微觀經(jīng)濟學消費者選擇理論_第1頁
微觀經(jīng)濟學消費者選擇理論_第2頁
微觀經(jīng)濟學消費者選擇理論_第3頁
微觀經(jīng)濟學消費者選擇理論_第4頁
微觀經(jīng)濟學消費者選擇理論_第5頁
已閱讀5頁,還剩45頁未讀, 繼續(xù)免費閱讀

下載本文檔

版權說明:本文檔由用戶提供并上傳,收益歸屬內(nèi)容提供方,若內(nèi)容存在侵權,請進行舉報或認領

文檔簡介

This

chapter

covers

topics

considered

advanced

for

the

typical

principles

course:

budget

constraints,

indifference

curves,

household

optimization,and

the

income

and

substitution

effects

of

price

changes.Most

students

find

it

more

difficult

than

average.The

first

half

of

the

chapter

develops

the

theory.

The

second

half

applies

the

theory

to

three

consumer

choice

problems:1)

Giffen

goods

and

positively-sloped

demand

curves2)

The

labor-leisure

choice3)

The

effects

of

interest

rates

on

household

savingNew

for

2008/2009:

The

first

half

of

this

PowerPoint

chapter

uses

a

different

example

than

the

text,

with

different

numerical

values.

(Theapplications

in

the

second

half

are

as

in

the

textbook.)?

2009

South-Western,

a

part

of

Cengage

Learning,

all

rights

reservedC

H

A

P

T

E

R消費者選擇理論經(jīng)濟學原理N.格里高利·曼昆21本章我們將探索這些問題的答案:·

預算約束如何代表了一個消費者能負擔得起的選擇?無差異曲線如何代表了消費者的偏好?什么決定了消費者如何將她的資源花在兩種物品上?消費者選擇理論如何解釋諸如消費者儲蓄多少,供給多少勞動等決策?23消費者選擇理論介紹·

第一章中的經(jīng)濟學十大原理之一:人們面臨權衡取舍?!?/p>

當消費者多買某種物品時,他只能買更少的其他物品·

工作時間更長意味著更多收入,更多消費,但更少的閑暇時間·

減少儲蓄會增加今天的消費,卻會減少未來的消費·

本章我們考察消費者面臨這些問題如何做出選擇The

two-good

assumption

greatly

simplifies

the

analysis

without

alteringthe

basic

insights

about

consumer

choice.If

your

students

remember

the

ProductionPossibilities

Frontier,

you

might

tell

themthata

budget

constraint

is,

in

essence,

a

“consumptionpossibilities

frontier”

for

the

consumer:

it

shows

all

combinations

(bundles)of

the

two

goods

that

the

consumer

can

afford

to

buy.預算約束:消費者能買得起什么4消費者選擇理論·

例如:Hurley把他的收入花在兩種物品上:魚和芒果一個“消費束"是物品的一個特定組合,比如:40條魚與300個芒果預算約束:對消費者可以支付得起的消費組合的限制Avery

straightforward

exercise.Hurley的收入:$1200價格:PF

=$4/每條魚,PM

=$1/每個芒果

如果Hurley將所有的收入都拿來買魚,那他能買多少條魚?

如果Hurley將所有的收入都拿來買芒果,那他能買多少個芒果?如果Hurley買了100條魚,那他還能買多少芒果?

將A

–C消費束畫在圖上,其中橫軸衡量魚的數(shù)量,縱軸衡量芒果的數(shù)量,并把這些點連接起來主動學習1預算約束5A.

$1200/$4=300條魚B.

$1200/$1=1200個芒果C.100條魚花

400美元,剩下的800美元買800個芒果主動學習1參考答案芒果的數(shù)量A魚的數(shù)量BCD.Hurley的預算約束表明他可以購買得起的消費束消費者選擇理論7預算約束線的斜率魚的數(shù)量芒果的數(shù)量D從C到D,

“縱軸”=–200個芒果“橫軸”=+50條魚斜率=–4Hurley為了得到1條魚必須放棄4個芒果C消費者選擇理論8預算約束線的斜率預算約束線的斜率等于:Hurley用芒果交換魚的比率用芒果來衡量魚的機會成本魚的相對價格:Another

straightforward

problemthat

will

not

take

much

class

time.

