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

  • James A. Mirrlees
Part of the International Economic Association Series book series (IEA)

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.

Keywords

Optimum Policy Optimal Path Deterministic Model Individual Decision Optimum Consumption 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

  1. [1]
    W. Brock and L. Mirman, ‘The Stochastic Modified Golden Rule in a One Sector Model of Economic Growth with Uncertain Technology’, mimeo, Rochester and Cornell, 1970.Google Scholar
  2. [2]
    F. H. Hahn, ‘Savings and Uncertainty’, Review of Economic Studies vol. XXXVII (1970), pp. 21–4.CrossRefGoogle Scholar
  3. [3]
    N. Hakansson, ‘Optimal Investment and Consumption Strategies Under Risk for a Class of Utility Functions’, Econometrica vol. XXXVIII (1970), pp. 587–607.CrossRefGoogle Scholar
  4. [4]
    D. Levhari and T. N. Srinivasan, ‘Optimal Savings under Uncertainty’, Review of Economic Studies vol. XXXVI (1969), pp. 153–63.CrossRefGoogle Scholar
  5. [5]
    E. Malinvaud, ‘First Order Certainty Equivalence’, Econometrica vol. XXXVII (1969), pp. 706–18.CrossRefGoogle Scholar
  6. [6]
    E. Phelps, ‘The Accumulation of Risky Capital: A Sequential Utility Analysis’, Econometrica vol. xxx (1962), pp. 729–43.CrossRefGoogle Scholar
  7. [7]
    M. Yaari, ‘Uncertain Lifetime, Life Insurance, and the Theory of the Consumer’, Review of Economic Studies vol. XXXII (1965), pp. 137–50.CrossRefGoogle Scholar
  8. [8]
    M. Yaari, ‘A Law of Large Numbers in the Theory of Consumer’s Choice Under Uncertainty’, Working Paper No. CP—330, Center for Research in Management Science, University of California, Berkeley, March 1971.Google Scholar

Copyright information

© International Economic Association 1974

Authors and Affiliations

  • James A. Mirrlees
    • 1
  1. 1.Nuffield CollegeOxfordUK

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