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Optimal price dynamics and speculation with a storable good. (English) Zbl 0674.90012

The paper studies a game theoretic problem of determining optimal price and storage strategies for a firm selling a storable good, facing an inflationary environment such that its costs and all aggregate prices increase at a constant rate per period. The firm incurs a fixed cost of changing its price and plans for an infinite horizon, seeking to maximize, in each period, the expected present value of profits. The other player of the game is a continuum of buyers maximizing in each period their expected discounted utilities. A buyer may either be a speculator (who can store the good) or a nonspeculator who faces a storage cost which renders storage unprofitable. The timing of decisions corresponds to a “repeated leader-follower” game such that the firm makes its pricing decision first (in each period). The author looks for a Markov perfect equilibrium and identifies the solution by a dynamic programming approach. In equilibrium there is, in general, a phase of mixed strategies where the seller attempts to deter speculation by introducing uncertainty into its pricing policy while speculators store in increasing numbers (with a possible “final run” on the good). Also some macroeconomic implications are dealt with and the results of the paper seem to provide a foundation for the often encountered claim that inflation causes price uncertainty.
Reviewer: S.Jørgensen

MSC:

91B62 Economic growth models
91A40 Other game-theoretic models
90C90 Applications of mathematical programming
90C39 Dynamic programming
91B24 Microeconomic theory (price theory and economic markets)
93A13 Hierarchical systems
91B38 Production theory, theory of the firm
91A15 Stochastic games, stochastic differential games
91A20 Multistage and repeated games
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