The Role of Saving in a Growth Model with Induced Inventions

Abstract

T HE theory of induced invention along Kennedy-Weizsacker lines has recently been incorporated into growth models with factor-augmenting technical progress by Samuelson [9], Drandakis and Phelps [4], Amano [1] and Fellner [5]. In these models they have shown that under the assumption of a proportional saving function, the condition that the elasticity of substitution (C-) be less than unity is sufficient for global stability of the long-run equilibrium. In this paper we attempt to generalize their results by employing a more general saving function and to examine the role of saving in a growth model of this type. We assume that the marginal propensity to save out of profits (s1) and out of wages (s2) are two different constant proportions. It turns out that, in the presence of a C-ambridge saving function, the condition C< 1 is not always sufficient to assure global stability of Kennedy's economy. The stability of the system, in general, depends upon not only the elasticity of substitution, but also the saving propensities. Furthermore, the position of the invention possibility frontier as well as its shape is an important element in stability analysis. This is due to an important feature of the generalization in which changes in income distribution between profits and wages resulting from factor substitution along the isoquants, and technological substitution along the invention possibility frontier, are taken into account in determining the changes of the rate of growth of capital. In section I we set up the model and derive the required dynamic equations. In section II we analyze the existence and global stability of the steady-state growth path. In particular, a local stability condition will be derived. Finally, in section III, after summarizing the principal findings, we interpret our stability condition and compare it with the condition which we found elsewhere in a model with exogenous Harrod-neutral technical change [2].