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Монополистическая конкуренция и олигополия

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IIIIIIEENOE*ANEAss EIIEO?AIOeEss E IEEAIIIEEss

Niaa?oaiiay eiieo?aioeey e /enoay iiiiiieey – aeaa e?aeieo neo/ay
?uii/iie no?oeoo?u.E oi e ae?oaia auaaao /?acau/aeii ?aaeei.
I?iiaaeooi/iie e ai?acaei aieaa ?aaeenoe/iie noaaeeae yaeyaony
iiiiiieenoe/aneay eiieo?aioeey.A yoii neo/aa oe?iu ,oioy e noaeeeaathony
n eiieo?aioeeae ni noi?iiu ae?oaeo oe?i,aoiaeyueo a io?aneue eee oaea
nouanoa. i?iaeaaoeia,ii iaeaaeatho iaeioi?ie aeanoueth iaae oeaiaie ia
naie oiaa?u.Aeey yoie ?uii/iie no?oeoo?u oaeaea oa?aeoa?ia
aeeooa?aioeeaoeey oiaa?ia,o.a. iiiaea oe?iu i?aaeeaaatho iioiaeea,ii ia
eaeaioe/iua oiaa?u.

?acee/ea iaaeaeo /enoie iiiiiieeae e niaa?oaiiie eiieo?aioeeae.

Ianiaa?oaiiay eiieo?aioeey nouanoaoao,eiaaea aeaa eee aieaa
i?iaeaaoeia,eaaeaeue ec eioi?uo iaeaaeaao iaeioi?ui eiio?ieai iaae
oeaiie ,eiieo?e?otho ca i?iaeaaee.Oaeia auaaao a aeaoo neo/ayo :

– oe?iu i?iaeatho ia noaiaea?oece?iaaiioth i?iaeoeoeeth

– eiaaea eiio?ieue iaae oeaiie iaoneiaeai ?uii/iie aeieae ioaeaeueiuo
oe?i.(ia oaeeo ?uieao eaaeae. i?iaeaaaoe i?iecaiaeeo aeinoaoi/ii
aieueooth /anoue i?iaeoeoa,/oiau cia/eoaeueii aeeyoue ia i?aaeeiaeaiea,a
,neaaeiaaoaeueii, e ia oeaiu.

Oaeaea ai iiiaeo neo/ayo eiio?ieue iaae oeaiie ia ?uiea iauyniei
ni/aoaieai yoeo aeaoo oaeoi?ia.

Iiiiiieenoe/aneay eiieo?aioeey

Iiiiiieenoe/aneay eiieo?aioeey inouanoaeyaony oiaaea,eiaaea iiiai
i?iaeaaoeia eiieo?e?otho ,/oiau i?iaeaoue aeeooa?aioee?iaaiiue i?iaeoeo
ia ?uiea ,aaea aiciiaeii iiyaeaiea iiauo i?iaeaaoeia.

Aeey ?uiea n iiiiiieenoe/aneie eiieo?aioeeae oa?aeoa?ii neaaeothuaa:

1.Oiaa? eaaeaeie oe?iu,oi?aothuae ia ?uiea ,yaeyaony ianiaa?oaiiui
caiaieoaeai oiaa?a

,?aaeecoaiiai ae?oaeie oe?iaie.

I?iaeoeo eaaeaeiai i?iaeaaoea iaeaaeaao eneeth/eoaeueiuie ea/anoaaie e
oa?aeoa?enoeeaie ,eioi?ua neoaeao oiio, /oiau iaeioi?ua iieoiaoaee
i?aaeii/ee aai oiaa? oiaa?o eiieo?e?othuae oe?ia.Aeeooa?eioeeaoeey
oiaa?a icia/aao ,/oi i?aaeiao ,i?iaeaaaaiue ia ?uiea ia yaeyaony
noaiaea?oece?iaaiiui.Yoi iiaeao i?ienoiaeeoue ec-ca aeaenoaeoaeueiuo
ea/anoaaiiuo ioee/ee iaaeaeo i?iaeoeoaie eee ec-ca i?aaeiieaaaaiuo
ioee/ee ,eioi?ua i?ienoaeatho ec ?acee/ee a ?aeeaia ,i?anoeaea oi?aiaie
ia?ee eee “eieaeaea” ,naycaiiui n iaeaaeaieai yoei oiaa?ii.

2.Ia ?uiea nouanoaoao ioiineoaeueii aieueoia /enei i?iaeaaoeia,eaaeaeue
ec eioi?uo

oaeiaeaoai?yao iaaieueooth,ii ia iee?ineiie/aneoth aeieth ?uii/iiai
ni?ina ia iauee oei

oiaa?a, ?aaeecoaiiaia oe?iie e aa niia?ieeaie.

I?e iiiiiieenoe/aneie eiieo?aioeee ?acia?u ?uii/iuo aeieae oe?i a
iauai i?aainoiaeyo 1% ,o.a. i?ioeaio,eioi?ue nouanoaiaae au i?e
niaa?oaiiie eiieo?aioeee.A oeie/iii neo/aa ia oe?io i?eoiaeeony io 1%
aei 10 % i?iaeaae ia ?uiea a oa/aiea aiaea.

3.I?iaeaaoeu ia ?uiea ia n/eoathony n ?aaeoeeae naieo niia?ieeia
,eiaaea auae?atho ,eaeoth

onoaiiaeoue oeaio ia naie oiaa?u eee eiaaea auae?atho i?eaioe?u ii
iauaio aiaeiauo

i?iaeaae.

Yoa iniaaiiinoue yaeyaony neaaenoaeai ana aea ioiineoaeueii aieueoiai
/enea i?iaeaaoeia ia ?uiea n iiiiiieenoe/aneie eiieo?aioeeae.o.a. anee
ioaeaeueiue i?iaeaaaoe nie?aoeo oeaio ,oi aa?iyoii,/oi i?e?ino iauaia
i?iaeaae i?iecieaeao ia ca n/ao iaeiie oe?iu, a ca n/ao iiiaeo.Eae
neaaenoaea , iaeiaa?iyoii , /oi eaeie-ieaoaeue ioaeaeueiue eiieo?aio
i?eianao aeinoaoi/ii cia/eoaeueiua iioa?e naiae aeiee ia ?uiea ec-ca
oiaiueoaiea i?iaeaaeiie oeaiu eaeie-ieaoaeue ioaeaeueiie
oe?iu.Neaaeiaaoaeueii ,o eiieo?aioia iao i?e/ei,/oiau io?aaae?iaaoue ia
yoi eciaiaieai naiae iieeoeee ,iineieueeo ?aoaiea iaeiie ec oe?i ia
aicaeaenoaoao a cia/eoaeueiie noaiaie ia eo aiciiaeiinoe ecaeaeaoue
i?eauee.Oe?ia ciaao yoi e ,neaaeiaaoaeueii,ia o/eouaaao eaeie-eeai
aiciiaeiie ?aaeoeee eiieo?aioia,eiaaea auae?aao naith oeaio eee oeaeue
ii i?iaeaaeai.

4.Ia ?uiea anoue oneiaey aeey naiaiaeiiai aoiaea e auoiaea

I?e iiiiiieenoe/aneie eiieo?aioeee eaaei iniiaaoue oe?io eee iieeiooue
?uiie. Auaiaeiay eiiuetheoo?a ia ?uiea n iiiiiieenoe/aneie
eiieo?aioeeae i?eaea/ao iiauo i?iaeaaoeia.Iaeiaei aoiae ia ?uiie ia
ianoieueei eaaie,eae ii aue i?e niaa?oaiiie eiieo?aioeee,iineieueeo
iiaua i?iaeaaoeu /anoi eniuouaatho o?oaeiinoe ni naieie iiauie aeey
iieoiaoaeae oi?aiauie ia?eaie e oneoaaie.Neaaeiaaoaeueii,oaea
nouanoaothuea oe?iu n onoiyaoaeny ?aiooaoeeae iiaoo nio?aiyoue naia
i?aeiouanoai iaae iiauie i?iecaiaeeoaeyie.Iiiiiieenoe/aneay
eiieo?aioeey iioiaea ia neooaoeeth iiiiiieee,iineieueeo ioaeaeueiua
oe?iu iaeaaeatho niiniaiinoueth eiio?iee?iaaoue oeaio naieo oiaa?ia.Iia
oaeaea iioiaea ia niaa?oaiioth eiieo?aioeeth,o.e. eaaeaeue oiaa?
i?iaeaaony iiiaeie oe?iaie, e ia ?uiea nouanoaoao naiaiaeiue aoiae e
auoiae.

Nouanoaiaaiea io?anee i?e iiiiiieenoe/aneie eiieo?aioeee.

Oioy ia ?uiea n iiiiiieenoe/aneie eiieo?aioeeae oiaa? eaaeaeiai
i?iaeaaoea oieeaeai,iaaeaeo ?acee/iuie aeaeaie i?iaeoeoia iiaeii iaeoe
aeinoaoi/ii noiaenoaa,/oiau iauaaeeieoue i?iaeaaoeia a oe?ieea
eaoaai?ee,iioiaeea ia io?aneue.

