巴罗宏观经济学：现代观点7

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