Introduction to Modern Economic Growth note that there are two senses in which there are limited scale effects in these models First, a faster rate of population growth translates into a higher equilibrium growth rate Second, a larger population size leads to higher output per capita (see Exercise 13.18) It is not clear whether the data support these types of scale effects either Put differently, some of the evidence suggested against the scale effects in the baseline endogenous technological change models may be inconsistent with this class of models as well For example, there does not seem to be any evidence in the postwar data or from the historical data of the past 200 years that faster population growth leads to a higher equilibrium growth rate In addition, the evidence that countries with larger markets are not necessarily richer is also inconsistent with the weaker scale effects implied by these models It is also worth noting that these models are sometimes referred to as “semiendogenous growth” models, because while they exhibit sustained growth, the per capita growth rate of the economy, (13.37), is determined only by population growth and technology, and does not respond to taxes or other policies Some papers in the literature have developed models of endogenous growth without scale effects, with equilibrium growth responding to policies, though this normally requires a combination of restrictive assumptions 13.4 Growth with Expanding Product Varieties Finally, we will briefly discuss the equivalent model in which growth is driven by product innovations, that is, by expanding product varieties rather than expanding varieties of inputs The economy is in continuous time and has constant population L It admits a representative household with preferences given by Z ∞ exp (−ρt) log C (t) dt, (13.38) where (13.39) C (t) ≡ "Z N(t) c (ν, t) ε−1 ε dν ε # ε−1 is the consumption index, which is a CES aggregate of the consumption of different varieties Here c (ν, t) denotes the consumption of product ν at time t, while N (t) is the total measure of products We assume throughout that ε > Therefore, 593