Uploaded by Alexandre Dalban

7 Slutsky Equation with notes

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dx
,
Tdp
I
I
I
I
I
I
Pix
,
+
pie
=
m
÷ pi
pit
•
Xun
Pz
,
F-
is
I:÷:¥¥÷¥÷
✗
,
=
=
✗
pi
to
*
dpi
,
if
M
,
✗
-
pain)
pi
>
-
×
i
,
( pi Pam )
,
Decompose
①
TE
into
SebÉEfEt
slope
=
_pP÷
and I F-
SE
rotate the BE
:
✗
°
slope
BCI with
get
to
pi
I
÷¥¥÷÷÷¥:÷÷÷¥⇐÷*÷
✗
F-
-
=
✗
=
=
☒
?
Ipf
,
-
✗
consumer✗
make
0
just affordable
to
in
SE
,
×
?
'
pain )
.
give
around
-
×
,
Cpi
,
pain )
②
Ia¥ct
Xun
:
shift BCI
income level
☐
÷÷÷÷÷÷÷
xFE=
✗
to
m to
-
F
-
the actual
get BC ?
✗
F
yj
.
H
PFRM-xpi
t
p.
m
g
(
+
:*
EESE
sxi-E-ax.SE
+
•
✗
FE
Slutsky equation/Identify
.
/ Decomposition
p <
Extra
practice
Pete C
general
case
*
Explain
steps
the
)
I
(x , x )
I
m =p x +p x
I
I
(p , p )
(p 0 , p )
m0
I m0 = p 0 x + p x
I
I
I
x (p 0 , p , m0 )
x SE = x (p 0 , p , m0 )
|
{z
}
intermediate dem.
x (p , p , m)
|
{z
}
initial dem.
p.tt
i
d✗i=E
( poorer )
( richer)
I
DXFE
<0
70
>
0
< 0
if
normal
if inferior
x (p 0 , p , m)
I
x IE = x (p 0 , p , m)
|
{z
}
final dem.
I
x IE
I
I
m0 > m
x
IE
x
p0 > p
m0
m
x (p 0 , p , m0 )
|
{z
}
intermediate dem.
I
I
x < x (p , p , m)
(p , p )
I
x < x (p , p , m)
I
x
I
x SE
p <
=x
(p 0 , p
, m0 )
x (p , p , m)
x (p , p , m)
I
x = x (p 0 , p , m)
I
Dp
Op
x (p , p , m)
>
,
←
°<
70
so
<o
%
x =
so
x SE +
x IE
Giffen good
trmcstbeñnfuior
.
inefñor
if
normal
if
Substitution e↵ect
z
}|
{
x (p , p , m) = [x (p 0 , p , m0 ) x (p , p , m)]
,
0
x (p , p , m)
Demand
curve
+ [x (p 0 , p , m) x (p 0 , p , m0 )]
|
{z
}
Income e↵ect
I
↳
ordinary
if
÷
,
slope
of
JPY-30 KD
I
normal
p
I
I
p >
p
x
IE

x 
x SE 
x IE
x SE 
x
-
I
I
I
I
I
I
I
I
I
p =$ .
I
p =$
①
u
↳
•
✗
✗
,
-1×2
k
a-
-
I
✓
slope
K
-
-
×
-
Before
•
_p¥
:
✗
pic pz
:
9- FILL
,
After :p
1
ftp.F.s.t.pt
>
BE
=
"
pmg
×
=
,
pz
•
Y÷
BCF
⑥
②
③
"
( slope of
Draw the Ics
① Draw BC
find
then
Find BCI
I
→
✗
Find BcF→
to
shift BCI
original income
Ax
?¥
✗
FE
✗
☐ ✗
it
F
-
-
II. 1>1
↳
original
Bc°
rotate
i
so that
✗
✗
°
around ✗
BCI has
slope
F
level
demand
BC )
_f
m
×
?
✗
F'
=
=
0
O
-
-
Xi
O
so
=
0
°
②
min {
u=
↳
×
""
|①
,
✗
,
"
if
Before
•
pi
:
"*
After :p
÷;¥÷÷÷÷:÷÷÷:÷÷¥÷÷
②
Find BCI
→
shift Bct
original income
DX
?
F-
BXFE
=
=
✗
F-
✗
original
find
✗
Ii
demand
rotate
F
level
×
F-
✗
Bc°
around ✗
_f
m
?
✗
=
F
°
0
<
°
BCI has
slope
✗
to
✗,
so that
③ Find BcF→
to
Bc
:
>
+
pie
steeper than
are
-
,
BCI and BCF
*
then
pain
"
"
•
① Draw BC
,
0
.
°
>
[
U
assam
=
p <p
✗ it ✗
z
p0 > p
p
p0
p
→ assume
①
Be
0
→
② BCI →
③
BcF→
✗
I
✗
F
✗
}
§
SE
I F-
U=
minx ,
>
☒ *}
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