linear production function, that for some utility functions the optimal initial consumption in the random case decreases for all values of initial wealth as compared with the initial consumption in the deterministic case. For other utility functions the optimal consumption always increases. Hence it seems, from these examples, that two divergent forces are at work. The first is the desire to consume more initially as a hedge against the uncertain future. The second force is the desire to consume less initially so as to increase the future consumption prospects. (It is assumed, of course, that increased inputs increase outputs for all possible random events, or states of the world). The relative strength of each of these forces, as implied by the utility function, is the key to the relationship between random consumption and deterministic consumption in this model. The major conclusion of this paper is that the qualitative difference between optimal consumption decisions in the two different models is very strongly influenced by the shape of the utility function. In particular the third derivative of the utility function plays a rather large role. It is this derivative that determines the attitude toward the skewness of a distribution in the theory of portfolio choices, as may be seen from the analysis of Pratt [7] and Tobin [10]. Even in these models, however, the third derivative cannot be ignored, since ignoring skewness distorts the results. Moreover, there does not seem to be any intuitive economic reason to make any assumptions concerning the third derivative of the utility function. The extent to which the utility function influences savings and consumption decisions is exhibited in a precise manner. It may be shown that the qualitative relationship between random and deterministic consumption depends in general on the initial wealth. It is not true, as one would infer from the papers cited above, that random consumption is always either greater than or less than deterministic consumption independently of the initial wealth. In other words, for many utility functions the initial wealth turns out to be a decisive factor in the qualitative relationship between the random and deterministic case. Naturally this relationship will also normally depend on -the probabilistic structure of the model. The key result of this paper is a theorem which gives a necessary and sufficient condition for determining the qualitative relationship between random consumption and deterministic consumption. This condition, which is both necessary and sufficient, is in a particularly simple form in that it depends only on the known parameters of the model (i.e., the production function, the utility function, and the distribution of the random variable) and also on the optimal deterministic policy which, in general, is much simpler to exhibit than its counterpart in the random case.

Richard E. Kihlstrom, Leonard J. Mirman; Constant, Increasing and Decreasing Risk Aversion with Many Commodities, The Review of Economic Studies, Volume 48, Iss

[This paper studies the effect of lifetime uncertainty on optimal consumption decisions. It is shown that for risk averters changing the distribution of lifetime uncertainty decreases consumption due to the higher probability of having a longer life and increases consumption due to the desire for sure consumption in the present. The stronger of these effects determines the effect of lifetime uncertainty on optimal consumption decisions. The major result is that if the utility function is Cobb-Douglas and the rate of return is not too large relative to the amount of future discounting then lifetime uncertainty will always increase consumption.]

This paper studies the effect of lifetime uncertainty on optimal consumption decisions. It is shown that for risk averters changing the distribution of lifetime uncertainty decreases consumption due to the higher probability of having a longer life and increases consumption due to the desire for sure consumption in the present. The stronger of these effects determines the effect of lifetime uncertainty on optimal consumption decisions. The major result is that if the utility function is Cobb-Douglas and the rate of return is not too large relative to the amount of future discounting then lifetime uncertainty will always increase consumption.

[A model is constructed in which a potential entrant uses prices to make inferences about industry conditions. Stochastic demand shocks occur after the incumbent firm's action, so that prices reveal only statistical information about the incumbent's private information. The equilibrium differs from standard signalling equilibria in that it can be unique, it depends on prior beliefs, and it is rich in comparative statics. Conditions are obtained for entry threats to result in limit pricing, lower entry probabilities, and lower expected profits for potential entrants.]

It is natural to consider the stock of any renewable resource as a capital stock and treat the exploitation of that resource in much the same way as one would treat accumulation of a capital stock. This has been done to some extent by Cohn Clark and Gordon Monro and by Ngo Van Long, whose papers contain a discussion of this point of view. However, the analysis is much simpler than it appears in the literature especially since the interaction between markets and the natural biological dynamics has not been made clear. Three issues which have been raised only tangentially are important for the understanding of the economics of renewable resources. The first arises from the fact that the fish population might not be able to sustain the market determined amount of fish and hence should be allocated optimally over time. Second, there is the cost externality. Here costs are affected by the size of the stock of fish which again affects the allocation over time. The third issue is how central (typically used in capital theory) can be employed as a tool in analyzing a decentralized economy with perfect futures markets and property rights. In this paper a simple framework, using only elementary mathematical techniques, will be provided in which many important results new to the literature, as well as many familiar results, can be derived. One bonus of this approach is that much of the previous literature can be organized and rationalized. The simplicity of the mathematics has the effect of revealing the underlying economic intuition of the subject. Throughout the paper, as a matter of convenience, the selfrenewing resource will be referred to as However, it should be clear that the analysis is perfectly general in that it can be applied to any self-renewing resource. In fact, by specializing the production function, an elementary exposition of the theory of exhaustible resources is implicit. There are two main sections to this work plus an Appendix. The first section analyzes the time path of prices, output, and resource stock under the assumption of free-entry competition, and the second section studies optimal planning (or perfect competition). In the first part of the discussion of each market structure, extraction costs are assumed to be independent of the size of the fish stock. In the second part of each section this assumption is relaxed. Finally the Appendix contains several of the results used in the body of the paper. The case of free-entry competition can be treated in a very simple manner. Each period's output is determined by the intersection of the demand and marginal harvesting cost curves (i.e., supply equals demand). Subtracting this output from the natural dynamics yields the dynamics of free-entry competition. Using this technique, it is easy to see the conditions under which free-entry competition leads to the exhaustion of the stock of fish. Furthermore, the free-entry case serves as a benchmark by which to evaluate the effects of the institution of property rights on the exploitation of the resource. The case of a centrally planned economy is studied next. This case is shown to be identical to a competitive outcome in which property rights are clearly defined and prices and outputs are endogenously determined so as to be consistent with demand conditions. One result, coincidentally, is that it is possible that the solution might be obtained without property rights. The tech*The Hebrew University; University of Virginia; University of Illinois and Northwestern University, respectively. Research support from the National Science Foundation under grants SOC 77-27340 and SOC 7905900 and the US-Israel BSF under grant 1828-79 is gratefully acknowledged.

Sanford J. Grossman, Richard E. Kihlstrom, Leonard J. Mirman; A Bayesian Approach to the Production of Information and Learning By Doing, The Review of Economic