Results of the Koopmans-Beckmann (K-B) analysis of the quadratic assignment problem [3] have perplexed many location theorists. K-B hold that indivisibilities of plant, in the presence of minimal interaction between spatially separated plants (namely, the shipment of intermediate goods at positive transportation rates), preclude the existence of a system of rents which will sustain an integral assignment, optimal or otherwise [3, p. 69]. Earlier in their paper K-B show that a sustaining price system does exist when the transportation of intermediate products is excluded; however, it is the presence of such interaction that leads to the more interesting quadratic assignment problem and the pessimistic conclusion reported above. The authors first present the quadratic assignment problem in a permutation search format, and then construct an equivalent linear programming problem which allows fractional assignments to be optimal without forfeiting any integral (one whole plant to each location) solutions that might exist:
[In this paper a mathematical theorem by Samuelson on what he calls the "LeChatelier principle" is generalized, the generalization being closer to the original formulation of the LeChatelier principle than Samuelson's theorem itself. The results obtained are formulated in terms of systems theory and mathematical programming. Examples concerning cost minimization or profit maximization are included.]
[The methods of Cochrane and Orcutt orr Hildreth and Lu to correct linear regressions for first-order autoregression in the disturbances, as usually implemented, underestimate the standard errors of the regression coefficients whenever a lagged dependent variable is included. A convenient transformation is derived from the information matrix to remove this bias. The asymptotic standard error of the estimated serial coefficient is a useful coproduct of the analysis.]
This paper attempts an international comparison of production structures, using the input-output framework. An earlier study in this field has shown that the production structures of advanced countries such as Italy, Japan, Norway, and the United States are similar, in spite of the wide differences in their levels of per capita income. This paper extends the analysis to a comparison of the production structure of India, a developing country with a very low per capita income, with those of the above developed countries. The result shows that in spite of the differences in the levels of development and per capita incomes, the similarity is preserved. THE PURPOSE of this study is to find out whether the structure of production of India is in any way comparable to those of Italy, Japan, Norway, and the United States. Looking at the present stage of India's development, low per capita income, and the overwhelming importance of the agricultural sector, the general impression would be that the production structure of India is unlikely to be in any way similar to the production structures of industrially developed countries. It might, therefore, be suggested that any attempt to compare the structure of production in India with that of a relatively more developed country like the United States or Italy would yield poor results. The results of a pioneering study by Chenery and Watanabe [1], however, indicated that there could be similarities in production and use of intermediate products among such countries as Italy (1950), Japan (1951), Norway (1950), and the United States (1947), though there were wide differences among these countries with respect to their resource endowments, per capita income, and the level of dependence on foreign trade. In a recent study [3] Simpson and Tsukui, while pointing out similarities in the structure of production of Japan and the United States, reported what appeared to them to be an important empirical regularity, the existence of a fundamental structure of production. The present study provides some further evidence that irrespective of differences in resource endowments and the level of economic development similarities in the production structures of different countries appear to exist. It would be of some interest to note here briefly the basic forces that tend to create similarities or dissimilarities in the national structure of production before
[A decomposition technique for linear programs is presented, in which the master program distributes the common resources and aims directly among the subprograms, rather than using price setting as is done in the Dantzig-Wolfe method. The technique is essentially a dual formulation of the Dantzig-Wolfe method. Consequently the optimum is reached in a finite number of steps. This is in contrast with the Kornai-Liptak method.]
Wallace and Hussain (1969) considered the use of an error components regression model in the analysis of time series of cross-sections and developed an estimator of the coefficient vector based on an estimated variance-covariance matrix of error terms. In this paper, we have shown that under the set of assumptions adopted by Wallace and Hussain there are an infinite number of estimators which have the same asymptotic variancecovariance matrix as the Wallace-Hussain estimator and also that it is not possible to choose an estimator on the basis of asymptotic efficiency. We have developed an alternative estimator of the variance-covariance matrix of error terms and have used this estimator in developing a feasible Aitken type estimator for the coefficient vector. We have derived some small sample properties of this estimator and have compared them with those of other estimators of the coefficient vector.
[This paper presents a new version of the factor-price equalization theorem. The numbers of outputs and of factor inputs are allowed to be unmatched. The domestic factor prices in a country facing the international commodity prices are uniquely determined in the neoclassical framework once the factor endowment is taken as given. This allows the factor-price equalization proposition to maintain the invariance of the derivatives of the social production possibility schedule with respect to input parameter perturbations, considering the possible repercussions in the outputs. A necessary and sufficient condition for this invariance is presented in terms of second derivatives of the social production possibility frontier with its economic interpretation. This condition is applied to the non-joint production case. The paper asserts that the equalization theorem holds true if the constant-returns to scale production functions are strictly concave except along rays and satisfy the full-rank condition on the input-coefficient matrix, and if the number of commodities is no less than that of factors. Several other varieties are also presented including the joint production case.]