គំរូគួកណូ​ (cournot Model)

 

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kic©karRsavRCavRbFanbT ³ “Cournot Model” ENnaMedaysa®sþacarü³ TYn-pløa cgRkgedaynisßit £ -lwm bBaØa -pl burI -Kg´ suFar¨a

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GarmÖkfa enAkñúgGaCIvkmμEbb pþac;mux Bak;kNþalpþac;mux nigRbkYtRbECgeBjelj mansar³sMxan;y:agxøaMg kñúgesdækic©Cati EdlGaCIvkmμTaMgGs;enHsuT§EtRtUv)anpþl;KMnity:agl¥eday esdæviTUmYyrUbeQμaH Autoine Augustin Cournot EdlCaBiess elak)anbegáItnUv KMrU Cournot EdlBiPakSaBI Duopoly. edaycg;[kan; Etyl;c,as;GMBI KMrU Cournot nigmanbMNgcg;TukCaÉksardl;nisiStCMnan;eRkay eTIbeyIg´CanisiStesdækic©én saklviTüal½y PUminÞnItisa®sþ nigviTüasa®sþesdækic© )anrYmKñaCaRkumtUcmYy edIm,IRsavRCav nigcgRkgesovePA mYyk,alenH EdlmancMngeCIgfa {KMrUCournot}. esovePAmYyk,alenHniyayGMBI Rbvtþi rbs;elak Cournot/ RTwsþIbTKMrU Cournot nig lMhat;énKMrU Cournot. edaysarEt eBlevlaxøI karyl;dwg nigkarRsavRCavrbs;eyIg´mankMrit RbEhlCaGaceFIV[Gtßn½y esovePAenHminmanPaBeBjelj. EteTaHCay:agNak¾eday eyIg´sgÇwmfaesovePAenH nwgkøayCa ÉksarCMnYydl;mitþnisiStTaMgT,ay. eTaHCaeyIg´)ansikSaRsavRCavy:agNakþI eyIg´eCOCak;fa eyIg´mankMhusedayGectna kñúgesovePAenH TaMgEpñkkarKNnaelx Gtßn½y nigGkçraviruT§. eyIg´sUmsVaKmn¾cMeBaH ral;mtiriHKn;edImI,sßabna BIRKb;mCÄdæan GñkGan. PMñeBj/ éf¶TI08 Exmifuna qñaM2009 pl burI/ lwm bBaØa/ Kg; suFar:a

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matika TMB½r 1-Rbvtþirbs;elak Autoine Augustin Cournot ¬28¼8¼1801 dl; 31¼3¼1877¦...............................................1 1-1-karsikSa nigkargardMbUgrbs; Cournot...........................................................................................................................1 1-2-karRsavRCav .............................................................................................................................................................................1 1-3-kargarviTüasa®sþepSgeTot ................................................................................................................................................ 2 2-RTwsþIKMrUKYkNU (Cournot Model) .................................................................................................................................................... 3 3-lMhat;énKMrUKYkNU (Exercise of Cournot Model).................................................................................................................. 3 4-GvsanbT ................................................................................................................................................................................................ 5 Éksareyag.................................................................................................................................................................................................. 6

