巴罗宏观经济学现代观点9章

Capital

Utilization

and

UnemploymentMacroeconomics

Chapter

91C

h

a

p

t

e

r

9Capital

InputMacroeconomics

Chapter

92·

Capital

utilization

rateThe

fraction

of

the

capital

stock

used

inproduction.κ

(the

Greek

letter

kappa)

representthe

utilization

rate

for

the

capital

stock,K.Y=

A·

F(κK,

L)Capital

InputMacroeconomics

Chapter

93·

κK,

rises

with

the

utilization

rate,

κ.Therefore,

an

increase

in

κ

raises

real

GDP,

Y,

for

a

given

technology

level,

A,

capital

stock,

K,

and

labor

input,

L.Capital

InputMacroeconomics

Chapter

94·

The

Demand

for

Capital

ServicesFirms

maximize

real

profitπ/P

=

A·F[(κK)d,

Ld)]–

(w/P)·Ld

−

(R/P)·(κK)dCapital

InputMacroeconomics

Chapter

95Capital

InputMacroeconomics

Chapter

96·

The

Demand

for

Capital

ServicesAssume

that

the

technology

level

risesfrom

A

to

A’.

This

change

raises

theMPK

at

a

given

quantity.Capital

InputMacroeconomics

Chapter

97Capital

InputMacroeconomics

Chapter

98The

Supply

of

Capital

ServicesFor

a

given

stock

of

capital,

K,

ownerscan

supply

more

or

less

capital

servicesper

year

by

varying

κ.One

reason

to

set

the

utilization

rate,

κ,below

its

maximum

is

that

increases

in

κtend

to

raise

the

depreciation

rate,

δ.δ

=

δ(κ)Other

reasons

include

utility

cost

ofcapital.Capital

InputMacroeconomics

Chapter

99·

The

Supply

of

Capital

ServicesNet

real

income

from

supplying

capitalservices=

real

rental

payments

−depreciation=

(R/P)

·

κK

−

δ(κ)

·

K=

K·[(R/P)·κ

−

δ(κ)]Rate

of

return

from

owning

capital=

(R/P)·κ

−

δ(κ)Capital

InputMacroeconomics

Chapter

910Capital

InputMacroeconomics

Chapter

911·

Owners

of

capital

(households)select

the

utilization

rate,

κ,

thatmaximizes(R/P)·κ−δ(κ)The

solution

is

κ

=

κ∗Capital

InputMacroeconomics

Chapter

912Capital

InputMacroeconomics

Chapter

913·

Thus,

an

increase

in

the

real

rentalprice

raises

the

capital

utilizationrate;

the

higher

real

rental

pricemakes

it

worthwhile

to

raise

κdespite

the

resulting

increase

in

thedepreciation

rate,

δ(κ).Capital

InputMacroeconomics

Chapter

914·

Market

Clearing

and

Capital

UtilizationThe

supply

curve

slopes

up

because

anincrease

in

the

real

rental

price,

R/P,motivates

a

higher

capital

utilization

rate,κ.·

The

technology

level,

A,

does

not

affect

thechoice

of

the

capital

utilization

rate,

κCapital

InputMacroeconomics

Chapter

915Capital

InputMacroeconomics

Chapter

916·

Market

Clearing

and

CapitalUtilizationWhen

the

technology

level

rises

to

A,the

demand

curve

for

capital

servicesshifts

to

the

right,

and

the

supply

curvedoes

not

shift.Therefore

the

market

clears

at

thehigher

real

rental

price,

[(R/P)∗],

andthe

larger

quantity

of

capital

services,[(κK)∗].Capital

InputMacroeconomics

Chapter

917·

We

now

have

three

reasons

why

real

GDPrises

in

a

boom

and

falls

in

a

recession.First

a

high

or

low

technology

level,

A,

causesreal

GDP

to

be

correspondingly

high

or

low.A

high

or

low

A

causes

L

to

be

correspondinglyhigh

or

lowA

high

or

low

A

causes

the

capital

utilization

rate,κ,

and,

thereby,

the

quantity

of

capital

services,κK,

to

be

correspondingly

high

or

low.Capital

InputMacroeconomics

Chapter

918·

Market

Clearing

and

Capital

Utilizationi

=

(R/

P)

·

κ

−

δ(κ)Rate

of

return

on

bonds=

rate

of

return

on

ownership

of

capitalIncrease

in

the

technology

level,

A,

raisesthe

rate

of

return

from

owning

capital,

theinterest

rate,

i,

increases.

