Investment in a Monopoly with Bayesian Learning
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 deÞning the distribution of the random demand. Observing prices reveals this information slowly. We Þrst 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 inÞnite-horizon program can be found either analytically or numerically for any kinds of distributions. We then use speciÞc distributions to study the monopolist?s behavior. SpeciÞcally, 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 Þndings 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.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- G. Berttocchi, 1995.
"Growth Under Uncertainty with Experimentation,"
95-12, Brown University, Department of Economics.
- Godfrey Keller & Sven Rady, 1998.
"Optimal Experimentation in a Changing Environment,"
Game Theory and Information
- Smith, L. & Sorensen, P., 1997.
"Informational Herding and Optimal Experientation,"
97-22, Massachusetts Institute of Technology (MIT), Department of Economics.
- Smith, L. & Sorensen, P., 1997. "Informational Herding and Optimal Experimentation," Economics Papers 139, Economics Group, Nuffield College, University of Oxford.
- Lones Smith & Peter Norman Sorensen, 2006. "Informational Herding and Optimal Experimentation," Cowles Foundation Discussion Papers 1552, Cowles Foundation for Research in Economics, Yale University.
- Lones Smith & Peter Norman Sørensen, 2005. "Informational Herding and Optimal Experimentation," Discussion Papers 05-13, University of Copenhagen. Department of Economics.
- Amparo Urbano Salvador & Larry Samuelson & Leonard J. Mirman, 1990.
Working Papers. Serie AD
1990-04, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
- Arthur Fishman & Neil Gandal, 1993.
"Experimentation and Learning with Network Effects,"
- Fishman, Arthur & Gandal, Neil, 1994. "Experimentation and learning with networks effects," Economics Letters, Elsevier, vol. 44(1-2), pages 103-108.
- Prescott, Edward C, 1972. "The Multi-Period Control Problem Under Uncertainty," Econometrica, Econometric Society, vol. 40(6), pages 1043-1058, November.
- 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.
- 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.
- Christos Koulovatianos & Leonard J. Mirman, 2004.
"The Effects of Market Structure on Industry Growth,"
2004 Meeting Papers
639, Society for Economic Dynamics.
- 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.
- Aghion, P. & Bolton, P. & Harris, C. & Jullien, B., 1990.
"Optimal Learning By Experimentation,"
DELTA Working Papers
90-10, DELTA (Ecole normale supérieure).
- Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
- 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.
- S. Baranzoni & P. Bianchi & L. Lambertini, 2000. "Multiproduct Firms, Product Differentiation, and Market Structure," Working Papers 368, Dipartimento Scienze Economiche, Universita' di Bologna.
- 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.
- Freixas, Xavier, 1981. "Optimal growth with experimentation," Journal of Economic Theory, Elsevier, vol. 24(2), pages 296-309, April.
- 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.
- 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.
- Tjalling C. Koopmans, 1963. "On the Concept of Optimal Economic Growth," Cowles Foundation Discussion Papers 163, Cowles Foundation for Research in Economics, Yale University.
- 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.
- 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.
- 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.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:vie:viennp:0603. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Paper Administrator)
If references are entirely missing, you can add them using this form.