This paper examines the effects of demand and cost uncertainty on a firm's investment, output, and pricing decisions. But unlike most earlier studies in which demand and cost are simply not known at the time an output (or pricing) decision is made, here I consider uncertainties over future demand and costs. It will be seen that the effects of such uncertainties depend critically on the characteristics of the firm's adjustment costs. I treat demand uncertainty in a dynamic context by letting the market-demand function shift randomly but continuously through time according to a stochastic process. This means that today's demand is known exactly, but future demand may be larger or smaller, and has a variance that increases with the time horizon. Likewise, uncertainty over factor costs is characterized by treating those variables as stochastic processes. I combine this characterization of uncertainty with a dynamic model of the firm in which some factor inputs can be adjusted freely in response to stochastic demand changes, but other factors are quasi fixed in that adjustment costs are incurred when they are changed. In this model the firm's price and output are random processes, but we can examine the firm's behavior in expected value terms. Of interest is whether the presence of uncertainty should cause competitive or monopolistic firms to invest and produce more or less than they would otherwise, how the effects of uncertainty are influenced by the presence of risk aversion, and how the use of inventories can alter the impact of uncertainty on capacity and sales. Of course these questions have been addressed by others in the past. Among the earliest studies of demand uncertainty are those of Edwin Mills (1959, 1962) and Samuel Karlin and Charles Carr (1962). Mills examined a single period monopolistic firm that sets both output and price, and showed that additive demand uncertainty (i.e., the demand function is of the form q = q( p) + u where u is a random variable) leads to a lower price if marginal cost is constant (so that the firm reduces the expected loss from discarding unsold production). Karlin and Carr confirmed, for both the static case and the multiperiod case with inventory carryover, that additive uncertainty tends to reduce the price and increase the output of a risk-neutral firm, while multiplicative uncertainty does the opposite. Other papers have been concerned with the way in which the error term enters the demand function (additively, multiplicatively, or nonlinearly), the implications of choosing price ex ante instead of output, the implications of risk aversion, and the use of inventories. For example, Agnar Sandmo (1971) and David Baron (1970) showed that a risk-averse competitive firm will produce less when the price is a random variable or subject to an additive error term, but a riskneutral firm will not alter its production.' Hayne Leland (1972) extended these results to a monopolistic firm whose demand can depend in a general way on a random error term (for example, q = q( p, u)), and showed that uncertainty reduces the production of a

The cartelization of world commodity markets is not a new phenomenon. In a historical survey of the experience of some international commodity cartels, Paul L. Eckbo shows that at one time or another there has been an attempt to cartelize the market for most of the major internationally traded commodities. The large majority of these attempts at cartelization, however, were failures-the cartel either dissolved after a short period of time, or in some cases the cartel remained in force officially, but had little or no real impact on price and member revenues. Of the fifty-one formal cartel organizations documented by Eckbo, only nineteen could be considered successful in the sense of being able to maintain a price significantly higher than what it would have been in the absence of agreements. But even the successful cartels were limited in their durability; the average lifetime of the formal agreements was about five years, and only five of the nineteen cartels lasted ten years or longer. What is new is the growing concern that the prospects for successful cartelization have suddenly become greater, and that in the future, world commodity markets are likely to be increasingly dominated by cartels. Much of this concern, of course, has been the result of the Organization of Petroleum Exporting Countries' (OPEC) spectacular success in quadrupling world oil prices, and the International Bauxite Association's (IBA) success in tripling the price of bauxite. Warranted or not, this concern now casts a shadow over predictions, policy prescriptions, and proposals for the international management of commodity markets. Buffer stocks and other instruments for price stabilization, for example, become the vehicles for cartelization and the establishment and maintenance of the monopoly price. And for some, cartelization, or more specifically, an implicit or explicit transfer of monopoly and monopsony power from developed to developing countries, is an essential and justifiable component of the New International Economic Order (NIEO). ' Given the historical success record of international cartels, is there any reason to expect new attempts at cartelization to succeed where similar attempts in the past have failed? Has the structure of world commodity markets-or the environment surrounding them-changed in such a way as to better facilitate the formation and success of cartels, so that over the next decade we are likely to witness a proliferation of international cartels that will succeed in raising the prices of a large number of key commodities? There are no simple answers to these questions. While the interest in cartelization on the part of some LDCs may indeed be greater, there appears to be no clear change in the structure of commodity markets that would facilitate their cartelization. It is difficult to agree with C. Fred Bergsten's assertion, for example, that the environment has shifted to one in which supplies of raw material commodities are shrinking as demand keeps growing, thereby encouraging cartelization. In the past some cartels succeeded while others failed for reasons specific to each market and to each cartel configuration. As a more recent example, IBA succeeded while CIPEC, the copper cartel, did not-and

Demand and reserve uncertainty are included in a simple model of an exhaustible resource market by allowing the demand function and the reserve level to fluctuate via continuous-time stochastic processes. Thus, producers always know current demand and reserves but do not know what demand and reserves will be in the future. I show that demand uncertainty has no effect on the expected dynamics of market price, while reserve uncertainty shifts the expected rate of change of price only if extraction costs are nonlinear in reserves. However, if the demand function is nonlinear, both demand, and reserve uncertainty affect the dynamics of production, whatever the character of extraction costs. The model is also extended to include exploration, first as a means of reducing uncertainty and second as a means of accumulating reserves, with uncertainty over the future response of discoveries to exploratory effort.

Demand and reserve uncertainty are included in a simple model of an exhaustible resource market by allowing the demand function and the reserve level to fluctuate via continuous-time stochastic processes. Thus, producers always know current demand and reserves but do not know what demand and reserves will be in the future. I show that demand uncertainty has no effect on the expected dynamics of market price, while reserve uncertainty shifts the expected rate of change of price only if extraction costs are nonlinear in reserves. However, if the demand function is nonlinear, both demand, and reserve uncertainty affect the dynamics of production, whatever the character of extraction costs. The model is also extended to include exploration, first as a means of reducing uncertainty and second as a means of accumulating reserves, with uncertainty over the future response of discoveries to exploratory effort.

Optimal Exploration and Production of a Nonrenewable Resource Earlier studies of exhaustible resource production and pricing usually assume that there is a fixed reserve base that can be exploited over time. In reality there is no "fixed " reserve base (in an economically meaningful sense), since as price rises, additional proved and potential reserves become economical. Here we view a resource like oil as being "nonrenewable " rather than "exhaustible." There is a proved reserve base which is the basis for production, and exploratory activity is the means of increasing or maintaining this proved reserve base. "Potential reserves " are unlimited, but as depletion ensues, given amounts of ex-ploratory activity result in ever-smaller discoveries. Thus resource producers must determine simultaneously their optimal rate of exploratory activity and their optimal rate of production. Optimal trajectories for exploratory activity and production are determined for both competitive and monopolistic producers, and are applied to a simple model of oil production in the Permian region of Texas.

Most studies of nonrenewable resource production and pricing assume there is a fixed reserve base to be exploited over time, but in fact, with economic incentives reserves can be increased. Here we treat the reserve base as the basis for production and exploratory activity as the means of increasing or maintaining reserves. "Potential reserves" are unlimited, but as depletion ensues, given amounts of exploratory activity result in ever smaller discoveries. Given these constraints, resource producers must simultaneously determine their optimal rates of exploratory activity and production. We solve this problem for competitive and monopolistic markets and show that if the initial reserve endowment is small, the price profile will be U-shaped; at first production will increase as reserves are developed, and later production will decline as both exploratory activity and the discovery rate fall.