲率 

分 类 号：O186.1[理学—数学]