Investment in a Monopoly with Bayesian Learning

Christos Koulovatianos, Leonard Mirman and Marc Santugini ()

Vienna Economics Papers from University of Vienna, Department of Economics

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.

JEL-codes: C61 D21 D42 D81 D84 D92 L12 Q20 (search for similar items in EconPapers)
Date: 2006-03
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Related works:
Working Paper: Investment in a Monopoly with Bayesian Learning (2011)
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Persistent link: https://EconPapers.repec.org/RePEc:vie:viennp:vie0603

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