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IMPARTIALITY IS THE MORAL IMPERATIVE requiring that conflicting claims be evaluated without prejudice. In this paper I propose an axiomatic definition of impartiality and examine its implications for the theory of social welfare functions. Following the seminal work of Harsanyi (1953, 1977) I take as given the set of individuals that constitute the society and the set of social alternatives, representing the constitutions, income distributions, institutions, or policies among which the society must choose. Moreover, the moral value judgment that should govern this choice is modeled as a preference relation of an ethical observer. However, unlike Harsanyi, who defines the observer's preference relation on the set of all extended lotteries (i.e., joint probability distributions on social alternatives and individuals) I define the observer's preference relation on a set of allocations whose elements are assignments of social-alternative lotteries (i.e., probability distributions on the set of social alternatives) to individuals. As in Harsanyi's theory, the observer's preference relation is supposed to govern the choice among social alternatives of individuals placed behind a veil of ignorance regarding their social position and preferences. Harsanyi assumes that the observer's preference relation on the set of extended lotteries and the individual preference relations on the set of social-alternative lotteries satisfy the axioms of expected utility theory and jointly satisfy the principle of acceptance.2 He shows that the observer's preference relation may be represented as a weighted sum of individual von Neumann-Morgenstern utilities and defines impartiality as the restriction that the individual utilities are assigned equal weights. This representation may be interpreted as assigning equal probabilities to the events of being each individual in society. Note, however, that given any preference relation that is representable as a weighted sum of individual utilities with strictly positive weights, a new set of individual utilities may be defined (by multiplying each utility function by its weight and dividing through by the inverse of the number of individuals) to obtain a new representation of the preference relation with uniform weights. In other words, the same observer's preference relation is represented as a weighted sum of individual utilities with equal weights. Since this manipulation does not change the underlying observer's preference relation, it does not make it impartial except in a tautological sense.
This paper develops a matrix-measure of multivariate risk aversion which is related to a notion of risk premium and states the restrictions that must be imposed upon the matrix-measures of two utility functions in order that one require a higher risk premium than another for every small multivariate risk. A necessary and sufficient condition for comparability of global attitude towards risk is that the local restrictions hold over the entire domain. The usefulness of the measures of risk aversion is discussed within the context of a multivariate risk-sharing problem. UNIVARIATE MEASURES OF ABSOLUTE and relative risk aversion were introduced in the seminal works of Pratt [8] and Arrow [1], and have since become indispensable tools for the analysis of risk bearing in situations involving unidimensional risks. Recent years witnessed numerous attempts to generalize various aspects of the Pratt-Arrow notions to the case of multivariate risk (Kihlstrom and Mirman [6], Keeney [5], Duncan [2], Paroush [7], and Stiglitz [9]). The univariate case is qualitatively different from the multivariate case in that the ordinal preferences of all decision makers are identical, whereas in the multivariate case the preference orderings may differ among decision makers. This fact has two important consequences. First, while the analysis of risk bearing in situations involving univariate risks turns out to depend solely upon the cardinal properties of the function representing the ordinal preferences of the decision makers involved, in situations involving multivariate risks, the ordinal preferences themselves play an important role in addition to that of the function representing them. Second, in the univariate case the local measure of absolute risk aversion permits a complete ordering of individuals according to the relation least as risk averse as, whereas in the multivariate case such ordering is not in general independent of the specific risk under consideration. Pratt [8] has shown that the univariate measure of absolute risk aversion satisfies a formal relation to a number which has the interpretation of risk premium. In this study I introduce a matrix measure of absolute multivariate risk aversion which satisfies a similar formal criterion. It should be noted at the outset, however, that in the multivariate case the risk premium may be regarded as a vector of commodities (see, for example, Duncan [2, 3]), and interpersonal comparison of risk aversion is not directional independent. I.e., the ranking of risk
The observed practice of contracting for labor services in advance introduces stickiness or friction into the economic system. In the presence of monetary and real stochastic disturbances the stability of the levels of employment and output hinges on the nature of the wage contracts. In this paper we demonstrate the existence of optimal indexation schemes that are capable of eliminating the aforementioned friction by duplicating the equilibrium that would obtain if labor services were contracted for after the stochastic disturbances were realized.
The observed practice of contracting for labor services in advance introduces stickiness or friction into the economic system. In the presence of monetary and real stochastic disturbances the stability of the levels of employment and output hinges on the nature of the wage contracts. In this paper we demonstrate the existence of optimal indexation schemes that are capable of eliminating the aforementioned friction by duplicating the equilibrium that would obtain if labor services were contracted for after the stochastic disturbances were realized.
This paper describes two alternative institutional setups for trading in assets and goods. One setup corresponds to a "beginning-of-period:" asset equilibrium specification; the other suggests both beginning and end-of-period equilibrium. It is shown that: (a) each model is internally consistent and the two models are consistent with each another; (b) the two models abide by Walra's law and in neither of them is there a need for a separate "balance-sheet constraint"; and (c) the continuous time version of the two models is well defined.
This paper describes two alternative institutional setups for trading in assets and goods. One setup corresponds to a "beginning-of-period:" asset equilibrium specification; the other suggests both beginning and end-of-period equilibrium. It is shown that: (a) each model is internally consistent and the two models are consistent with each another; (b) the two models abide by Walra's law and in neither of them is there a need for a separate "balance-sheet constraint"; and (c) the continuous time version of the two models is well defined.