The

interestrate

is

still

procyclical

in

the

model.Capital

InputMacroeconomics

Chapter

919·

The

Cyclical

Behavior

of

CapacityUtilizationThe

Federal

Reserve

computes

capacity

utilization

by

expre

sing

a

sector’s

output

of

g

ods

as

a

percentage

of

the

estimated

“normal

capacity”

of

each

sector

to

produce

g

odsCapital

InputMacroeconomics

Chapter

920The

Labor

Force,

Employment,

andUnemploymentMacroeconomics

Chapter

921Basic

Concepts

and

EmpiricalPatternsu

=

number

unemployed/labor

force=

(

labor

force−

number

employed)/labor

force=

1

−

(number

employed/labor

force)=

1

−

employment

rateemployment

rate=

1

−

uThe

Labor

Force,

Employment,

andUnemploymentMacroeconomics

Chapter

922Employment

=（1

−

u）·

Labor

forceTotal

working

hours=

（1

−

u）·

Laborforce

·

working

hours

per

workerThe

Labor

Force,

Employment,

andUnemploymentMacroeconomics

Chapter

923The

Labor

Force,

Employment,

andUnemploymentMacroeconomics

Chapter

924The

Labor

Force,

Employment,

andUnemploymentMacroeconomics

Chapter

925The

Labor

Force,

Employment,

andUnemploymentMacroeconomics

Chapter

926The

equilibrium

business-cycle

model

isprobably

satisfactory

for

understandingfluctuations

in

the

labor

force

and

hoursworked

per

worker.The

real

wage

rate,

w/P

adjusts

to

equatethe

quantity

of

labor

supplied,Ls,

to

thequantity

demanded,

Ld.However,

thisapproach

leavesunexplained

the

most

important

factor—the

fluctuations

in

the

employment

rate

or,equivalently,

in

the

unemployment

rate.The

Labor

Force,

Employment,

andUnemploymentMacroeconomics

Chapter

927·

A

Model

of

Job

FindingThe

Labor

Force,

Employment,

andUnemploymentMacroeconomics

Chapter

928The

Labor

Force,

Employment,

andUnemploymentMacroeconomics

Chapter

929·

A

Model

of

Job

FindingDistribution

of

wage

offers.For

each

real

wage

rate,

w/P,

on

thehorizontal

axis,

the

value

on

thevertical

axis

shows

the

probability

ofreceiving

that

offer.The

value

ω,

which

is

the

effective

realincome

received

while

unemployed.Key

decision

is

whether

to

accept

a

realwage,

w/P,

when

it

is

greater

than

ω.The

Labor

Force,

Employment,

andUnemploymentMacroeconomics

Chapter

930·

A

Model

of

Job

FindingReservation

real

wage,

denoted

by(w/P)’.

Offers

below

(w/P)’

arerejected,

and

those

above

(w/P)’

areaccepted.The

Labor

Force,

Employment,

andUnemploymentMacroeconomics

Chapter

931For

a

given

distribution

of

wage

offers

an

increasein

ω

makes

it

more

likely

that

w/P

<

ω

will

apply,because

ω

increases.Job

offers

will

be

rejected

more

often.

It

followsthat

job

searchers

tend

to

take

longer

to

find

aposition

when

ω

increases.

