Global analysis of the growth and cycles of multi-sector economies with constant returns: A turnpike approach

In Section 1, we explain the neoclassical optimal growth model, which includes multi capital goods, and is derived from neoclassical production functions; the transformations to the reduced model are also explained. Section 2 pertains to the explanation of the methods for proving the consumption turnpike theorem demonstrated by Scheinkman (1976) and McKenzie (1983). Also, the case in which the essentials of the von Neumann-McKenzie facet, which plays an important role in the next part, became a two-sector model and is explained using figures. In Section 3, we postulate a two-sector neoclassical optimal growth model, and the optimal path behavior in the vicinity of the optimal steady state path (modified golden rule path) are classified using the characteristics of von Neumann-McKenzie facet. Also, we will use these results to prove, based on a weaker hypothesis, that the theorem that the optimal path local stability and the optimal path attained by Benhabib and Nishimura（1985）becomes a two-term periodic solution. In Section 4, the generalization of the global asymptotic stability conclusion achieved with two divisions into a case that includes two or more types of capital goods. In Addendum, the important fundamental principles used in the main text will be defined, and a number of theorems will be proved.