Yet,

students

will

learn

these

concepts

better

by

figuring

out

for

themselveshow

the

budget

line

moves

in

response

to

income

and

price

changes.Hurley的預算約束線在下列情況會發(fā)生什么樣的變化:他的收入減少到800美元芒果的價格上升到PM

=$2/每個芒果主動學習2預算約束線9主動學習2參考答案:A魚的數(shù)芒果的數(shù)現(xiàn)在Hurley

量能買$800/$4=200條魚或$800/$1=800個芒果或這兩者之間的任意組合收入減少使預算約束線向下移動量主動學習2參考答案:B魚的數(shù)芒果的數(shù)Hurley仍然能量買300條魚.但他現(xiàn)在只能買$1200/$2=

600個芒果.注意:斜率變小,魚的相對價格現(xiàn)在是兩個芒果一種物品價格的上升使預算約束線向內(nèi)轉(zhuǎn)動量偏好:消費者想要什么魚的數(shù)量芒果的數(shù)量無差異曲線:一條表示給消費者相同滿足程度的消費組合的曲線。在I1上的A,B以及其他消費束使Hurley感到同樣快樂–他在它們之間無差異I1Hurley的一條無差異曲線BA12消費者選擇理論無差異曲線的四個特征魚的數(shù)量芒果的數(shù)量如果魚的數(shù)量減少,那芒果的數(shù)量必須

增加,以使Hurley保持相同的滿足AHurley的一條無差異曲線I11.無差異曲線向右下方傾斜B13消費者選擇理論無差異曲線的四個特征魚的數(shù)量芒果的數(shù)量Hurley的幾條無差異曲線I1I2I0D2.消費者對較高無差異曲線的偏好大于較低無差異曲線他對I1

上的每個消費束(比如消費束A)的偏好要大于I0上的每個消費束(比如D)CA14消費者選擇理論相對于I1上的每個消費束(如消費束A),Hurley更喜歡I2

上的每個消費束(如消費束C)無差異曲線的四個特征魚的數(shù)量芒果的數(shù)量Hurley的無差異曲線I13.

無差異曲線不相交如果相交由于消費束B的兩種物品的數(shù)量都大于消費束C的兩種物品的數(shù)量,相對于C,Hurley會更偏好B。然而,Hurley卻是在B與C之間無差異:他在A與C之間無差異(兩個消費束都在I4)他在A與B之間無差異(兩個消費束都在I1)BCI4A15消費者選擇理論Hurley

has

more

fish

at

B

than

at

A,

so

an

extra

fishwould

be

less

valuable

atB

than

at

A.無差異曲線的四個特征魚的數(shù)量芒果的數(shù)量相對于消費束B,Hurley在消費A時愿意放棄更多的芒果來交換一條魚4.無差異曲線凸向原點I1116

A

B216消費者選擇理論At

A,

Hurleyhas

fewfish,

so

an

additional

fish

is

veryvaluable

to

him.At

B,

Hurley

already

has

lotsof

fish,

so

an

additional

one

is

not

as

valuable

to

him.邊際替代率魚的數(shù)量芒果的數(shù)量Hurley的邊際替代率是他愿意為多得到一條魚所愿意放棄的芒果數(shù)量I111AB邊際替代率(MRS):消費者愿意以一種物品交換另一種物品的比率MRS=無差異曲線的斜率MRS

=

617消費者選擇理論MRS

=

2沿著無差異曲線向右下方移動,MRS不斷減少It

is

hard

to

thinkof

examples

of

perfect

substitutes.

(Even

nickels

and

dimes

are

probably

not

perfect

substitutes:

I’d

rather

carry

10

dimes

inmy

pocket

than

20

nickels.)But

it’s

easy

to

think

of

examples

that

are

close

substitutes,

and

therefore

are

likely

to

have

indifference

curves

that

are

not

very

bowed:1)

Movies(atthe

movie

theater)

and

videos

at

home.

A

consumer

mightbe

willing

to

trade

two

videos

for

one

night

at

the

movies.2)

Coke

and

Pepsi

(for

consumers

that

do

not

perceive

much

difference

between

them).3)

Vacations

in

Hawaii

and

vacations

in

the

Bahamas一個極端的例子:

完全替代品完全替代品:無差異曲線為直線的兩種物品,有不變的

MRS例如:5美分的(Nickel)硬幣與10美分的(Dimes)硬幣消費者總是愿意以2個5美分的硬幣來交換換1個10美分的硬幣18消費者選擇理論Again,

It

is

hard

to

thinkof

examples

of

perfect

complements.

