Knowledge that Transforms

[This paper deals with rules suitable for evaluating risky consequences of economic projects when various forms of stochastic dependence have to be taken into account. The Validity of various certainty-equivalence results, including the Arrow-Lind theorem, are reexamined in this framework.]

between schooling and wages: Schooling raises wages. The standard empirical questions of when are wages raised and by how much have gone unaddressed. The purpose of this paper is to demonstrate that the conventional efficiency units model of human capital accumulation provides answers to these questions. The model deals with investment both in school and on the job. The existence of post-schooling investment implies a path of wages that rises over time. Proposition 1 is that the marginal impact of schooling on the log of wages at each point in time is a constant equal to the interest rate if and only if the human capital production function is locally unit elastic in accumulated stocks of capital. A constant marginal effect on log wages is what is usually assumed in empirical work. Further, extrapolating from a model with no post-schooling investment, the constant effect is expected to equal the interest rate. Proposition 1 indicates that this assumption severely restricts the underlying structure. Propositions 2 and 3 deal with intertemporal variation in the marginal effect of schooling on wages. For example, if the output elasticity of accumulated stocks in the human capital production function falls short of one, the marginal impact of schooling on log wages is shown to decline over time. Further, under a reasonable additional assumption, the marginal impact of schooling on the level of wages rises over time. The propositions arise from the fact that wealth maximization involves maximization of an appropriately discounted flow of rents. Wages at a point in time provide information on the current flow of rents. The relationship between wealth maximization and the implied optimal pattern of flow rents yields the results. The model is laid out in Section 2. Section 3 deals with optimal schooling choice. Propositions 1-3 are presented in Section 4. In Section 5 the results are employed to discuss several stylized facts in the empirical literature on the wage-schooling relation. Proofs of the propositions are straightforward and are therefore presented in an appendix.

THE ARROW-PRATT MEASURES of risk aversion for von Neumann-Morgenstern utility functions have become workhorses for analyzing problems in the microeconomics of uncertainty. They have been used to characterize the qualitative properties of demand in insurance and asset markets, to examine the properties of risk taking in taxation models, and to study the interaction between risk and life-cycle savings problems to name just a few applications. Equally importantly, they have generated the linear risk tolerance class of utility functions which has provided canonical examples in such diverse areas as portfolio theory and the theory of teams. Despite these successes, there have been a number of areas for which the results have been weaker than hoped. It is natural to use the risk aversion measures to compare the behavior of individuals in risky choice situations. For example, consider the individual portfolio choice problem in a two asset world with a riskless asset and a risky asset. If individual A has a uniformly higher Arrow-Pratt coefficient of risk aversion than individual B, then B will always choose a portfolio combination with more wealth invested in the risky asset. But, suppose that both assets are risky. Now, there is no obvious sense in which the more risk averse individual can be said to hold a less risky portfolio, but it seems strange that such a simple alteration should destroy the analytics which support the basic intuition. Similarly, consider the basic insurance problem. If one individual, A, is more risk averse than another, B, in the Arrow-Pratt sense, it follows that A will pay a larger premium to insure against a random loss than will B. Typically, though, an individual evaluates partial rather than total insurance, that is, only some gambles can be insured against and others must be retained. In this case, even when the gambles which are retained are independent from those which are insured, it is no longer true that the individual whose Arrow-Pratt measure of risk aversion is higher will pay a larger insurance premium. The situation is no better when we consider comparative statics exercises for a single individual. Decreasing absolute risk aversion in the sense of Arrow and

This paper presents a model of myopic tastes, both in the context of intertemporal decision making and choice under uncertainty. Infinite dimensional consumption plans arise naturally in both contexts, either involving a denumerable number of periods or a countable number of states of the world. The essential feature of our model is that myopic behavior is formalized by defining topologies, on the space of consumption plans, which discount the future or improbable events.

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Two theorems are derived about social choice functions, which are defined on comprehensive convex subsets of utility allocation space. Theorem 1 asserts that a linearity condition, together with Pareto optimality, implies that a social choice function must be utilitarian. Theorem 2 asserts that a concavity condition, together with Pareto optimality and independence of irrelevant alternatives, implies that a social choice function must be either utilitarian or egalitarian. These linearity and concavity conditions have natural interpretations in terms of the timing of social welfare analysis (before or after the resolution of uncertainties) and its impact on social choices.

[Recent advances in optimal mechanism design are used to show that a certain type of auction, similar to the "open English auction," is an optimal mechanism in a certain class of environments.]

[This paper investigates the implications for asset price dispersion of conventional security valuation models. Successively sharper variance bounds on asset prices are derived. Large-sample tests of the bounds are determined and applied to aggregated and disaggregated price and earnings data of U.S. corporations.]