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1-Rbvtþirbs;elak Autoine Augustin Cournot ¬28¼8¼1801 dl; 31¼3¼1877¦ 1-1-karsikSa nigkargardMbUgrbs;elak Cournot elak Autoine Augustin Cournot EdlCa esdæviTUpg/ TsSnviTUpg nigKNitviTU)araMgpgenaH )anekIt enAéf¶28 ExsIha qñaM1801 kñúgTIRkugtUcmYyén Gray (Haute‐Saône)  kñúgRbeTs)araMg. elak)ancUlsikSaenA salamFümsikSa  Collège de Gray rvagqñaM1809 nig1816. kñúgv½y19qñaM elak)ancuHeQμaHcUleronkñúgvKÁsikSa KNitviTüamYyénsala kñúg  Besançon ehIybnÞab;mk elak)anCab;eQμaHkñúg  École  Normale  Supérieure  kñúgTIRkug Paris RbeTs)araMgkñúgqñaM 1821. edaybBaðaneya)ay  École  Normale  Supérieure RtUv)anbiT/ dUecñHqñaM1822 elakCournot )anepÞreTA Sorbonne ehIyKat;TTYl)anbriBaØabRtEpñkKNitviTüakñúgqñaM1823. elak)ansuxcitþ RblUkxøÜnKat;eTAkñúg BiPBGñkRsavRCav ehIyEdl elak)ancUlrYmkñúgsalaCan;x<s;mYyenA Academie des Sciences ehIy)anTTYlCYbCamYy esdæviTUmYyrUb KWelak Joseph Droz. cab;BIqñaM1823 elak Cournot RtUv)an[cUleFVIkarCaGñkRbwkSaGkSrsa®sþenA Marshal Gouvoin Saint Cyr. kñúgqñaM 1829 elak)anTTYl)ansBaØabRtfñak;bNÐitEpñkviTüasa®sþEdlepþatelI ynþkarI nigtarasa®sþ. RTwsþI nig GtßbTmYycMnYnrbs;elak Cournot )anTak;Tajkarcab;GarmμN_rbs; KNitviTU Siméon‐Denis  Poisson ehIyelak Poisson k¾GeBa¢Ijelak Cournot mkcUlmYykñúgbNÐitsPa. dMbUgelak Cournot bdiesF/ EteRkayBI)ancb;kic©snüaCamYy RKYsar Saint CyrkñúgqñaM1833/ elakCournot k¾cUleTAbNÐitsPa CabeNþaH GasnñkñúgTIRkug Paris. kñúgqñaM1934 elak Cournot )ankøayCasa®sþacarüEpñkkarviPaK nigynþkarI enAÉ Lyons. ehIykñúgqñaM 1835 elak Cournot eFVICasaRsþacarüKNitviTüa enA Grenoble ehIyCa saklviTüaFikar enATIenaH. bIqñaMeRkaymk Kat;)aneFVIkarCa GFikarelIRbB½n§Gb;rMrdæ. 1-2-karRsavRCav elak Cournot )ancab;epþImkarsegátdMbUgelI tYnaTIrbs; KNitviTüaeTAelI viTüasa®sþsgÁm. elak eCOfa esdæviTU RtUvEteRbI]bkrN_KNitviTüa. Kat;EfmTaMgGHGagfa kareRbIR)as;KNitviTüa kñúgesdækic©minTak;TgsMxan; RkumnisiStesdækic©qñaMTI2  

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elIPaBRtwmRtUv\tex©aHelIelxnBVnþenaHeT/ eKalbMNgrbs;Kat;kñúgkareRbIR)as;KNitviTüa KWsMxan;edIm,IENnaM nUvesckþIsMGagelIRTwsþIrbs;Kat; CaCagkarKNnaelx. kñúgqñaM1838 elak Cournot )anecjpSayesovePAmYyman cMNgeCIgfa {Recherches  sur  les  principes  mathématiques  de  la  théorie  des  richesses} EdlkñúgesovePAenH Kat;BiPakSaBI esdækic©KNitsaRsþ CaBiessKW TsSnrbs;Kat;elI Monopoly, Oligopoly, Perfect Competition nig muxgarénkarpÁt;pÁg; nigtMrUvkar. kñúgkarbgðajlMnwgénEl,gOligopoly rbs;elak Cournot/ elak)anbBa©ÚlnUvTMrg; famkb,nal¥bMput EdlshRKasnImYy²eRbIedIm,I eRCIserIsbrimaNplitplb¤ Output Edlpþl;R)ak;cMenjGtibrma kñúgkareqøIytb nwgbrimaNplitplb¤ Outputsrub rbs;shRKas kalBIeBlmun. 1-3-kargarviTüasaRsþepSgeTot kñúgqñaM1841 elak Cournot )anecjpSay BI Lyon nUvesovePAbeRgónelIkarviPaK. kñúgqñaM1843 Kat;)anesckþIBüayamdMbUgrbs;elakelI RTwsþIRbU)ab‘ÍelIet (Probability Theory). elak)aneFVIkarEbgEck rvag RbU)abbIRbePT KW Objective, Subjective nig Philosophical Probability. bnÞab;BIqñaM1848 énbdivtþn_/ elak Cournot RtUv)anEtgtaMgCa KN³kmμakarGb;rMCan;x<s; Commission des  Hautes  Études. kñúgry³eBlenaHehIy Edlelak)ansresrkarBnül;dMbUgrbs;Kat; sþIBITsSnviC¢aén viTüasa®sþ ¬1851¦. Éqña1854/ Kat;)aneFVICasaklviTüaFikar kñúg sala Dijon. b:uEnþbBaðaEPñkb¤ ckçúRbsaT ¬exSayEPñk¦ rbs;Kat; )ankøaykan;EtF¶n;F¶reTA². elak)anQb;beRgónenAqñaM 1862 ehIyRtlb;eTA TIRkug Parisvij. kñúgqñaM 1859 elak Cournot )ansresrRbvtþiGnusSavrIy_rbs;Kat; ¬ecjpSayqñaM1913¦. fVIebImanKMnit Tutidæiniym elIkarfmfyénKMnitécñRbDitrbs;elak Cournot/ k¾elakminTan;bBa©b;enAeLIyeT. elak)an ecjpSaynUvesovePABIrk,aleTotniyayBiIkarsegátTsSnviC¢a kñúgqñaM 1861 nig 1872 Edl)andak; PaBl,Il,ajrbs;elak eTAkñúgshKmn_TsSnviTU)araMg. elak Cournot )anTTYlmrN³PaBenA éf¶31 ExmIna qñaM1877 EdlenAeBlKat;erobnwgBikarEPñkpgEdr.

