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Management of a Capital Stock by Strotz's Naive Planner

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.

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Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number 2006-W01.

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Length: 25 pages
Date of creation: 30 Mar 2006
Date of revision:
Handle: RePEc:nuf:econwp:0601
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  1. Per Krusell & Anthony A Smith, Jr., 2001. "Consumption Savings Decisions with Quasi-Geometric Discounting," NajEcon Working Paper Reviews 625018000000000251,
  2. Harris, Christopher & Laibson, David, 2001. "Dynamic Choices of Hyperbolic Consumers," Econometrica, Econometric Society, vol. 69(4), pages 935-57, July.
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  4. Ted O' Donoghue and Matthew Rabin., 2000. "Choice and Procrastination," Economics Working Papers E00-281, University of California at Berkeley.
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  6. Asheim, G.B., 1991. "Individual and Collective Time Consistency," Papers 9169, Tilburg - Center for Economic Research.
  7. Christopher Harris & David Laibson, 2006. "Instantaneous Gratification," Levine's Bibliography 321307000000000635, UCLA Department of Economics.
  8. Ted O'Donoghue & Matthew Rabin, 1997. "Incentives for Procrastinators," Discussion Papers 1181, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. Ted O'Donoghue and Matthew Rabin ., 1997. "Doing It Now or Later," Economics Working Papers 97-253, University of California at Berkeley.
  10. H. Stuart Burness, 1976. "A Note on Consistent Naive Intertemporal Decision Making and an Application to the Case of Uncertain Lifetime," Review of Economic Studies, Oxford University Press, vol. 43(3), pages 547-549.
  11. Tjalling C. Koopmans, 1959. "Stationary Ordinal Utility and Impatience," Cowles Foundation Discussion Papers 81, Cowles Foundation for Research in Economics, Yale University.
  12. Paul A. Samuelson, 1937. "A Note on Measurement of Utility," Review of Economic Studies, Oxford University Press, vol. 4(2), pages 155-161.
  13. George Loewenstein & Drazen Prelec, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, Oxford University Press, vol. 107(2), pages 573-597.
  14. Shane Frederick & George Loewenstein & Ted O'Donoghue, 2002. "Time Discounting and Time Preference: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 40(2), pages 351-401, June.
  15. Bezalel Peleg & Menahem E. Yaari, 1973. "On the Existence of a Consistent Course of Action when Tastes are Changing," Review of Economic Studies, Oxford University Press, vol. 40(3), pages 391-401.
  16. R. A. Pollak, 1968. "Consistent Planning," Review of Economic Studies, Oxford University Press, vol. 35(2), pages 201-208.
  17. 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.
  18. Fishburn, Peter C & Rubinstein, Ariel, 1982. "Time Preference," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(3), pages 677-94, October.
  19. Robert J. Barro, 1999. "Ramsey Meets Laibson in the Neoclassical Growth Model," The Quarterly Journal of Economics, Oxford University Press, vol. 114(4), pages 1125-1152.
  20. Charles Blackorby & David Nissen & Daniel Primont & R. Robert Russell, 1973. "Consistent Intertemporal Decision Making," Review of Economic Studies, Oxford University Press, vol. 40(2), pages 239-248.
  21. Schelling, Thomas C, 1984. "Self-Command in Practice, in Policy, and in a Theory of Rational Choice," American Economic Review, American Economic Association, vol. 74(2), pages 1-11, May.
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