Summary
In this paper we present new results on the local and global convergence property of solutions to an optimization model where the objective function is a discounted sum of stationary one-period utilities. The asymptotic local turnpike is given without differentiability assumptions but imposing some mild curvature restrictions on the utility function. This approach allows us to get easy estimates on the range of discount factors and the size of the neighborhood for which the asymptotic property occurs. The paper concludes by providing two global turnpike theorems. The first one is an asymptotic theorem derived from a result similar to Scheinkman's visit lemma. The second one turns out to be a restatement of McKenzie's neighborhood turnpike theorem.
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Araujo, A., Scheinkman, J.A.: Smoothness, comparative dynamics and the Turnpike property. Econometrica45, 601–620 (1977)
Benveniste, L.M., Scheinkman, J.A.: On the differentiability of the value function in dynamic models of economics. Econometrica47, 727–732 (1979)
Boldrin, M., Montrucchio, L.: On the indeterminacy of capital accumulation paths. J. Econ. Theory40, 26–39 (1986)
Cass, D.: Optimum growth in an aggregative model of capital accumulation: a Turnpike theorem. Econometrica34, 833–850 (1966)
Cass, D., Shell, K.: The structure and stability of competitive dynamical systems. J. Econ. Theory12, 31–70 (1976)
Deneckere, R., Pelikan, S.: Competitive chaos. J. Econ. Theory40, 13–25 (1986)
McKenzie, L.W.: A primal route to the Turnpike and Liapounov stability. J. Econ. Theory27, 194–209 (1982)
McKenzie, L.W.: Optimal economic growth and Turnpike theorems. In: Arrow, K.J., Intriligator, M. (eds.) Handbook of mathematical economics, vol.III. Amsterdam: North-Holland 1986
Montrucchio, L.: Dynamic complexity of optimal paths and discount factors for strongly concave problems. J. Optim. Theory Application (forthcoming)
Nishimura, K., Sorger, G. and Yano, M.: Ergodic chaos in optimal growth models with low discount rates. Econ. Theory4 (forthcoming)
Rockafellar, T. R.: Saddle points of Hamiltonian systems in convex Lagrange problems having a nonzero discount rate. J. Econ. Theory12, 71–113 (1976)
Scheinkman, J. A.: On optimal steady states ofn-sector growth models when utility is discounted. J. Econ. Theory12, 11–30 (1976)
Stokey, N. L., Lucas, R. E., Prescott, E.: Recursive methods in economic dynamics. Cambridge, MA: Harvard University Press 1989
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This research was partially supported by MURST, National Group on Nonlinear Dynamics in Economics and Social Sciences.
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Montrucchio, L. A new turnpike theorem for discounted programs. Econ Theory 5, 371–382 (1995). https://doi.org/10.1007/BF01212324
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DOI: https://doi.org/10.1007/BF01212324