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Irreversible investment under weighted discounting: effects of decreasing impatience

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  • Pengyu Wei
  • Wei Wei

Abstract

This paper employs an intra-personal game-theoretic framework to investigate how decreasing impatience influences irreversible investment behaviors in a continuous-time setting. We consider a capacity expansion problem under weighted discount functions, a class of nonexponential functions that exhibit decreasing impatience, including the hyperbolic discount function as a special case. By deriving the Bellman system that characterizes the equilibrium, we establish the framework for analyzing investment behaviors of agents subject to decreasing impatience. From an economic perspective, we demonstrates that decreasing impatience prompts early investment. From a technical standpoint, we warn that decreasing impatience can lead to the failure of the smooth pasting principle.

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  • Pengyu Wei & Wei Wei, 2024. "Irreversible investment under weighted discounting: effects of decreasing impatience," Papers 2409.01478, arXiv.org.
    • Handle: RePEc:arx:papers:2409.01478
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    References listed on IDEAS

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    1. Grenadier, Steven R. & Wang, Neng, 2007. "Investment under uncertainty and time-inconsistent preferences," Journal of Financial Economics, Elsevier, vol. 84(1), pages 2-39, April.
    2. Karp, Larry, 2007. "Non-constant discounting in continuous time," Journal of Economic Theory, Elsevier, vol. 132(1), pages 557-568, January.
    3. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    4. Charles Harvey, 1995. "Proportional Discounting of Future Costs and Benefits," Mathematics of Operations Research, INFORMS, vol. 20(2), pages 381-399, May.
    5. R. H. Strotz, 1955. "Myopia and Inconsistency in Dynamic Utility Maximization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 23(3), pages 165-180.
    6. Ted O'Donoghue & Matthew Rabin, 2001. "Choice and Procrastination," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 116(1), pages 121-160.
    7. Erzo G. J. Luttmer & Thomas Mariotti, 2003. "Subjective Discounting in an Exchange Economy," Journal of Political Economy, University of Chicago Press, vol. 111(5), pages 959-989, October.
    8. Erhan Bayraktar & Jingjie Zhang & Zhou Zhou, 2021. "Equilibrium concepts for time‐inconsistent stopping problems in continuous time," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 508-530, January.
    9. repec:dau:papers:123456789/11473 is not listed on IDEAS
    10. Ebert, Sebastian & Wei, Wei & Zhou, Xun Yu, 2020. "Weighted discounting—On group diversity, time-inconsistency, and consequences for investment," Journal of Economic Theory, Elsevier, vol. 189(C).
    11. George Loewenstein & Drazen Prelec, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(2), pages 573-597.
    12. Christopher Harris & David Laibson, 2013. "Instantaneous Gratification," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 128(1), pages 205-248.
    13. Jane E. J. Ebert & Drazen Prelec, 2007. "The Fragility of Time: Time-Insensitivity and Valuation of the Near and Far Future," Management Science, INFORMS, vol. 53(9), pages 1423-1438, September.
    14. Dumas, Bernard, 1991. "Super contact and related optimality conditions," Journal of Economic Dynamics and Control, Elsevier, vol. 15(4), pages 675-685, October.
    15. Tomas Björk & Mariana Khapko & Agatha Murgoci, 2017. "On time-inconsistent stochastic control in continuous time," Finance and Stochastics, Springer, vol. 21(2), pages 331-360, April.
    16. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 443-478.
    17. E. S. Phelps & R. A. Pollak, 1968. "On Second-Best National Saving and Game-Equilibrium Growth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(2), pages 185-199.
    18. Steven R. Grenadier, 2002. "Option Exercise Games: An Application to the Equilibrium Investment Strategies of Firms," The Review of Financial Studies, Society for Financial Studies, vol. 15(3), pages 691-721.
    19. Abel, Andrew B, 1983. "Optimal Investment under Uncertainty," American Economic Review, American Economic Association, vol. 73(1), pages 228-233, March.
    20. Bleichrodt, Han & Rohde, Kirsten I.M. & Wakker, Peter P., 2009. "Non-hyperbolic time inconsistency," Games and Economic Behavior, Elsevier, vol. 66(1), pages 27-38, May.
    21. Yu-Jui Huang & Zhou Zhou, 2021. "Strong and Weak Equilibria for Time-Inconsistent Stochastic Control in Continuous Time," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 428-451, May.
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