THE USE OF the geometric distributed lag in economics is widespread. The Liviatan [6] method for estimating its parameters is simple and provides consistent estimates. Moreover, it can be used to provide initial estimates for more sophisticated techniques [2]. Not much is known about the statistical properties of these estimators, especially their small sample properties. We do know that their asymptotic efficiencies are inferior to most alternatives [1], and recently Nagar and Gupta [7] have provided approximations to the small sample biases. The purpose of this note is to derive a simple way of displaying the Liviatan estimators which makes their nature clear and which allows the small sample distribution of one of them to be easily deduced. The main result is that the estimator of the parameter which defines the geometric distributed lag is a ratio of two ordinary least squares estimators. With this and the assumption that the error terms form a sequence of independent, identically distributed normal variables, it is possible, using the work of Geary [4], to derive the small sample distribution of this estimator. This result forms the main part of this note, which concludes with a brief discussion of the problem of setting confidence limits along the lines suggested by Fieller [3].

The concepts of conditional risk aversion, the conditional risk premium, and risk independence pertaining to multiattributed utility functions are defined. The latter notion is then generalized to what is called utility independence. A number of theorems useful for simplifying the assessment of multiattributed utility functions given certain risk independence and utility independence assumptions are stated.

TO AN ECONOMIST the study of economic development is in large part an investigation into the mechanics of capital formation. At least in theory, the output options open to a developing economy are more restricted in the case where possibilities for obtaining foreign exchange via trade or aid are relatively limited. Society's menu of choices is even easier to enumerate if it is further assumed that labor is surplus in the sense that labor supply is a non-binding constraint on economic development now and for some time to come. These conditions are roughly descriptive of the historical situation confronting some large underdeveloped nations wishing to industrialize rapidly; the U.S.S.R. in the thirties is a classic example. In such situations the key to economic growth is the capacity of the domestic capital goods sector. Increasing that capacity by ploughing back a high proportion of investment goods for purposes of self-reproduction will permit high consumption levels eventually, but not just in the near future. The reverse is true if, by bolting down a substantial percentage of investment goods there, the consumer goods sector is presently expanded. These thoughts underlie a very interesting model of economic development first propounded by the Soviet engineering economist G. A. Fel'dman in 1928 [7] 2 We are indebted to Professor Domar [6] for pointing out the significance of this model and for relating it to current growth theory as well as to the Soviet industrialization debate of the twenties. The same model has been independently formulated by the Indian statistician P. C. Mahalanobis [9] who places somewhat greater emphasis on making it operational enough to serve as a rough guide of sorts for Indian long term planning.3 In its simplest form this model splits an economy into two departments, investment and consumption. Investment goods are general ex ante and can be used to increase the capacity of either sector. But ex post, capital is specific to the

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

In this paper a family of functional iterations is introduced. One member of this family is the Newton-Raphson method and another member, obtained from a generalization of Steffensen's method to a system of equations, has been considered in [7]. The general member of the family is derived from a regulafalsi construction, due to Gauss, for a particular choice of points in the iteration. From the computational point of view, all the members of the family of iterations, except the Newton-Raphson method, have the property that the partial derivatives of the system of equations are used almost never if a computing device with unlimited precision is utilized. Further, the asymptotic speed of convergence for any member is at least of order two. In view of the difficulties of obtaining the functional form of the second order partials of the likelihood function for general linear and nonlinear simultaneous systems, the method proposed here may be recommended in the computation of full information maximum likelih Dod estimates. Even if the partials of the system of equations are easily calculated, then some member of the family may still lead to convergence if the Newton-Raphson method does not. Practically speaking, the proposed method can be used to determine an approximate solution and this approximate solution will be closer to the solution if the precision of the computations is higher.

Arc elasticity is estimated for liquor by simply comparing state sales before and after price increases, standardized by states in which price did not change. The technique can be used wherever there are several economic units independent with respect to price changes; it allows causal interpretation and it permits comparison of various length-of-run elasticities.

Economic production systems may break up into subeconomies of goods and processes that can function independently of each other. This article first explores the various kinds of decompositions that may exist in production schemes, nonlinear as well as linear. Some recent techniques developed in graph theory are adopted to ascertain the decompositions possible for a given production system and the precedence relations between the subeconomies of the decomposition. Finally, I show how the concept of tearing from simultaneous equations theory might be used to analyze square input-output models for potential decompositions.