Introduction to Modern Economic Growth Let us now define the consumption index as àZ N ả 1 C ci ε di An identical analysis leads to utility maximizing decisions given by (12.8) and to the ideal price index P = µZ N p1−ε di i ¶ 1−ε The expression for the semi-indirect utility function is similar U (C, y) = C + v (y) , and using Using the definition of the ideal price index and (12.8), we obtain the budget constraint as P C + y ≤ m Equation (12.10) then determines y and C Since the supplier of each variety is infinitesimal, their prices have no effect on P and C Consequently, the profitmaximizing pricing decision in (12.12) obtains exactly, and each firm has profits given by à ảả ε − 1 0−1 N ε−1 ψ m−v π= εN εψ Now using this expression, we can endogenize the entry margin Imagine, for example, that there is an infinite number of potential different varieties, and a particular firm can adopt one of these varieties at some fixed cost µ > and enter the market Consequently, as in the Chamberlin’s (1933) model of monopolistic competition, in equilibrium all varieties will make zero profits because of free entry This implies that the following zero-profit condition has to hold for all entrants and thus for all varieties: (12.14) γ−1 γN Ã m−v 0−1 Ã N ε−1 εγ !! = µ As we will see in the next chapter, there is an intimate link between entry by new products (firms) and technological change Leaving a detailed discussion of this connection to the next chapter, here we can ask a simpler question: the aggregate demand externalities imply that there is too little entry in a model of this sort? The answer is not necessarily While the aggregate demand externalities 560