But

it’s

easy

to

think

of

examples

that

are

good

though

not

perfect

complements,and

therefore

are

likelyto

have

indifference

curves

that

are

very

bowed:1)Tickets

to

rock

concerts

and

parking

at

the

arena

in

which

the

concert

takes

place2)

Hot

dogs

and

hot-dog

buns3)

Brewed

Starbucks

coffee

and

20

spoons

of

sugar

(If

you

don’t

get

this

one,

you

probably

haven’t

tried

brewed

Starbucks

coffee!)另一個極端例子:

完全互補品完全互補品:無差異曲線為直角形的兩種物品。例如:左腳鞋,右腳鞋{7只左腳鞋,5只右腳鞋}等同于{5只左腳鞋,5只右腳鞋}19消費者選擇理論When

the

two

goods

are

close

but

not

perfect

substitutes

(like

Coke

and

Pepsi),

indifference

curves

are

slightly

bowed.When

the

two

goods

are

close

but

not

perfect

complements

(like

hot

dogs

and

buns),

indifference

curves

are

very

bowed,

having

a

very

sharp(but

not

quite

90-degree)

angle.Later

in

this

PowerPoint

chapter,

an

Active

Learningexercise

asks

students

to

illustrate

the

substitution

effect

for

these

two

cases.

Theywill

seethat

a

relative

price

change

causesa

muchbigger

movement

along

an

indifference

curve

when

the

goods

are

substitutes

than

when

they

arecomplements.不那么極端的例子:近替代品與近互補品可口可樂的數(shù)量百事可樂的數(shù)量近替代品的無差異曲線不是很彎曲熱狗的數(shù)量熱狗面包的數(shù)量近互補品的無差異曲線非常彎曲Simply

put,

optimizationmeans

buying

the

bundle

that

makes

the

consumer

happiest,

given

his

or

her

income.最優(yōu)化:

消費者選擇什么魚的數(shù)量芒果的數(shù)量1200600300150A是最優(yōu)點:

預算約束線上位于最高無差異曲線上的一點ACDHurley偏好B勝過A,但他買不起B(yǎng)Hurley買得起C和D,但A在更高的無差異曲線上B最優(yōu)點是Hurley負擔得起的所有消費束中最偏好的消費束21消費者選擇理論Consumer

optimization

is

another

example

of

“thinking

at

the

margin.”Remember

that

MRS

=marginal

value

of

the

good

on

the

X-axis

(fish)

in

termsof

the

good

on

Y-axis

(mangos).If

MRS

>

Pf/Pm,

the

value

of

another

fish

is

greater

than

its

cost,

so

Hurley

canmake

himself

happier

by

decreasing

his

mango

purchases

andusing

the

proceeds

to

buy

another

fish.If

MRS

<

Pf/Pm,

the

value

of

another

fish

is

less

than

its

cost,

so

Hurley

should

move

along

his

budget

line

toa

bundle

with

less

fish

and

moremangos

to

make

himself

happier.最優(yōu)化:消費者選擇什么魚的數(shù)量芒果的數(shù)量1200600300150在最優(yōu)點,無差異曲線的斜率等于預算約束線的斜率MRS

=

PF/PMA魚的邊際價值(用芒果來衡量)魚的價格

(用芒果來衡量)消費者最優(yōu)化是“考慮邊際量”的另一個例子22消費者選擇理論In

Active

Learning2,

students

determined

that

afall

in

income

shifts

the

budget

constraint

downward.

They

should

readily

accept,

then,

that

anincrease

in

income

shifts

the

budget

line

upward/outward.收入增加的影響芒果的數(shù)量收入增加使預算約束線向外移動如果這兩種物品都是“正常物品”,AB赫雷會多買些這兩種物品魚的數(shù)量23消費者選擇理論Instead

of

merelyshowing

students

the

diagram

for

the

case

where

one

of

the

goods

is

inferior,

let’s

just

remind

themof

the

definition

and

see

ifthey

canfigure

out

howto

draw

the

diagram.收入增加會使正常物品的需求量增加,低檔物品的需求量減少如果魚是正常物品,而芒果是低檔物品用圖形表示出收入增加對Hurley的魚與芒果的最優(yōu)消費量的影響主動學習3低檔物品與正常物品24In

Active

Learning

2,

students

determined

that

an

increase

in

the

priceof

a

good

pivots

the

budget

constraint

inward.

