In long-run planning, targets may be set further in the future than economic technologies can be estimated. How costly in hindsight is limited foresight? Following Los, we say K is an e-horizon if knowledge of economic possibilities for the next K time periods permits decisions with results at most E worse than optimal. For a dynamic Leontief model, we show that any T-period efficient path is almost as big as all feasible T-period paths during the first T - K periods. Thus, given K periods notice, we can plan an E-optimal growth path no matter how technologies change after T.
1. INTIRODUCTION ANALYSES OF THE STABILITY of general competitive equilibrium2 have typically concerned themselves with the case of pure exchange. Sometimes that restriction has been inessential. In the tatonnement case, for example, if we are willing to make the assumption that all goods are gross substitutes, then it makes little difference where the excess demand functions come from.3 In less highly special cases, the restriction to pure exchange is a more serious matter. This is particularly so in the richer world of non-tatonnement processes. The difficulties raised by the abandonment of the pure exchange assumption in such models are three. First, such models, in assumptions or proofs, rest on considerations of utility maximization which are not immediately applicable to firms. Second, it is not fully natural to assume that stocks of goods are bounded, an important feature when non-tatonnement is being considered. Third, the creation and destruction of goods in the course of the adjustment process itself must be taken into account. The present paper shows how the first and, to some extent, the second of these problems can be handled in the context of the most appealing of the non-tatonnement models, that of the Hahn process.4 The third problem, that of the creation and disappearance of goods during the adjustment process is far more difficult. It is also not special to the introduction of firms, since the pure exchange models do not allow consumption to take place until equilibrium has been reached. Thus, this
[This paper demonstrates how the short-run static stability conditions of the two-sector growth model can be derived by converting the problem into a two-person, two-good exchange model. It is shown that the only necessary and sufficient condition for short-run stability is the Marshall-Lerner condition, and that the Drandakis (sufficient) condition follows easily from the former.]
R. L. Basmann, D. H. Richardson, R. J. Rohr, An Experimental Study of Structural Estimators and Test Statistics Associated with Dynamical Econometric Models, Econometrica, Vol. 42, No. 4 (Jul., 1974), pp. 717-730
[This paper looks at some aspects of the three stage least squares approach to estimating simultaneous econometric models. Three stage least squares is derived along the lines of best linear unbiased estimators in classical regression, whereby it is indicated that the usual assumption of non-singularity of the disturbance covariance matrix is unnecessary. Consistency of the estimator is shown as is the irrelevance of exactly identified equations to the estimation of other equations in a model when three stage least squares is used. Also included are an easily computed test for the validity of all specified overidentifying restrictions, and a method of efficiently estimating the reduced form using only the information contained in structural equations that are thought to be well specified.]
Decentralized decision making is consistent if it is executed without cost (i.e., without a loss of output or utility). Consistency requires that the objective function be appropriately structured. In this paper, a hierarchical decision making structure is rationalized by an objective function which combines some of the properties of homothetic separability and asymmetric separability. THIS PAPER EXAMINES consistent decentralized decision making in a hierarchical structure. The decision making process is rationalized by a class of objective functions which combines some of the properties of homothetic separability [1, 3] and recursive, or asymmetric, separability [5,8]. We refer to these functions as homothetically recursive. After introducing our basic notation and definitions, we prove a representation theorem for homothetically recursive functions in Section 1. In Section 2 we prove two duality theorems for homothetically recursive structures. A recursively decentralized decision making process, described in Section 3, is made manifest in the structure of the associated cost function. The analysis is carried out in the context of the theory of the firm but other applications are discussed briefly in Section 4.
James L. Kenkel, Some Small Sample Properties of Durbin's Tests for Serial Correlation in Regression Models Containing Lagged Dependent Variables, Econometrica, Vol. 42, No. 4 (Jul., 1974), pp. 763-769
The purpose of this paper is to give a systematic account of the significance that antagonism among opinions of individuals has on the theory of social choice. We define an intensity of antagonism among individuals and an index of possibility of constructing social welfare functions, and show that when there is less antagonism in a society, then there is more possibility of constructing social welfare functions. Since antagonism is an opposite concept to similarity, this relation can be viewed as a formal realization of Arrow's assertion [1, Ch. 7] that sets preference similarity as the basis of social welfare judgement.
[Cette note discute les conditions d'existence d'un noyau non vide dans une économie de propriété privée où des possibilités de production sont associées à chaque coalition en fonction de sa composition. On étudie les relations entre noyau et équilibre concurrentiel dans le cas particulier où il existe un ensemble d'entreprises et où l'ensemble de production d'une coalition est égal à la somme des ensembles de production des entreprises dont les membres de la coalition possèdent une majorité des parts.]