Mathematical Modeling of the Marxian Economics Based on Neoclassical Growth Model

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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.