The representative agent has preferences described by the utility function U = log C, whereC is...

The representative agent has preferences described by the utility function U = log C, whereC is consumption. The production technology is Y = zLaN(1-a) with 0 < a < 1, z is totalfactor productivity (TFP), L is land, and N is labor. The agent has 1 unit of time availablefor leisure, l, and work, N. That is, l + N = 1. The representative firm demands labor andpays the wage w.A. Calculate equilibrium leisure l* and labor N*;B. Assume land is fixed at L. Calculate the equilibrium profits of the firm p*;C. Assume there is a competitive rental market for land. The firm has to pay R per unitof land rented. Calculate the equilibrium profits of the firm p*;D. Assume land is fixed at L and population N grows according to N0 = g (C/N) N,where g (C/N) = d (C/N)?, with d > 0 and 0 < ? < 1. Calculate N*in steady state;E. Assume z changes to z+ with z+ > z. Does the new N*increase/decrease?12 Solow Model (50 points)The production technology is Y = zF(K, N) = zKaN(1-a) with 0 < a < 1, z is totalfactor productivity (TFP), K is capital, and N is labor. Capital accumulates accordingK0 = K - dK + I, where K0is the capital stock tomorrow, K is the capital stock today, dis the rate at which capital depreciates, and I is investment.A. Show that the production technology has constant returns to scale (CRS);B. Given Y = zKaN(1-a), calculate output per worker y = f(k), with k = K/N;C. Calculate the investment Iss that makes the capital stock to be constant over time.Interpret the result.D. Assume the economy saves a constant fraction s of output per worker y = f(k) suchthat i = sy, where i is investment. Calculate k*in steady state;E. Assume z changes to z+ with z+ > z. Does the new k*increase/decrease?