Oiaa?iay a?oiia i?aaenoaaeyao niaie ianeieueei aeecei naycaiiuo ,ii ia
eaeaioe/iuo oiaa?ia,eioi?ua oaeiaeaoai?ytho iaeio e oo aea iio?aaiinoue
iieoiaoaeae.A eaaeaeie oiaa?iie a?oiia i?iaeaaoeia iiaeii ?anniao?eaaoue
eae eiieo?e?othuea oe?iu a i?aaeaeao io?anee.Oioy anoue i?iaeaiu n
ii?aaeaeaieai a?aieoe io?aneae,o.a. i?e ii?aaeaeaiee io?anee iaaei
naeaeaoue ?yae aeiiouaiee, e i?eiyoue ?yae niioaaonoaothueo
?aoaiee.Iaeiaei i?e iienaiee io?anee iiaeao ieacaoueny iieaciie ioeaiea
ia?ae?anoiie yeanoe/iinoe ni?ina ia oiaa?u niia?ie/athueo oe?i,o.e. a
io?anee n iiiiiieenoe/aneie eiieo?aioeeae ia?ae?anoiay yeanoe/iinoue
ni?ina ia oiaa?u niia?ie/athueo oe?i aeieaeia auoue iieiaeeoaeueiie e
ioiineoaeueii aieueoie,/oi icia/aao,/oi oiaa?u eiieo?e?othueo oe?i
yaeythony ae?oa aeey ae?oaa i/aiue oi?ioeie caiaieoaeyie,/oi
icia/aao,/oi anee oe?ia iiaeieiao oeaio auoa eiieo?aioiie,oi iia iiaeao
iaeeaeaoue iioa?e cia/eoaeueiiai iauaia i?iaeaae a iieueco eiieo?aioia.

Iau/ii ia ?uieao n iaeaieueoae iiiiiieenoe/aneie eiieo?aioeeae ia /aou?a
e?oiiaeoea oe?iu i?eoiaeeony 25% iaueo aioo?aiieo iinoaaie,a ia ainaiue
e?oiiaeoeo oe?i – iaiaa 50%.

E?aoein?i/iia ?aaiiaanea oe?iu i?e iiiiiieenoe/aneie eiieo?aioeee.

E?eaay ni?ina oae,eae iia aeaeeony iiiiiieueii-eiieo?aioiie
oe?ia,iaeeiiaia aiec.I?aaeiieiaeei,/oi i?iaeaaaoe no?aieoueny
iaeneiece?iaaoue i?eaueue e aai oiaa? ioee/aaony io niia?ie/athueo ii
eaeei-eeai oa?aeoa?enoeeai.Oiaaea i?iaeaaaoe iiaeao iiaeiyoue oeaio aac
iaaeaiey o?iaiy i?iaeaae,o.e. iaeaeoony iieoiaoaee,aioiaua ieaoeoue
iiauoaiioth oeaio ca yoio i?iaeoeo.(inoaeueiia caaeneo io yeanoe/iinoe
ni?ina ia yoio oiaa?,o.a. iie?iao ee i?eaueue io oaaee/aiey oeaiu
iioa?e io nie?auaiey i?iaeaae eee iao).Ni?in e i?aaeaeueiue aeioiae
caaenyo oaeaea io oeai,onoaiiaeaiiuo eiieo?e?othueie oe?iaie,o.e. anee
au iie nieceee naie oeaiu, oi i?iaeaaaoe iieo/ee au iaiueooth i?eaueue
io iiieaeaiey / iiauoaiey oeaiu.Ii ,eae oaea aiai?eeinue ?aiaa,
iiiiiieueii-eiieo?aioiay oe?ia ia o/eouaaao ?aaeoeeth eiieo?aioia ia
naie aeaenoaey.

E?aoein?i/iia ?aaiiaanea oe?iu iieacaii ia ?enoiea 1.

Oeaia e naaano.

IN

P1 A

AN

?2 A

D

MR

Q
Eie-ai.

Iaeneiece?othuaa i?eaueue eie- ai oiaa?a =Q .Yoio auione niioaaonoaoao
oi/ea ,a eioi?ie MR=MC .*oiau i?iaeaoue yoi eie-ai oe?ia onoaiiaeo
oeaio ,?aaioth ?1,i?e yoie oeaia eie-ai oiaa?a,ia eioi?ia anoue
ni?in,niioaaonaoao o. A ia e?eaie i?aaeeiaeaiey e ninoaaeyao
iaeneiece?othuee i?eaueue auione.I?e onoaiiaeaiee oeaiu,?aaiie ?1 oe?ia
iieo/aao i?eaueue n aaeeieoeu oiaa?a ?aaioth io?aceo AA,a ni anaai
auionea-?aaioth ieiuaaee caoo?eoiaaiiiai i?yiioaieueieea.

?aaiiaanea oe?iu a aeieain?i/iii ia?eiaea

Ii iieo/aiea i?eauee aiciiaeii oieueei a e?aoein?i/iii ia?eiaea,o.e. a
aeieain?i/iii a io?aneue i?eaeoo iiaua oe?iu,eioi?ua neiie?otho
aeinoeaeaiey i?iaeaaoea eee i?iaeaaaoe nai ia/iao ?anoe?youeny e
i?eaueue oiaaeao aei ii?iaeueiie,o.e. ii ia?a ?inoa eiee/anoaa
i?aaeeaaaaiiai oiaa?a,oeaia ca aaeeieoeo oiaa?a,eioi?oth iiaeao
iacia/eoue eaaeaeue ioaeaeueiue i?iaeaaaoe,aoaeao
nieaeaoueny.I?iaeaaaoe,eioi?ue ia?aui auionoee oiaa? ia
?uiie,iaia?oaeeo,/oi eae e?eaay ni?ina,oae e e?eaay i?aaeaeueiiai
aeioiaea ia oiaa?,?aaeecoaiue oe?iie, aoaeao niauaoueny aiec.Yoi
icia/aao,/oi oeaia e i?aaeaeueiue aeioiae ,eioi?ue oe?ia iiaeao
iaeeaeaoue,oiaaeoo a aeieain?i/iii ieaia ec-ca aic?inoaai i?aaeeiaeaiey
oiaa?a.Iethn e yoiio,ni?in ia oiaa? eaaeaeie ioaeaeueiie oe?iu oaeaea
aoaeao no?aieoueny noaoue aieaa yeanoe/iui i?e aeaiiie oeaia,o.e.
oaaee/aiea /enea niia?ie/athueo oe?i oaaee/eaaao /enei caiaieoaeae.Iiaua
oe?iu aoiaeyo ia ?uiie aei oao ii?,iiea ia noaiao iaaiciiaeiui iieo/aiea
i?eauee.Neaaeiaaoaeueii,aeieain?i/iia ?aaiiaanea ia ?uiea n
iiiiiieenoe/aneie eiieo?aioeeae iioiaea ia eiieo?aioiia ?aaiiaanea a
oii,/oi ie iaeia oe?ia ia iieo/aao i?eaueue aieueoa ii?iaeueiie.

Ia ?enoiea 2 iieacaii aeieain?i/iia ?aaiiaanea io?anee i?e
iiiiiieenoe/aneie eiieo?aioeee.

Oeaia e naaano.

LRAC
LRMC

A AN

?

D

MR

Q1 Q2 Eie-ai

Io?aneue ia iiaeao iaoiaeeoueny a ?aaiiaanee,iiea oe?iu iiaoo
cai?aoeaaoue ca oiaa? aieueoa,/ai n?aaeiea cao?aou i?e iaeneiece?othuai
i?eaueue auionea,o.a. oeaia aeieaeia auoue ?aaia n?aaeiei cao?aoai ia
yoio auione.I?e aeieain?i/iii ?aaiiaanee e?eaay ni?ina yaeyaony
eanaoaeueiie e aeieain?i/iie e?eaie n?aaeieo ecaea?aeae.Oeaia,eioi?oth
iaaei onoaiiaeoue ,/oiau i?iaeaoue Q1 oiaa?a , ninoaaeyao
?,niioaaonaoao o.A ia e?eaie ni?ina.I?e yoii n?aaeiea cao?aou oiaea
?aaiu ? ca oooeo, e, neaaeiaaoaeueii i?eaueue ?aaia ioeth eae n iaeiie
oooee,oae e a oeaeii.Naiaiaeiue aoiae ia ?uiie i?aiyonoaoao oe?iai
ecaeaeaoue yeiiiie/aneea i?eauee a aeieain?i/iii ieaia.Yoio aea i?ioeann
?aaioaao e a ia?aoiii iai?aaeaiee.Anee au ni?in ia ?uiea nieceeny au
iinea aeinoeaeaiey ?aaiiaaney,oi oe?iu iieeioee au ?uiie,o.e.nie?auaiea
ni?ina naeaeaei au iaaiciiaeiui iie?uoea yeiiiie/aneeo ecaea?aeae.Eae
iieacaii ia ?enoiea 3,i?e auionea Q1 ,i?e eioi?ii MR=LRMC iinea
nie?auaiey ni?ina,oeie/iue i?iaeaaaoe iaoiaeeo,/oi oeaia ?1,eioi?oth ii
aeieaeai onoaiiaeoue./oiau i?iaeaoue yoi eie-ai oiaa?a,iaiueoa,/ai
n?aaeiea cao?aou AN1 ia aai i?iecaiaenoai.O.e. i?e yoeo ianoiyoaeuenoaao
oe?iu ia iiaoo iie?uoue naie yeiiiie/aneea ecaea?aeee,iie aueaeoo ec
io?anee e ia?aianoyo naie ?ano?nu a aieaa auaiaeiua i?aaei?eyoey.Eiaaea
yoi i?iecieaeao,e?eaay ni?ina e e?eaua i?aaeaeueiiai aeioiaea inoaeueiuo
oe?i nianoyony aaa?o.Yoi i?iecieaeao iioiio,/oi nie?auaiea eiathuaainy
a iaee/ea oiaa?a oaaee/eo iaeneiaeueiua oeaiu e i?aaeaeueiue
aeioiae,oa?aeoa?iua aeey ethaiai aai auionea. e eioi?ua iiaee au
iieo/aoue inoaaoeany i?iaeaaoeu.Auoiae oe?i ec io?anee aoaeao
i?iaeieaeaoueny aei oao ii?,iiea ia aoaeao aeinoeaiooi iiaia
?aaiiaanea,i?e eioi?ii e?eaay ni?ina iiyoue yaeyaony eanaoaeueiie e
e?eaie LRAC,a oe?iu iieo/atho ioeaaua yeiiiie/aneea i?eauee.I?ioeann
auoiaea oe?i n ?uiea iia au oaeaea i?iecieoe a ?acoeueoaoa oiai,/oi
oe?iu caauneee au ioeaieo aiciiaeiiai io i?iaeaae ia ?uiea i?aaeaeueiiai
aeioiaea.Ecauoi/iia /enei oe?i iiaei au naeaeaoue oiaa? ianoieueei
eciaeeueiui,/oi oe?iu ia ?uiea ia niiaee au iie?uoue naie n?aaeiea
ecaea?aeee i?e oeaia,i?e eioi?ie i?aaeaeueiue aeioiae ?aaiyaony
i?aaeaeueiui cao?aoai.

