Knowledge that Transforms

Abstract : In many situations involving interaction among parties, the individual welfare of each party can be improved by cooperation. This requires a cooperative decision, which specifies the course of action to be followed by each party, and a rule for sharing the total payoff resulting from that decision. In general, the total payoff will depend on the value of a random variable that is unknown at the time of the decision making. This study determines the conditions under which the parties are willing to delegate cooperative decision making to a group. In arriving at its optimal decision, this group does not take into account the division of the total payoff among the parties. Furthermore, the parties are willing to form this group independent of the set of alternative payoff functions. The results are based on the assumption of complete information; that is, each party knows his own and his opponents' utility functions, subjective probability distributions, available strategies, and payoff functions. (Author)

T. Takayama, A. D. Woodland, Equivalence of Price and Quantity Formulations of Spatial Equilibrium: Purified Duality in Quadratic and Concave Programming, Econometrica, Vol. 38, No. 6 (Nov., 1970), pp. 889-906

The object of this note is to generalize a result of Dummet and Farquharson [3] on the existence of a choice set,2 i.e., the existence of an alternative socially considered to be best under a system of majority voting. In the first section the motivation of the exercise is explained and the relevance of the problem is discussed. In the second, the generalization is stated in the shape of a theorem and is proved. In the third, some observations are made on the nature of the theorem and its relation to conditions of transitivity of majority decision.

The use of numerical techniques for solving dynamic nonlinear multisectoral models for development planning is analyzed. A four sector model with nonlinear welfare, production, and investment functions is developed and solved using conjugate gradient and neighboring extremal methods. The model draws on recent developments in nonlinear theoretical growth models and linear development planning models. Sensitivity tests on the turnpike properties of the model and on changes in the elasticity of substitution parameters in the production function are discussed. The numerical techniques used have their origins in control theory applications and exploit the dynamic structure of the planning model. THIS PAPER discusses the application of numerical methods to the solution of nonlinear planning models of a type that could be used in the formulation of development programs for less developed countries. The numerical methods were originally developed by control theorists and our chief interest has been in testing their capability to solve moderately sized economic problems. In general, we have been satisfied with the results of these tests, and wish to demonstrate the usefulness of the nonlinear specification with a realistically formulated four sector model. This model is based on ideas drawn from two recent lines of thought about economic growth over time. The first is that of neoclassical theoretical models designed to analyze the characteristics of an economy in asymptotic optimal growth, viz. Samuelson and Solow [24] and Koopmans [19]. The other line is that of finite horizon linear programming planning models, viz. Bruno [4], Eckaus and Parikh [10], and Chakravarty and Lefeber [7]. We have attempted to blend the nonlinear production and welfare functions of the neoclassical models with the disaggregation and emphasis on foreign trade of the linear programs. In future applications this combination should offer growth theorists the possibility of using greater disaggregation than their present closed-form solution methods permit and at the same time give economic planners the opportunity to specify their models with nonlinear functions in both the performance index and the constraints.2

Consider a committee or society attempting to order the alternatives (X_1, X_2, X_3) by use of majority rule. Each individual is assumed to have a strong ordering (called a profile) on the alternatives. "Indifference" is not a property of the profiles. The committee is said to "prefer" X_i to X_j, denoted X_iCX_j if X_i is preferred to X_j on a majority of the individual profiles. It is well known that if certain individual profiles are chosen, the resulting "social ordering" may be cyclical, i.e., X_iCX_j, X_jCX_k, X_kCX_i. Such a result is called a "cycle."