Journal of Economic Theory 96, 180207 (2001) Optimal Environmental Management in the Presence of Irreversibilities Jose A. Scheinkman 1 Department of Economics, Princeton University, Princeton, New Jersey 08544-102 josesprinceton.edu and Thaleia Zariphopoulou 2 Business School and Department of Mathematics, University of Wisconsin, Madison zariphopmath.wisc.edu Received December 16, 1998; revised October 9, 1999; final version received October 22, 1999 We consider an environment of a fixed size that can be converted to another use. This conversion can be made in steps, but it is irreversible. The future benefits (per unit) from the original use, and from the alternative use, follow a diffusion process. For a fairly general case, we show that the value function must be the unique (viscosity) solution to the associated Hamilton-Jacobi-Bellman equation. We also exhibit several properties of the solution for the case of constant relative risk aver- sion between 0 and 1, and a log-linear diffusion for the benefits. Journal of Economic Literature Classification Numbers: C61, D90, Q30.  2001 Academic Press 1. INTRODUCTION In this paper we study a class of dynamic optimization problems, inspired by questions on the economics of environmental management, which are characterized by uncertainty and irreversibility. We consider an environment of a fixed size that can be converted to another use. Though this conversion can be made in steps, it is irreversible. The future flow of benefits from each possible use is uncertain. We model these future flows as following a diffusion. The utility flow in turn depends on these benefit flows. The presence of irreversibilities, together with the increase over time doi:10.1006jeth.1999.2607, available online at http:www.idealibrary.com on 180 0022-053101 35.00 Copyright  2001 by Academic Press All rights of reproduction in any form reserved. 1 Research partially funded by the Fondazione Eni Enrico Mattei and the National Science Foundation. 2 Research partially supported by a Romnes Fellowship and the Graduate School of the University of Wisconsin, Madison and the Alfred Sloan Foundation.