A Model of Endogenous Growth: The Case of an Innovative Economy

The main aim of this paper is to bring some improvements to the model developed by Funke and Strulik, having as starting point the basic model proposed by Grossman and Helpman. We will prove that the competitive equilibrium solution is locally unique. Nevertheless, at least as regards the stability of equilibrium point, we confirm the results obtained by Funke and Strulik. 1. Introduction A large number of papers have been published in the last years on this subject, following the line developed by Grossman and Helpman [1]. Among them, to our knowledge, the first are the papers of Romer [2] and Eriksson [3]. Eriksson works out a model that is only a slight modification to those developed by Grossman and Helpman. The formal model of the economy of Romer has three sectors. The research sector uses human capital and the existing stock of knowledge to produce new knowledge. The intermediate-goods sector uses the designs from the research sector together with forgone output to produce the large number of intermediates that are in fact durable goods that are available for use in final goods production at any time. The final goods sector uses labor, human capital, and the set of intermediates that are available to produce final output. Output can be either consumed or saved as new capital. Few years later, the balanced growth path of the endogenous growth model with physical capital, human capital, and R&D has been explored by Funke and Strulik [4] and then by Arnold [5] (henceforth FSA). FSA suggest that the typical advanced economy follows three development phases, characterized by physical capital accumulation, human capital formation, and innovation. In their paper, FSA claim that consumption goods, investment goods, and intermediate goods are all produced with the same technology and they can be transformed one to one without further cost from output of the industrial sector which is produced with Cobb-Douglas technology. In other words, one unit of each intermediate can be obtained from one unit of final output. Gómez [6] analyzes the equilibrium dynamics of this model and corrects the analysis of FSA. Sequeira [7] incorporates an erosion effect into the endogenous growth model and claims that this effect significantly improves the fit between the model and the data. Iacopetta [8, 9] extends the earlier analysis of FSA and argues that other sequences of the phases of development are possible and shows that the model can generate a trajectory in which innovation precedes human capital formation. This trajectory accords with the observation that the rise