Optimal Investment Policy
We wish to discuss here a small-scale problem which is condiderably less abstract than most of the contributions so far in this conference. On the other hand, being more concrete, it may serve to illustrate some of the concepts introduced by earlier speakers, and some of the possible applications of control theory in particular problems in economics. The example has served two purposes for us: in the first place it provided a little experience in approaches to computing an optimal path for a problem with an essential state-space constraint and singular arcs; in the second place, it served as a starting point in a more extensive program of research. Perhaps it is not out of place here to sketch a rough outline of the general direction of this work.
KeywordsCapital Stock Optimal Path Employment Rate Physical Capital Terminal Condition
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- A.E. Bryson and Y.C HO, Optimal Programming, Estimation, and Control. New York: Blaisdell (to be published).Google Scholar
- S.E. Dreyfus, Dynamic Programming and the Calculus of Variations. New York: Academic Press, 1905.Google Scholar
- H.J. Kelley, R. Kopp, and G. Moyer, “Singular extremals in optimal control”, in Optimization Techniques, vol. 2, G. Leitman, Ed. New York: Academic Press (to be published).Google Scholar
- T.C. Koopmans, “On the concept of optimal economoc growth”, Cowles Foundation. Yale University, Discussion Paper 163, 1963.Google Scholar
- P.A. Samuelson, “A catenary theorem involving consumption and the Golden Rule”, Am. Econ. Rev, pp.486-496, June 1965.Google Scholar
- K. Shell, “Optimal programs of capital accumulation for an economy in which there is exogenous technical change”, Mass. Inst. Tech., Cambridge, Mass., Discussion Paper, undated.Google Scholar
- K.S. Tait, “A generalized Legendre condition for singular optimal control problems”, Ph.D dissertation, Harvard University, Cambridge, Mass. 1965 (unpubished).Google Scholar
- Dobell, A.R. and Ho, Y.C.: “A Control Problem in Economic Theory”, in Mathematical Systems Theory and Economics, Proceedings of a Conference at Varenna, Italy, (June 1967).Google Scholar