3. Carry out a simulation of the model over the periods 0 to 100, and show in a diagram the evolution of yo, c,, and the growth rate (y, - y,)/y,_ (or the approximate one Iny, - Iny,,), over the 100 periods. Comment with respect to what a developing country can obtain by birth control according to the Solow model. Does there seem to be any systematic difference with respect to the speed of convergence to the new steady state (or the speed by which the benefits arrive) between a decrease in the population growth rate as considered here, and an increase in the savings rate as considered in the example of section 5? For instance, for the two experiments (approximately from the figures) compare the number of periods it takes until half of the distance between the old and the new steady state values for y has been eliminated. Try to explain the difference (Exercise 3 may be useful)