Efficient Stationary Capital Accumulation Structures of a Biconvex Production Technology
A classical theorem by H. Poincaré asserts that the characteristic roots at a rest point of a continuous-time autonomous variational or Hamiltonian dynamical system come in opposite-signed pairs. This result confirms the catenary motion of efficient capital accumulation paths around a saddle-point turnpike in finite-horizon models of efficient economic growth. Poincaré’s theorem will be extended to the non-autonomous case of a time-dependent biconvex production technology which can be represented by a separable transformation frontier function. This extension may prove useful to integrate into optimum growth theory areas of economic analysis such as externalities and public goods.
KeywordsCapital Stock Jacobian Matrice Rest Point Aggregate Production Function Hamiltonian Dynamical System
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