?en. 3. (Iiiiiieueii eiieo?aioiay oe?ia,oa?iyuay oauoee)

Oeaia e naaanoieiinoue

LRMC

AN1

?1
LRAC

D

MR

Q
Eie-ai

Caoo?eoiaaiiue i?yiioaieueiee – iioa?e oe?iu.

N?aaiaiea n enoiaeiui eiieo?aioiui ?aaiiaaneai.

Iio?aaeoaee ieaoyo aieaa aunieea oeaiu,eiaaea i?iaeoeou
aeeooa?aioee?iaaiu ii n?aaiaieth n oaie oeaiaie,eioi?ua iie ieaoeee
au.anee au oiaa? aue noaiaea?oece?iaai e auioneaeny au eiieo?aioiuie
oe?iaie.Yoi aa?ii,aeaaea anee LRMC iiiiiieueii eiieo?aioiie oe?iu
eaeaioe/ia e?eaie niaa?oaiii eiieo?aioiie oe?iu.Aeiiieieoaeueiue ?ino
oeaiu eiaao ianoi,eiaaea aicieeatho aeiiieieoaeueiua ecaea?aeee ii
aeeooa?aioeeaoeee oiaa?a.Neaaeiaaoaeueii i?e iiiiiieenoe/aneie
eiieo?aioeee yeiiiie/aneay i?eaueue iaaeaao aei ioey ?aiueoa,/aioeaiu
aeinoeaatho o?iaiy,iicaieythuaai iie?uoue oieueei naie i?aaeaeueiua
ecaea?aeee. I?e o?iaia auionea,aeey eioi?iai oeaia ?aaiyaony n?aaeiei
cao?aoai,oeaia i?aauoaao i?aaeaeueiua ecaea?aeee.I?e/eia yoiai
ianiaiaaeaiey iaaeaeo n?aaeieie e i?aaeaeueiuie ecaea?aeeaie
caeeth/aaony a eiio?iea iaae oeaiaie.,eioi?ue iicaieyao inouanoaeyoue
aeeooa?aioeeaoeey i?iaeoeoa.(iia iaoneaaeeaaao iaeeii ni?ina aiec,/oi
i?eaiaeeo e oiio,/oi i?aaeaeueiue aeioiae ia aeinoeaaao aaee/eiu oeaiu
i?e ethaii iauaia auionea).A ?aaiiaanee oe?ia anaaaea ?aaoee?oao
oeaio,iiea ia onoaiiaeo ?aaainoaa MR=MC.Iineieueeo oeaia anaaaea
i?aauoaao MR ,oi iia a ?aaiiaanee aoaeao i?aauoaoue IN.Iiea oiaa?
aeeooa?aioee?iaai n?aaee oe?i,iaaiciiaeii,/oiau a aeieain?i/iii
?aaiiaanee n?aaeiea ecaea?aeee i?iecaiaenoaa aeinoeaee naiaai
iaeneiaeueii aiciiaeiiai o?iaiy.En/aciaaiea yeiiiie/aneie i?eauee
o?aaoao oiai,/oiau e?eaay ni?ina yaeyeanue eanaoaeueiie e e?eaie
ecaea?aeae.Yoi iiaeao i?iecieoe oieueei i?e auionea ,niioaaonoaothuai
LRAC min,anee e?eaay ni?ina yaeyaony ai?eciioaeueiie eeieae ,eae i?e
niaa?oaiiie eiieo?aioeee.Iiiiiieueii eiieo?aioiua oe?iu ia aeiaeaathony
anaai aiciiaeiiai a aeieain?i/iii ieaia nieaeaiey ecaea?aeae.Eae
iieacaii ia ?enoiea 2 a ?aaiiaanee oeie/iay iiiiiieueii eiieo?aioiay
oe?ia i?iecaiaeeo Q1 i?iaeoeoeee,iaeiaei LRACmin aeinoeaaaony i?e
auionea Q2 i?iaeoeoeee,neaaeiaaoaeueii Q1-Q2=ecauoi/iay
iiuiinoue.Neaaeiaaoaeueii oaeie aea auuione iiaeii au auei i?aaeeiaeeoue
iio?aaeoaeth i?e aieaa ieceeo n?aaeieo ecaea?aeeao.Oi aea eie-ai oiaa?a
iiaeii auei i?iecaanoe iaiueoei /eneii oe?i,eioi?ua au auioneaee
aieueoaa eie-ai oiaa?a i?e ieieiaeueii aiciiaeiuo ecaea?aeeao.Ii
?aaiiaanea i?e yoeo oneiaeyo iiaeii aeinoe/ue eeoue anee i?iaeoeo
yaeyaony noaiaea?oece?iaaiiui.Neaaeiaaoaeueii aeeooa?aioeeaoeey oiaa?a
ianiaianoeia n yeiiiieae iaeniieueciaaiiuo ?ano?nia.I?e i?i/eo ?aaiuo
oneiaeyo,/ai auoa a ?aaiiaanee oeaia,oai aieueoa ecauoi/iay iiuiinoue.

Auaiae.:

Iiiiiieueii eiieo?aioiia ?aaiiaanea iioiaea ia /enoi iiiiiieueiia
?aaiiaanea a oii,/oi oeaiu i?aauoatho i?aaeaeueiua ecaea?aeee
i?iecaiaenoaa.Iaeiaei i?e /enoie iiiiiieee oeaia iiaeao oaeaea
i?aauoaoue a aeieain?i/iii ieaia e n?aaeiea ecaea?aeee ec-ca aa?uea?ia
aeey aoiaea ia ?uiie iiauo i?iaeaaoeia.I?e iiiiiieenoe/aneie
eiieo?aioeee naiaiaeiue aoiae ia ?uiie i?aaeioa?auaao aeeeoaeueiia
nouanoaiaaiea yeiiiie/aneie i?eauee.I?eaueue yaeyaony i?eiaieie,eioi?ay
i?eaeaeaao iiaua oe?iu ,e oaea?aeeaaao oeaiu ieaea o?iaiy,eioi?ue
nouanoaiaae au i?e /enoie iiiiiieee,ii oeaiu i?aauoatho oa,eioi?ua
nouanoaiaaee au ia noaiaea?oece?iaaiiua oiaa?u i?e /enoie eiieo?aioeee.

?aeeaia e i?iaeaeaeaiea oiaa?a ia ?uiee n iiiiiieenoe/aneie
eiieo?aioeeee.

Ecaea?aeee iaoeaiiaie eiieo?aioeee.

