Schumpeterian evolution of firms' capital-labor ratio distribution

A. Leonidov and E. Vasilyeva
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A. Leonidov: P.N. Lebedev Physical Institute, Moscow, Russia
E. Vasilyeva: P.N. Lebedev Physical Institute, Moscow, Russia

Journal of the New Economic Association, 2020, vol. 48, issue 4, 12-40

Abstract: 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.

Keywords: Schumpeterian evolution; economic growth; capital-labor ratio; firms' distribution; Burgers' equation (search for similar items in EconPapers)
JEL-codes: C61 C65 E22 O33 (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:nea:journl:y:2020:i:48:p:12-40

DOI: 10.31737/2221-2264-2020-48-4-1

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