1. Suppose that the augmenter'l Solow model represents the world well enough. Assume that Y; : ArrnthtG. (a) Find the new transitional dynamics equations of the model= in el'lieiency units terms [TD2]. (Backward engineering." given that the model displays long-run equilibrium in ef- ciency units, we divide everything by ZtNt) (h) Find an expression for the. steady state Value of F: : ZALN and k : % How do we know that if\" exists? (c) Find an expression for the steady state value of y % and y : % g (d) Find an expression for the steady state. value of 1 = % and e = N (e) Use. the maerohistorv data set .lSTdatasetRLLdta to compute the growth rate of population in the US for the period 186072016. Plot a graph, clearly labeling the axis. Do you observe any trend or structural change in n? (f) \"That are the 1'1'1odel's ii'nplieations on ywk and r from the observed el'ianges in n in the US? (g) Is the observed evolution of y,c and r consistent with these predictions? Discuss how the model can (or cannot) make sense of the evolution of these. variables more broadly