A aeiaaaeaiea e ecaea?aeeai,naycaiiui n ecauoi/iie
iiuiinoueth,nouanoaotho oaeaea ecaea?aeee,eioi?ua ianoo oe?iu ia ?uieao
n iiiiiieenoe/aneie eiieo?aioeeae oiaaea,eiaaea oe?ia no?aieoueny
oaaaeeoue iio?aaeoaey a oii,/oi aa oiaa?u ioee/athony io oiaa?ia
eiieo?aioia.Iiiiiieueii eiieo?aioiua ?uiee oa?aeoa?ecothony iaee/eai
oiaa?iuo ciaeia e iai?a?uaiie ?ac?aaioeie iiauo oiaa?ia e oeo/oaieai
noa?uo.Iiiaeo iio?aaeoaeae oaaaeeee,/oi ea/anoai oiaa?ia n ecaanoiuie
ia?eaie i?aainoiaeeo ea/anoai eiieo?aioiie i?iaeoeoeee..Aa?iyoii,/oi
oe?iu ia ?uieao n iiiiiieenoe/aneie eiieo?aioeeae aeey oaaee/aiey
i?iaeaae aoaeoo nei?aa eiieo?e?iaaoue n iiiiuueth oeo/oaiey oiaa?ia eee
?ac?aaioee iiauo,/ai i?e iiiiue iiieaeaiey oeai.Oeo/oaiea oiaa?a
ioaeaeueiie oe?iie iicaieeo ae ecaeaeaoue i?eauee iiea inoaeueiua oe?iu
ia neiie?otho yoe oeo/oaiey.*anoi yoe oeo/oaiey auaatho iiaa?oiinoiuie e
ianouanoaaiiuie.Ii eae oieueei oiaa? oeo/oai,oe?ia iau/ii ia/eiaao
?aeeaio,/oiau i?ieioi?ie?iaaoue iio?aaeoaeae ia yoeo eciaiaieyo.

Ecaea?aeee ?aaeecaoeee

?aeeaia e ?aaeecaoeey oiaa?ia yaeythony i?ioeannaie,o?aaothueie
cao?ao.Ecaea?aeee ?aaeecaoeee – yoi ana oa ecaea?aeee,eioi?ua ianao
oe?ia,/oiau iiaeeyoue ia i?iaeaaee naiaai oiaa?a.Inouanoaeyy ?aeeaiiua e
i?i/ea naycaiiua n i?iaeaaeae ?anoiaeu,oe?ia iaaeaaony oaaee/eoue
iinooieaiey,au?o/eo.?aeeaia iiaeao aicaeaenoaiaaoue ia o?iaaiue ni?ina
ia oiaa? oe?iu e ia oeaiiaoth yeanoe/iinoue yoiai ni?ina. Iia iiaeao
oaeaea aicaeaenoaiaaoue ia ia?ae?anoioth yeanoe/iinoue ni?ina ia
i?iaeoeo i?eiaieoaeueii e oeaiai ia oiaa?u eiieo?e?othueo oe?i.?aeeaia
oaeaea iiaeao oaaee/eoue ni?in ia oiaa?u anao i?iaeaaoeia a oiaa?iie
a?oiia.Ia iieiinoueth eiieo?aioiuo ?uieao iao noeioeia ianoe ecaea?aeee
?aaeecaoeee,o.e. oiaa?u yaeythony niaa?oaiiuie caiaieoaeyie,e iieoiaoaee
yaeythony iieiinoueth eioi?ie?iaaiiuie. eaaeiaaoaeueii,i?e yoeo
ianoiyoaeuenoaao ?aeeaia aaniieacia.Oe?iu caieiathony ?aeeaiie e ae?oaie
aeayoaeueiinoueth ii i?iaeaeaeaieth oiaa?a oiaaea,eiaaea iie iiaoo
oeacaoue ia oieeaeueiua noi?iiu naieo oiaa?ia e eiaaea eioi?iaoeey ia
eiaaony a naiaiaeiii ?anii?yaeaiee o iieoiaoaeae.

E?eaua ecaea?aeae ?aaeecaoeee e iaeneiece?othuay i?eaueue ?aeeaia.

N ?aeeaiie e ae?oaie aeayoaeueiinoueth ii i?iaeaeaeaieth oiaa?a naycaiu
cia/eoaeueiua ecaea?aeee.*oiau eii?aeeie?iaaoue ana yoe oneeey ioaeai
ooao,eioi?iio iaaei ieaoeoue.Ecaea?aeee ?aaeecaoeee aeene?aoiu,yoi
cia/eo./oi iie ia ana a?aiy yaeythony iaiaoiaeeiuie aeey i?iecaiaenoaa
oiaa?a.Eiaaea oe?ia ?aeeaie?oao naie oiaa? iia oioneaao aiciiaeiinoue
i?iaeaaaoue aieueoa oiaa?a, oaea?aeeaay ecaea?aeee
e,neaaeiaaoaeueii,oeaio ia aieaa aunieii o?iaia.?aeeaia yaeyaony
iiiuoeie eiaoue aieueoee iauai i?iaeaae i?e ethaie oeaia.Oaeiai aea
i?e?inoa i?iaeaae ,aiciiaeii,iiaeii auei au aeinoe/ue nie?auaieai oeaiu.

Aa?iyoii,/oi n?aaeiea ecaea?aeee ?aaeecaoeee (ia aae. auionea) nia/aea
oiaiueoathony ,a iioii aic?anoatho.Aic?anoatho ii ia?a ?inoa
aeaenoaeoaeueiuo i?iaeaae.N?aaeiea iinoiyiiua ecaea?aeee nieaeathony n
oaaee/aieai i?iaeaae,o.e. ecaea?aeee,aaaine?iaaiiua ia
?aaeecaoeeth,?ani?aaeaeythony ia aieueoaa /enei aaeeieoe
oiaa?a.Ecaea?aeee ?aaeecaoeee ia aae. oiaa?a nieaeathony oaeaea
oiaaea,eiaaea aeaaony aieueoay ?aeeaia,anee oeaia ca iaeii ?aeeaiiia
iauyaeaiea iaaeaao n ?inoii eo /enea.Aiciiaeii oaeaea,/oi aieueoea iauea
?anoiaeu ia ?aeeaio,icia/ay aieueoa iauyaeaiee,i?eaiaeyo e
i?iii?oeeiiaeueii aieueoei i?e?inoai i?iaeaae.Iiaoi? ?aeeaiiuo
iauyaeaiee a ?aciuo NIE iiaeao ieacuaaoue aicaeaenoaea ia oaaee/aiea
i?iaeaae.

Iiaeii i?aaenoaaeoue e?eaoth n?aaeieo ecaea?aeae ?aaeecaoeee (ANs
),eioi?ay iieacuaaao , eaeei ia?acii eciaiythony ecaea?aeee ?aaeecaoeee
aae. oiaa?a i?e ?aciuo o?iaiyo i?aaeiieaaaaiiai ni?ina.*ai aieueoa ni?in
ia oiaa?,oai iaiueoa n?aaeiea ecaea?aeee ?aaeecaoeee,naycaiiua n
i?iaeaaeae ia ?uiea aeaiiiai eie-aa oiaa?a.Neaaeiaaoaeueii,eciaiaiea
ni?ina ia oiaa? iiaeao nianoeoue e?eaoth ecaea?aeae
?aaeecaoeee.Eciaiaiea ethaiai oaeoi?a,aeeythuaai ia ni?in ia oiaa?
oe?iu ,nianoeo e?eaoth n?aaeieo ecaea?aeae ?aaeecaoeee eeai aaa?o,eeai
aiec.U-ia?aciay e?eaay n?aaeieo ecaea?aeae ?aaeecaoeee ecia?aaeaia ia
?en. 4.Yoa e?eaay iieacuaaao ?anoiaeu ia ?aaeecaoeeth aaeeieoeu
i?iaeaaaaiiai oiaa?a,anee aeaiu ni?in ia oiaa? oe?iu e noiia ?aeeaiiuo
?anoiaeia eiieo?e?othueo oe?i.Nie?auaiea ni?ina niauaao e?eaoth
n?aaeieo ecaea?aeae ?aaeecaoeee aaa?o,eae e i?e?ino ?anoiaeia ia ?aeeaio
o eiieo?e?othueo oe?i.Oaeei ia?acii,n?aaeiea ecaea?aeee
?aaeecaoeee,naycaiiua n aeaiiui auioneii,oai ieaea,/ai neeueiaa ni?in ia
oiaa? e /ai iaiueoa ecaea?aeee ?aaeecaoeee,eioi?ua ianoo eiieo?aiou.

I?iaeaaeiay oeaia ca aae.

ACs

Aiaeiaie auione

?aeeaia,aoaeo/e oniaoiie,oaaee/eaaao ni?in ia oiaa? oe?iu.?en. 5
iieacuaaao,eae inouanoaeaiea ?aeeaiu iiaeao i?eaanoe e ?inoo i?eaueae
o iiiiiieueiieiieo?aioiie oe?iu.

P`,Q`,MR1,D1 – oeaia , eie-ai,i?aaeaeueiue aeioiae e ni?in aei ?aeeaiu

Pa,Qa ,MR2,D2- oeaia , eie-ai ,i?aaeaeueiue aeioiae e ni?in iinea
?aeeaiu.

IN+MCs-i?aaeaeueiua ecaea?aeee i?iecaiaenoaa +i?aae. ecaea?aeee
?aaeecaoeee

AN+ACs – n?aaeiea ecae. i?iecaiaenoaa +n?aaeiea ecae. ?aaeecaoeee.

Caoo?eoia. i?yiioaieueiee-i?eaueue a e?aoein?i/iii ieaia iinea
?aeeaie?iaaiey.

