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Consumption,
Saving
andInvestmentMacroeconomics
Chapter
71Chapter
7Consumption
and
SavingMacroeconomics
Chapter
72·
Household
budget
constraintC
+
(1/P)
·
?B+
?K
=π/P
+
(
w/P
)·L
+
i·(
B/P
+
K)π
/P
=
0C+(1/P)·?B+?K=(w/P)·L+i·(B/P+K)
consumption+
real
saving
=
real
incomeConsumption
and
SavingMacroeconomics
Chapter
73Consumption
and
SavingMacroeconomics
Chapter
74Consumption
Over
Two
YearsYear1·
C1
+
(
B1/
P
+
K1)
?
(
B0/
P
+
K0)
=(
w/P)1
·
L
+
i0
·
(
B0/
P
+
K0)consumptionin
year1
+
real
saving
in
year1
=real
income
in
year1Year2C2
+
(
B2/
P
+
K2)
?
(
B1/
P
+
K1)
=(
w/
P)
2
·
L
+
i1
·
(
B1/
P
+
K1)consumption
in
year
2
+
real
saving
in
year
2=
real
income
in
year
2Consumption
and
SavingMacroeconomics
Chapter
75·
Consumption
Over
Two
Years
Combine
the
budget
constraints
to
describe
ahousehold’s
choice
between
consumingthisyear,
C1,
and
next
year,
C2.B1/P
+K1
=B0/P
+
K0
+
i0·(B0/P
+
K0)
+
(
w/P)1·L?
C1Real
assets
end
year1
=real
assets
end
year0
+
real
income
year1–
consumption
year1Consumption
and
SavingMacroeconomics
Chapter
76Consumption
and
SavingMacroeconomics
Chapter
77Consumption
and
SavingMacroeconomics
Chapter
78·
Consumption
Over
Two
YearsB1/P
+K1
=(1+i0)
·
(B0/P
+
K0)
+
(w/P)1
·
L
?
C1
B2/P
+K2
=(1+
i1)
·
(B1/P
+
K1)
+
(w/P)2
·
L
?
C2
B2/P
+K2
=(1+i1)
·
[(1+i0)·(
B0/P
+
K0)
+
(w/P)1·L
?
C1]+
(w/P)2
·
L
?
C2Consumption
and
SavingMacroeconomics
Chapter
79Consumption
Over
Two
YearsC2+(1+i1)·
C1
=
(1+i1)·(1+i0)·(B0/P+K0)+(1+i1)·(w/P)1·L+(w/P)2·L
-
(B2/P
+
K2)Two-year
household
budget
constraint:C1
+
C2/(1+i1)
=
(1+
i0)·(B0/P+K0)
+(w/P)1·L+(w/P)2·L/(1+i1)?(B2/P+K2)/(1+i1)Consumption
and
SavingMacroeconomics
Chapter
710·
Present
valueIf
the
interest
rate,
i1,
is
greater
thanzero,
$1
received
or
spent
in
year
1
isequivalent
to
more
than
$1
in
year
2.Dollarsreceived
or
spent
in
year
2must
be
discounted
to
make
themcomparable
to
dollars
in
year
1.The
term
1+i1
is
called
a
discountfactor.Consumption
and
SavingMacroeconomics
Chapter
711Household
chooses
the
time
path
ofconsumption—in
this
case,
C1
and
C2—to
maximize
utility,
subject
to
thebudget
constraint.Consumption
and
SavingMacroeconomics
Chapter
712·
Choosing
consumption:
income
effectsC1
+
C2/(1+i1)
=
(1+
i0)·(B0/P+K0)
+(w/P)1·L+(w/P)2·L/(1+i1)?(B2/P+K2)/(1+i1)p.v.
of
consumption
=
value
of
initialassets
+
p.v.
of
wage
incomes
?
p.v.
ofassets
end
year
2V
=
(1
+
i0)·(B0/P+K0)
+
(w/P)1·L
+
(w/P)2·L/(1+i1)p.v.
of
sources
of
funds
=
value
of
initialassets
+
p.v.
of
wage
incomesConsumption
and
SavingMacroeconomics
Chapter
713·
Choosing
consumption:
incomeeffectsC1
+
C2/(1+i1)
=
V
?
(B2/P+K2)/(1+i1)p.v.
of
consumption
=p.v.
of
sources
of
funds–
p.v.
of
assets
end
year
2Consumption
and
SavingMacroeconomics
Chapter
714·
Choosing
consumption:
income
effectsSuppose
that
V
increases
due
to
a
rise
in
wageincomes.
