Schumpeterian evolution of firms' capital-labor ratio distribution

According to J. Schumpeter innovation and imitation are two key drivers of economic growth. A quantitative realization of this idea using the formalism of kinetic equations was described in a number of papers. In most of these studies only one firm efficiency factor, the total factor productivity, was considered. In general, a description of economic evolution should include more efficiency factors such as, e.g., total factor productivity (TFP) and capital-labor ratio. The present study makes a preliminary step in the direction of two factor model development by considering central planner's problem of endogenous growth driven by the capital-labor ratio. The model describes an evolution of a distribution of firms on an odel developmentefficient path by considering a difference-differential analogue of the Burgers' type equation operating at a set of discrete capital-labor ratio levels. It is shown that if investment efficiency does not depend on the investment size, and production is characterised by decreasing returns to scale then firms concentrate at a certain level of capital-labor ratio. In the case of decreasing efficiency of investment with respect to its size, one observes widening of the distribution of firms in the capital-labor ratio. In addition, it is shown that the latter result holds in the case of increasing returns to scale.