Oe?ia,aeaaiaea?y ?anoiaeai ia ?aeeaio niauaao naith e?eaoth ni?ina n
D1 aei D2 e e?eaoth i?aae. aeioiaea n MR1 aei MR2.Iaeneiece?othuei
i?eaueue auioneii yaeyaony oio,aeey eioi?iai MR2 ?aaiyaony i?aaeaeueiui
ecaea?aeeai ia i?iecaiaenoai iethn i?aaeaeueiua ecaea?aeee
?aaeecaoeee.I?e ionoonoaee ?aeeaiu oe?ia iieo/eea au ioeaaoth
yeiiiie/aneoth i?eaueue.?aeeaia iicaieyao oe?ia ecaeaeaoue
iieiaeeoaeueioth yeiiiie/aneoth i?eaueue a e?aoein?i/iii ieaia.?aeeaia
iiae?acoiaaaao,/oi oe?ia iiaeao oaaee/eoue ni?in e i?aaeaeueiue
aeioiae,iany aieueoea cao?aou.I?e?ino ni?ina,anee ii
iinoiyiai,oiaiueoaao ecaea?aeee ?aaeecaoeee,iaiaoiaeeiua ,/oiau
i?iaeaoue aeaiiia eie-ai oiaa?a e,neaaeiaaoaeueii,iiaoaeaeaao oe?io
niiaa nie?aoeoue ?anoiaeu ia ?aeeaio.Acaeiicaaeneiinoue iaaeaeo MR e MC
a neo/aa,eiaaea ?aeeaia yaeyaony oniaoiie,aeaeaao iaaiciiaeiui
i?aaeneacaiea ?aaiiaaniiai o?iaiy ?aeeaiiuo ?anoiaeia.

P e naaano.

Pa D
MC+MCs

AC+ACs

AC

C A

D2

P`

D1

MR2

MR1

Q` Qa
Q

?aaiiaanea a aeieain?i/iii ieaia n inouanoaeaieai ?aeeaiiie
aeayoaeueiinoe i?e

iiiiiieenoe/aneie eiieo?aioeee.

?aeeaia,eioi?ay i?eaiaeeo e i?eaueyi a iiiiiieueii eiieo?aioiie
io?anee aeaao ia/aei i?ioeanno,eioi?ue oie/oiaeeo yoe i?eauee.Iineieueeo
i?e iiiiiieenoe/aneie eiieo?aioeee nouanoaoao naiaiaeiue aoiae a
io?aneue,oi iiaeii iaeeaeaoue,/oi ?aeeaia,iaoneaaeeaathuay
yeiiiie/aneoth i?eaueue,i?eaea/ao ia ?uiie iiauo
i?iaeaaoeia.Neaaeiaaoaeueii,e?eaay ANs nianoeoueny aaa?o ec-ca
aic?inoeo ?aeeaiiuo ?anoiaeia eiieo?aioia,a e?eaua D e MR nianoyony
aiec.Ni/aoaiea yoeo oaeoi?ia naaaeao ia iao yeiiiie/aneoth
i?eaueue.Ii,o.e. ?aeeaia iineoaeeea oaaee/aieth ni?ina aeey anao
i?iaeaaoeia ia ?uiea e niinianoaiaaea iiyaeaieth iiauo
i?iecaiaeeoaeae,oi iauaa eie-ai iio?aaeyaiiai oiaa?a oaaee/eaaaony.

E?eaay ni?ina eaaeaeie oe?iu aeieaeia auoue eanaoaeueiie,e e?eaie
AC+ACs i?e iaeneiece?othuai i?eaueue auionea Ql .I?e oeaia ?1 oe?ia
iieo/aao ioeaaoth yeiiiie/aneoth i?eaueue.?aaiiaaniia eie-ai Ql aieueoa
Q` ,eioi?ue nouanoaiaae au i?e ionoonoaee ?aeeaiu.Neaaeiaaoaeueii a
io?anee nieaeaaony ecauoi/iay iiuiinoue.(io?acie Q`Ql).Yoi niinianoaoao
nieaeaieth n?aaeieo ecaea?aeae i?iecaiaenoaa,/oi iaeiaei ia i?eiineo
auaiae iio?aaeoaeth,o.e. oeaia ia oiaiueoaaony,a
iaiai?io,aic?anoaao,o.e. a iae io?aaeathony n?aaeiea ecaea?aeee
?aaeecaoeee,iaiaoiaeeiua aeey i?iaeaaee Ql i?iaeoeoa.?aeeaia oaeaea
ioaeaeaao ?ano?nu io i?iecaiaenoaa ae?oaeo oiaa?ia.A aeieain?i/iii ieaia
oe?ia ia auea?uaaao io ?aeeaiu,o.e. /oi n iae,/oi aac iaa oe?ia
iieo/aao ioeaaoth i?eaueue.?aeeaia,iaeiaei,iiaeao auiieiyoue aaaeioth
nioeeaeueioth caaea/o,niaaaeay iio?aaeoaeae eioi?iaoeeae e nie?auay
iia?aoeeiiiua ecaea?aeee i?e iieoiea.Anee ?aeeaia iaania/eaaao
i?eciaiea i?iaeoeoo e aaaeao e i?eaueaieth o iio?aaeoaey,oi iia
iicaieyao i?iaeaaoeai iiaeieiaoue oeaiu aac iioa?ue a i?iaeaaeao a
iieueco eiieo?aioia.Oaeaea iaia?oaeeaaaony iieiaeeoaeueiay caaeneiinoue
iaaeaeo i?eaueyie e ?aeeaiie.Yoi eioa?i?aoe?oaony eae iieacaoaeue
oiai,/oi ?aeeaia oaaee/eaaaoiiiiiieueioth aeanoue.Iaeiaei ae?oaea
enneaaeiaaiey iieacuaatho,/oi eioi?iaoeey,i?aaeinoaaeyaiay
?aeeaiie,niinianoaoao oiaiueoaieth i?eaa?aeaiiinoe iio?aaeoaeae e
ii?aaeaeaiiiio aeaeo i?iaeoeoeee.Yoi iiae?acoiaaaao ,/oi ?aeeaia
oaaee/eaaao oeaiiaoth yeanoe/iinoue ni?ina aeey i?eaueae eaaeaeie
ioaeaeueiie oe?iu.

?en. 6 ecia?aaeaao ?aaiiaanea a aeieain?i/iii ieaia n inou. ?aeeaiiie
aeayoaeueiinoe.

MC+MCs
AC+ACs

Pl
min

AC

P`

D

MR

Q` Ql

Ieeaiiieey

Ieeaiiieey – yoi ?uii/iay no?oeoo?a,i?e eioi?ie a ?aaeecaoeee
eaeiai-eeai oiaa?a aeiieie?oao i/aiue iaiiiai i?iaeaaoeia,a iiyaeaiea
iiauo i?iaeaaoeia cao?oaeiaii eee iaaiciiaeii.Oiaa?,?aaeecoaiue
ieeaiiieenoe/aneeie oe?iaie,iiaeao auoue e aeeooa?eioee?iaaiiui e
noaiaea?oece?iaaiiui.

Iau/ii ia ieeaiiieenoe/aneeo ?uieao ainiiaenoaoao io aeaoo aei aeanyoe
oe?i,ia eioi?ua i?eoiaeeony iieiaeia e aieaa iaueo i?iaeaae i?iaeoeoa.

Ia ieeaiiieenoe/aneeo ?aieao,ii iaiueoae ia?a,iaeioi?ua oe?iu iiaoo
aeeyoue ia oeaio aeaaiaea?y eo aieueoei aeieyi a iauai auioneaaiii
eie-aa oiaa?a.I?iaeaaoeu ia ieeaiiieenoe/aneii ?uiea ciatho,/oi eiaaea
iie eeai eo niia?ieee eciaiyo oeaiu eee auioneaaiue iauai i?iaeaae,oi
iineaaenoaey neaaeoony ia i?eaueyo anao oe?i ia ?uiea.I?iaeaaoeu
iniciatho naith acaeiicaaeneiinoue.I?aaeiieaaaaony,/oi eaaeaeay oe?ia a
io?anee i?eciaao,/oi eciaiaiea aa oeaiu eee auionea auciaao ?aaeoeeth ni
noi?iiu ae?oaeo oe?i.?aaeoeey,eioi?oth eaeie-eeai i?iaeaaaoe iaeeaeaao
io niia?ie/athueo oe?i a ioaao ia eciaiaiey onoaiiaeaiiuo ei oeaiu
,iauaia auionea eee eciaiaiey aeayoaeueiinoe a iaeanoe
ia?eaoeiaa,yaeyaony iniiaiui oaeoi?ii,ii?aaeaeythuei aai
?aoaiey.?aaeoeey,eioi?ie ioaeaeueiua i?iaeaaoeu aeaeoo io naieo
niia?ieeia,aeeyao ia ?aaiiaanea ia ieeaiiieenoe/aneeo ?uieao.

Ai iiiaeo neo/ayo ieeaiiieee caueuaiu aa?uea?aie aeey aoiaea ia
?uiie,noiaeeie n oaie,eioi?ua nouanoaotho aeey iiiiiieueiuo
oe?i.Anoanoaaiiay ieeaiiieey nouanoaoao,eiaaea ianeieueei oe?i iiaoo
iinoaaeyoue i?iaeoeoeeth aeey anaai ?uiea i?e aieaa ieceeo aeieain?i/iuo
ecaea?aeeao,/ai auee au o iiiaeanoaa oe?i.

