Article Contentsp.289p.290p.291p.292p.293p.294p.295p.296p.297p.298p.299p.300p.301p.302p.303Issue Table of ContentsThe Review of Economic Studies, Vol. 51, No. 2, Apr., 1984Front MatterThe Theoretical Limits to Redistribution [pp.177-195]Prices, Product Qualities and Asymmetric Information: The Competitive Case [pp.197-207]Bertrand, the Cournot Paradigm and the Theory of Perfect Competition [pp.209-230]The Identifiability of the Proportional Hazard Model [pp.231-241]Estimating Distributed Lags in Short Panels with an Application to the Specification of Depreciation Patterns and Capital Stock Constructs [pp.243-262]Profiles of Fertility, Labour Supply and Wages of Married Women: A Complete Life-Cycle Model [pp.263-278]A Price Discrimination Analysis of Monetary Policy [pp.279-288]Uncertainty in the Theory of Renewable Resource Markets [pp.289-303]Optimal Nonuniform Prices [pp.305-319]Value of an Additional Firm in Monopolistic Competition [pp.321-332]Mixed-Strategy Equilibrium in a Market with Asymmetric Information [pp.333-342]Notes and CommentsA Note on Aoki's Conditions for Path Controllability of Continuous-Time Dynamic Economic Systems [pp.343-349]A Note on "The Optimal Depletion of Exhaustible Resources" [p.351]Back Matterhttp://www.jstor.orgUncertainty in the Theory of Renewable Resource MarketsAuthor(s): Robert S. PindyckSource: The Review of Economic Studies, Vol. 51, No. 2, (Apr., 1984), pp. 289-303Published by: The Review of Economic Studies Ltd.Stable URL: http://www.jstor.org/stable/2297693Accessed: 06/08/2008 00:06Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available athttp://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unlessyou have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and youmay use content in the JSTOR archive only for your personal, non-commercial use.Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained athttp://www.jstor.org/action/showPublisher?publisherCode=resl.Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printedpage of such transmission.JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with thescholarly community to preserve their work and the materials they rely upon, and to build a common research platform thatpromotes the discovery and use of these resources. For more information about JSTOR, please contact [email protected] of Economic Studies (1984) LI 289-303 0034-6527/84/00200289$00.50 ? 1984 The Society for Economic Analysis Limited Uncertainty in the Theory of Renewable Resource Markets ROBERT S. PINDYCK Massachusetts Institute of Technology The natural growth rate of most renewable resource stocks is in part stochastic. This paper examines the implications of such ecological uncertainty for competitive equilibrium in a market with property rights. We show that stochastic fluctuations add a risk premium to the rate of return required to keep a unit of stock in situ, and we examine the effects of fluctuations on resource rent. Examples are used to show that extraction can increase, decrease, or be left unchanged as the variance of the fluctuations increases, depending on the extent of market "self-correction". Regulatory implications are also discussed. 1. INTRODUCTION Renewable resource economics has traditionally been concerned with the study of dynami- cally optimal harvesting policies given a deterministic function for the natural growth of the resource stock. Issues have included the existence and characteristics of steady-state equilibria for the optimally managed resource, the need for and design of regulatory policies to prevent over-exploitation, and conditions under which (as a social optimum or otherwise) the resource will be exploited to extinction.1 Much of this work has been based on the assumption of a fixed and exogenous price for the harvested resource (typically resulting in "bang-bang" solutions for the harvesting policy). However some recent papers make price endogenous, and thereby describe how the extraction rate, and the rate of return and asset value of the resource behave in a competitive market with property rights.2 For virtually all resources, the natural rate of growth of the stock (or "biomass") is in fact stochastic. This is well appreciated by biologists and ecologists, and a growing body of literature in population ecology has focused on the development of stochastic models of resource growth dynamics, and the characterization of steady-state probability distributions for resource stocks that are either unexploited or else harvested according to some fixed rule.3 The presence of "ecological" uncertainty raises interesting questions about the behaviour of renewable resource markets. First, how does such uncertainty affect the value and (expected) rate of return dynamics of the in situ resource stock? Second, how does it affect the rate of extraction in a competitive market with property rights? Related to this, what are the implications for the degree of regulation needed in cases where property rights cannot be assigned or maintained? These are the questions that are addressed in this paper. Other papers have already examined the optimal rate of extraction from a stochasti- cally growing resource stock (typically to maximize the expected flow of utility from net revenue). For example, using a continuous-time geometric random walk for the biomass growth function (i.e. infinite carrying capacity), Gleit (1978) finds the optimal extraction rate that maximizes the expected integral of an isoelastic utility function of net revenue. 289290 REVIEW OF ECONOMIC STUDIES He shows that as the variance of the growth rate increases, the optimal extraction rate increases. Smith (1978) solves the same problem but using a reciprocal utility function and the more realistic logistic growth function, and finds the optimal extraction rate reduced by uncertainty. Also, Ludwig (1979) and Ludwig and Varah (1979) use perturba- tion methods to obtain approximate numerical solutions to the stochastic harvesting problem for a logistic growth function. However, in these and related papers (as in much of the deterministic literature), price is fixed and