Growth Cycles with Induced Technical Change

Abstract

This paper concerns itself with two related topics: the relative shares of workers and capitalists in the national income and the labour augmenting bias of technical change. Both have been dealt with, in contrasting fashion, in two seminal papers on distribution theory. Kennedy (I964) attempts to explain the then observed constancy of relative shares with the help of the now famous invention possibility frontier. However, the wage and profit rates are exogeneous to his model. Goodwin (I967), on the other hand, presents a model of cycles in growth rates in which the share of labour, the wage rate and the profit rate are endogenously determined. However, unlike the Kennedy analysis, technical change is assumed to be constant and exogeneously given. Given that these pioneering works have addressed themselves to important questions, it seems a worthwhile task to build a model in which the shares of labour and capital, the wage rate, the profit rate, and technical change are all endogenously determined. The perspective we have chosen here introduces the key element of Kennedy's perception, induced technical change, into the Goodwin scheme and the consequences of so doing are traced out in the following terse account. There are two classes in the economy, workers and capitalists. Only one good q(t) is produced and it can be either consumed or invested. Capital stock k(t) is homogeneous and, for simplicity, also assumed to be non-depreciating. The capital-output ratio at time t is denoted by o(t). Labour, I(t) is also homogeneous and its productivity at time t, a(t) = q(t)/l(t), improves at the rate ac(t). Labour's share in the national income denoted by u(t) is