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2-RTwsþIbTKMrUKYkNU (Cournot Model) RTwsþInaHRtUv)anbegþIteday elak Autoine Augustin Cournot. elak)anEcgRTwsþIKMrUKYkNUenH edaysnμt;fa ³ manRkumh‘unBIr plit niglk;plitpldUcKña Rkumh‘unnImYy² kMrit brimaNplitplb¤ Output énKURbkYtRbECgrbs;xøÜnfaenAefr bnÞab;eTIb eFVIkarsMerccitþfaRtUvplit niglk;b:unμan. 3-lMhat;énKMrUKYkNU (Exercise of Cournot Model) lMhat;³ ]bmafa kñúgTIpSarplitplmYyRbePT manRkumh‘un A nig B lk;plitpldUcKña EdlshRKasTaMgBIr RbQmnwgExSekagtMrUvkar P=50-4Q (PKWCaéfø KitCa$, QKWCabrimaNOutput KitCaÉkta) ehIy Q=Q1+Q2 Edl Q1 nig Q2 tagbrimaN Output rbs;shRKas A nig B erogKña. ehIyGnuKmn_cMnaymFüm nig GnuKmn_ cMNaylMeGogrbs;Rkumh‘un A nig B KW AC1=MC1=14 nig AC2=MC2=14. Rkumh‘unnImYy²maneKaledAplit Output Edlpþl;R)ak;cMeNjGtibrma edaysnμt;faRkumh‘undéTeTotrkSa OutputenAefr. k¼ cUrrkExSekagRbtikmμrbs;Rkumh‘un A nig B. x¼ KNnalMnwgrbs;shRKasnImYy². „

„

cMelIy³ k¼rkExSekagRbtikmμrbs;Rkumh‘un A nig B -ExSekagRbtikmμrbs;Rkumh‘un A tamrUbmnþ ³ TR1=PQ1 , Et P=50-4Q ¬smμtikmμ¦ TR1=50Q1-4QQ1 eday Q=Q1+Q2 ¬smμtikmμ¦ 2

TR1=50Q1-4(Q1) -4Q1Q2

eday MR1=(TR1)l=50-8Q1-4Q2 ehIy MC1=14 ¬smμtikmμ¦ T

π

max

MR1=MC1

50-8Q1-4Q2=14

8Q1=36-4Q2

Q1=4.5-0.5Q2 (1)

-ExSekagRbtikmμrbs;Rkumh‘un B tamrUbmnþ ³ TR2=PQ2 , Et P=50-4Q ¬smμtikmμ¦ RkumnisiStesdækic©qñaMTI2  

