Public Economics Lectures Part 1: Introduction

Life Cycle Model: Time Separability
By assuming time separability can rewrite the problem as:
U =
T
∑ β t u(c t , l t )
t=0
Leads to simpler first order conditions
l t : β t u lt + λw t /(1 + r) t = 0
c t : β t u ct + λ/(1 + r) t = 0
Combining yields: −u l (l t ) = w t u c
Intratemporal f.o.c. same as in static model
Intertemporal f.o.c.: u ct /u ct+1 = β(1 + r)
Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 131 / 217