Iiaeii auaeaeeoue neaaeothuea /a?ou ieeaiiieenoe/aneeo ?uieia.:

1.Anaai ianeieueei oe?i niaaaeatho aanue ?uiie.I?iaeoeo iiaeao auoue
eae aeeooa?aioee?iaaiui,oae e noaiaea?oece?iaaiiui.

2.Ii e?aeiae ia?a, iaeioi?ua oe?iu a ieeaiiieenoe/aneie io?anee
iaeaaeatho e?oiiuie ?uii/iuie aeieyie.Neaaeiaaoaeueii,iaeioi?ua oe?iu ia
?uiea niiniaiu aeeyoue ia oeaio oiaa?a,aa?uee?oy aai iaee/ea ia ?uiea.

3.Oe?iu a io?anee niciatho naith acaeiicaaeneiinoue.

Iao aaeeiie iiaeaee ieeaiiieee,oioy ?ac?aaioai oeaeue ?yae iiaeaeae.

Niciaoaeueiia niia?ie/anoai:ieeaiiieenoe/aneea oeaiiaua aieiu.

Anee i?aaeiieiaeeoue ,/oi ia ianoiii ?uiea nouanoaoao oieueei ai?noea
i?iaeaaoeia,?aaeecothuay noaiaea?oece?iaaiiue oiaa?,oi iiaeii
?anniio?aoue iiaeaeue “niciaoaeueiiai niia?ie/anoaa”.Eaaeaeay oe?ia ia
?uiea no?aieoueny iaeneiece?iaaoue i?eaueue e aeiionoei,eaaeaeay
i?aaeiieaaaao,/oi aa eiieo?aiou aoaeoo oaa?aei i?eaea?aeeaaoueny
ecia/aeueiie oeaiu.

Oeaiiaay aieia – oeeee iineaaeiaaoaeueiuo oiaiueoaiee oeaiu
niia?ie/athueie ia ieeaiiieenoe/aneii ?uiea oe?iaie.Iia yaeyaony iaeiei
ec iiiaeo aiciiaeiuo iineaaenoaee ieeaiiieenoe/aneiai
niia?ie/anoaa.Aieiu oeai oi?ioe aeey iio?aaeoaeae,ii ieioe aeey i?eaueae
i?iaeaaoeia.

Eaaei iiiyoue,eae oe?iu aoyaeaathony a yoo aieio.Iineieueeo eaaeaeue
i?iaeaaaoe aeoiaao,/oi ae?oaie ia aoaeao ?aaae?iaaoue ia aai iiieaeaiea
oeaiu,oi o eaaeaeiai ec ieo anoue eneooaiea oaaee/eoue
i?iaeaaee,nie?auay oeaiu.Nieaeay oeaio ieaea oeaiu naiaai
eiieo?aioa,eaaeaeue i?iaeaaaoe iiaeao caoaaoeoue aanue ?uiie – eee ii
oae aeoiaao – e iiaeao oai naiui oaaee/eoue i?eaueueIi eiieo?aio
ioaa/aao iiieaeaieai oeaiu.Aieia oeai i?iaeieaeaaony aei oao ii?,iiea
oeaia ia iaaeaao aei o?iaiy n?aaeieo ecaea?aeae.A ?aaiiaanee iaa
i?iaeaaoea iacia/atho iaeio e oo aea oeaio P=AC=MC .Iauee ?uii/iue
auione oaeie aea,eaeie eiae au ianoi i?e niaa?oaiiie
eiieo?aioeee.I?aaeiieaaay,/oi eaaeaeay oe?ia anaaaea iiaeaea?aeeaaao
naith oaeouoth oeaio,ae?oaay oe?ia anaaaea iiaeao oaaee/eoue
i?eaueue,o?aaoy ia 1 ?oaeue iaiueoa,/ai aa niia?ieoea.Eiia/ii ,ae?oaay
oe?ia ia nio?aieo i?aaeithth oeaio,o.e. iia iniciaao,/oi iiaeao
iieo/eoue aieueooth i?eaueue,o?aaoy ia 1 eiiaeeo iaiueoa eiieo?aioa.

?aaiiaanea nouanoaoao oiaaea,eiaaea ie iaeia oe?ia aieueoa ia iiaeao
iieo/aoue auaiaeu io iiieaeaiey oeaiu.Yoi i?ienoiaeeo.eiaaea ?=AN,a
yeiiiie/aneea i?eauee ?aaiu ioeth.Nieaeaiea oeaiu ieaea yoiai o?iaiy
i?eaaaeao e oauoeai.Iineieueeo eaaeaeay oe?ia aeiioneaeao,/oi ae?oaea
oe?iu ia aoaeoo iaiyoue oeaio,oi o iaa iao noeioea oaaee/eaaoue
oeaiu.Naeaeaoue oae cia/eei au iioa?youe ana i?iaeaaee a iieueco
eiieo?aioia,eioi?ay,eae i?aaeiieaaaaony,oaea?aeeaaao naith oeaio
iaeciaiiie ia o?iaia ?=AN .Yoi oae iacuaaaiia ?aaiiaanea Aa?o?aia.A
iauai ia ieeaiiieenoe/aneii ?uiea ?aaiiaanea caaeneo io
i?aaeiieiaeaiee,eioi?ua aeaeatho oe?iu i ?aaeoeee naieo niia?ieeia.

E ian/anoueth aeey iio?aaeoaeae ,oeaiiaua aieiu iau/ii
iaaeieaiaa/iu.Ieeaiiieenoe/aneea oe?iu eniuouaatho eneooaiea aneoieoue
iaaeaeo niaie a nio?oaeie/anoai,/oiau onoaiaaeeaaoue oeaiu e aeaeeoue
?uiee oaeei ia?acii,/oiau ecaaaeaoue ia?niaeoeau oeaiiauo aiei e eo
iai?eyoiiai aicaeaenoaey ia i?eaueue.

No?aoaaey iiaaaeaiey i?e ieeaiiieee e oai?ey ea?

Oai?ey ea? aiaeece?oao iiaaaeaiea eeoe e i?aaiecaoeee n
i?ioeaiiieiaeiuie eio?anaie. ?acoeueoaou ?aoaiey oi?aaeaiey oe?i caaenyo
ia oieueei io naieo yoeo ?aoaiee,ii e io ?aoaiee eiieo?aioia.Oai?eth ea?
iiaeii i?eiaieoue e oeaiiaie no?aoaaee ieeaiiieenoe/aneeo
oe?i.Neaaeothuee i?eia? eeethno?e?oao aiciiaeiinoe oai?ee ea?.

A i?aaeuaeouae iiaeaee oeaiiaie aieiu i?aaeiieaaaaony,/oi eiieo?aio
aoaeao nio?aiyoue oeaio iaeciaiiie.Iie aun/eouaatho i?eaueue io naiaai
?aoaiey i oeaia,aeiioneay,/oi niia?iee ia aoaeao ioaa/aoue iiieaeaieai
oeaiu.I?aaeiieiaeei,/oi ?oeiaiaenoai aieaa i?eaeeaeaii e ?aaeueiinoe.Iie
ia i?eaea?aeeaathony oi?yii iiaiey,/oi eiieo?aio nio?aieo naith oeaio
iaeciaiiie,a iniciatho,/oi i?ioeaiee eeai ioaaoeo iiieaeaieai oeaiu,eeai
nio?aieo aa ia i?aaeiai o?iaia.O.a. i?eaueue,eioi?oth iiaeao iieo/eoue
oe?ia caaeneo io ?aaeoeee niia?ieea.A aeaiiii neo/aa,iaiaaeaea?u
iiaen/eouaatho naie i?eauee eae aeey neo/ay,a eioi?ii eiieo?aio
nio?aiyao oeaio iaeciaiiie,oae e aeey neo/ay eciaiaiey oeaiuEoiaii yoiai
yaeyaony iao?eoea ?acoeueoaoia.,eioi?ay iieacuaaao auaiaeo eee oauoie io
eaaeaeie aiciiaeiie no?aoaaee aeey eaaeaeiai aiciiaeiiai ioaaoa
niia?ieea ii ea?a.Neieueei ea?ie iiaeao auea?aoue eee i?iea?aoue caaeneo
io no?aoaaee niia?eea.

Oaaeeoea 1 iieacuaaao iao?eoeo ?acoeueoaoia ?aoaiee iaiaaeaea?ia
eiiiaiee A e A.

Iao?eoea ?acoeueoaoia oi?aaeai/eneeo ?aoaiee a oeaiiaie aieia

N o ? a o a a e y A

Nieceoue oeaio
Iiaeaea?aeeaaoue oeaio Iaeneioi

ia 1 ?/oo

iioa?ue

aeey A

N Nieceoue Eciaiaiea i?eaueae Eciaiaiea
i?eaueae

o oeaio eiii. A =-O
eiii. A =+Y – X

? ia 1 ?/oo

a Eciaiaiea i?eaueae
Eciaiaiea i?eaueae

o eiii. A =-O
eiii. A =-Z

a

a Iiaeaea?- Eciaiaiea i?eaueae Eciaiaiea
i?eaueae

e aeeaaoue eiii. A = -Z
eiii. A=0 – Z

y oeaio

Eciaiaiea i?eaueae
Eciaiaiea i?eaueae

A eiii. A =+Y
eiii. A=0

Iaeneioi iioa?ue – X
– Z

aeey A

X LRACmin iioaioeeaeueiuo
iiauo i?iecaiaeeoaeae,oi ea?oaeue ia?a/ai ia i?iaae,anee oieueei ia
nouanoaoao aa?uea?a aeey aoiaea ia ?uiie.Neaaeiaaoaeueii,oe?iu
ciatho,/oi onoaiaaeeaaoue iiiiiieueioth oeaio ouaoii.I?e iiiiiieueiie
oeaia aieueoa oe?i aieaeao ia ?uiie e i?aaeeaaaaiia aeey i?iaeaaee
eie-ai oiaa?a aic?anoao.neaaeiaaoaeueii,oeaia e i?eauee oiaaeoo.