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naM[ TR2=50Q2-4QQ2 eday Q=Q1+Q2 ¬smμtikmμ¦ naM[ TR2=50Q2-4(Q2)2-4Q1Q2 eday MR2=(TR2)l=50-8Q2-4Q1 ehIy MC2=14 ¬smμtikmμ¦ T

π

max

MR2=MC2

50-8Q2-4Q1=14

8Q2=36-4Q1

Q2=4.5-0.5Q1 (2)

dUecñH ExSekagRbtikmμRkumh‘un A KW Q1=4.5-0.5Q2 ExSekagRbtikmμRkumh‘un B KW Q2=4.5-0.5Q1 x¼ KNnalMnwgrbs;shRKasnImYy² tamsmμtikmμ ³ edayRkumh‘unnImYy² maneKaledAplit Output Edlpþl;R)ak;cMeNjGtibrma edaysnμt;fa Rkumh‘undéTeTotrkSa OutputenAefr enaHnaM[vaCalMnwgKYkNU. tam (1)nig(2)³ Q1=4.5-0.5[4.5-0.5Q1]=4.5-2.25+0.25Q1 0.75Q1=2.25 naM[ Q1=3Ékta ykCMnYskñúg(2) eyIg)an ³ Q2=4.5-(0.5)(3)=3Ékta ehIy Q=Q1+Q2=3+3=6Ékta P=50-4x6=$26 -R)ak;cMenjGtibrmaTπ1 nig Tπ2 rbs;Rkumh‘un A nig B Tπ1=(P-AC1)Q1 eday AC1=14

π =(26-14) 3=$36 Tπ =(P-AC )Q eday AC =14 Tπ =(26-14) 3=$36

T

x

1

2 2

2

2

2

x

dUecñH lMnwgshRKasnImYy²KW ³

P=$26 , Q=6Ékta Q1=Q2=3Ékta T

π =Tπ =$36 1

2

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ExSekagRbtikmμRkumh‘un A : Q1=4.5-0.5Q2 ExSekagRbtikmμRkumh‘un B : Q2=4.5-0.5Q1 Q1  9 

Q1

0

4.5

Q2

9

0

Q1

0

9

Q2

4.5 0

Q2=4.5-0.5Q1 

4.5 

lMnwgKYkNU

3 

z

0 

3 

Q1=4.5-0.5Q2 

4.5 

9

Q2 

4-GvsanbT eyIgsegáteXIjfaeTaHCa RTwsIþ Cournot manGayukalrab;ryqñaMehIyenaH k¾enAman\T§iBldl;brisßan esdækic© enAeBlbc©úb,nñCaBiesscMeBaHRTwsþI\riyabf Monopolies nig Duopolies EdleRbIR)as;GnuKmn_KNitviTüa ExSekagpÁt;pÁg; nigtMrUvkarCaGnuKmn_énéfø EdlRtUv)anerobcMedIm,Ipþl;nUvcMeNHdwgsMxan; elIkarBüakrN_esdækic© elIkMriténGaCIvkmμepSg² k¾dUcCa esdækic©Cati. edaykarxMRbwgERbgRtYsRtaypøÚv elak Cournot )anbegáItKMnit kñúgkarGPivDÆesdækic© kñúgviFI EdlGac[sgÁmmnusS karBar nig eFVI[rIkcMerInnUvkMeNInesdækic©.

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Éksareyag

1-dkRsg;BIesovePA {Microeconomics Thoery} niBn§eday Dominick Sanlvatore, 1974, 1983, 1992. 2-tam website: http://www.-history-www.gap-system.org//cournot.html 3- http://newworldencyclopedia.com/entry/AntoineAugustinCournot, Rbvtþi nigRTwsþIrbs; elak Cournot cuHéf¶TI 3 Ex4 qñaM 2008. 4- http://en.wikipedia.org/wiki/Cournot, Rbvtþirbs;elak Cournot/ cuHéf¶TI 31¼01¼2009. 5- http://economyprofessor.com/theorists/antoineaugustincournot.php.mht, RbvtiþrUbrbs; elak Antoine Augustin Cournot.

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