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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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    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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