Summary
In this paper we consider a class of time discrete intertemporal optimization models in one dimension. We present a technique to construct intertemporal optimization models with nonconcave objective functions, such that the optimal policy function coincides with any pre-specifiedC 2 function. Our result is a variant of the approach presented in a seminal paper by Boldrin and Montrucchio (1986). Whereas they solved the inverse problem for the reduced form models, we address the different question of how to construct both reduced and primitive form models. Using our technique one can guarantee required qualitative properties not only in reduced, but also in primitive form. The fact that our constructed model has a single valued and continuous optimal policy is very important as, in general, nonconcave problems yield set valued optimal policy correspondences which are typically hard to analyze. To illustrate our constructive approach we apply it to a simple nonconcave model.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Benhabib, J., Nishimura, K.: Competitive equilibrium cycles. J. Econ. Theory35, 284–306 (1985)
Boldrin, M., Montrucchio, L.: On the indeterminacy of capital accumulation paths. J. Econ. Theory40, 26–39 (1986)
Clark, C. W.: Mathematical bioeconomics — The optimal management of renewable resources. New York: Wiley 1976
Dechert, W. D., Nishimura, K.: A complete characterization of optimal growth paths in an aggregated model with a non-concave production function. J. Econ. Theory31, 332–354 (1983)
Deneckere, R., Pelikan, S.: Competitive Chaos. J. Econ. Theory40, 13–25 (1986)
Feichtinger, G., Hartl, R. F.: Optimale Kontrolle ökonomischer Prozesse: Anwendungen des Maximumprinzips in den Wirtschaftswissenschaften. Berlin: de Gruyter 1986
Hommes, C. H.: Chaotic dynamics in economic models. Some simple case studies. Groningen: Wolters-Noordhoff 1991
Li, T., Yorke, J.: Period three implies chaos. Am. Math. Month.82, 985–992 (1975)
Lorenz, H. W.: Nonlinear dynamical economics and chaotic motion. 2nd Edn., Berlin Heidelberg New York: Springer 1993
Majumdar, M., Mitra, T.: Intertemporal allocation with a non-convex technology: the aggregative framework. J. Econ. Theory27, 101–136 (1982)
Majumdar, M., Mitra, T.: Periodic and chaotic programs of optimal intertemporal allocation in an aggregative model with wealth effects. Econ. Theory4, 649–679 (1994)
Neumann, D., O'Brien, T., Hoag, J., Kim, K.: Policy functions for capital accumulation paths. J. Econ. Theory46, 205–214 (1988)
Sethi, S. P., Thompson, G. L.: Optimal control theory — applications to management science. Martinus Nijhoff l981
Sethi, S. P.: A survey of management science applications of the deterministic maximum principle. In: Bensoussan, A., Kleindorfer, P. R. Tapiero, Ch. S. (eds.) Applied optimal control. Studies in the management sciences, vol. 9. Amsterdam: North Holland 1978
Stepan, A., Hillinger, C.: The optimal life time of capital goods and pricing for replacement components and repair costs. Technovation15, 111–120 (1995)
Stokey, N. L., Lucas, R. E.: Recursive methods in economic dynamics. Cambridge: Harvard University Press (1989)
Author information
Authors and Affiliations
Additional information
We are grateful for the helpful comments of L. Montrucchio, K. Nishimura, T. Mitra and an anonymous referee. Financial support of the Austrian Science Foundation under contract No. P7783-PHY and No. J01003-SOZ is gratefully acknowledged. This paper was written while M. Kopel was visiting the Department of Economics, Cornell University.