Contribution to optimal growth theory, endogenous growth theory, and nonlinear dynamics

What is it about?

The present paper constructs a family of three-sector models of optimal endogenous growth, and conducts exactbifurcation analysis. In so doing, original six-dimensional equilibrium dynamics is decomposed into fivedimensionalstationary autonomous dynamics and one-dimensional endogenously growing component. It is shown that the stationary dynamics thus decomposed undergoes supercritical Hopf bifurcation. It is inferred from the convex structure of our model that the dimension of a stable manifold of each closed orbit thus bifurcated in this five-dimensional dynamics should be two.

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Why is it important?

This study presents the first example of a multisector optimal endogenous growth model that generates a limit cycle around its balanced growth path.

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