Introduction to Modern Economic Growth aspect is entirely missing from the baseline model of competitive innovations, where not only any firm can engage in research to develop the next higher-quality machine, but the Arrow’s replacement effect implies that incumbents not undertake R&D A more realistic description of the research process may involve only a few firms engaging in innovation and competition in a particular product or machine line In this section, we will analyze a model of cumulative innovation of this type Following Aghion, Harris, Howitt and Vickers (2001), we will refer to this as a model of step-by-step innovation Such models are not only useful in providing a different conceptualization of the process of competitive innovations, but they also enable us to endogenize the equilibrium market structure and allow a richer analysis of the effects of competition and intellectual property rights policy In particular, both the model presented in the previous section and the models of expanding varieties imply that weaker patent protection and greater competition reduce economic growth Existing empirical evidence, on the other hand, suggests that typically industries that are more competitive experience faster growth (or at the very least, there is a non-monotonic relationship between competition and economic growth, see, for example, Blundell (1999), Nickell (1999) and Aghion, Bloom, Blundell, Griffith and Howitt (2005)) Schumpeterian models with an endogenous market structure show that the effects of competition and intellectual property rights on economic growth are more complex, and greater competition (and weaker intellectual property rights protection) sometimes increases the growth rate of the economy The model presented in this section will allow us to investigate these issues and also illustrate a range of other implications of models of competitive innovations 14.3.1 Preferences and Technology Consider the following continuous time economy with a unique final good The economy is populated by a continuum of measure of individuals, each with unit of labor endowment, which they supply inelastically To simplify the analysis, we assume that the instantaneous utility function takes a logarithmic form Thus the representative household has preferences given by (14.31) Z ∞ exp (−ρt) log C (t) dt, 630