Knowledge that Transforms

[Production correspondences are defined and their properties explored. Properties of the distance function of a production structure are studied and are related to properties of the correspondence. Homotheticity is generalized to allow discontinuities in returns to scale and to take cognizance of several outputs. The factorization of the distance function into the product of two functions, one depending only on output and the other only on input, is demonstrated. The cost function is then shown to give rise to a production structure. A Shephard-type duality theorem is proven which implies, among other things, that the cost function and the distance function are dually related; that is, given one, a minimization proglem yields the other. The duality theorem is then used to deduce necessary and sufficient conditions, in terms of the cost function, for a production correspondence to be homothetic. A few simple applications of the duality theorem are given which relate properties of the cost function to geometric properties of the correspondence.]

[The relationship between efficiency and competitiveness of production programs is explored in a general disaggregated model.]

[Hitherto, studies of the impact of government taxation and expenditure on the distribution of national income or product among income classes have used arbitrary rules of thumb for the distribution of the benefits from pure public goods or bads. This article demonstrates the logically correct method for distribution of these public good benefits. Application of this method requires information on consumer preferences for public goods; since this information is unavailable, we illustrate the application of the method to the 1961 United States income distribution by showing how various distributions would result from various consumer preference structures.]

Sufficient conditions are given for the existence of continuous numerical representations (utilities) for partially ordered topological spaces. (Author)

Simultaneity as a LimitA well-known and highly convincing position on the nature of simultaneity in econometric models is that such models are only approximations to the true state of affairs.In fact, causation takes time, and the reactions given by the equations of the model truly occur not instantaneously but with a very small time lag.Unfortunately, however, data do not come to us sufficiently finely divided in time to allow us to observe such fastmoving reactions, so we take simultaneous instantaneously-holding relations as approximations, valid between the observations which nature allows us.Time lags are thus considered negligible provided they are sufficiently small.The consequences of this position for parameter estimation when observations occur at discrete points of time separated by an interval much larger than that in which the true reactions take place have been discussed 2 in the literature.In fact, however, this particular variant of the above view does not seem a very realistic one, We very seldom have observations on the value of a particular variable at precise discrete moments in time, 3 and, if we do, we seldom use the observations in that form.Much more common is the case in which the observations either by necessity or by choice are in the form of averages or sums over a non-zero time interval.Simultaneous This view has been discussed at length by Bentzel and Hansen [2].The basic position on causation has been vigorously maintained by H. Wold in several works, e.g., Wold and Jureen [11]. 2 Strotz [10]; but see also Gorman [6].

A method is shown for finding all solutions to the generalized von Neumann model formulated by Kemeny, Morgenstern, and Thompson. The method uses results from decomposing economic production systems to extend the algorithm of Hamburger, Thompson, and Weil. THIS ARTICLE shows how the results derived by Weil [5, 6] for decomposable production systems can be used to extend the results of Hamburger, Thompson, and Weil [1] for performing calculations on the generalized von Neumann model of an expanding economy formulated by Kemeny, Morgenstern, and Thompson [2]. A method is shown for finding all solutions to a generalized von Neumann model. The model represents an economy of m goods and n fixed-coefficient, constantreturns-to-scale processes for producing those goods. The set of processes form an m by n input matrix A and an m by n output matrix B. When the jth process is operated at unit intensity the amount ai of the ith good must be supplied at the beginning of the production period and the amount bij of the jth good is produced at the end of the period. The element xj, xj > 0, Ixj = 1, of the stochastic column vector x is the level at which the jth activity is operated. The element yi of the stochastic row vector y is the price of the ith good. Von Neumann required that