Journal Article Optimal Depletion of an Uncertain Stock Get access Richard J. Gilbert Richard J. Gilbert University of California Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 46, Issue 1, January 1979, Pages 47–57, https://doi.org/10.2307/2297171 Published: 01 January 1979 Article history Received: 01 July 1976 Accepted: 01 May 1977 Published: 01 January 1979

The paper examines the question of whether land rents should be considered costs. The motivation for this paper arose from a study of a search model of resource exploration. The study showed that when no new information is revealed in the process of search, exploration can be completely characterized by a reservation cost rule. If probability distributions are known and firms are risk-neutral, the sequence of extraction would be efficient. The area with the lowest reservation cost would be and should be exploited first. It is implied that, for the purpose of resource allocations, unexplored land can be considered a commodity with essentially the same characteristics as known deposits. The author then examines a specific example which shows that, when the characteristics of nonreplenishable resources can be screened, it may not be desirable to screen all resources at the same intensity. He also examines the allocation of screening effort in a decentralized economy with complete futures markets. A final note concerns the general intuitive explanation of the differentiated screening equilibrium. (MCW)

Economists in an antitrust case have at their disposal quite a large bag of tools and truisms, but for the most part these are derived from studies of static models. In many industries the policy issues concern the implications of firm behavior on market structure and performance over time. A case in point is a recent Federal Trade Commission complaint against the DuPont Corporation. The FTC alleged that DuPont had engaged in a strategy designed to monopolize the market for titanium dioxide, better known as the coloring agent in white paint. The alleged strategy was, in essence, what some would recognize as the Boston Consulting Group story: When a firm has a lead in an industry with significant learning economies, the firm should price below competitors' costs and expand to take further advantage of learning effects and, in the process, to increase market share.' This paper summarizes the results of an analysis of dynamic competition with scale and learning effects. The research is a preliminary exploration. All results are obtained under rather special assumptions about the production technology, the effects of experience on costs, and the strategic interactions between firms. Two kinds of strategic behavior are considered. In the first case, each firm takes the production decisions of competitors as given (the Nash assumption). In the second case, firms consider pre-emptive capacity investments, taking into account that competitors will alter their future investment plans to achieve nonnegative profits. We call this a Stackelberg (CS) game. Using the maximization of net surplus as a socially optimal benchmark, neither form of competition yields an efficient outcome when new investment exhibits increasing returns to scale. In the absence of learning effects, smaller firms in a Nash competition have a greater incentive to add new capacity than do larger firms, and the equilibrium industry structure approaches equal market shares. Introducing learning effects in the Nash game causes a tendency toward increased concentration, but monopoly is not an inevitable consequence. The CS game is competitive than the Nash game in the sense that firms compete for the right to invest at each instant of time. With identical firms and no learning effects, the market structure in a CS equilibrium is indeterminate, although the sequence of industry investments is well defined. Introducing firm-specific and nonstochastic learning has a dramatic effect on the CS equilibrium. All new investment is undertaken by a single firm, even if the learning economies are small. Moreover, the level of output could be lower (and price higher) in a CS equilibrium than it would be in a Nash equilibrium. In this sense more competition can lead to a lower rate of output over time.

Stephen Salant takes issue with a single paragraph of our 1982 paper (Section IIC, p. 518) and then claims that our conclusions result either from faulty logic or from our implicit assumption that a market fails to operate. We respond by showing that our conclusions are logically consistent, and that Salant's argument is flawed by its incompleteness. The preemptive patenting results hold whenever equally efficient firms compete with nonzero transaction costs (a point which is not contested by Salant), and whenever any cost disadvantage experienced by the incumbent is less than the transaction costs incurred in the process of bargaining for production rights. Furthermore, we will show that if the incumbent's cost disadvantage exceeds transaction costs, then the preemption result hinges on the relative transaction costs in the markets for R&D outputs and inputs. The conditions derived by Salant are erroneous, and indeed irrelevant to the incentives for preemption. Salant mounts his main argument on the assumption that transaction costs are zero, but fails to realize the full implications of this counterfactual assumption. Ronald Coase told us many years ago that bargaining in the absence of transaction costs (broadly interpreted) will eliminate cost inefficiencies and yield a Pareto optimal allocation. By selecting excerpts from two different papers and then providing his own emphasis, Salant constructs the impression that our results contradict the Coase argument. We feel this creative journalism is an inaccurate representation of our conclusions. The implications for preemptive patenting depend on transaction costs, as Salant shows. For any finite transaction cost, an equally efficient monopolist can preempt competitors (subject to the technological and strategic assumptions in our model). Salant argues that if a monopolist is less efficient than a rival, and if the cost penalty exceeds transaction costs, then the rival firm will preempt the monopolist. As it stands, this conclusion is false. It is arbitrary to restrict bargaining, as Salant does, to a single market or group of markets. If firms can negotiate in the patent market, they can also negotiate in markets for inputs to the R&D process. Assuming (as we had explicitly done) no diseconomies that are solely due to management, technological inefficiency must be the result of inferior R&D inputs. These inputs can be bargained for as well.

This article takes a different tack and inquires whether institutions such as the patent system create opportunities for firms with monopoly power to maintain their monopoly power. The results apply to other situations such as brand identification, spatial location, and capacity expansion, which share the characteristic that early, or preemptive, actions may lower the returns to potential competitors.