Here,

the

priceof

a

good

isfalling,

so

the

budget

line

pivots

outward.350價格變動的影響芒果的數(shù)量1200600500300150600

魚的數(shù)量原來的最優(yōu)點新最優(yōu)點最初,PF

=

$426消費者選擇理論MP

=

$1如果

PF

下降到

$2

預算約束線向外移動,Hurley會買更多的魚和更少的芒果On

the

previous

slide,

the

fall

in

the

price

of

fish

caused

a

net

decrease

in

Hurley’s

demand

for

mangos:

the

substitution

effect

is

greater

than

theincome

effect,

as

depicted

on

the

following

slide.However,

it

could

have

gone

the

other

way:

if

the

income

effect

were

greater

than

the

substitution

effect,

thenHurley’s

demand

for

mangos

wouldhave

risen.魚價格的下降對Hurley兩種物品的最優(yōu)消費有兩種效應:收入效應PF

的下降增加了Hurley收入的實際購買能力,允許他購買更多的芒果和魚替代效應PF

的下降使芒果相對于魚的價格上升,會使Hurley買更少的芒果和更多的魚注意:對芒果的凈效應并不確定27消費者選擇理論收入效應與替代效應This

diagramdecomposes

the

movement

from

the

old

optimum(A)

to

the

newone

(C)

into

two

parts.The

first

part,

from

A

to

B,

represents

the

substitution

effect.

It

shows

the

change

in

the

optimal

bundle

due

to

the

relative

price

change,

holdingconstant

the

consumer’s

level

of

well-being.The

second

part,

from

B

to

C,

represents

the

income

effect.

It

shows

the

change

in

the

optimal

bundle

due

to

the

increase

in

the

purchasingpower

of

the

consumer’s

income.

The

dashed

line

through

point

B

is

parallel

to

the

newbudget

line

through

point

C,

indicating

that

we

areholding

relative

prices

constant

to

see

how

the

increase

in

income

affects

the

optimal

bundle.收入效應與替代效應原來的最優(yōu)點在APF下降替代效應:從A到B,買更多的魚和更少的芒果收入效應:從B到C,買更多的這兩種物品魚的數(shù)量芒果的數(shù)量ABC在這個例子中,對芒果的凈效應是負的28消費者選擇理論This

exercise

is

similar

to

Problem

2

in

the

back

of

the

chapter.It

reviews

these

concepts:indifference

curves

for

substitutes

and

complements

have

different

shapesthe

substitution

effect

shows

the

movement

alongan

indifference

curve

froma

relative

price

change你認為哪種物品的替代效應會更大,完全替代品還是完全互補品?在一張圖上畫出百事可樂與可口可樂的無差異曲線,在另一張圖上畫出熱狗與熱狗面包的無差異曲線在每張圖中,表示出相對價格變動的影響(保持消費者效用在最初的無差異曲線上)主動學習4兩種情形中的替代效應29The

size

of

the

substitution

effect

can

be

measured

by

how

far

the

consumer

moves

along

her

indifference

curve

in

response

to

agiven

relativeprice

change.Why

this

exercise

is

relevant:Previously,

we

saw

that

the

income

and

substitution

effects

work

in

opposite

directions

on

the

good

whose

price

does

not

change.

Whatdetermines

which

effect

is

bigger?

The

answer

depends

on

the

extent

to

which

the

goods

are

close

substitutes

or

complements.

The

closer

thegoods

are

to

being

perfect

substitutes,

the

bigger

the

substitution

effect,

and

the

more

likelythe

substitution

effect

will

be

greater

than

the

incomeeffect.主動學習4參考答案可口可樂數(shù)量百事可樂數(shù)量在但兩替張代圖品中的,替相代對效價應格要變大動于相互同補的品幅的度替代效應熱狗數(shù)量熱狗面包數(shù)量ABABThis

slide

shows

that

the

familiar

demand

curve

we’ve

been

using

all

semester

comes

fromconsumer

optimization.$2DFishHurley對魚的需求曲線的推導350魚的數(shù)量芒果的數(shù)量魚的數(shù)量魚的價格150AB150$4A350B31A:當PF

=$4,Hurley購買150條魚B:當PF

=$2,Hurley購買350條魚32消費者選擇理論應用1:

吉芬物品所有的物品都遵守需求定理嗎?假設有兩種物品:土豆和肉,其中土豆是低檔物品如果土豆的價格上升,替代效應:少買土豆收入效應: 多買土豆如果收入效應>替代效應,那土豆是一種吉芬物品:價格上升引起需求量增加的物品。An

increase

in

the

price

of

potatoes

rotates

the

budget

line

inward.The

substitution

effect

would

cause

the

consumer

to

buy

fewer

potatoes.

