Investment in a Monopoly With Bayesian Learning

34 Pages Posted: 18 Nov 2004 Last revised: 15 May 2011

See all articles by Christos Koulovatianos

Christos Koulovatianos

Department of Finance, University of Luxembourg

Leonard J. Mirman

University of Virginia - Department of Economics

Marc Santugini

University of Virginia - Department of Economics

Date Written: April 18, 2011

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 a¤ect 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.

Keywords: Dynamic programming, Investment, Learning, Monopoly.

JEL Classification: C61, D21, D42, D80, L12.

Suggested Citation

Koulovatianos, Christos and Mirman, Leonard J. and Santugini, Marc, Investment in a Monopoly With Bayesian Learning (April 18, 2011). Available at SSRN: https://ssrn.com/abstract=619387 or http://dx.doi.org/10.2139/ssrn.619387

Christos Koulovatianos

Department of Finance, University of Luxembourg ( email )

4 Rue Albert Borschette
Luxembourg, L-1246
Luxembourg

Leonard J. Mirman

University of Virginia - Department of Economics ( email )

1818 Winston Rd
Charlottesville, VA
United States

Marc Santugini (Contact Author)

University of Virginia - Department of Economics ( email )

P.O. Box 400182
Charlottesville, VA 22904-4182
United States

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