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For IIT-JAM, JNU, GATE, NET, NIMCET and Other Entrance Exams
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UGC NET ECONOMICS
SAMPLE THEORY
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eqæk dh ekax
lglEcU/k
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lkoZtfud jktLo
[ksy fl)kUr
C SIR NET, GATE, IIT-JAM, UGC NET , TIFR, IISc , JEST , JNU, BHU , ISM , IBPS, CSAT, SLET, NIMCET, CTET
Phone: 0744-2429714 Mobile: 9001297111, 9829567114, 9001297243 Website: www.vpmclasses.com E-Mail: [email protected] /[email protected] Address: 1-C-8, Sheela Chowdhary Road, SFS, TALWANDI, KOTA, RAJASTHAN, 324005
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eqnzk dh ekaxeqnzk dh ekaxeqnzk dh ekaxeqnzk dh ekax
eqnzk ds nks egRoiw.kZ dk;ksZa ds dkj.k eqnzk dh ekax mRiUu gksrh gSA izFke ;g gS fd eqnzk fofue; ds
ek/;e dk dk;Z djrh gS vkSj nwljk ;g fd eqnzk ewY; dk lap; (store of value) gSA vr% O;fDr
vkSj O;kikjh eqnzk dks vkaf”kd +:i ls udnh ds :i esa vkSj vkaf”kd :i ls ifjlEifr;ksa ds :i eas
j[kuk pkgrs gSaA
eqnzk dh ekax ds fuEu er gSa & Dyklhdy] uo Dyklhdy (neo classical), dsUth; rFkk
dsUtksijkUr (Post Keynesian) A bu erksa dh fuEufyf[kr foospuk dh xbZ gSA
Dyklhdy er Dyklhdy er Dyklhdy er Dyklhdy er (Classical Approach)
Dyklhdy vFkZ”kkfL=;ksa us eqnzk ds lap;u osx (velocity of circulation) ds :i esa eqnzk dh ysu&nsu
ekax ij cy fn;k A bldk dkj.k ;g gS fd Dyklhdy fopkj /kkjk ds vuqlkj eqnzk fofue; ds
ek/;e dk dk;Z djrh gS vkSj oLrqvksa rFkk lsokvksa ds fofue; dks lqxe cukrh gSA fQ”kj ds
^fofue;fofue;fofue;fofue; ds lehdj.kds lehdj.kds lehdj.kds lehdj.k esa MV = PT
tgka M eqnzk dh dqy ek=k, V eqnzk dk lap;u osx, P dher Lrj rFkk T eqnzk esa fofu;e dh x;h
dqy oLrqvksa vkSj lsokvksa dh ek=k gSA
bl lehdj.k esa PT eqnzk dh ekax dks O;Dr djrk gS
MV eqnzk dh iw frZ dks O;Dr djrk gS vkSj larqyu Lrj ij eqnzk dh ekax ds cjkcj gksrh gSSA bl
izdkj eqnzk dh ekax dk lehdj.k gksxk&
Md = PT
Tkgka Md eqnzk dh ekax gS A
uo&Dyklhdy fl}kUr uo&Dyklhdy fl}kUr uo&Dyklhdy fl}kUr uo&Dyklhdy fl}kUr (Neo-Classical Theory)
eqæk ds ekax ds uo&Dyklhdy fl}kUr dks dSfEczt vFkZ”kkL=h ek”kZy vkSj ihxw us fn;k Fkk A
dSfEczt er ds vuqlkj eqnzk dh ekax dk lehdj.k gS&
Md=KPY
C SIR NET, GATE, IIT-JAM, UGC NET , TIFR, IISc , JEST , JNU, BHU , ISM , IBPS, CSAT, SLET, NIMCET, CTET
Phone: 0744-2429714 Mobile: 9001297111, 9829567114, 9001297243 Website: www.vpmclasses.com E-Mail: [email protected] /[email protected] Address: 1-C-8, Sheela Chowdhary Road, SFS, TALWANDI, KOTA, RAJASTHAN, 324005
Page 3
tgka Md eqnzk dh ekax K okLrfod ekSfnzd vk; dk Hkkx gS ftls yksx udnh ds :i eas j[kuk
pkgrs gSa] P dher Lrj gS A ;g lehdj.k crkrk gS fd vU; ckrsa leku ;g lehdj.k crkrk gS fd vU; ckrsa leku ;g lehdj.k crkrk gS fd vU; ckrsa leku ;g lehdj.k crkrk gS fd vU; ckrsa leku jgus ij lkekU; :i eas jgus ij lkekU; :i eas jgus ij lkekU; :i eas jgus ij lkekU; :i eas
eqnzk dh ekax izR;sd O;fDr ds udnh vk; Lrj ds lekuqikfrd gksxhAeqnzk dh ekax izR;sd O;fDr ds udnh vk; Lrj ds lekuqikfrd gksxhAeqnzk dh ekax izR;sd O;fDr ds udnh vk; Lrj ds lekuqikfrd gksxhAeqnzk dh ekax izR;sd O;fDr ds udnh vk; Lrj ds lekuqikfrd gksxhA
dSfEczt ekax Qyu dks fuEu js[kkfp= dh lgk;rk ls fn[kk;k tk ldrk gS SA
Income
K
O
M
js[kkfp= % Cambridge Demand for Money Function.
