On the Transition Dynamics in Endogenous Recombinant Growth Models

Abstract

Tsur and Zemel (2007) developed an endogenous growth model in which balanced long-run growth is obtained by assuming that the stock of knowledge evolves according toWeitzman’s (1998) recombinant expansion process and is used, together with physical capital, as input factor by competitive firms in order to produce a unique physical good. At each instant new knowledge is produced by an independent R&D sector directly controlled by a “regulator” who aims at maximizing the discounted utility of a representative consumer over an infinite horizon. The optimal resources required for new knowledge production are obtained by the regulator in the form of a tax levied on the consumers. The economy, thus, envisages two sectors, a competitive one devoted to the production of the unique physical good, and a regulated R&D sector in which the public good “knowledge” is being directly financed by the regulator and produced according toWeitzman’s production function.

In such framework Tsur and Zemel provide conditions under which the economy performs sustained constant balanced growth in the long run; moreover, when balanced growth occurs, they also characterize the asymptotic optimal tax rate and the common growth rate of all variables. Hence, by endogenizing the optimal choice for investing in knowledge production, their result generalizes Weitzman’s (1998) endogenous growth model in which the investment in knowledge production was assumed to be constant and exogenously determined.