For

a

group

of

persons,we

therefore

predict

that

a

rise

in

ω

reduces

thejob-finding

rate,

which

is

the

rate

at

which

jobseekers

find

positions.Correspondingly,

a

rise

in

ω

raises

the

expectedduration

of

unemployment,

which

is

theamount

of

time

that

the

typical

unemployedperson

stays

unemployed.The

Labor

Force,

Employment,

andUnemploymentMacroeconomics

Chapter

932The

effect

of

the

increase

in

AThe

real

offer

risesReservation

real

wage

increases,

butnot

so

large

as

the

increase

in

the

realofferShort

run

effect

of

AThe

effect

of

ωThe

Labor

Force,

Employment,

andUnemploymentMacroeconomics

Chapter

933·

Search

by

Firms

is

important

in

a

well-functioning

labor

market,

the

allowance

for

this

search

does

not

change

our

major

conclusions.It

still

takes

time

for

workers

to

match

with

jobs,

sothat

the

expected

durations

of

unemployment

andvacancies

are

greater

than

zero.An

increase

in

workers’

effective

real

incomes

whileunemployed,

ω,

lowers

the

job-finding

rate

and

raises

the

expected

duration

of

unemployment.A

favorable

shock

to

productivity

raises

the

job-finding

rate

and

lowers

the

expected

duration

ofunemployment.The

Labor

Force,

Employment,

andUnemploymentMacroeconomics

Chapter

934Job

SeparationsJob-separation

rate,

the

rate

atwhich

job

matches

dissolve.This

rate

is

high

among

inexperiencedworkers

who

are

hard

to

evaluate

oramong

young

persons

who

are

likely

toexperience

changes

in

family

size

or

jobpreferences.The

separation

rate

is

also

high

inindustries

that

are

subject

to

frequentshocks

to

technology

or

product

demand.The

Labor

Force,

Employment,

andUnemployment·

Job

Separations,

Job

Finding,

andthe

Natural

Unemployment

RateMacroeconomics

Chapter

935The

Labor

Force,

Employment,

andUnemploymentMacroeconomics

Chapter

936The

Labor

Force,

Employment,

andUnemploymentMacroeconomics

Chapter

937·

Job

Separations,

Job

Finding,

andthe

Natural

Unemployment

RateJob−finding

rate

=

(number

of

hiresper

month)

/UThe

Labor

Force,

Employment,

andUnemploymentMacroeconomics

Chapter

938The

Labor

Force,

Employment,

andUnemploymentMacroeconomics

Chapter

939·

Job

Separations,

Job

Finding,

andthe

Natural

Unemployment

RateThe

natural

unemployment

rate

isthe

unemployment

rate

that

economytends

towards,

given

the

rates

at

whichpeople

lose

and

find

jobsThe

Labor

Force,

Employment,

andUnemploymentMacroeconomics

Chapter

940The

Labor

Force,

Employment,

andUnemploymentMacroeconomics

Chapter

941Job

Separations,

Job

Finding,

andthe

Natural

Unemployment

RateThe

change

in

the

number

of

persons

employed

over

a

month,

∆L,

is

given

by∆

L

=

ϕ

U

−

σ

L=

job

findings−

job

separationsThe

long-run

levels

of

L

and

U

areconstant.∆L=0ϕ

U

=

σ

Ljob

findings=

job

separationsThe

Labor

Force,

Employment,

andUnemploymentMacroeconomics

Chapter

942·

Job

Separations,

Job

Finding,

andthe

Natural

Unemployment

RateKey

equation

(natural

unemploymentrate):un

=

σ/(ϕ

+

σ)·

A

higher

job-separation,

σ

,

raises

thenatural

unemployment

rate,

un,

whereasa

higher

job-finding

rate,

ϕ,

lowers

un.The

Labor

Force,

Employment,

andUnemploymentMacroeconomics

Chapter

943·

Economic

Fluctuations,

Employment,and

UnemploymentAn

adverse

shock

to

the

technologylevel,

A,

reduces

the

marginal

productof

labor

for

the

typical

worker

and

job.The

job-finding

rate,

ϕ,

falls

becausemarket

opportunities

became

p