The problems associated with interpersonal comparisons are particularly intractable. This paper presents a procedure whereby the relative importance of any particular individual varies over the set of social states. In one sense, the stronger (relative to some norm) a person feels about any particular pairwise decision, the larger his say in that outcome. This procedure leads to a nested sequence of aggregate partial orderings which reflects this strength of preference. Under the assumptions presented it is also possible, given any two social states, to characterize the minimal amount of interpersonal comparison which is necessary in order to arrive at an aggregate ordering.
[Recently, a partial ordering "more risky than" on the set of distribution functions has been established by several authors. The following problem is investigated in this paper: characterize the maximal elements (efficient points) in the above ordering of a given set X of random variables. For a closed and convex set X of discrete random variables we give an essentially complete characterization of the efficient random variables by means of their systems of efficiency prices.]
This paper discusses the asymptotic behavior of the neoclassical two-sector growth model when the steady-state conditions are not fulfilled, and derives the asymptotic growth rates for cases in which Hicks neutral technical progress occurs in the investment sector, or Harrod neutral technical progress occurs at different rates in the two sectors. The last section compares the asymptotic properties of this model with the standard steady-state properties of the two-sector growth model. IN THE EIGHTEEN YEARS following the publication of Professor Solow's classic one-sector model [8], much work has been done in attempting to explain the stylized facts of growth by means of aggregate models. However, almost without exception, these models have concentrated on analyzing the properties of the steady-state equilibrium, ignoring the behavior of the economy should a steady state fail to exist. Even those models that have implicitly dealt with the singularity of the steady-state solution2 have done so by attempting to explain why the steady state should occur (for example, Kennedy [5] and Chang [4]), rather than by explaining the non-steady-state properties of their models. In this paper we shall study the behavior of a two-sector economy in which the steady-state conditions are not fulfilled. Our analysis will follow, for the most part, the technique developed by Vanek [12 and 13] and extended by Bertrand and Vanek [2]. In these papers the authors study the behavior of the aggregate capitallabor ratio in a one-sector model in which the steady-state condition is not fulfilled. However, they do not explicitly discuss the asymptotic behavior of the economy, nor do they contrast the asymptotic behavior of the non-steady-state economy to those characteristics attributed to the steady-state world. It is the purpose of this paper to examine both of these issues for a two-sector growth model.3
This paper formulates the notion of stochastic equilibria as invariant probability distributions consistent with the behavior patterns of individuals and the disequilibrium adjustment mechanism of the economy. Conditions for existence, uniqueness, and stability of such equilibria are examined. WE CONSIDER A CLASS of problems in this paper in which the economic environment is stochastic. We will be concerned primarily with developing an equilibrium concept for general equilibrium models of this type. However the essential ideas can be carried over directly to partial equilibrium applications. The choice of the specific general equilibrium model used results primarily from a desire to facilitate comparisons with earlier work on alternative equilibrium concepts for this model (see Hildenbrand [9] and Majumdar and Bhattacharya [2 and 3]). Randomness can arise from several sources. We will be considering, for concreteness, a simple exchange economy in which the basic data are the preferences and endowments of the economic agents. Either of these can be random. Typically, randomness of endowments can be allowed for by creating contingent markets in which case the Arrow-Debreu deterministic equilibrium suffices. It is conceptually much more difficult to create markets contingent on tastes due to the difficulties of discovering the true taste pattern of an individual, difficulties which do not arise in the case of endowment vectors which can be observed directly. We will be considering an economy without markets for every future contingency and thus there will remain some randomness. This residual uncertainty in the economy necessitates equilibrium concepts other than the Arrow-Debreu system of market clearing prices. 2. NOTATION
[The problem under consideration is to select the smallest majority size such that at least one social state is not defeated by any other when restrictions on possible voters' preferences are explicitly known, and when populations of arbitrary size are possible. This problem is formulated in mathematical programming terms. The special structure of the formulation is discussed, and some results concerning bounds on the majority sizes are established.]
[Changes in asset prices are shown to produce only substitution effects in a broad class of portfolio-choice models. Wealth effects are identically zero unless the individual's stocks of assets are subject to unanticipated changes.]
Zellner [11], and Chow [3], is to deal with the uncertainty by treating the model parameters as independent, identically distributed random variables in each period,' yielding what Zellner calls rules. Although the sequential updating rules do capture the uncertainty, they ignore the possibility of ongoing estimation in the formulation of decision rules. The purpose of this paper is to develop an adaptive learning decision rule for the multiperiod problem. This rule incorporates the effect of policy variables on the learning which is expected to occur throughout the remainder of the planning period. It is a generalization of the rules described above in the sense that both of them can be derived as special cases of this rule. Finally, this decision rule yields to economic analysis in terms of the stock and value of information, a feature which is not found in previous work. Section 2 of the paper describes the multiperiod decision problem with unknown parameters, discusses the assumptions associated with the certainty equivalence and sequential updating rules, and then presents the assumptions employed in this paper. Adaptive learning decision rules are derived in Section 3 and a mathe
[A preference ordering R is called "self-dual" by Samuelson if and only if there exists a direct utility function U representing R such that U(Z) = - U*(Z) is any non-negative n-vector and U* is the indirect utility function corresponding to U. Samuelson showed that the Cobb-Douglas preference ordering is self-dual and asked the open question as to the existence of any other self-dual case. If a preference ordering R is both self-dual and homothetic, then for the two-good case Samuelson claims to have proved that R is Cobb-Douglasian and conjectures the same to be true in the three-or-more good-case. Swamy has claimed that the Cobb-Douglas case is the only example of a preference ordering which is self-dual and either homothetic or additive. In this paper, we give two non Cobb-Douglasian examples of self-duality, one additive and the other homothetic, in order to answer the open question and refute the claims.]