Question 1.3 Show that the growth rate of output is equal to the growth rate of ideas. I Now plug in the same numbers as those in Problem 7 in Chapter 6 of the textbook (page 160). Let i: 0.05, z = 30100, E = 1,000 . Also , let the initial stock of ideas (in period 0) be A0 = 100. Question 1.4 Using these numbers , what is the growth rate of output per capita in the economy? I Question 1.5 What is the initial level of output per peson 'E' What is the level of output per person after 100 years? I 2 Experiments in the Romer model This problem assumes the baseline Romer model without capital . Question2.1 Assume that the economy is on the balanced growth path . Assume that there is a technology breakthrough that suddenly increases the amount of knowledge (measured by At) by 10%. 0 Describe in words what happens immediately after this breakthrough? o What will be the growth rate of the economy in the years after this breakthrough ? 0 Plot the trajectory of output per capita in the economy before and after the break - through (similar to that in Figures 6.3 and 6.4 in the textbook ). Question 2.2 Repeat question 2.1 with the following experiments 1. Smart people become more interested in nance than in research ,and the share of reseachers 1 decreases 2. The government allows an inflow of educated people from abroad that keeps the number of workers L!\" the same but increases the number of researchers , Lat (notice that from the perspective of the model parameters , there are two effects , one on f, and one on I). 3. The government decides that part of the tax revenue will be invested in research and development rather than spent on government consumption. This increased RSCD spending increases the productivity of the researchers 2