?en. 10.

a?. A

P`=

LRACmin

A?. A

Pm
MC

P`

MR
D

Qm Ql

Oeaiie ,ia?aie/eaathuae aoiae ia ?uiie,yaeyaony oeaia,aeinoaoi/ii
ieceay,/oiau i?aaeioa?aoeoue iiyaeaiea ia ?uiea a ea/anoaa i?iaeaaoeia
iiauo iioaioeeaeueiuo i?iecaiaeeoaeae.I?aaeiieiaeei,/oi e?eaua n?aaeieo
ecaea?aeae oe?i auaeyaeyo oae aea,eae e o iiauo i?iecaiaeeoaeae.A yoii
neo/aa ethaay oeaia auoa P` ni?iaioee?oao aoiae
“/oaeaeia”.Neaaeiaaoaeueii,oe?iai io?anee i?eaeaony oaea?aeeaaoue oeaio
ia o?iaia P`=LRACmin.Ii yoie oeaia iie i?iaeaaeoo Ql i?iaeoeoa,/oi
aieueoa,/ai iie i?iaeaee au,anee au oeaia auea aeinoaoi/ii aunieie,/oiau
niinianoaiaaoue anooieaieth ia ?uiie iiauo oe?i,ii oiaaea iie iieo/atho
ioeaaoth yeiiiie/aneoth i?eaueue.

Anee,iaeiaei ,oe?iu iaeaaeatho i?aeiouanoaii ieceeo cao?ao,eioi?uo iao
o iiauo iioaioeeaeueiuo i?iecaiaeeoaeae,oi iie niiaoo ecaeaeaoue a
aeieain?i/iii ieaia yeiiiie/aneoth i?eaueue i?e oeaia P` e a oiaea a?aiy
oaea?aeeaaoue iioaioeeaeueiuo i?iecaiaeeoaeae io aoiaea ia ?uiie.

Oeaiiia?aciaaiea,ia?aie/eaathuaa aoiae ia ?uiie ,iieacuaaao,eaeei
ia?acii iianaiey ia?aae iiyaeaeai ia ?uiea iiauo eiieo?aioia iiaoo
iiaeoieeiooue iaeneiece?othuea i?eauee oe?iu a?aiaiii ia eniieueciaaoue
naith iiiiiieueioth aeanoue ia ?uiea.

Iiaeaeue aeoiiieee Eo?ii

Aeoiiieey – yoi ?uii/iay no?oeoo?a,i?e eioi?ie aeaa
i?iaeaaoea,caueuaiiua io iiyaeaiey aeiiieieoaeueiuo
i?iaeaaoeia,yaeythony aaeeinoaaiiuie i?iecaiaeeoaeyie
noaiaea?oece?iaaiiie i?iaeoeoeee,ia eiathuae aeeceeo
caiaieoaeae.Yeiiiie/aneea iiaeaee aeoiiieee iieaciu ,/oiau
i?ieeethno?e?iaaoue,eae i?aaeiieiaeaiey ioaeaeueiiai i?iaeaaoea ian/ao
ioaaoa niia?ieea aicaeaenoaotho ia ?aaiiaaniue auione.Eeanne/aneay
iiaeaeue aeoiiieee – yoi iiaeaeue,noi?ioee?iaaiiay a 1838 a.
o?aioeocneei yeiiiienoii Iathnoaiii Eo?ii.Yoa iiaeaeue aeiioneaao,/oi
eaaeaeue ec aeaoo i?iaeaaoeia i?aaeiieaaaao,/oi aai eiio?aio anaaaea
aoaeao oaea?aeeaaue naie auione iaeciaiiui,ia oaeouai o?iaia.Iia oaeaea
i?aaeiieaaaao,/oi i?iaeaaoeu ia ociatho i naieo ioeaeao.A
aeaenoaeoaeueiinoe i?aaeiieiaeaiey i?iaeaaoeia i ?aaeoeee
eiieo?aioa,aa?iyoii,iiiaiythony,eiaaea iie ociatho i naieo i?aaeuaeoueo
ioeaeao.

Aeiionoei,/oi a ?aaeiia anoue oieueei aeaa i?iecaiaeeoaey oiaa?a
O.Ethaiio aeaeathuaio i?eia?anoe oiaa? O i?eoiaeeony i?eia?aoaoue aai o
iaeiiai ec yoeo aeaoo i?iecaiaeeoaeae.Oiaa? O eaaeaeie oe?iu
noaiaea?oece?iaai e ia eiaao ea/anoaaiiuo ?acee/ee.Ieeaeie ae?oaie
i?iecaiaeeoaeue ia iiaeao aieoe ia ?uiie.Aeiionoei,/oi iaa
i?iecaiaeeoaey iiaoo auioneaoue oiaa? O i?e iaeeiaeiauo cao?aoao e /oi
n?aaeiea ecaea?aeee iaeciaiiu e ?aaiu,neaaeiaaoaeueii,i?aaeaeueiui
ecaea?aeeai.A?aoee A ?en. 11,iieacuaaao ?uii/iue ni?in ia oiaa?
O,iiia/aiiue Dm,aianoa ni n?aaeieie e i?aaeaeueiuie ecaea?aeeaie
i?iecaiaenoaa.Anee au oiaa? O i?iecaiaeeeny ia eiieo?aioiii ?uiea,oi
auione aue au Qc aae ,a oeaia auea au Pc=AC=MC.

Aeaoiy oe?iaie,auioneathueie oiaa? O yaeythony oe?ia A e oe?ia A.Oe?ia
A ia/aea i?iecaiaeeoue oiaa? O ia?aay.Aei oiai,eae oe?ia A ia/eiaao
i?iecaiaenoai,oe?ia A iaeaaeaao anai ?uieii e i?aaeiieaaaao,/oi auione
niia?ie/athueo oe?i anaaaea aoaeao ?aaai ioeth.Iineieueeo iia
n/eoaao,/oi iaeaaeaao iiiiiieeae,oi i?iecaiaeeo iiiiiieueiue
auione,niioaaonoaothuee oi/ea,a eioi?ie MRm=MC.Iieo/athuayny a eoiaa
oeaia ?aaia Pm.I?aaeiieiaeei eeiaeioth e?eaoth ni?ina.Yoi
iiae?acoiaaaao,/oi i?aaeaeueiue aeioiae aoaeao iaaeaoue n ?inoii auionea
aaeaia auno?aa oeaiu.Iineieueeo e?eaay ni?ina aeaeeo io?acie ?nA
iiiieai,oi iiiiiieueiue auione ninoaaeyao iieiaeio eiieo?aioiiai
auionea.Neaaeiaaoaeueii,ia?aiia/aeueiue auione oe?iu A,iaeneiece?othuee
aai i?eaueue ninoaaeyao Qm aae.

N?aco aea iinea oiai,eae oe?ia A ia/eiaao i?iecaiaenoai,ia ?uiea
iyaeyaony oe?ia A.Iiyaeaiea iiauo oe?i iaaiciiaeii.Oe?ia A
i?aaeiieaaaao,/oi oe?ia A ia aoaeao ioaa/aoue eciaiaieai
auionea.Iia,neaaeiaaoaeueii,ia/eiaao i?iecaiaenoai,i?aaeiieaaay,/oi
oe?ia A aoaeao i?iaeieaeaoue auioneaoue Qm aae oiaa?a O.E?eaay ni?ina
,eioi?ue oe?ia A aeaeeo aeey naiaai oiaa?a,iieacaia ia a?. A ?en. 11.Iia
iiaeao ianeoaeeoue anao oao iieoiaoaeae,eioi?ua eoieee au oiaa? O ,anee
au oeaia oiaea ieaea oaeouae oeaiu oe?iu A,Pm.Neaaeiaaoaeueii,e?eaay
ni?ina ia aa auione ia/eiaaony i?e oeaia Pm,eiaaea ?uii/iue ni?in
ninoaaeyao Qm aae. oiaa?a .Yoa e?eaay ni?ina Db1, i?iaeaaee aaeieue yoie
e?eaie i?aaenoaaeytho niaie i?eaaaeo,iaania/eaaaioth oe?ia A e oaeouaio
?uii/iiio auioneo Qm aae,eioi?ua aei yoiai iiiaioa auioneaea oe?ia A.

