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Investment in a Monopoly with Bayesian Learning

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Abstract

We study how learning affects an uninformed monopolist's supply and investment decisions under multiplicative uncertainty in demand. The monopolist is uninformed because it does not know one of the parameters defining the distribution of the random demand. Observing prices reveals this information slowly. We first show how to incorporate Bayesian learning into dynamic programming by focusing on sufficient statistics and conjugate families of distributions. We show their necessity in dynamic programming to be able to solve dynamic programs either analytically or numerically. This is important since it is not true that a solution to the infinite-horizon program can be found either analytically or numerically for any kinds of distributions. We then use specific distributions to study the monopolist's behavior. Specifically, we rely on the fact that the family of normal distributions with an unknown mean is a conjugate family for samples from a normal distribution to obtain closed-form solutions for the optimal supply and investment decisions. This enables us to study the effect of learning on supply and investment decisions, as well as the steady state level of capital. Our findings are as follows. Learning affects the monopolist's behavior. The higher the expected mean of the demand shock given its beliefs, the higher the supply and the lower the investment. Although learning does not affect the steady state level of capital since the uninformed monopolist becomes informed in the limit, it reduces the speed of convergence to the steady state.

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  • Christos Koulovatianos & Leonard J. Mirman & Marc Santugini, 2011. "Investment in a Monopoly with Bayesian Learning," Cahiers de recherche 11-05, HEC Montréal, Institut d'économie appliquée.
  • Handle: RePEc:iea:carech:1105
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    1. Godfrey Keller & Sven Rady, 1999. "Optimal Experimentation in a Changing Environment," Review of Economic Studies, Oxford University Press, vol. 66(3), pages 475-507.
    2. Philippe Aghion & Patrick Bolton & Christopher Harris & Bruno Jullien, 1991. "Optimal Learning by Experimentation," Review of Economic Studies, Oxford University Press, vol. 58(4), pages 621-654.
    3. Christos Koulovatianos & Leonard J. Mirman, 2003. "The Effects of Market Structure on Industry Growth," University of Cyprus Working Papers in Economics 7-2003, University of Cyprus Department of Economics.
    4. El-Gamal, Mahmoud A. & Sundaram, Rangarajan K., 1993. "Bayesian economists ... Bayesian agents : An alternative approach to optimal learning," Journal of Economic Dynamics and Control, Elsevier, vol. 17(3), pages 355-383, May.
    5. Sanford J. Grossman & Richard E. Kihlstrom & Leonard J. Mirman, 1977. "A Bayesian Approach to the Production of Information and Learning By Doing," Review of Economic Studies, Oxford University Press, vol. 44(3), pages 533-547.
    6. Tjalling C. Koopmans, 1963. "On the Concept of Optimal Economic Growth," Cowles Foundation Discussion Papers 163, Cowles Foundation for Research in Economics, Yale University.
    7. Trefler, Daniel, 1993. "The Ignorant Monopolist: Optimal Learning with Endogenous Information," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(3), pages 565-581, August.
    8. Michel Demers, 1991. "Investment under Uncertainty, Irreversibility and the Arrival of Information Over Time," Review of Economic Studies, Oxford University Press, vol. 58(2), pages 333-350.
    9. Fishman, Arthur & Gandal, Neil, 1994. "Experimentation and learning with networks effects," Economics Letters, Elsevier, vol. 44(1-2), pages 103-108.
    10. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
    11. Mirman, Leonard J & Samuelson, Larry & Urbano, Amparo, 1993. "Monopoly Experimentation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(3), pages 549-563, August.
    12. Prescott, Edward C, 1972. "The Multi-Period Control Problem Under Uncertainty," Econometrica, Econometric Society, vol. 40(6), pages 1043-1058, November.
    13. McLennan, Andrew, 1984. "Price dispersion and incomplete learning in the long run," Journal of Economic Dynamics and Control, Elsevier, vol. 7(3), pages 331-347, September.
    14. Manjira Datta & Leonard J. Mirman & Edward E. Schlee, 2002. "Optimal Experimentation in Signal Dependent Decision Problems," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(2), pages 577-608, May.
    15. Smith, L. & Sorensen, P., 1997. "Informational Herding and Optimal Experimentation," Economics Papers 139, Economics Group, Nuffield College, University of Oxford.
    16. Huntley Schaller & Fanny Demers & Michel Demers, 1993. "Investments Under Uncertainty and Irreversibility," Carleton Economic Papers 93-10, Carleton University, Department of Economics, revised Sep 1990.
    17. Easley, David & Kiefer, Nicholas M, 1989. "Optimal Learning with Endogenous Data," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(4), pages 963-978, November.
    18. Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, vol. 4(3), pages 479-513, June.
    19. S. Baranzoni & P. Bianchi & L. Lambertini, 2000. "Multiproduct Firms, Product Differentiation, and Market Structure," Working Papers 368, Dipartimento Scienze Economiche, Universita' di Bologna.
    20. Freixas, Xavier, 1981. "Optimal growth with experimentation," Journal of Economic Theory, Elsevier, vol. 24(2), pages 296-309, April.
    21. Creane, Anthony, 1994. "Experimentation with Heteroskedastic Noise," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(2), pages 275-286, March.
    22. Balvers, Ronald J & Cosimano, Thomas F, 1990. "Actively Learning about Demand and the Dynamics of Price Adjustment," Economic Journal, Royal Economic Society, vol. 100(402), pages 882-898, September.
    23. Bertocchi, Graziella & Spagat, Michael, 1998. "Growth under uncertainty with experimentation," Journal of Economic Dynamics and Control, Elsevier, vol. 23(2), pages 209-231, September.
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    More about this item

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D42 - Microeconomics - - Market Structure, Pricing, and Design - - - Monopoly
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • D92 - Microeconomics - - Micro-Based Behavioral Economics - - - Intertemporal Firm Choice, Investment, Capacity, and Financing
    • L12 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Monopoly; Monopolization Strategies
    • Q20 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - General

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