Investment in a Monopoly with Bayesian Learning
AbstractWe 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.
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Bibliographic InfoPaper provided by University of Vienna, Department of Economics in its series Vienna Economics Papers with number 0603.
Date of creation: Mar 2006
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Web page: http://www.univie.ac.at/vwl
Other versions of this item:
- 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 and Pricing - - - 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 - - Intertemporal Choice and Growth - - - Intertemporal Firm Choice and Growth, Financing, Investment, and Capacity
- 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-04-08 (All new papers)
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