Introduction to Modern Economic Growth we have replaced expanding input varieties with expanding product varieties The log specification in this utility function is for simplicity, and can be replaced by a CRRA utility function The patent to produce each product ν ∈ [0, N (t)] belongs to a monopolist, and monopolist who invents the blueprints for new products receives a fully enforced perpetual patent on this product Each product can be produced with the technology (13.40) y (ν, t) = l (ν, t) , where l (ν, t) is labor allocated to the production of this variety Since we have closed economy, y (ν, t) = c (ν, t) As in model with knowledge spillovers of Section 13.2, we assume that new products can be produced with the production function N˙ (t) = ηN (t) LR (t) (13.41) The representative household now determines both the allocation of its expenditure on different varieties and the time path of consumption expenditures We assume that the economy is closed and there is no capital, thus all output must be consumed Nevertheless, the consumer Euler equation will now apply to determine the equilibrium interest rate Labor market clearing requires that Z N(t) l (ν, t) dν + LR (t) ≤ L (13.42) Let us start with expenditure decisions Since the representative household has Dixit-Stiglitz preferences, the following consumer demands can be derived (see Exercise 13.22): (13.43) c (ν, t) = ³ R N(t) χ (ν, t)−ε 1−ε χ (ν, t) dν −ε C (t) , ´ 1−ε where χ (ν, t) is the price of product variety ν at time t, and C (t) is defined in (13.39) The term in the denominator is the ideal price index raised to the power −ε As before, it is most convenience to set this ideal price index as the numeraire, 594