E?eaay i?aaeaeueiiai aeioiaea,niioaaonoaothuay e?eaie ni?ina Db1 –
MRb1.Oe?ia A i?iecaiaeeo iauai i?iaeoeoeee,niioaaonoaothuee ?aaainoao
MRb1=MC.Noaey ii ion/aoo ia ine auionea io oi/ee, a eioi?ie auione
oiaa?a O ?aaai Qm aae. ,aeaeei,/oi yoio iauai ninoaaeyao 0.5.O aae.
oiaa?a. Oaaee/aiea ?uii/iiai i?aaeeiaeaiey oiaa?a O n O aei 1.5 O
aae,iaeiaei,oiaiueoaao oeaio aaeeieoeu oiaa?a O n Pm aei ?1.A oaaeeoea
2 i?aaenoaaeaiu aeaiiua auionea i?iaeoeoeee eaaeaeie oe?iu ca ia?aue
ianyoe aeayoaeueiinoe.Iaeneiece?othuee i?eaueue auione eaaeaeie oe?iu
anaaaea ninoaaeyao iieiaeio ?acieoeu iaaeaeo Qc e oai iauaiii
i?iecaiaenoaa ,eioi?ue ,eae iia i?aaeiieaaaao, aoaeao eiaoue ae?oaay
oe?ia.Eiieo?aioiue auione – yoi auione ,niioaaonoaothuee oeaia ? =IN – a
yoii neo/aa 2O aae. oiaa?a.Eae iieacuaaao oaaeeoea oe?ia A ia/eiaao n
i?iecaiaenoaa 0.5 Qc ,i?e oneiaee,/oi auione aa niia?ieea ?aaai ioeth.
Oiaaea oe?ia A a yoii ianyoea auioneaao 0.5 O oiaa?a O,/oi ninoaaeyao
0.5(0.5Qc)=0.25 Qc.Yoi iieiaeia ?aciinoe iaaeaeo eiieo?aioiui auioneii e
iiiiiieueiui auioneii,eioi?ue ia?aiia/aeueii iaania/eaaea oe?ia A.

Iaaeaiea oeaiu oiaa?a O ,aucaaiiia aeiiieieoaeueiui i?iecaiaenoaii
oe?iu A ,i?eaiaeeo e eciaiaieth e?eaie ni?ina oe?iu A.Oe?ia A oaia?ue
i?aaeiieaaaao,/oi oe?ia A aoaeao i?iaeieaeaoue auioneaoue 0.5.O aae.
oiaa?a.Iia aeaeeo ni?in ia naie oiaa? O eae ia/eiathueeny a oi/ea e?eaie
?uii/iiai ni?ina ,niioaaonoaothuae iany/iiio auioneo 0.5. O aae.Aa ni?in
oaia?ue ?aaai Da1,eae iieacaii ia a?. N,?enoiie 11.Iaeneiece?othuee aeey
iaa i?eaueue auione ?aaai oaia?ue iieiaeia ?aciinoe iaaeaeo
eiieo?aioiui auioneii e oai iauaiii,eioi?ue a ianoiyuaa a?aiy
i?iecaiaeeo oe?ia A.Yoi i?ienoiaeeo, eiaaea MRa1=MC.Oe?ia A
i?aaeiieaaaao,/oi oe?ia A aoaeao i?iaeieaeaoue auioneaoue 0.5.O aae.
oiaa?a iinea oiai,eae ii io?aaoee?oao naie auione,neaaeiaaoaeueii,
iaeneiece?othuee i?eaueue auione ?aaai o oe?iu A

1/2(2X – 1/2X)=3/4 X .

Yoi iiaeii caienaoue a aeaea:

1/2(Qc – 1/4Qc)=3/8 Qc,

/oi e iieacaii a oaaeeoea 2.

Iiaeaeue aeoiiieee Eo?ii.(?en. 11)

Ia?aue ianyoe.

A?. A

Oeaia

Pm

Pc E
MC=AC

Mrm Dm

Qm=1/2Qc Qc
Q

A?. A

Oeaia

Pm

P1

MC=AC

MRb1 Db1

1/2Qc 3/4 Qc Qc
Q

Aoi?ie ianyoe.

A?. N

Oeaia

?2

IN=AN

MRa1 Da1

1/4 Qc 5/8 Qc Qc

A?. D

P3

MC=AC

MRb2 Db2

3/8Qc11/16QcQc

Ieii/aoaeueiia.(a?. A)

Pe

MC=AC

D

1/3Qc 2/3Qc Qc

Aeoiiieueiia ?aaiiaanea Eo?ii oaae. 2

Ianyoe Aui. oe?iu A Aui. oe?iu A

1 1/2Qc 1/2(1/2Qc)=1/4Qc

2 1/2(Qc-1/4Qc)=3/8Qc 1/2(Qc-3/8Qc)=5/16Qc

3 1/2(Qc-5/10Qc)=11/32Qc 1/2(Qc-11/32Qc)=21/64Qc

4 1/2(Qc-21/64Qc)=43/128Qc 1/2(Qc-43/128Qc)=85/256Qc

Eiia/iia ?aaiiaanea

Qa=(1-(1/2Qc+1/8Qc+1/32Qc+…))Qc=(1-1/2(1-1/4))Qc=1/3Qc

Qb=(1/4+1/16+1/64+…)Qc=(1/4(1-1/4))Qc=1/3Qc

Iauee auione =2/3Qc

Oaia?ue i/a?aaeue oe?iu A ioaa/aoue niiaa.Oe?ia A nieceo naia
i?iecaiaenoai N 1/2 Qc aei 3/8Qc yoi i?eaiaeeo e nieaeaieth iauaai
i?aaeeiaeaie oiaa?a O n 3/4Qc aei 5/8Qc.A ?acoeueoaoa yoiai oeaia
oiaa?a au?anoaao aei ?2.Oe?ia A i?aaeiieaaaao,/oi oe?ia A aoaeao
i?iaeieaeaoue auioneaoue yoi eie-ai.Iia ?anniao?eaaao naith e?eaoth
ni?ina eae eeieth,ia/eiathuothny a oi/ea,aaea ?uii/iue auione ?aaai
3/8Qc.Yoa e?eaay ni?inaDb2,oeacaiiay ia a?. D,?en. 11.Iaeneiaeueiay
i?eaueue nouanoaoao a oie oi/ea,aaea MRb2=MC.Yoi ?aaiyaony iieiaeia
?aciinoe iaaeaeo eiieo?aioui auioneii e aaee/eiie a 3/8 eiieo?aioiiai
auionea,eioi?oth a ianoiyuaa a?aiy iinoaaeyao oe?ia A.Eae iieacaii a
oaaeeoea 2,oe?ia A oaia?ue i?iecaiaeeo 5/16 eiieo?aioiiai auionea.Iauee
?uii/iue auione ?aaai oaia?ue 11/16Qc,a oeaia nieaeaaony aei ?3.Ca
eaaeaeue ianyoe eaaeaeue aeoiiieeno i?iecaiaeeo iieiaeio ?aciinoe
iaaeaeo eiieo?aioiui auioneii e auioneii,inouanoaeyaiui eiieo?aioiie
oe?iie.

Eae iieacaii ia a?. A,?en.11 ,eaaeaeay oe?ia auioneaao 1/3 Qc,a oeaia
?aaia ?a.Yoi ?aaiiaanea Eo?ii aeey aeoiiieee.Iii nouanoaiaaei au.anee
oieueei eaaeaeay oe?ia oii?ii iieaaaea au,/oiae?aaay ia aoaeao
?aaoee?iaaoue naie auione,/oi iiae?acoiaaaao,/oi oi?aaeaiea oe?iu ia
o/eouaaao naieo ioeaie.,/oi ,eiia/ii,yaeyaony aieueoei oi?iuaieai.Ii i?e
aieaa neiaeiuo aeiiouaieyo noaiiaeony neiaeii ii?aaeaeeoue oneiaey
?aaiiaaney.

E?eaua ?aaae?iaaiey.

Oi aea naiia ?aaiiaanea iiaeii ecia?aceoue e ae?oaei niiniaii.E?eaua
?aaae?iaaiey iieacuaatho iaeneiece?othuea i?eaueue ?acia?u
auionea,eioi?ue aoaeao inouanoaeyoueny iaeiie oe?iie,anee aeaiu ?acia?u
ae?oaie oe?iu-niia?ieea.

E?eaay ?aaae?iaaiey1 i?aaenoaaeyao auione oe?iu A eae o-oeeth io
auionea oe?iu A.,a e?eaay ?aaae?iaaiey 2 – iaiai?io.

Qa

Qc

Eeiey ?aaae?iaaiey 1

1/2Qc

3/8Qc

1/3Qc Eeiey ?aaae?iaaiey 2

1/4Qc

Qb

1/4Qc1/3Qc 1/2Qc Qc

Ethaie auione auoa Qc iaauaiaeai,o.e. oeaia iaaeaao ieaea o?iaiy
n?aaeieo ecaea?aeae.Neaaeiaaoaeueii,anee auione iaeiie ec oe?i ?aaai Qc
aae.,oi aoi?ay ioaa/aao ioeaaui auioneii.?aaiiaanea aeinoeaaaony,eiaaea
aeaa e?eaua ?aaae?iaaiey ia?anaeathony e eaaeaeay oe?ia auioneaao
1/3Qc.I?e ethaii ae?oaii auionea oe?iu acaeiii ?aaae?otho ia auai? ae?oa
ae?oaii aaee/eiu auionea.

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