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Optimal capital accumulation under price uncertainty and costly reversibility

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  • Alvarez, Luis H.R.

Abstract

We consider the optimal capital accumulation policy of a competitive firm operating in the presence of decreasing returns to scale, price uncertainty, and costly reversibility of investment. We characterize the optimal accumulation policy and derive the value of the firm by focusing on the marginal investment decision and solving the associated optimal timing problem characterizing the option value of the associated opportunity to either disinvest or acquire a marginal unit of capacity. We also characterize the required exercise premia associated with the optimal policies and demonstrate that hysteresis prevails within this class of accumulation problems as well.

Suggested Citation

  • Alvarez, Luis H.R., 2011. "Optimal capital accumulation under price uncertainty and costly reversibility," Journal of Economic Dynamics and Control, Elsevier, vol. 35(10), pages 1769-1788, October.
    • Handle: RePEc:eee:dyncon:v:35:y:2011:i:10:p:1769-1788
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    References listed on IDEAS

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    1. Luis Alvarez & Jukka Virtanen, 2006. "A class of solvable stochastic dividend optimization problems: on the general impact of flexibility on valuation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(2), pages 373-398, June.
    2. Dixit, Avinash, 1995. "Irreversible investment with uncertainty and scale economies," Journal of Economic Dynamics and Control, Elsevier, vol. 19(1-2), pages 327-350.
    3. Shepp, Larry & Shiryaev, Albert, 1996. "Hiring and firing optimally in a large corporation," Journal of Economic Dynamics and Control, Elsevier, vol. 20(9-10), pages 1523-1539.
    4. Andrew B. Abel & Avinash K. Dixit & Janice B. Eberly & Robert S. Pindyck, "undated". "Options, the Value of Capital, and Investment," Rodney L. White Center for Financial Research Working Papers 15-95, Wharton School Rodney L. White Center for Financial Research.
    5. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    6. Caballero, Ricardo J., 1999. "Aggregate investment," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 12, pages 813-862, Elsevier.
    7. Wong, Kit Pong, 2007. "The effect of uncertainty on investment timing in a real options model," Journal of Economic Dynamics and Control, Elsevier, vol. 31(7), pages 2152-2167, July.
    8. repec:bla:econom:v:41:y:1974:i:163:p:241-55 is not listed on IDEAS
    9. Anders ûksendal, 2000. "Irreversible investment problems," Finance and Stochastics, Springer, vol. 4(2), pages 223-250.
    10. Andrew B. Abel & Janice C. Eberly, 1996. "Optimal Investment with Costly Reversibility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(4), pages 581-593.
    11. Brennan, Michael J & Schwartz, Eduardo S, 1985. "Evaluating Natural Resource Investments," The Journal of Business, University of Chicago Press, vol. 58(2), pages 135-157, April.
    12. Abel, Andrew B. & Eberly, Janice C., 1999. "The effects of irreversibility and uncertainty on capital accumulation," Journal of Monetary Economics, Elsevier, vol. 44(3), pages 339-377, December.
    13. Shackleton, Mark B. & Sodal, Sigbjorn, 2005. "Smooth pasting as rate of return equalization," Economics Letters, Elsevier, vol. 89(2), pages 200-206, November.
    14. Pindyck, Robert S, 1988. "Irreversible Investment, Capacity Choice, and the Value of the Firm," American Economic Review, American Economic Association, vol. 78(5), pages 969-985, December.
    15. Ben S. Bernanke, 1983. "Irreversibility, Uncertainty, and Cyclical Investment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 98(1), pages 85-106.
    16. Caballero, R.J., 1996. "Fixed Costs: The Demise of Marginal q," Working papers 96-14, Massachusetts Institute of Technology (MIT), Department of Economics.
    17. Shackleton, Mark B. & Wojakowski, Rafal, 2007. "Finite maturity caps and floors on continuous flows," Journal of Economic Dynamics and Control, Elsevier, vol. 31(12), pages 3843-3859, December.
    18. Sarkar, Sudipto, 2000. "On the investment-uncertainty relationship in a real options model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(2), pages 219-225, February.
    19. Shackleton, Mark B. & Sødal, Sigbjørn, 2010. "Harvesting and recovery decisions under uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 34(12), pages 2533-2546, December.
    20. Samuel Bentolila & Giuseppe Bertola, 1990. "Firing Costs and Labour Demand: How Bad is Eurosclerosis?," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(3), pages 381-402.
    21. Andrew B. Abel & Avinash K. Dixit & Janice C. Eberly & Robert S. Pindyck, 1996. "Options, the Value of Capital, and Investment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 111(3), pages 753-777.
    22. Dias, José Carlos & Shackleton, Mark B., 2011. "Hysteresis effects under CIR interest rates," European Journal of Operational Research, Elsevier, vol. 211(3), pages 594-600, June.
    23. Pindyck, Robert S, 1991. "Irreversibility, Uncertainty, and Investment," Journal of Economic Literature, American Economic Association, vol. 29(3), pages 1110-1148, September.
    24. Stephen Nickell, 1974. "On the Role of Expectations in the Pure Theory of Investment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 41(1), pages 1-19.
    25. Dixit, Avinash K, 1989. "Entry and Exit Decisions under Uncertainty," Journal of Political Economy, University of Chicago Press, vol. 97(3), pages 620-638, June.
    26. Avinash Dixit, 1992. "Investment and Hysteresis," Journal of Economic Perspectives, American Economic Association, vol. 6(1), pages 107-132, Winter.
    27. Bertola, Giuseppe, 1998. "Irreversible investment," Research in Economics, Elsevier, vol. 52(1), pages 3-37, March.
    28. Baldursson, Fridrik M., 1998. "Irreversible investment under uncertainty in oligopoly," Journal of Economic Dynamics and Control, Elsevier, vol. 22(4), pages 627-644, April.
    29. Abel, Andrew B., 1990. "Consumption and investment," Handbook of Monetary Economics, in: B. M. Friedman & F. H. Hahn (ed.), Handbook of Monetary Economics, edition 1, volume 2, chapter 14, pages 725-778, Elsevier.
    30. Guiseppe Bertola & Ricardo J. Caballero, 1994. "Irreversibility and Aggregate Investment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(2), pages 223-246.
    31. John V. Leahy, 1993. "Investment in Competitive Equilibrium: The Optimality of Myopic Behavior," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(4), pages 1105-1133.
    32. Hayashi, Fumio, 1982. "Tobin's Marginal q and Average q: A Neoclassical Interpretation," Econometrica, Econometric Society, vol. 50(1), pages 213-224, January.
    33. Baldwin, Carliss Y, 1982. "Optimal Sequential Investment When Capital Is Not Readily Reversible," Journal of Finance, American Finance Association, vol. 37(3), pages 763-782, June.
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    Cited by:

