This paper explores a new approach to the Nash bargaining problem in which the axiom of symmetry is dropped and it is assumed that the final allocation depends on both the status quo and the threat point. The resulting final allocation, unlike that formalized by Nash, cannot be represented by a simple analytic expression; rather, it leads to a whole class of solutions. Properties of the final allocation are analyzed. It is shown that for every initial allocation there exists a Nash fiber, corresponding to the Nash allocation, that it is possible to determine the sign of the derivatives of the final allocation with respect to changes in the threat point, and that a Slutsky-like equation relates these derivatives to the derivatives with respect to the initial allocation. It is also shown that, under certaiia conditions, as play is repeated the final allocation asymptotically converges to the Nash allocation.
In this paper we study the possibility of constructing satisfactory social choice mechanisms whose outcomes are determined by a combination of voting and chance. The following theorem is obtained: if a social choice mechanism does not leave too much to chance and satisfies a unanimity condition, then it is either uniformly manipulable or dictatorial. The result contributes to the program suggested by Gibbard [2] for the study of the extent to which social choice mechanisms in which chance plays a role can be freed from 2 strategic manipulation.
In recent studies of the temporary competitive equilibrium, agents' current decision correspondences are derived using a standard recursion procedure, which is only applicable when the planning horizon is finite. This paper presents a general derivation of the current decision rule without restrictions on the time horizon or the number of states of the world in any period. It is shown that if utility is continuous in the product topology and if, in each period, expectations and the current constraint correspondence are continuous, then the current decision rule is upper semi-continuous. This result is obtained by associating with each current decision a set of feasible future plans. The expected utility of a current decision is then the expected utility of the best feasible future plan. The feasible future plan correspondence is shown to be continuous and the Maximum Theorem completes the proof.
WE PROPOSE to study here the relationship between externalities, public goods, and returns to scale. The ideas behind this connection are certainly not new. Indeed, Marshall frequently spoke of external economies and diseconomies of scale. He had in mind situations in which expansion of one firm conferred external benefits on the industry and led to increased efficiency of the agggregate operations. The quantitative relationship has been explored from time to time in a number of specific contexts. For example, Arrow [1] showed that the presence of learning by doing (a public good) introduced an element of increasing returns into the aggregate relationships. We are after a general quantitative relationship. Our first task is to construct a general measure of returns to scale for multiproduct technologies. A starting point is the theory of homogeneous functions (see Henderson and Quandt [8] for a general discussion of this subject). The degree of returns to scale of a homogeneous function is naturally measured by its degree of homogeneity. This measure is used as a matter of course by economists (see for example, Intriligator [9]) and can be extended to multiproduct technologies. We certainly want our measure to agree with this one for homogeneous functions. However, it is very unlikely that the aggregate technology can be represented by a function which is homogeneous of any particular degree. Thus, we must find a measure which will apply to more general functions. In the next section we develop a measure which has some intuitive appeal and can be shown to be the ideal measure under some circumstances. It can be thought of as a generalization of the well known elasticity of production used by many authors (see, e.g., Carlson [2], Frisch [4] or Johansen [10]). We will show that our measure is a natural one from several different points of view. Having developed a measure, we will use it to quantify the returns to scale effect of public goods (or bads). This is done in Sections 5 and 6.
This paper extends earlier studies in this field by Chenery-Watanabe [2] and Santhanam-Patil [3] to a comparison of the production structure of Korea at present with those of other countries and with that of Korea at various points in the past. The results of this study provide additional evidence in support of the main findings of earlier studies. It is suggested that existing methods for computing inter-industry linkages and for comparing production structures could be improved by including an analysis of both domestic and international linkages.
This paper analyzes a one-commodity model in which alternative investment projects are characterized by return functions indicating the output intensities over time resulting from an initial unit investment. Saving is generated partly by households as a constant fraction of net income, and partly by business firms in accordance with a depreciation (or replacement) policy. It is shown that when a declining value depreciation policy is adopted, the ordering of consumption streams in terms of their present values, at any fixed interest rate for which these converge, induces an ordering of investment projects in terms of their internal rates of return. The same ordering of projects is also induced by applying the overtaking criterion to the consumption streams.
