Problem Set 8 (Hand-In)
2
Problem Set 8: Towards Real Business Cycle Theory From: Mash-Erdene Ganbold (1154248) Exercise 1: Two-Period Model It’s known that s t = w t 2+Ρ agent' s optimal saving decision y t = f Hk t L = K t Α production function per capita where MP K = f ' Hk L MP N = A@f Hk t L - f ' Hk t LD with A = 1 (a) 1.Order Condition (4.2.12): w t = Y N Y N = MP N MP K = f ' Hk L =ΑK t Α-1 MP N = K t Α H1 -ΑL = ! w t We know that capital stock changes over time as per: K t +1 = H1 -ΔL K t + I t with Δ= 1 here. k t +1 = H1 - 1L k t + i t = i t k t +1 = i t = s t k t +1 = w t 2+Ρ = MP N 2+Ρ = k t Α 1-Α 2+Ρ (b) i. K t +1 = K t k t *Α H1-ΑL 2+Ρ = k t * | : k t * | : H1-ΑL 2+Ρ k t *Α k t * = 2+Ρ 1-Α k t *Α-1 = 2+Ρ 1-Α | ^ 1 1-Α k t * = J 1-Α 2+Ρ N 1 1-Α & k t * = 0 ii. k t Α = w t 1-Α | ^ 1 Α k t * = I w t 1-Α M 1 Α | set equal to above equation I w t 1-Α M 1 Α = J 1-Α 2+Ρ N 1 1-Α | ^Α I w t 1-Α M = J 1-Α 2+Ρ N Α 1-Α |·(1-Α) w t = H1 -ΑLJ 1-Α 2+Ρ N Α 1-Α = w t * iii.
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Solutions to Problem Set for the Macroeconomics course (BA) at University of Vienna
Transcript of Problem Set 8 (Hand-In)
-
Problem Set 8: Towards Real Business Cycle Theory
From: Mash-Erdene Ganbold (1154248)
Exercise 1: Two-Period Model
Its known that
st =wt
2+agent ' s optimal saving decision
yt = f HktL =Kt production function per capita
where MPK = f ' HkL MPN = A@f HktL - f ' HktLDwith A = 1
(a)
1.Order Condition (4.2.12): wt =YN
YN =MPN
MPK = f ' HkL = Kt-1 MPN =Kt
H1 - L =! wtWe know that capital stock changes over time as per: Kt+1 = H1 - LKt + It with = 1 here.kt+1 = H1 - 1L kt + it = itkt+1 = it = st
kt+1 =wt
2+=
MPN
2+= k
t
1-
2+
(b)
i.
Kt+1 =Kt
kt
*H1-L2+
= kt
*| : k
t
*| :
H1-L2+
kt
*
kt
*=
2+
1-
kt
*-1=
2+
1-| ^
1
1-
kt
*= J 1-
2+N
1
1- & kt
*= 0
ii.
kt
=
wt
1-| ^
1
k
t
*= I wt
1-M 1 | set equal to above equation
I wt1-
M 1 = J 1-2+
N1
1- | ^
I wt1-
M = J 1-2+
N
1- |(1-)
wt = H1 - L J 1-2+
N
1- =wt
*
iii.
We know that as per (4.2.14): y 'k+1 = r +
For = 1: y 'k+1 = r + 1
steady state: y=y
MPk = y ' = y
kt
-1= r + 1 | - 1
r = kt
-1- 1 | substitute k
t
-1 with k
t
*-1=
2+
1-
r*= J 2+
1-N - 1
Exercise 2: The RBC Model
1. The main problem with the theory behind Keynesian models used prior to the revival of business
cycle in the 1970s was the fact that it was not consistent with how agents decided.
2. Lucas argued that outcomes depend on policy because of agents expectations. This led to the
term expectations revolution of macroeconomics. (Additionally Freedman critique states that
unemployment does not dependent on inflation in the long run)
3. Keynesian model states that cycle is demand driven and government spending can affect the
demand while in the RBC model Lucas argued if government changes behaviour now private
agents would also change its expectations.
4. Solow-Swan model of Economic Growth which is classified as a Neoclassical Model.
5. The source of variations in the RBC model usually comes from technology and productivity
shocks.
6. If theres no source of variation in the RBC model the output will converge to steady state.
7. A positive transitory productivity shock causes the output to increase in the short-term but then to
retract to the initial level.
8. On the other hand a permanant productivity shock increases the output in the long run.
9.
10. To assess the RBC model typically sample moments are used.
11. It explains especially positive fluctuations of output well attributing it to positive productivity
shocks.
12. The model has its shortcomings when it comes to explaining negative fluctuations in output
through the concept of productivity shocks as a driving force behind such a change.
-
(b)
i.
Kt+1 =Kt
kt
*H1-L2+
= kt
*| : k
t
*| :
H1-L2+
kt
*
kt
*=
2+
1-
kt
*-1=
2+
1-| ^
1
1-
kt
*= J 1-
2+N
1
1- & kt
*= 0
ii.
kt
=
wt
1-| ^
1
k
t
*= I wt
1-M 1 | set equal to above equation
I wt1-
M 1 = J 1-2+
N1
1- | ^
I wt1-
M = J 1-2+
N
1- |(1-)
wt = H1 - L J 1-2+
N
1- =wt
*
iii.
We know that as per (4.2.14): y 'k+1 = r +
For = 1: y 'k+1 = r + 1
steady state: y=y
MPk = y ' = y
kt
-1= r + 1 | - 1
r = kt
-1- 1 | substitute k
t
-1 with k
t
*-1=
2+
1-
r*= J 2+
1-N - 1
Exercise 2: The RBC Model
1. The main problem with the theory behind Keynesian models used prior to the revival of business
cycle in the 1970s was the fact that it was not consistent with how agents decided.
2. Lucas argued that outcomes depend on policy because of agents expectations. This led to the
term expectations revolution of macroeconomics. (Additionally Freedman critique states that
unemployment does not dependent on inflation in the long run)
3. Keynesian model states that cycle is demand driven and government spending can affect the
demand while in the RBC model Lucas argued if government changes behaviour now private
agents would also change its expectations.
4. Solow-Swan model of Economic Growth which is classified as a Neoclassical Model.
5. The source of variations in the RBC model usually comes from technology and productivity
shocks.
6. If theres no source of variation in the RBC model the output will converge to steady state.
7. A positive transitory productivity shock causes the output to increase in the short-term but then to
retract to the initial level.
8. On the other hand a permanant productivity shock increases the output in the long run.
9.
10. To assess the RBC model typically sample moments are used.
11. It explains especially positive fluctuations of output well attributing it to positive productivity
shocks.
12. The model has its shortcomings when it comes to explaining negative fluctuations in output
through the concept of productivity shocks as a driving force behind such a change.
2 Problem Set 8 (hand-in).nb
