Explain what kind of behavior and features these periods capture.
Suppose X = 1; = 0:6; = 0:225, = 0:879, = 0:2,c~ = 1, = 1. Assume the initial conditions are given by g = 0:125, A = 3:17, L = 0:77, e = 0. Finally, in order to ensure the model converges to a balanced growth path in the long run, assume that gt+1 = (et + )minf Lt;a g with a = 8; instead of the assumption that we made in class that gt+1 = (et + ) Lt: Note that the new assumption ensures that at some high enough level of population, further expansions in the population level do not increase the rate of technological growth. Again, the assumption ensures that technology will stop accelerating and will simply grow at some constant rate in the long run.
a. Solve the model for the equilibrium time paths of all the variables by hand for the Örst 2 periods. Carefully explain every step of the way and show all of your work.
b. Solve the model in Excel for the equilibrium time paths of all the variables. Copy paste the answers for the Örst 10 periods into your hw solution.
c. Make a line plot of education (place this in secondary axis) and the growth rates of At;Lt and zt: Submit the plot.
d. What periods capture the Malthusian regime, post-Malthusian regime and the modern growth regime? Explain what kind of behavior and features these periods capture.