This paper attempts to determine conditions under which distributed lag analysis is appropriate. Results indicate that lag functions are stable and linear under fairly general (but constant) objective criteria and decision constraints as long as the underlying economic environment is characterized by a stationary Gauss-Markov process, and observed environmental variables are Gaussian perturbations of that process. The results appear particularly useful for specifying the lag distribution inherent in subjective parameters in specific decision problem contexts. 1. INTRODUC'TION IN AN EARLIER PAPER, Taylor [11] dealt with the problem of determining lag distributions on the basis of optimization assumptions in a dynamic model of uncertainty. Taylor's conclusions, however, are somewhat disturbing in that they indicate only a narrow class of decision problems with uncertainty can be studied in a distributed lag framework. Taylor addresses only an exemplary model of inventory control and by assuming that (i) the firm's cost function can be expressed as a sum of strictly quadratic and linear terms, (ii) all production constraints are linear equalities, and (iii) observed demands are perturbations of unobserved components which follow a Gauss-Markov process, he is able to show that a distributed lag exists in the decision rule. By making yet additional assumptions, he is also able to demonstrate stability of the lag distribution. The purpose of this paper is to generalize the class of decision-makers' objective criteria and the constraint set description under which distributed lag analysis can find some theoretical justification. Although Taylor relies heavily on Kalman filtering theory to derive his results, the equivalent Bayesian approach is used explicitly in this paper for purposes of completeness and continuity.2 Results show that the lag function is stable and linear under more general conditions than Taylor's, although the lag function may enter the resulting econometric model nonlinearly. If econometric investigators are willing to consider nonlinear functions of lag distributions (or approximation of nonlinear functions by linear functions), the results should provide a basis for distributed lag analysis in a much broader class of problems than do Taylor's previous results. Furthermore, it is found that econometric equations which include the distributed lag linearly may exist outside of the set of cases considered by Taylor. The following section begins by specifying the general decision theoretic framework in which we shall operate throughout the paper. The existence of lag functions is made evident. In Section 3, Taylor's environmental system is
[A new formulation of the linear quadratic control, LQC, problem with known coefficients, called the LAG, is presented. The LAG generally does not generate a recursive Ricatti system. For models with long lags an important issue is whatformulation leads to an efficient algorithm both with respect to storage and speed. At present the most efficient known formulation is the minimum state variable representation, MSV. The LAG requires much less storage than the MSV as the LAG does not require conversion to state space representation. For short time horizons the LAG is computationally faster than the MSV. As the time horizon increases, the efficiency of the LAG relative to the MSV declines. Numerical comparisons of the Theil, Chow, MSV, and LAG formulations are shown.]
abstract: the conventional approach to the design of stochastic systems operates, either directly or indirectly, by minimising the variance of the model. this procedure can be regarded as a natural extension of the stability analysis of a deterministic system, according to which the degree of stability is inversely related to the absolute value of its largest characteristic root. very often, however, the policymaker is not indifferent to the frequency composition of economic fluctuations. he may, for example, have a marked dislike for short-term fluctuations. we formalize this notion by setting up a spectral utility function as a criterion for steady-state optimisation, and show that the results from such an optimisation may conflict with those yielded by the conventional approach. large characteristic roots may not necessarily be bad! the scheme of the paper is as follows. because the ideas involved may be unfamiliar we shall spend some time on a rather intuitive motivation for what follows. this is done in section i. in section ii the notion of a spectral utility function is introduced and its evaluation discussed. we then return to the example of section i to give it a more precise treatment. section iii contains extensions, principally to the multivariate case.;
The first part of this article integrates the concept of (relative) risk aversion with respect to income (r) with the static analysis of demand for many commodities. Alternative representations of preferences and demand functions, using duality, give rise to many alternative representations and interpretations of r, and to theorems regarding attitudes towards risk in bundles of quantities and in prices. In the second part, a previous analysis by Deschamps is corrected and completed by specifying the general form of preferences and demands such that r is a function of the utility level only, independent of relative prices. Finally, preferences and demand functions associated with constant r (previously analyzed by Stiglitz and Deschamps) are specified more explicitly and completely. A general conclusion emerging is that demand behavior under certainty can hardly throw any light on the nature of attitudes towards risk. THE CONCEPT OF THE relative risk aversion function as a unit-free measure of individual aversion to income risk under expected utility maximization, was defined by Arrow [1] and Pratt [15], and has proved useful in various applications. Stiglitz [21] studied relations between an individual's aversion to income risk, and his indirect utility and demand functions for many commodities, obtained under certainty in competitive markets. In particular, he analyzed the cases of risk indifference and constant relative risk aversion (r). Deschamps [4] extended this analysis to study implications of alternative assumptions: (i) That absolute risk aversion R = rly is independent of prices, nominal or relative, for given income. This is equivalent, however, to constant r (which is the case analyzed by Stiglitz) for both cases. (ii) That R or r are constant on each indifference surface. This is shown to be impossible for R, but meaningful and interesting for r = r(u). Unfortunately, however, Deschamps could not show the utility and demand functions for this case, and conducted an indirect analysis based on the second-order differential equation implied, failing to note that any such r(u) is compatible with homothetic preferences. In addition, his analysis contains errors (e.g., the case r = 1 constant) and may be subject to misleading interpretations. The purpose of this article is twofold: (i) To complete the analysis of risk aversion with many commodities, by using various alternative formulations of the relative risk aversion function to study general relations between income risk aversion and attitudes towards risk with respect to quantities (e.g., when both relative prices and income are subject to risk), or with respect to prices. (ii) To complete the analysis of Deschamps by showing the general forms of utility and demand functions when r = r(u), and to correct some errors of analysis and interpretation.