Imagine

moving

down

alongindifference

curve

I1

until

reaching

the

point

where

its

slope

just

equals

the

slopeof

the

new

budget

line.

At

that

point,

demand

for

potatoes

is

lower,

because

consumers

are

substitutingmeat

for

potatoes.But

if

potatoes

are

an

inferior

good,

the

income

effect

causes

demand

for

potatoes

to

rise:

the

price

increase

makes

the

consumer

generallyworseoff.

The

consumer

responds

by

buying

less

meat

(the

normal

good)

and

more

potatoes

(the

inferior

good).If

potatoes

are

a

Giffen

good,

the

income

effect

exceeds

the

substitution

effect,

so

the

net

effect

of

a

price

increase

on

demand

for

potatoes

ispositive!!!As

the

book

notes,

Giffen

goods

are

extremely

rare–

if

they

existatall!應用1:吉芬物品33消費者選擇理論34消費者選擇理論應用2:工資與勞動供給預算約束線:表明一個人消費與閑暇的權衡取舍取決于她如何分配閑暇時間和工作時間1小時閑暇的相對價格是她一小時工資能購買的消費量無差異曲線:表示能給她相同滿意程度的消費和閑暇的“消費束”Here,

the

marginal

rate

of

substitution

measures

the

marginal

value

of

an

hourof

leisure,

in

termsof

(dollars’

worth

of)

consumption.The

slope

of

the

budget

line

simply

equals

the

wage:

each

additional

hourof

leisure

requires

working

one

fewer

hour,

whichcauses

consumptionto

fall

by

an

hour’s

wages.At

the

optimum,

the

marginal

value

of

leisure

(in

terms

of

consumption)

must

equal

the

relative

price

of

leisure

(in

terms

of

consumption),

or

thewage.IfMRS

>wage,

then

the

valueof

leisure

is

greater

than

its

price,

so

take

more

leisure

(and

work

fewer

hours)

to

raise

happiness.IfMRS

<

wage,

then

the

value

of

leisure

is

less

than

its

price,

so

take

less

leisure

(and

work

more

hours)

to

raise

happiness.應用2:工資與勞動供給在最優(yōu)點,閑暇與消費的邊際替代率等于工資35消費者選擇理論The

relative

magnitude

of

the

substitution

and

income

effects

determine

the

slope

of

the

labor

supply

curve,

as

the

following

slides

show.應用

2:

工資與勞動供給36消費者選擇理論工資增加對勞動的最優(yōu)供給量有兩種效應:替代效應(SE):高工資使閑暇相對于消費更昂貴她會減少閑暇時間那就是說,會增加勞動供給量收入效應(IE):更高的工資使她能負擔得起更多的兩種物品她會增加閑暇時間那就是說,會減少勞動供給量A

personwiththe

preferences

depicted

in

the

left

graph

will

have

a

positively-sloped

labor

supply

curve,

as

shownin

the

right

graph.應用2:工資與勞動供給如果SE

>IE工資增加,她的勞動供給量也增加37消費者選擇理論A

personwith

the

preferences

depicted

in

the

left

graph

will

have

a

negatively-sloped

labor

supply

curve,

as

shown

in

the

right

graph.應用2:工資與勞動供給如果SE

<IE工資增加,她的勞動供給量減少38消費者選擇理論Typically,

we

assume

the

substitution

effect

is

at

least

as

big

as

the

income

effect,

and

we

draw

labor

supply

curves

as

upward-sloping

or

perhapsvertical.This

slide

notes

examples

froma

case

study

in

this

chapter

in

which

the

income

effect

is

very

strong.I

would

add

an

additional

possibility

(not

mentioned

in

thebook):

A

person’s

labor

supply

curve

may

slope

upward

for

low

wages,

becomesteeper,

and

bend

backward

at

high

wages.

