Extension to a Multi-Period Overlapping Generations Model: Based on the Two-Period Overlapping Generations Model

In macroeconomics, the Ramsey model and the two-period overlapping generations (OLG) model are regarded as standard frameworks. The latter is widely used due to its simplicity and its ability to explain a variety of economic phenomena. Although three-period models also exist, they are often constrained by analytical limitations, such as the inability to incorporate capital accumulation. As multi-period models, the altruism-based Ramsey model and the continuous-time OLG model have been developed; however, neither is well-suited for analyzing independent decision-making across generations, elderly labor supply, or pay-as-you-go pension schemes. Against this background, this paper constructs a four-period model consisting of youth, middle age, early old age, and late old age. By incorporating Romer-type capital externalities, it analytically derives the complex capital accumulation equations and theoretically demonstrates the existence, stability, and potential multiplicity of steady states.