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.

This paper examines the interactions between market structure and resource allocation over time when there is endogenous technical progress. The structures considered are a planned economy, pure monopoly, and competition with patent rights. In an efficient allocation the date of invention coincides with the date of innovation (the date at which technology is used). This is also true with a pure monopoly, but monopoly retards technical progress relative to the efficient level. Competition for patents rights to a new technology results in excessively rapid technical progress if the resource endowment of the economy is sufficiently large. Also, competition may lead to “sleeping patents” where invention strictly precedes the date of innovation.