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.
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