Here’s

why:The

size

of

the

substitution

effect

depends

on

a

comparison

of

the

wage

to

the

marginal

rate

of

substitution

between

leisure

and

consumption.

Thehigher

the

wage

relative

to

the

MRS,

the

stronger

the

incentive

to

substitute

away

from

leisure

and

toward

consumption.As

a

person

works

more

hours,

consumption

becomes

more

plentiful

while

leisure

becomes

dearer.

The

marginal

value

of

leisure

rises

relative

toconsumption.

I.e.,

the

MRS

risesasthe

person

moves

up

an

indifference

curve.As

this

occurs,

it

takes

increasingly

large

wage

increases

to

make

the

person

willing

to

sacrifice

another

hourof

leisure.

I.e.,

the

substitution

effectfroma

given

increase

in

the

wage

gets

weaker.Meanwhile,

the

income

effect

is

as

strong

as

ever

a

person

with

very

high

wages

can

afford

to

take

more

time

off

than

a

person

with

lowerwages.在現(xiàn)實世界中這可能發(fā)生嗎???39消費者選擇理論下述例子中勞動供給的收入效應非常強:·

在過去的100多年間,技術進步增加了勞動需求和實際工資,而平均工作日卻從每周6天減少為每周

5天·

當一個人獲得巨額彩票獎金或繼承了一筆遺產(chǎn)的同時,他的工資并沒有改變—因此沒有替代效應但這樣的人很可能會減少工作時間,意味著有很強的收入效應Why

the

interest

rate

determines

the

relative

price

of

current

in

terms

of

future

consumption:If

you

reduce

current

consumptionby

$1,

and

save

this

$1,

then

your

future

consumptionwill

rise

by

$(1

+

r),

where

r

denotes

the

interest

rate.Similarly,

if

youwish

to

increase

current

consumptionby

$1,

then

you

must

sacrifice

the

$(1

+

r)

that

you

would

have

been

able

to

consume

in

thefuture.Notice

that

the

slide

does

not

say

“the

interest

rate

equals

the

relative

price…”.

In

fact,

the

relative

priceof

current

in

terms

of

futureconsumption(and

also

the

slope

of

the

budget

constraint)

equals

(1

+

r),

not

r.應用3:

利率與家庭儲蓄40消費者選擇理論人的一生分為兩個時期:·

時期1:年輕,工作,掙$100,000消費=$100,000-儲蓄量·

時期

2: 老年,

退休消費=時期1的儲蓄+儲蓄得到利息利率決定年輕時消費與年老時消費的相對價格The

marginal

rate

of

substitution

is

the

marginal

value

of

current

consumptionin

terms

of

future

consumption;

it

tells

you

how

much

futureconsumptionthe

person

is

willing

to

give

up

for

aunitof

current

consumption.If

the

consumer

is

optimizing,

then

the

MRS

must

equal

(1

+

r):

the

marginal

valueof

current

consumption

must

equal

the

relative

price

of

currentconsumption(both

in

terms

of

future

consumpt

溫馨提示

  • 1. 本站所有資源如無特殊說明,都需要本地電腦安裝OFFICE2007和PDF閱讀器。圖紙軟件為CAD,CAXA,PROE,UG,SolidWorks等.壓縮文件請下載最新的WinRAR軟件解壓。
  • 2. 本站的文檔不包含任何第三方提供的附件圖紙等,如果需要附件,請聯(lián)系上傳者。文件的所有權益歸上傳用戶所有。
  • 3. 本站RAR壓縮包中若帶圖紙,網(wǎng)頁內(nèi)容里面會有圖紙預覽,若沒有圖紙預覽就沒有圖紙。
  • 4. 未經(jīng)權益所有人同意不得將文件中的內(nèi)容挪作商業(yè)或盈利用途。
  • 5. 人人文庫網(wǎng)僅提供信息存儲空間,僅對用戶上傳內(nèi)容的表現(xiàn)方式做保護處理,對用戶上傳分享的文檔內(nèi)容本身不做任何修改或編輯,并不能對任何下載內(nèi)容負責。
  • 6. 下載文件中如有侵權或不適當內(nèi)容,請與我們聯(lián)系,我們立即糾正。
  • 7. 本站不保證下載資源的準確性、安全性和完整性, 同時也不承擔用戶因使用這些下載資源對自己和他人造成任何形式的傷害或損失。

最新文檔

評論

0/150

提交評論