Endogenous Growth Model (20 points) Consider an economy with a total population of 100. Each individual in this economy accumulates human capital. Each period, a person has one unit of time to split between work and human capital accumulation. Initially, each person devotes 0.9 units of time to work in each period. The efficiency parameter of the human capital accumulation technology "b." is 14. Aggregate output in period is given by Y=100u,H., where He is the human capital level of a person at the beginning of period t and ut is time spent working in period t. Let Ho =1. The human capital level at the beginning of period t+1 is given by Ht+1=bt(1-Ut)Ht where b: is the efficiency parameter of period t respectively. Assume z=1 a) What is the economy-wide human capital growth rate between periods 0 and 1? Now suppose that at the beginning of period 2, the government introduces a policy that raises the efficiency of the human capital accumulation technology to 20 (b2=20). However, since this policy was financed by taxing labour income, the per-period work hours u goes down to 0.8. b) Calculate per-person consumption for periods 2 and 3. Show your calculations in detail. c) What is the new human capital growth rate for periods 2 and above? d) Draw the time path for consumption for periods 0,1,2 and 3. Label the graph (show the time on the x-axis and c on y axis, show the slopes, label c for T=0,1,2,3)