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On Irreversible Investment

  • Xia Su
  • Frank Riedel

    ()

This paper develops a general theory of irreversible investment of a single firm that chooses a dynamic capacity expansion plan in an uncertain environment. The model is set up free of any distributional or any parametric assumptions and hence encompasses all the existing models. As the first contribution, a general existence and uniqueness result is provided for the optimal investment policy. Based upon an alternative approach developed previously to dynamic programming problems, we derive the optimal base capacity policy such that the firm always keeps the capacity at or above the base capacity. The critical base capacity is explicitly constructed and characterized via a stochastic backward equation. This method allows qualitative insights into the nature of the optimal investment under irreversibility. It is demonstrated that the marginal profit is indeed equal to the user cost of capital in free intervals where investment occurs in an absolutely continuous way at strictly positive rates. However, the equality is maintained only in expectation on average in blocked intervals where no investment occurs. Whenever the uncertainty is generated by a diffusion, the investment is singular with respect to Lebesgue measure. In contrast to the deterministic and Brownian motion case where lump sum investment takes place only at time zero, the firm responses in general more frequently in jumps to shocks. Nevertheless, lump sum investments are shown to be possible only at information surprises which is defined as unpredictable stopping time or unanticipated information jump even at the predictable time. Furthermore, general monotone comparative statics results are derived for the relevant ingredients of the model. Finally, explicit solutions are derived for infinite time horizon, a separable operating profit function of Cobb--Douglas type and an exponential Levy process modelled economic shock.

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Paper provided by University of Bonn, Germany in its series Bonn Econ Discussion Papers with number bgse13_2006.

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Length: 45
Date of creation: Jun 2006
Date of revision:
Handle: RePEc:bon:bonedp:bgse13_2006
Contact details of provider: Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
Fax: +49 228 73 6884
Web page: http://www.bgse.uni-bonn.de

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  4. Svetlana Boyarchenko & Sergei Levendorskii, 2005. "General option exercise rules, with applications to embedded options and monopolistic expansion," Finance 0511001, EconWPA.
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  9. Andrew B. Abel & Janice C. Eberly, 1995. "The Effects of Irreversibility and Uncertainty on Capital Accumulation," NBER Working Papers 5363, National Bureau of Economic Research, Inc.
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  12. Abel, Andrew B & Eberly, Janice C, 1996. "Optimal Investment with Costly Reversibility," Review of Economic Studies, Wiley Blackwell, vol. 63(4), pages 581-93, October.
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  14. Avinash Dixit, 1992. "Investment and Hysteresis," Journal of Economic Perspectives, American Economic Association, vol. 6(1), pages 107-132, Winter.
  15. Bertola, Giuseppe, 1998. "Irreversible investment," Research in Economics, Elsevier, vol. 52(1), pages 3-37, March.
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  17. McDonald, Robert & Siegel, Daniel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, MIT Press, vol. 101(4), pages 707-27, November.
  18. Peter Bank & Frank Riedel, 1999. "Optimal Consumption Choice under Uncertainty with Intertemporal Substitution," GE, Growth, Math methods 9908002, EconWPA.
  19. Hindy, Ayman & Huang, Chi-fu & Kreps, David, 1992. "On intertemporal preferences in continuous time : The case of certainty," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 401-440.
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