Journal Article A Note on Elasticity of Substitution Functions Get access Lawrence J. Lau Lawrence J. Lau Stanford University Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 43, Issue 2, June 1976, Pages 353–358, https://doi.org/10.2307/2297330 Published: 01 June 1976

W E shall motivate our investigation of exact index numbers by presenting an example of application of index number theory. We consider a profit-maximizing, price-taking firm endowed with a continuously differentiable non-decreasing and concave production function F(q). Suppose we have observations on the normalized prices p (nominal prices divided by the price of output) and the quantities of the inputs q at two distinct points in time, but not the outputs. An index number formula for the unobserved output is a function of the normalized prices and the quantities of the inputs at the two points, say I(P1,P2,q1,q2), which gives a measure of the ratio of the outputs at the two points, that is,

PpTHE application of duality in economic analysis was initiated by Hotelling (1932) and Roy (1942) in the area of consumer demand. Subsequently, Shephard (1953) in his pioneering work on cost and production functions extended the duality concepts to the theory of production and derived many of the fundamental results, including the basic duality theorems and Shephard's (1953) Lemma, which asserts that the gradient of the dual function is equal to the supply and demand correspondences. More recently McFadden (1972) generalized the duality concepts in production theory to include profit and revenue functions. The profit function is a function of the output and input prices which gives the value of the maximized profit of a profit-maximizing and pricetaking firm endowed with a given technology. Because of Shephard's (1953) Lemma, the partial derivatives of the profit function with respect to the output and input prices give the supply and demand functions. Thus, the econometric analysis of the behavior and technology of the profit-maximizing and price-taking firms is greatly facilitated.' In this paper we are concerned with the properties of the profit functions of technologies with multiple inputs and outputs. Several theorems which relate the properties of the transformation functions to the properties of the profit functions and vice versa are proved. The specific properties considered are: (1) homogeneity, (2) separability, and (3) nonjointness. The properties of the profit function have been studied by McFadden (1972), Diewert (1969), and Jorgenson, Christensen and Lau (1970), among others. In addition, Hall (1972) has approached the problem of multi-output, multi-input firms from the point of view of joint cost functions.

[The economic theory of individual choice most frequently assumes that individual preferences are weak orders; this implies, among other things, a virtually perfect discriminating power on the part of individual decision makers. R. D. Luce's theory of semiorders generalizes the weak order concept to allow imperfect discrimination when choices are close. This paper examines the demand implications of the semiorder axioms and states conditions on demand that are necessary and sufficient for the revealed ordering to be a semiorder.]

A LTERNATIVE strategies for economic development have frequently invoked the doctrines of balanced and unbalanced growth.' Policy recommendations in favor of balanced or unbalanced growth are based on a priori notions about the relationship between (lack of) balance and the process of development. For balanced-unbalanced growth to become an empirical hypothesis, rather than a doctrine, it has to be formulated in a way that it is given the chance to be proven wrong. An operational formulation involves three steps: balance (or imbalance) is defined in an unambiguous way that renders itself to quantification; an observable relationship between balance and economic development is postulated; this observable relationship is further specified by establishing causality and by determining the flow of causation. The hypothesized observable relationship between balance and economic development is sufficiently clear in the literature. The proponents of the balanced growth theory specify positive association between balance on the one hand and overall growth rate in national income (per capita). The relationship is reversed for the unbalanced growth theorists. The discussion on causality between balance and development is less unequivocal. In general, the flow of causation is supposed to run from balance (or imbalance) to development.2 Two examples will suffice for illustrative purposes. Nurkse [8] [31 advocates balanced growth on the grounds that it increases the reinvestible surplus, it provides inducements to invest, it creates external economies in complementary industries and as a result it leads to higher economic development. On the opposite side of the field Hirschman [4] perceives the causal link between imbalance and development in terms of external economies of vertical type and in terms of decision-making which is induced by disequilibria.3 The operational definition of the concept of balance or imbalance is probably the weakest part in the formulation of the theory. In a recent article Swamy [9] formulated the criterion of balance in terms of the dispersion of sectoral growth rates and he tested the hypothesis by correlating the resulting index with the overall rate of growth for an international cross section and time periods between 1948-1960. In this article we basically employ the same operational framework, data sources and time periods with Swamy. The significant divergence in results is due to the more suitable index of imbalance and the more refined data set that we use. In section I we discuss the different variants of balanced-unbalanced growth and we introduce the appropriate for each measure of dispersion. After a brief description of the data in section II, section III presents the evidence on the relationship between growth rates and indices of imbalance. In section IV the indices of imbalance are related to the level of development, as determined by a country's national income per capita. Finally, we draw the conclusions from our analysis and we compare our results with parallel investigations.

Dale W. Jorgenson, Lawrence J. Lau; The Duality of Technology and Economic Behaviour12, The Review of Economic Studies, Volume 41, Issue 2, 1 April 1974, P