Since
we
are
holding
fixed
the
term(B2/P+K2)/(1
+
i1),thetotal
present
value
ofconsumption,
C1
+
C2/(1
+
i1),
must
rise
bythe
same
amount
as
V.Since
households
like
to
consume
at
similarlevels
in
the
two
years,
we
predict
that
C1
andC2
will
rise
by
similar
amounts.
These
responses
of
consumptionto
increasesin
initialassets
or
wage
incomes
are
called
incomeeffects.Consumption
and
SavingMacroeconomics
Chapter
715·
Choosing
consumption:
theintertemporal-substitution
effect.C1
+
C2/(1+i1)
=
V
?
(B2/P+K2)/(1+i1)p.v.
of
consumption
=p.v.
of
sources
of
funds–
p.v.
of
assets
end
year
2Consumption
and
SavingMacroeconomics
Chapter
716·
Choosing
consumption:
theintertemporal-substitution
effect.A
higher
i1
provides
a
greater
rewardfor
deferring
consumption.
Therefore,the
household
responds
to
an
increasein
i1
by
lowering
C1
and
raising
C2.This
response
is
called
theintertemporal-substitution
effect.Consumption
and
SavingMacroeconomics
Chapter
717·
Choosing
consumption:
theintertemporal-substitution
effect.C1
+(B1/P
+
K1)
?
(
B0/P+K0)
=(w/P)1·L
+
i0·(B0/P
+K0)Consumption
in
year1
+
real
saving
inyear1
=
real
income
in
year
1Consumption
and
SavingMacroeconomics
Chapter
718·
Choosing
consumption:
theintertemporal-substitution
effect.We
know
from
the
intertemporal-substitution
e
fect
that
an
increase
inthe
interest
rate,
i1,
motivates
thehousehold
to
postpone
consumption,
sothat
this
year’s
consumption,
C1,fa
ls
on
the
left-hand
side.Consumption
and
SavingMacroeconomics
Chapter
719·
Choosing
consumption:
theintertemporal-substitution
effect.Since
year
1’s
real
income
is
given,the
decline
in
C1
must
be
matched
bya
rise
in
year1’s
real
saving,
(B1/P
+K1)
?
(B0/P
+
K0).The
intertemporal-substitution
effectmotivates
the
household
to
save
morewhen
the
interest
rate
rises.Consumption
and
SavingMacroeconomics
Chapter
720The
income
effect
from
a
change
in
theinterest
rateC2
+
(
B2/
P
+
K2)
?
(
B1/
P
+
K1)
=(
w/
P)
2
·
L
+
i1
·
(
B1/
P
+
K1)The
income
effect
from
i1 i1(B1/P)i1K1Consumption
and
SavingMacroeconomics
Chapter
721The
income
effect
from
a
change
inthe
interest
ratei1(B1/P)For
a
holderofbonds,
the
income
effectfrom
an
increase
in
i1
is
positive.For
an
issuer
of
bonds,theincome
effectfrom
an
increase
in
i1
is
negative.For
the
economy
as
a
whole,
lending
andborrowing
must
balancethe
income
effect
from
the
term
i1·(B1/P)is
zero.Consumption
and
SavingMacroeconomics
Chapter
722The
income
effect
from
a
change
inthe
interest
ratei1K1Average
household’s
holding
of
claimson
capital,
K1,
is
greater
than
zero.The
term
i1K1,
the
income
effect
from
anincrease
in
i1
is
positive.Consumption
and
SavingMacroeconomics
Chapter
723·
The
income
effect
from
a
change
inthe
interest
rateIn
the
aggregate,
the
income
effect
from
an
increase
in
i1
consists
of
a
zeroeffect
from
the
term
i1·(B1/P)
and
apositive
effect
from
the
term
i1K1.The
full
income
effect
from
an
increasein
i1
is
positive.Consumption
and
SavingMacroeconomics
Chapter
724Combining
income
and
substitutioneffectsThe
effect
of
an
increase
in
the
interestrate,
i1,
on
year
1’s
consumption,
C1The
intertemporal
substitution
effectmotivates
the
household
to
reduce
C1.An
increase
in
i1
also
has
a
positiveincome
effect,
which
motivates
thehousehold
to
raise
C1.The
overall
effect
from
an
increase
in
i1on
C1
is
ambiguous.Consumption
and
SavingMacroeconomics
Chapter
725Consumption
