Consider the following growth Model (C) Nt Ct = (1-s) Yt (Y) Y = AK N-8 (K) Kt+1 = (1-6)K, + syt = Pt (N) Nt+1= N(1 + YN) Pt (P) Pt+1 1+YK The new element in this model is that the price of capital falls each period by rate yk. The idea is that each period one unit of output saved can buy converted into a greater quantity of physical capital because improvements in the technology for producing machines. For example, in 2010 one unit of output saved could be converted into one machine, but in 2020 that same unit of output saved could be converted into 2 machines. a. Take the Aggregate representation above and convert it into its per capita representation. b. Solve for the growth rate of the per capita output, per capita capital, the price of capital, the wage rate and the rental price of capital.