The Implications of Steady State Growth for Endogenous and Embodied Technological Change

Abstract

THE CONCERN OF THIS PAPER is with necessary, rather than sufficient, conditions for the existence of steady state growth paths. In a sense this is a negative approach to growth theory but it does have its positive aspects. Firstly, it enables us to appreciate the restrictive nature of our assumptions concerning technological change if a steady state growth path is to exist. Secondly, it emphasizes the fact that if one wishes to study the implications of technological change in any but its simplest forms, it will be fruitless to investigate the properties of steady state growth paths. One may classify growth models according to the technological change assumptions that they embody. Technological change may be either exogenous or endogenous. Under either of these categories one may further classify the model according to whether technological change is embodied or disembodied. Lastly, if technological change is embodied, one then classifies the model according to whether there is a general or fixed coefficient production function. The simplest class of models are those in which technological change is both exogenous and disembodied. Swan [9] has shown the well known result that for a steady state growth path to exist for all time, technological change must be labor augmenting and change at a constant exponential rate. Not so well known is the extension of this result to the case where technological change is embodied and there is a fixed coefficient production function. Recently Inada [3] has shown that Swan's result is applicable in this case also if we assume the existence of the steady state growth path for any value of the savings ratio 's' in a non-degenerate closed interval and also that the economic lifetime of capital goods is constant on this path. If the latter assumption is dropped the problem remains open. Also open is the same problem but with a general production function replacing the previous fixed coefficient production function. Sufficient conditions for a steady state growth path to exist when technological change is endogenous and embodied and there is a fixed coefficient production function have been studied by Arrow [1] and the model extended to a general production function by Levhari [5]. Sufficient conditions have also been studied by Sheshinski [8] for the case where technological change is endogenous but disembodied. In all these learning by doing models technological change is purely