= wt , b
wt
=
(1 − α ) Yt
lt Nt
⇒
ln
⎢⎡(1
⎣
−
st
)
Yt Nt
⎤ ⎥ ⎦
−
ln(1
−
lt
)
=
ln
⎢⎡(1
⎣
−
α
)
Yt lt Nt
⎤ ⎥ ⎦
−
ln
b
( ) ⇒ ln lt − ln(1− lt ) = ln(1−α )− ln 1− s∗ − ln b
( ) l∗
=
1−α
(1−α )+ b 1−
consumption in next period will not change the expected utility.
The cost of this change:
e−ρt ⎜⎜⎝⎛
1 ct
⎟⎟⎠⎞ ×
∆c
3
The benefit of this change:
Et
⎨⎧e− ⎩
ρ
(t
+1)
U
=
∞
∑e
t =0
−
ρtu(ct
,1
−
lt
)
Nt H
ln Nt = N + nt, where N = ln N0
ut = ln ct + b ln(1− lt ) b > 0
z Shocks: First autoregressive process with white-noise disturbances ε 1) ln At = A + gt + A~t A~t = ρ A A~t−1 + ε A,t −1 < ρ A < 1
