Group
PSet2 Solutions .
.
Macro 2025
.
Question 1
_
a
In SS :
=>
K
Ke
<tr
Aks
K
=>
=
=
=
=
so
k(l-d)kI
I
54
=>
FTJT,
=> KAKIT
Il
YAKSEFIE
·
b) Ad
&
KtM
y a
+
2) -
↳
-
snock
c+
d)
-
N
·"as A,
5)
%
F
-
cas =
·
after
>t
es
N
·
got
.
.
a
smaller fraction
of
adj
t
i
·
adj
0 3 < 0 5
So we consume
O
su
=
.
-
se
yozy
as
but 5
same
Gyz
adjustment
ec"
·
3 t
.
output
the
question
Akz grikes
gggg
=
>
-
G
-
4
=*
.
Aki (d +)k
-
b)
+
=
Jk* (d n)k
+
=
=
c ( j)y (1 5) AEs
=
+
SS :
-
-
Ako ;
=k k or
=
jAbs-(ath) Mess O
J
kss(a m)
=
+
Rss
=
=
↳
c) We
·
max's
want to find 5 that
wrt 5
take a derivative C
·
set it
to 0
fing
,
C
of
Smax
]FrsF
.
-]
:
=
Fo c
.
-F
LS
22-1
-
251-1
2
-
=
=
;
0 ;7 divide
both sides
by
Fr
1
25F2
=
_
5F
0
=
-
1
=
0%
1E
5
=
2
.
·
&
a)
N SS
·
S
Y1
-
-
-
-
-
-
y
b)k
slope
in
same
Y
+
k
A
=
A
I
SS
k.
su
Y
>
t
su
ope
>
t
W
same
=
Y
=
SS
Y
su
a)
>
-
.
In
t
girl n
in
o
su
gya
-
>
su
isn
Go
-
>
O
t
-
-
t
~
it
>
t
~
i
-
su
>
t
.
Question 4
a) akz ? Gadg
=
81
GG g(z gN g4
-
-
=
-
;
l
= jk
kt
&
>
-
T
=
ggk
+
=-( )k
=
(can
also be
-
(a n)k ;
+
5yz-(d (k)
+
~
b)
bk + -
5k
(n :)ks
]
=
+
possible correct answers, the most likely ones are a one-time decrease in K and
C) Many
a one-time decrease in L.
fi
fi
• For the decrease in K, the justi cation could be that the natural disaster has led to
destruction of factories and equipment
• For the decrease in L, the justi cation could be loss of life associated with natural
disaster
But could also justify changes in other parameters too.
↓h ji
d)
giat
La
oh
In
) For
+
=
* ·
M
T
-
1
e)
>
k
-
1
kt
su
su
S
y+
y+
--
job
su
ys
su
S
S
Cxx
Cxx
&
S
o
-
-
-
-
& SS
su
C
su
C
-
si
-
question
-2)Akw
ForK
b)
:
= (1
0
-
2) A
LARL
=L K O
=
LAR""LEUPK
a
&
D
A
&
c) In
=
equilibrium ,
*
12
*
(
=
=
1
=
T
=
notation important
40]
50
* 47 3
" 1 40750
R**
Y*
&
:
.
=
3
75070
400
***** 0 25
.
.
%
* 2k
r
.
%25 80 7
-
w
* (1
*
2)k "
*
-
*
0 75
.
:
40
.
-"
·
-
-
-
-
-
-
y
sir
·
↑
Y
ksu
1
2
large
possibilities
2
. ↓Lis
2
.
↑
:
to
push Knock
/L still increases
way
to
new
so
above new so
not all the
but
knock
For scario 1 : Rsu] kss
b)
K+
k
A
=
stopt-A
-
n
su
>
Y+
A
slope
s
=
=
t
su
>
t
Ye
Ith,
A
lo
-
--S
SS
Yo
su
c)
>
-
su
t
>
t
gr
gi
I ·
No-
su
>
isn
t
Go
g
>
t
&
No-
T ·
O
---T
su
>
t
su
>
t
For
b)
scenario 2 : Es < ks
K+
↓
A
=
slope
Slope
=
k
1 +1
15.
=
A
=
X
ks-
su
>
t
su
in1
Y+
slope
A
>
t
ya
=
y
su
c)
>
su
t
gk+
gi
>
-
Li
su
>
t
gya
-
in
-
No
1
-
-
----
⑧
su
>
t
I
su
Go
t
>
t
-
o
i
su
>
t
Question 7
a)
.
CAUKBL"de
MPU :
BAU"KB71-59
(1-a-plaut-h-B
MPK :
UPLi
)
I
wL
r(u
UKPL"
it =
-
8)
max
K ,U , L
-B
=
O C K:
,
4
F
.
.
F02
.
.
.
"B
:
U
BAUP"
simplify p*
<
Combine :
:
Bk"
=
or
K
B
24
*
=
P
=
-
r
r
CAU""B" GB
cu R
**
=
+
&4 1
,
d) With
1
=
0
.
10 p
=
0 2
.
,
U*
=
***.
Firms want the level of land quality to be twice the amount of capital, but quality is fixed at only 10% the
amount of capital. This means two of the conditions for profit maximizing cannot both be simultaneously
true, specifically, the rental rates of capital will be different across the FOCs for K and U. Therefore the
economy is not in equilibrium because firms are not profit maximizing.
e)
Relaxing the constraint means letting quality of land rise, since in part d we saw quality was
fixed too low. As a result, the rental rate of capital would rise until it reaches its equilibrium
value where both FOCs for K and U agree. Intuitively, firms are willing to pay more for
capital when the quality of land is higher, so the equilibrium rental rate is larger than the
rental rate with quality fixed arbitrarily low.