Economic growth and economic development 593

Introduction to Modern Economic Growth Therefore, given the BGP interest rate we can simply determine the long-run growth rate of the economy as: (13.20) g∗ = (ηβL − ρ) θ We next assume that (13.21) ηβL > ρ and (1 − θ) ηβL < ρ, which will ensure that g∗ > and that the transversality condition is satisfied We then obtain: Proposition 13.1 Suppose that condition (13.21) holds Then, in the abovedescribed lab equipment expanding input-variety model, there exists a unique balanced growth path in which technology, output and consumption all grow at the same rate, g ∗ , given by (13.20) Proof The preceding discussion establishes all the claims in the proposition except that the transversality condition holds You are asked to check this in ExerÔ cise 13.6 An important feature of this class of endogenous technological progress models is the presence of the scale effect, which we encountered in Section 11.4 in Chapter 11: the larger is L, the greater is the growth rate The scale effect comes from a very strong form of the market size effect discussed in the previous chapter As illustrated there, the increasing returns to scale nature of the technology (for example, as highlighted in equation (13.12)) is responsible for this strong form of the market size effect and thus for the scale effect We will see below that it is possible to have variants of the current model that feature the market size effect, but not the scale effect 13.1.4 Transitional Dynamics It is also straightforward to see that there are no transitional dynamics in this model To derive this result, let us go back to the value function for each monopolist Substituting for profits, this gives r (t) V (ν, t) − V˙ (ν, t) = βL 579