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Optimum Accumulation Under Uncertainty: the Case of Stationary Returns to Investment

In: Allocation under Uncertainty: Equilibrium and Optimality

Author

Listed:
  • James A. Mirrlees

    (Nuffield College)

Abstract

In the theory of optimum growth it has been found that models with discrete time are easier to treat rigorously than models with continuous time. But continuous-time models often have the advantage of providing simpler results. I shall illustrate this tension in the present paper by discussing the model for optimum growth under uncertainty that has received most attention in the literature (Phelps [6], Levhari and Srinivasan [4], Hahn [2], Hakansson [3], Brock and Mirman [1]). An existence theorem will be proved for the discrete-time case. By a heuristic argument, I obtain an equation for the optimum under continuous-time which makes possible results about the effects of uncertainty on the optimum policy more general than are available in discrete time. These latter results are somewhat surprising. By way of prelude I outline the reasons for research into optimum growth under uncertainty, and offer a classification of models. The model discussed in this paper is less appealing than some others; but it seems to be the easiest one.

Suggested Citation

  • James A. Mirrlees, 1974. "Optimum Accumulation Under Uncertainty: the Case of Stationary Returns to Investment," International Economic Association Series, in: Jacques H. Drèze (ed.), Allocation under Uncertainty: Equilibrium and Optimality, chapter 3, pages 36-50, Palgrave Macmillan.
    • Handle: RePEc:pal:intecp:978-1-349-01989-2_3
    DOI: 10.1007/978-1-349-01989-2_3
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    Cited by:

    1. Posch, Olaf, 2009. "Structural estimation of jump-diffusion processes in macroeconomics," Journal of Econometrics, Elsevier, vol. 153(2), pages 196-210, December.
    2. Lars J. Olson & Santanu Roy, 2006. "Theory of Stochastic Optimal Economic Growth," Springer Books, in: Rose-Anne Dana & Cuong Le Van & Tapan Mitra & Kazuo Nishimura (ed.), Handbook on Optimal Growth 1, chapter 11, pages 297-335, Springer.
    3. Mauro Baranzini, 1977. "The Effects of Interest Uncertainty in a Life-Cycle Model," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 113(IV), pages 407-423, December.

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