Abstract
We study a rational expectations partial equilibrium model of a market for a single storable commodity whose output each period is a function of previous period effort on production and a realization of a shock that affects equally all producers. I'he final demand is non-random and depends only on each period's price. Risk-neutral producers make production and storage decisions based on forecasts of future price distributions. Existence of equilibrium is proved, and for the case of i.i.d. shocks several comparative statics results are established as well as the existence and stability of a unique stationary distribution. and whose output at each period is a (multiplicative) function of previous period's planting and of the realization of a shock that affects equally all producers. The final demand for this good is non-random and depends only on this period's price. This describes approximately markets for agricultural products which are not traded internationally and where most of the price uncertainty stems from supply shocks. Risk-neutral producers make their decisions based on forecasts of future price distributions and of known cost functions of storage and production to maximize their discounted profits. In order to close the model an assumption on how such price forecasts are made is needed. We assume that agents make equilibrium forecasts, i.e. that their forecast is common and that when producers act, taking the forecasted prices as given, they make decisions that yield the forecasted prices as equilibrium prices. This is, of course, what has been sometimes called rational expectations. The assumption of equilibrium expectations and the presence of risk neutral pro- ducers will imply that the equilibrium variables may be obtained by considering a related market surplus maximization problem.1 This places strong restriction on the stochastic process of equilibrium prices. For the case where the basic shocks are assumed to be independently and identically distributed over time one may thus show that equilibrium prices are a function of a certain state variable-the total stocks kept from last period plus this period's output-and this allows us to derive properties of equilibrium solutions. Our main results concerning this case are: (a) Storage is a non-increasing function of price and expected production a non-decreasing one. (b) The elasticity of expected future prices with respect to today's prices is positive and less than one. (c) This elasticity is non-constant, being zero for high enough prices. (d) The price process follows a renewal process: If prices are low
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