and
SavingMacroeconomics
Chapter
726·
Consumption
Over
Many
YearsTwo-year
budget
constraint·
C1
+
C2/(1+i1)
=
(1+
i0)·(B0/P+K0)+
(w/P)1
·
L
+
(w/P)2·L/(1+i1)–
(
B2/P+K2)/(1+i1)Relax
our
simplifying
assumption
thatthe
household
could
not
change
thepresent
value
of
assets
held
at
the
endofyear
2Consumption
and
SavingMacroeconomics
Chapter
727Consumption
and
income
in
future
years.overall
present
value
of
consumption=
C1+
C2/(1
+
i1)+
C3/[(1
+
i1)·(1
+
i2)]+
·
·
·overall
present
value
of
wage
incomes=
(w/P)1·L+
(w/
P)2·L/(1+
i1)+
(w/P)2·L/[(1+i1)·(1+i2)]+
·
·
·Consumption
and
SavingMacroeconomics
Chapter
728·
Multiyear
budget
constraint:C1
+
C2/(1
+
i1)
+
C3/[(1+i1)·(1+i2)]
+
·
·
·=(1+
i0)·(B0/P+K0)
+
(w/P)1·L+
(w/P)2·L/(1+
i1)
+
(w/P)2·L/[(1+i1)·(1+i2)]+
·
·
·Consumption
and
SavingMacroeconomics
Chapter
729·
Multi-Year
budget
constraint
allowsthe
comparison
of
the
effects
oftemporary
and
permanent
changesin
income.Consumption
and
SavingMacroeconomics
Chapter
730·
Temporary
change
in
income·
We
predict
that
the
household
would
respondto
a
rise
in
(w/P)1
·
L
byraising
consumptionby
similar
amountsin
each
year:
C1,
C2,
C3,
and
so
on.
This
response
means,
however,that
consumption
in
any
particular
year,
suchas
year
1,
cannot
increase
very
much.Therefore,
if
(w/P)1
·
L
rises
by
one
unit,
wepredict
that
C1
increases
by
much
less
than
one
unit.
To
put
it
another
way,
thepropensity
to
consume
in
year
1
out
of
anextra
unit
of
year
1’s
income
tends
to
besmall
when
the
extra
income
is
temporary.Consumption
and
SavingMacroeconomics
Chapter
731temporary
change
in
incomeIf
(w/P)1·L
rises
by
one
unit
on
the
right-hand
side,
C1
rises
by
much
less
thanoneunit
on
the
left-hand
side.Year
1’s
real
saving,
(B1/P
+
K1)
?(B0/P
+
K0),
must
rise
by
nearly
one
uniton
the
left-hand
side.The
propensity
to
save
in
year
1
out
ofan
extra
unit
of
year
1’s
income
isnearly
one
when
the
extra
income
istemporary.Consumption
and
SavingMacroeconomics
Chapter
732·
Permanent
increase
in
wage
income·
(w/P)1·L,
(w/P)2·L,
(w/P)3·L,
and
so
oneach
rise
by
one
unit.·
It
would
be
possible
for
the
household
torespond
by
increasing
consumption
byoneunit
in
each
yearConsumption
and
SavingMacroeconomics
Chapter
733Permanent
increase
in
wage
incomeThe
prediction
is
that
the
propensity
toconsume
out
of
an
extra
unit
of
year
1’sincome
would
be
high—close
to
one—whenthe
extra
income
is
permanent.The
propensity
to
save
in
year
1
outofanextra
unit
ofyear
1’s
income
is
small
whenthe
extra
income
is
permanent.Consumption
and
SavingMacroeconomics
Chapter
734·
Consumption
Over
Many
YearsPermanent
income.·
Consumption
depends
on
a
long-termaverage
of
incomes—which
he
calledpermanent
income—ratherthan
currentincome.Consumption,
Saving,
and
Investmentin
EquilibriumMacroeconomics
Chapter
735Determine
the
aggregate
quantitiesof
consumption
and
saving.Determine
the
aggregate
quantityof
investment.Consumption,
Saving,
and
Investmentin
EquilibriumMacroeconomics
Chapter
736·
Budget
ConstraintC
+
(1/P)·?B+
?K
=
(w/P)·L
+
i·(B/P)+
iK·
i
=
(R/P
?
δ
)C+
(1/P)·?B+
?K
=(w/P)·L
+
i·(B/P)
+
(R/P)
·
K
?δ
KB
=
0
and
?B
=
0Consumption,
Saving,
and
Investmentin
EquilibriumMacroeconomics
Chapter
737·
Budget
ConstraintC+
?K
=
(w/P)·L
+
(R/P)·K
?
δ
K·
(w/P)·L
+
(R/P)·K
=
Y
(Real
GDP).C
+
?K
=
Y
?δKConsumption
+
net
investment
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