a. Why do the varieties model of technological change from section 6.1 exhibit a scale effect in the sense that the growth rate rises with the aggregate quantity of labor, L? Is it reasonable to identify L empirically with a country’s population?

The varieties model of technological change propounds that the firms indulge into research and development. This leads to innovation. The innovation is non rival in nature i.e.it is available to entire economy. Because of this the model has scale effect. The cost of invention gets distributed among the population. Therefore lager the population less is the per capita invention cost. Thus population growth tends to raise growth.
It is not reasonable to associate L empirically with the country’s population as the scale in the model tends towards two facts. First the amount of production for which the technology is employed in non rival manner. Secondly, the scope of patent. The countries may not define the proper unit in the first context if the idea is readily available. Countries may not be appropriate in the second context as well as the property right may be applicable internationally or there can be situation of monopoly if the secrecy is maintained. Although, Kremer opines that the scale effect can be visible over a longer period. It is widely accepted that this hypothesis is counterfactual and thus needs to be altered.
b. What happens in this model if population, L, grows at a constant positive rate?
Answer: if the population, L , grows at a constant positive rate the economy would not move to steady state with a constant growth rate. The higher level of population corresponds to higher innovation and thus more GDP and consumption. It have a scale effect.
c. What types of modifications to the model would eliminate the scale effects?

To eliminate the scale effect the assumption for research and development