Mathematical Modeling of the Marxian Economics Based on Neoclassical Growth Model

在本研究中，我们将2002年首次建立的马克思最优增长理论扩展到各个领域。第一个领域是将我们的模型改进为两类模型，尽管我们最初的模型是一类模型，但通过这些改进，我们现在能够研究增长路径中的开发动态。特别是，我们的主要成就是阶级划分在一定条件下造成了过度积累，为了避免这种积累，社会倾向于产生社会民主主义、反生产主义和工会主义以及马克思主义。我们还发现了零增长社会下减少剥削的条件及其与劳动价值论的关系。第二个字段是单类模型本身的扩展。例如，生产性产品的生产函数变化为以资本品为生产资料，从社会计划模型向分散的市场导向模型的延伸，从工业革命模型向农业革命模型或知识革命模型的延伸，从确定性模型向随机模型的延伸，解释日本目前零增长社会的各种现象。第三个领域是研究我们的剥削定义与罗默的剥削定义的关系，以及什么条件使前者与后者相同。这项研究开辟了新的领域。

In this research, we extended our Marxian Optimal Growth Theory which was first established our paper in 2002 into various fields.The first field is improvements of our model for the two-class model although our original model was one-class model, by these improvements now we are able to study the dynamics of exploitation in the growth path. Especially, our main achievement is that class division makes over-accumulation under certain conditions, and to avoid it, society tend to cause social democrats, anti-productivism and trade unionism as well as Marxism. We also found some conditions which diminish exploitation under zero-growth society and its relationship with labor theory of value.The second field is the extensions of the one-class model itself. For example, change of the production function of the productive goods to have capital goods as its means of production, extension from the social planner model to decentralized market-oriented model, extension from the Industrial revolution model to the Agricultural revolution model or Knowledge revolution model, extension from the deterministic model to the stochastic model, extension to explain the present various phenomena of zero growth society in Japan.The third field is the study of the relations of our definition of exploitation with Roemer's, and what conditions make the former same as the latter. This study opened new field.