Question 3 Please complete question giving all of the steps

Let's modify the first Romer model we developed in class. Let's assume that the production function is Yt=AtLyt and knowledge accumulation process is At+1=At+zLat, where Lyt,Lat and z are number of workers, number of researchers and productivity of researchers in developing new ideas, respectively. Let's assume that the number of workers and the number of researchers are always a constant fraction of total population, Lt, i.e Lat=(1l)Lt and Lat=lLt. Population, Lt grows at the constant rate of n. Question 3 Part a Find the growth rate of the per capita output on a balance growth path. Question 3 Part b Let's assume that the economy is currently on a balance growth path and the government contemplates an idea to encourage more people to become researchers. You can imagine that the government implements a new education dizes firms R\&D efforts. In our models igch a policy corresponds to a permanent increase in the value of the l parameter. Show how such a policy would impact the growth rate of the per capita output on a new balance growth path. Show the effect of this policy on the time path of the output per capita (it is easier to show it on log scale as oppose to the original scale) Question 3 Part c Let's assume again that the economy is currently on the balance growth path, but this time quality of graduate education improves that makes researchers more productive, i.e. z increases. Show the impact of such an increase on the growth rate of the per capita output on a new balance growth path. Show the effect of this policy on the time path of the output per capita