Civil Engineering Reference
In-Depth Information
Capital transfer equation changes to
s
t
s
t
−
1
s
t
(
1
+
γ
)
k
t
+
1
(
)=(
1
−
δ
)
k
t
(
)+
x
t
(
)
which
β
=
ρ
(
1
+
g
n
)
,
1
+
γ
=(
1
+
g
n
)(
1
+
g
z
)
.
The enterprise's profit maximization problem changes to
s
t
s
t
−
1
s
t
s
t
s
t
−
1
s
t
s
t
max
{
k
t
(
s
t
)
,
l
t
(
s
t
)
}
A
t
(
)
F
(
k
t
(
)
,
l
t
(
))
−
r
t
(
)
k
t
(
)
−
ω
t
(
)
l
t
(
)
.
(2)
Resource constraint of the society changes to
s
t
s
t
s
t
s
t
c
t
(
)+
x
t
(
)+
g
t
(
)=
y
t
(
)
.
(3)
2.1.2
The Equilibrium Conditions of the Model
Assume:
k
α
l
1
−
α
F
(
k
,
l
)=
u
(
c
,
l
)=
log
(
c
)+
ψ
log
(
1
−
l
)
we can get
s
t
ψ
c
t
(
)
s
t
s
t
s
t
−
1
)
α
l
t
s
t
)
−
α
)
=(
−
α
)[
−
τ
lt
(
)]
(
)
(
(
1
1
A
t
k
t
(4)
1
−
l
t
(
s
t
1
c
t
(
1
c
t
+
1
(
s
t
+
1
s
t
s
t
+
1
s
t
)
(
1
+
γ
)[
1
+
τ
xt
(
)] =
β
∑
s
t
+
1
π
(
|
)
s
t
)
s
t
+
1
s
t
s
t
+
1
1
−
α
s
t
+
1
{
α
A
t
+
1
(
)
k
t
+
1
(
)
l
t
+
1
(
)
+(
1
−
δ
)[
1
+
τ
xt
+
1
(
)]
}.
(5)
Production function
s
t
s
t
s
t
−
1
)
α
l
t
s
t
1
−
α
(
)=
(
)
(
(
)
.
y
t
A
t
k
t
(6)
The equilibrium conditions of the model are described by optimal conditions (
4
),
(
5
), production function (
8
), and resource constraints (
3
).
2.1.3
Steady-State Calculation
It is easy to obtain
ψ
−
1
(
1
−
α
)[
1
−
τ
l
]
A
l
=
1
−
α
1
ψ
−
1
(
−
α
)[
−
τ
l
]
A
−
(
γ
+
δ
)
ξ
+(
−
ξ
2
)
A
1
1
1
=
ψ
−
1
ξ
1
(
c
(
1
−
α
)[
1
−
τ
l
]
A
1
−
l
)
ξ
1
y
=
A
l
.
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