Question

2. (20 POINTS) Consider an economy with one representative consumer and one representative firm. There is no government (no taxes). The consumer's utility function is U = log(C) - N where cis consumption and N$ is labor supply. The consumer's budget constraint is c = WNS + it in real terms. The representative firm has a standard Cobb-Douglas production function F(z,K,N) = zkN1-4. Suppose z=1 and K=1 so that the production function is simplified to F(N) = N1-4. Set up the labor market clearing condition and derive an equation that implicitly determines the equilibrium wage.

Answer 1

Solution: & Given Urlog Ce) - NS C = consumption NS = labor supply. c=WNS+T F (2,K,N) = 2kYNx F(N) = NIE equation that The labor market cleasing Condition and implicity determines Equilibrium wage is: ) Demand for Labor is given by [MPL = f (2, K, N) = zky na have = 2K*(1-x)(wyl-cd-1 z =1, k=1

X (N2(x-1) 1*1 = Marow mon = men = o NX = (1-a) e demand fore(n = {Cina) £"* labor U = wge-NS c = UNS U = logu NS NS u= logut wgNs_ws dos to-1

3 Substituting dy co - ANS tos - 1 =0 ANS=1] = supply for laber At Equilibrium labor dd = laborss 15 (CN) )! - a= (1-9) h :. So equilibrium real wage o -