Question

In the In the two-period neoclassical model with production, which expression is the tangency condition corresponding to the consumption function C d ?

1) 1 + rt = uC(Ct , 1 − Nt) / βuC(Ct+1, 1 − Nt+1)

2) wt = uL(Ct , 1 − Nt) / uC(Ct+1, 1 − Nt+1)

3) rt + ft = At+1FK((1 − δ)Kt + It , Nt+1) − δ

4) wt = AtFN (Kt , Nt)

5) None of the above

Answer 1

Answer is option 2)

Let in two period intertemporal leisure-consumption model

Let utility function, U = U(Ct, (1-Nt)) + β*U(Ct+1, (1-Nt+1))

Nt : Labor supply in year t

Nt+1 : labor supply in t+1

β : discount factor

.

Then at eqm,

Slope of BC = slope of IC

wt= U'(Ct , 1-Nt) / β*U'(Ct+1, 1-Nt+1)

wt : Wage rate