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Unformatted text preview: Chapter 5. CapitalLabour Substitution and Economic Growth (in collaboration with Robert M. Solow) Ever since its emergence in John Hicks&s Theory of Wages (1932), the elasticity of substitution has Figured primarily in the theory of distribution. The standard proposition states that, with two factors, constant returns to scale, and cost minimization, the fastergrowing factor increases or decreases its share in income according as this parameter is larger or smaller than one. However, the elasticity of substitution is by de¡nition a technological fact, a characteristic of a production function which would turn out to play an important role. Indeed, as shown in La Grandville (1989) and extended in sections 2, 3 and 4, a higher value of the elasticity of substitution ce teris paribus does more than merely alter production possibilities, it expands them. Naturally, then, the elasticity of substitution should have signi¡cance in all branches of economics where technology matters. And it does. The purpose of this paper is to explore the role of the elasticity of substitution in the aggregative theory of economic growth. There are historical overtones to this technical theme. Broadly speak ing, the capitallabor ratio has probably been rising since the beginning of sedentary agriculture made largescale accumulation of capital possible. The ratio of the wage to the rental rate of capital has presumably also increased through history, though less regularly than the factor ratio. In the tradition of economics, accounting for these characteristics of the longterm growth path involves an interplay between technical progress and the evolution of capitallabor substitution possibilities (along with possible nonmarket forces that are not our concern here). In practice, growth theory has placed more emphasis on the analysis of technical change. We propose to focus our at tention on the signi¡cance of a changing elasticity of substitution. It is understood that in any onecompositegood representation of a many good economy, substitution on the consumption side between goods of dif ferent capital intensity will function much like direct input substitution. An early reference on this is R. Jones (1965); see also the more recent work by Klump and Preissler (2000) and E. Malinvaud ((2002) and (2003)). Most of 1 the time we will use the CES (constantelasticityofsubstitution) production function, so that & , as it is almost always denoted, is a parameter, not a pointwise varying characteristic of a more general production function. It will usually be clear from context when a particular statement would be true at a point even if & were not constant. It has been known since the beginning of &neoclassical¡ growth theory that permanently sustained growth is possible even without technological progress, provided that diminishing returns to capitalintensity operates very weakly. We underline the verb &is¡only because this fact is sometimes ca sually denied in the literature. In sections 2 and 3 of this paper we showsually denied in the literature....
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 Fall '08
 OLIVIERDELAGRANDVILLE
 Economics, Order theory, Capital accumulation, Monotonic function

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