    1. Peter Bank & Helena Kauppila, 2014. "Convex duality for stochastic singular control problems," Papers 1407.7717, arXiv.org.
    2. Hanno Dihle, 2015. "Real Options in a Ramsey style Growth Model," Discussion Paper Series 32, Department of International Economic Policy, University of Freiburg, revised Dec 2015.
    3. Mike Ludkovski, 2022. "Regression Monte Carlo for Impulse Control," Papers 2203.06539, arXiv.org.
    4. Salvatore Federico & Mauro Rosestolato & Elisa Tacconi, 2018. "Irreversible investment with fixed adjustment costs: a stochastic impulse control approach," Papers 1801.04491, arXiv.org, revised Feb 2019.
    5. Xin Guo & Pascal Tomecek, 2008. "Solving Singular Control from Optimal Switching," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 15(1), pages 25-45, March.
    6. Pekka Matomäki, 2012. "On solvability of a two-sided singular control problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(3), pages 239-271, December.
    7. Andrianos Tsekrekos, 2013. "Irreversible exit decisions under mean-reverting uncertainty," Journal of Economics, Springer, vol. 110(1), pages 5-23, September.
    8. Shibata, Takashi & Wong, Kit Pong, 2019. "Investment under uncertainty with variable costly reversibility," International Review of Economics & Finance, Elsevier, vol. 59(C), pages 14-28.
    9. Alain Bensoussan & Benoît Chevalier-Roignant, 2019. "Sequential Capacity Expansion Options," Operations Research, INFORMS, vol. 67(1), pages 33-57, January.

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