taffordabletheco
sumerpicksexactlythei
itialbu
dleas
mmwellsothattheow
pricesubstitutio
effectforcommodity1iszeroA
dthei
comeeffectiswhichis
p1p1
positiveifthepriceofcommodity1becomeslessviceversaCase2
p1
p2

1a

sothata
ybu
dle
satisfyi
g
p1x1

p2x2
mis
probably
selectedSuppose
that
fi
allythe
bu
dle
x1x2
is
1233
fchose
bytheco
sumerU
derthefi
alpricesa
dgive
thei
itialbu
dleca
bejustaffordabletherearealso
i
fi
itebu
dleswhichmaybeselectedAssume
owtheco
sumerpicksx1x2The
thesubstitutio
effectfor
commodity
1
is
x1

mp1

a
d
the
i
come
effect
is
x1x1
Case3
p1p2

1a
sothatthefi
albu
dlechose
bytheco
sumeris0

mp2
Si
ceu
derthe
ewpricesthei
itialbu
dleis
alsoexactlyaffordablethebu
dlepickedbytheco
sumeris

0
mp1p1p2


So
the
substitutio

effect
for
commodity
1
isma
dthei
comeeffectforcommodity1iszerop1
Nowassume
i
itially
p1p2

1a

so
thatthe
i
itial
bu
dle
is0

mp2

the

the
priceofcommodity1
becomes
p1
A
alogouslythefollowi
gsholdCase4
If
p1p2

1a

the
fi
al
bu
dle
is
mp1
0

A
d
the
substitutio

effect
for
commodity
1
is
mp1

a
d
the
i
come
effect
is
zeroCase5
If
p11a
dassumethefi
albu
dleselectedbytheco
sumerisp2a
x1x2
the
substitutio
effectforcommodity1
isx1a
dthei
comeeffectiszero
Case6
Ifp11thefi
albu
dleisthe
thei
itialbu
dleThe
boththesubstitutio
effecta
di
comeeffectforcommodityp2a
1arezero
A
dthe
supposei
itially
p11the
a
ybu
dlesatisfyi
gp2a
p1x1p2x2misprobablyselectedassume
thatx1x2isi
itiallychose
Case7
1333
fIf
p1p2

1a

the

the
fi
al
bu
dle
is
mp1
0
The
substitutio

effect
for
commodity
1
is
p1x1p2x2p1
x1
p2x2p1

a
dthei
comeeffectismp2x2p1p1
A
d
oteit’simpossiblethatp11Otherwisethepriceofcommodity1does
’tvaryatallp2a
Case8If
p1p2

1a

the

the
fi
al
bu
dle
is0

mp2


U
der
the
fi
al
prices
if
the
i
itial
bu
dle
is
just
affordable
the
co
sumer
shall
select
thebu
dle0

p1x1
p2x2p2


so
the
substitutio

effect
for
commodity
1
is
x1a
dthe
i
comeeffectiszeroE
d
11．Itiseasytofi
dthei
itialco
sumptio
ofyism3075thefi
alo
eism3010a
dthebu
dle
2py4
2
p

y
3
chose
ifo
efacesthebudgetli
ewiththesameslopeofthefi
albudgetli
ea
dthroughthei
itialco
sumptio

bu
dlewhichispxxpyy2625875
2py
3
Sothesubstituteeffectis87575125a
dthei
comeeffectis10875125E
d
12．Forexamplethepriceofcommodity1decreaseswiththepriceofcommodity2fixedweca
drawalir