@article{LI2024, 
author = {Bangxi LI and Yihan ZHAO and Rui LU},
title = {Price, Activity Equilibrium, and Stability of Marx-Sraffa Joint Production: A Further Proof Based on the Moore-Penrose Pseudo Inverse},
year = {2024},
journal = {Political Economy Quarterly},
volume = {3},
number = {4},
pages = {25-41},
keywords = {Marx-Sraffa, joint production, linear production model, Moore-Penrose pseudo inverse, Perron-Frobenius theorem},
url = {https://www.sciopen.com/article/10.26599/PEQ2024.9310402},
doi = {10.26599/PEQ2024.9310402},
abstract = {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.}
}