Nancy L. Schwartz

Optimal Exhaustible Resource Depletion with Endogenous Technical Change

The prospect of imminent exhaustion of some natural resources, especially those employed in energy generation, has prompted calls for conservation through reduction or even cessation of economic growth. A natural framework for analysing such proposals is a hybrid offspring of Ramseys optimal growth model [8] and Hotellings model of exhaustible resources [4]. Specifically, Anderson [1], Solow [10] and Stiglitz [11], among others, have recently studied optimal growth models modified to incorporate production requirements for an essential exhaustible resource. It has been shown that while resource irreplenishability limits growth in per capita consumption, this limitation may be offset by technical progress along with increasing capital accumulation and substitution. Reliance upon technical progress, in particular, to offset the constraining irreplenishability of a vital natural resource is based on its role as a major source of past economic growth. Along with the discovery of the past importance of technical progress has come awareness that it proceeds neither smoothly nor without effort. It is affected by the resources devoted to it. Unpredictability in technical progress results from our partial ignorance of the principles underlying natural and social phenomena. The randomness can be reduced at a cost, but it cannot be eliminated. These features of technical advance have typically not been incorporated in most of modern growth theory, wherein progress is regarded as proceeding steadily, costlessly and exogenously. In contrast, a few papers have considered more abrupt and significant changes in technology used. Smith [9] assumes that two alternate technologies are available from the outset, one requiring an exhaustible resource at low initial cost and the other employing an inexhaustible factor at high initial cost. He shows that maximum output will be achieved by using only the exhaustible resource technology at the beginning but gradually supplementing and then replacing it with the high-cost alternative. Dasgupta and Heal [2] considered the possibility that a new technology will eventually appear that does not employ limited natural resources. The technical advance could be costlessly achieved but the date of its availability was both random and exogenous. In a subsequent paper, Dasgupta, Heal and Majumdar [3] extended this model by making development of the new technology endogenous. Their model is very similar to and consistent with the one independently developed by us and described below. Our view is that technical advance is in large part neither costless nor exogenous [6]. The rate and direction of technical progress are influenced in the long run by the economic resources allotted to it, guided by the quest for profits and government policy. In this paper we follow the framework used by Dasgupta and Heal [2] while making technical advance endogenous. We omit steady technical progress that reduces unit factor requirements in favour of emphasizing a drastic technical change that relaxes the limitation imposed by

On the Degree of Rivalry for Maximum Innovative Activity

Introduction, 245. — Model I — the framework, 250. — Model I — rivalry and speed of innovation, 253. — Model II — the framework. 255. — Model II — rivalry and speed of innovation, 256. — Summary and conclusions, 258. — Appendix, 259.

A Generalized Hazard Rate

Abstract We present a general class of probability functions in which the hazard rate depends on both time and a shift parameter. It is used, for example, to generalize a model of innovation due to Loury and Dasgupta and Stiglitz.