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Management of a Capital Stock by Strotz's Naive Planner

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Abstract

A generalized version of the capital management problem posed in a classic paper by R. H. Strotz is analyzed for the case of the "naive" planner who fails to anticipate any impending change in his own preferences. By imposing progressively stronger restrictions on the primitives of the problem --- namely, the planner's discounting function, his utility index function, and the investment technology --- the path of the capital stock is characterized first implicitly as the solution to a differential equation and then explicitly via formulae that may or may not be expressible in closed form. Inasmuch as this procedure turns out to leave the discounting function essentially unrestricted, the theory can accommodate, in particular, decision makers who discount time according to the type of hyperbolic curve said to be suggested by psychological studies. Strategies for numerical computation of capital paths are discussed and are demonstrated in sample planning problems.

Suggested Citation

  • Christopher J. Tyson, 2006. "Management of a Capital Stock by Strotz's Naive Planner," Economics Papers 2006-W01, Economics Group, Nuffield College, University of Oxford.
    • Handle: RePEc:nuf:econwp:0601
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    1. Per Krusell & Anthony A. Smith, Jr., 2003. "Consumption--Savings Decisions with Quasi--Geometric Discounting," Econometrica, Econometric Society, vol. 71(1), pages 365-375, January.
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    1. Tyson, Christopher J., 2008. "Management of a capital stock by Strotz's naive planner," Journal of Economic Dynamics and Control, Elsevier, vol. 32(7), pages 2214-2239, July.
    2. Borissov, Kirill, 2013. "Growth and distribution in a model with endogenous time preferences and borrowing constraints," Mathematical Social Sciences, Elsevier, vol. 66(2), pages 117-128.
    3. Tyson, Christopher J., 2008. "Management of a capital stock by Strotz's naive planner," Journal of Economic Dynamics and Control, Elsevier, vol. 32(7), pages 2214-2239, July.

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    More about this item

    Keywords

    consumption; computation; hyperbolic discounting; time preference.;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

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