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2 Experiments in the Romer model In the questions in this section, we will use the Romer model, described by equations YtAt+1Lyt+LatLat=AtLyt=zAtLat=L=lL with a given initial value A0. Question 2.1 What is the growth rate of the stock of ideas? What is the growth rate of output per capita? Question 2.2 Plot the trajectory of output and output per capita (two separate graphs, time on horizontal axis, output on vertical axis in logarithmic scale) for the following experiment. The economy is on the balanced growth path, when the government grants permanent residence permits for people from abroad. These new immigrants split between workers and researchers in the same shares as the original population. In both graphs, always plot the trajectory without the policy change and with the policy change, so that the two trajectories can be clearly compared. Question 2.3 How long will it take after the experiment until the economy settles on the new balanced growth path? Question 2.4 According to the model, which country should grow faster in the long run, the United States or the Netherlands? Why? Is this empirically correct? Question 2.5 Explain why a technology with a fixed cost of production exhibits increasing returns to scale