Innovation and Capital Accumulation in a Vintage Capital Model: an Infinite Dimensional Control Approach

Emilio Barucci - University of Florence and F. Gozzi - Pisa University

In this paper we present a model of capital accumulation and technology innovation/adoption in a vintage capital framework. The model is an infinite horizon/infinite dimensional optimal control model, the firm employs a continuum of technologies (a continuum of heterogeneous capital goods). Capital goods are technology specific, their technology is related to vintage and technology progress. The entrepreneur maximizes the profits obtained by employing a continuum of technologies under the assumption of constant returns to scale and bearing adjustment costs for gross investments. The diffusion of a new technology is established under some conditions, i.e. the long run stationary equilibrium stock of capital is a single-peaked function of the vintage, first increasing and then decreasing. Two different models are considered: quality differentiation of vintage capital goods with no technology progress and exogenous technology progress.

Scheduled for Session 4.3 Innovation And Pricing