[This paper begins by formulating a finite horizon linear programming model for economic development. The formulation allows for heterogeneous capital goods and for nonnegativity constraints upon investment in each sector. It is then proved that a certain set of conditions are sufficient to ensure that an optimal solution to this T period, finite horizon plan will also coincide with an optimal solution during the first T periods of an infinite horizon plan. Among the restrictive conditions imposed to prove this sufficiency theorem are the following: gradualist consumption paths, no primary factors that cannot themselves be produced within the economy, a Leontief technology, and a characterization of the optimal finite horizon solution as one in which the terminal investment and output levels are positive. An illustrative numerical example is provided.]

THE CELEBRATED factor price equalization theorem has a curious history. Ohlin (1933) introduced to English-speaking readers an important modification to international trade theory, replacing the classical simplification, of constant costs but differing production functions among countries, with the alternative simplification of identical production functions but differing factor endowments. While many economists have remarked on the unrealism of Ohlin's simplification, an important aspect of it has not, it would seem, always been sufficiently appreciated. This is the fact that the classical model assumed that production relations in different countries differed in a quite arbitrary fashion; no satisfactory way had been provided for explaining how such production relations differed. In the Ohlin model, on the other hand, an element of continuity was introduced, since continuous variation of factor endowments would yield continuous (rather than arbitrary) variation in production relations. Even if differences in production relations (specifically, in transformation functions) cannot be completely explained in terms of differences in factor endowments, the Ohlin model is nevertheless susceptible to amendments that preserve meaningful relationships between different countries' production functions. Ohlin's writings were greatly influenced by Heckscher (1919), whose work was not made available in English until 1949. Heckscher, in turn, acknowledged the influence on his thought of Wicksell (1919).' Ohlin asserted that there was a tendency towards factor price equalization as a result of free trade, but he tempered his argument with many qualifications, even to the point of asserting that equalization would never be complete. The partial equalization argument was taken up and made rigorous by Stolper and Samuelson (1941), and later Samuelson (1948,

IT IS GRATIFYING that my paper on Additive Preferences has been the occasion for the preceding note by Samuelson, and also for an independent comment by W. M. Gorman which with characteristic modesty he has withdrawn from publication because its results were similar to Samuelson's. These admirable contributions do not call for extended comment on my part.' I take the opportunity, however, to answer an open question raised by Samuelson.2 This question concerns the existence of a nontrivial self-dual preference ordering, that is a preference ordering with a direct utility function that can be written in the same mathematical form as the corresponding indirect utility function. Writing x for the vector of quantities and y for the vector of prices (each divided by income),3 while 4 and ,G, denote a direct and indirect utility function respectively, a preference ordering is self-dual if it has a +(x) that is the same kind of function of x as at least one jGr(y) is of y. If so, the demand functions x=f(y) and the inverse demand functions y=g(x) must also have the same form. More precisely, there must be a function F such that x=F(y, A) and y=F(x, B), where A and B are sets of m parameters;4 note that Fis a single function, not a class of functions involving arbitrary parameters. Substituting the expression for y into that for x we get the functional equation

This paper gives a non-linear growth model, which explains the development of an economy through stages somewhat similar to the Rostovian stages. Non-linearity is introduced by including the inaugmentable factor of land or natural resources in the production function along with labor and capital, and by recognising that net saving is not a linear homogeneous function of income alone, but might be affected by the distribution of income and the interest rate and tends to be negative when per capita income is very low. Furthermore, population growth is assumed to follow a NeoMalthusian pattern. The effects of non-neutral as well as neutral technical progress are discussed in this paper.

PROFESSOR THEIL [5] recently gave the derivation of the best linear (B. L.) index number formulae for price and quantity. In an application of the formulae to Dutch import and export data, Kloek and DeWit [3] found that there is some slight, though persistent, bias to the effect that the index vectors yield larger current values than the individual data do. As this feature is related conceptually to the factor reversal test, they considered it desirable to devise a method which would control this bias on the average and worked out what may be called the best linear average unbiased (B. L. A. U.) index number. The aim of the present note is to indicate what relationship the B. L. and the B. L. A. U. indexes bear to the factorial indexes, that is, to those obtained through the factorial approach [1, 2, 4]. We conclude that the factorial indexes2 appear to compare well with the B. L. A. U. indexes. Incidentally, it is also pointed out that it might be possible to obtain a closer algebraic approximation to the B. L. index number formulae.