马克思-斯拉法联合生产下的价格、数量均衡与稳定性——基于摩尔-彭诺斯伪逆的再证明  

Price,Activity Equilibrium,and Stability of Marx-Sraffa Joint Production:A Further Proof Based on the Moore-Penrose Pseudo Inverse

作　　者：李帮喜 赵奕菡 卢睿 LI Bangxi;ZHAO Yihan;LU Rui(Institute of Economics,School of Social Sciences,Tsinghua University,Beijing,China;School of Economics,Beijing Institute of Technology,Beijing,China;Department of Automation,School of Information Science and Technology,Tsinghua University,Beijing,China)

机构地区：[1]清华大学社会科学学院 [2]北京理工大学经济学院 [3]清华大学信息科学技术学院自动化系

出　　处：《政治经济学季刊》2024年第4期25-41,共17页Political Economy Quarterly

基　　金：国家社会科学基金重点项目(23AZD016);中央高校基本科研业务费专项资金;北京理工大学青年教师学术启动计划的资助。

摘　　要：华罗庚1984年提出了一个大规模经济规划下全局最优解的分析框架。Li and Fujimori(2011)和Li(2017)将其推广到了只包含固定资本的联合生产的情况,利用摩尔-彭诺斯(Moore-Penrose,MP)伪逆的性质,给出了计算最优价格均衡pB=αpM和数量均衡Bx=βMx的方法,并证明了均衡价格体系的解和矩阵MB+的特征体系是等价的。在上述文献的基础上,本文提出了一种更有效的计算均衡解的方式,并在马克思-斯拉法联合生产模型下推广了经典的佩龙-弗罗宾尼斯(Perron-Frobenius,PF)定理。本文的研究结果表明,在联合生产情况下,生产价格和数量体系都无法实现稳态均衡。In 1984,Hua Luogeng proposed an analytical framework for the global optimal solution under large-scale economic planning.Li and Fujimori(2011)and Li(2017)extended it to the case of joint production containing fixed capital,and used the properties of Moore-Penrose(MP)pseudo inverse to calculate the optimal price equilibrium pB=αpM and activity equilibrium Bx=βMx.They also proved that the solution of the equilibrium price system is equivalent to the characteristic system of the matrix MB+.On the basis of the above literature,this thesis proposes a more effective way to calculate equilibrium solutions and extends the classical Perron-Frobenius(PF)theorem under the Marx-Sraffa joint production model.The research results indicate that in the case of joint production,both the price and activity system cannot achieve steady-state equilibrium.

关 键 词：马克思-斯拉法 联合生产 线性生产模型 摩尔-彭诺斯伪逆 佩龙-弗罗宾尼斯定理 

分 类 号：G63[文化科学—教育学]