Introduction to Modern Economic Growth stealing effect we encountered in Chapter 12 and raises the possibility of excessive innovations Finally, and perhaps most importantly, competitive innovations bring us to the realm of Schumpeterian creative destruction, since economic growth takes place with new firms replacing incumbents For this reason, the models discussed in this chapter are often referred to Schumpeterian growth models, though we prefer the term competitive innovations here, since it emphasizes the distinctive feature of this class of models relative to models of expanding varieties This description suggests that a number of new and perhaps richer issues arise when we model competitive innovations One may then expect models of competitive innovations to be significantly more complicated than expanding varieties models This is not necessarily the case, however In this chapter, we will present the basic models of competitive innovations, first proposed by Aghion and Howitt (1992) and then further developed by Grossman and Helpman (1991a,b) and Aghion and Howitt (1998) The literature on models of competitive innovations and Schumpeterian economic growth is now large and an excellent survey is presented in Aghion and Howitt (1998) Our purpose here is not to provide a detailed survey, but to emphasize the most important implications of these models for understanding crosscountry income differences and the process of economic growth We will also present these models in a way that parallels the mathematical structure of the expanding varieties models, both to emphasize the similarities and clarify the differences A number of distinct applications of these models are also discussed later in the chapter and in the exercises 14.1 The Baseline Model of Competitive Innovations 14.1.1 Preferences and Technology In this section, we present a tractable model of Schumpeterian growth We choose the economy to be as similar to the baseline (lab equipment) expanding machine variety model as possible, both to emphasize the parallels in the mathematical structures between these models and to highlight the basic economic differences that come from the presence of competitive innovations The economy is in continuous time and admits a representative household with the standard CRRA preferences, (13.1), as in the previous chapter Population is constant at L and labor is supplied inelastically The resource 610