Dyklhdy vFkZ”kkfL;ksa us dsoy eqnzk ds fofu;e ds ek/;e dk;Z ds Åij gh cy fn;k gSA muds
vuqlkj vFkZO;oLFkk esa eqnzk fu’izHkkoh Hkwfedk fuHkkrh gS A ;g ,d xyr /kkj.kk gS D;ksafd eqnzk
ifjlEifr dk dk;Z Hkh djrh gS tc ;g fcyksa] ckaMkas] izfrHkwfr;ksa] _.ki=ksa] okLrfod ifjlEifŸk;ksa
tSls edku] tehu vkfn vU; izdkj dh ifjlEifŸk;kas eas ifjofrZr dj nh tkrh gSA vr % eqnzk dh
ekax ds Dyklhdy fl)kUr dh eq[; deh eqnzk ds ifjlEifŸk dk;Z dh mis{kk Fkh ftls dsUt us nwj
fd;kA
eqnzk dh ekax dk dssUth; fl}kUr eqnzk dh ekax dk dssUth; fl}kUr eqnzk dh ekax dk dssUth; fl}kUr eqnzk dh ekax dk dssUth; fl}kUr
dsUt ds viuh iqLrd General Theory eas eqnzk dh ekax ds fy, ,d u;k “kCn ‘rjyrk vf/kekurjyrk vf/kekurjyrk vf/kekurjyrk vf/keku’
dk iz;ksx fd;k gSA dsUt ds vuqlkj vFkZO;oLFkk eas eqnzk dh ekax rhu mÌs”;kas ds dkj.k gksrh gS&
1- ysu&nsu mÌs”;
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2- lrdZrk mÌs”;
3- lV~Vk mÌs”;
dsUt ds vuqlkj eqnzk dh ekax bUgha rhu mÌs”;kas ds dkj.k gk srh gSA bUgha rhuksa mÌs”;ksa ds dkj.k gqbZ
eqnzk dh ekax dks eqnzk dh dqy ekax (Aggregate demand for money) dgrs gSaA Lej.k jgs] dsUt
ds ^eqnzk dh ekax* ls vHkhizk; eqnzk dh ml jkf”k ls gS tks yksx vius ikl j[krs gSa (The demand
for money in the Keynesian sense is the demand to hold money) A
1111---- ysu&nsu mÌs”; &ysu&nsu mÌs”; &ysu&nsu mÌs”; &ysu&nsu mÌs”; & ;g jkstkuk ds ysu&nsu ds fy, eqnzk dh ekax ls lEcfU/kr gSA bl izdkj
ysu&nsu mÌs”; ds fy, eqnzk dh ekax eqnzk ds fofue; ds ek/;e dk;Z ls mRiUu gksrh gSA
dsUt ds vuqlkj] vU; rRoksa ds fn, gksus ij eqnzk dh ysu&nsu mÌs”; ls lEcfU/kr ekax vk; Lrj
dk izR;{k lekuqikfrd vkSj /kukRed Qyu gSA bls bl izdkj O;Dr fd;k tk ldrk gS &
Lt = kY
tgka Lt eqnzk dh ysu&nsu ekax] k vk; dk og Hkkx tks ysu&nsu mÌs”; ds fy, j[kk tkrk gS] vkSj
Y vk; gSA
bl lehdj.k dks fuEu js[kkfp= dh lgk;rk ls n”kkZ;k x;k gSA tgak kY js[kk eqnzk dh ysu&nsu
ekax vkSj vk; Lrj eas js[kh; (linear) vkSj lkekuqikfrd lEcU/k O;Dr djrh gSA
;gka /;ku nsus ;ksX; ckr ;g gS fd dsUt us eqnzk dh ysu&nsu ekax dks C;kt c syksp ekuk gSA
IncomeO
Ky
js[kfp= % eqnzk dh ysu&nsu ekax
2222---- lrdZrk mÌs”;lrdZrk mÌs”;lrdZrk mÌs”;lrdZrk mÌs”; & O;fDr rFkk O;kolkf;d QesZa vkikr fLFkfr dk lkeuk djus ds fy, Hkh dqN
vfrfjDr jkf”k udnh ds :i eas j[krs gSA bls gh lrdZrk mÌs”; ds fy, eqnzk dh ekax dgrs gSA
C SIR NET, GATE, IIT-JAM, UGC NET , TIFR, IISc , JEST , JNU, BHU , ISM , IBPS, CSAT, SLET, NIMCET, CTET
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Page 5
vizR;kf”kr vko”;drkvksa dks iqjk djus ds fy, O;fDr vkSj O;kikjh nksuksa gh dqN udnh fjtoZ esa
j[krs gSaA O;fDr rks chekjh] nq?kZVuk] csjkstxkjh vkSj viwoZ–‘V laHkkO;rkvkas (unforeseen
contingencies) dh O;oLFkk djus ds fy, dqN udnh fjtoZ j[krk gSA blh izdkj] O;kikjh izfrdwy
fLFkfr;kas dks ikj djus ds fy, ;k vizR;kf”kr lkSnksa ls ykHk mBkus ds fy, dqN udnh fjtoZ j[krk
gSA bUgh lHkh mÌs”;ksa ds fy, j[kh xbZ eqnzk dh ekax dks lrdZrk Ekkax dgrs gSaA
dsUt ds vuqlkj eqnzk dh ysu &nsu ekax dh rjg] lrdZrk ekax Hkh vk; Lrj dk Qyu gksrh gSA
3333---- lV~Vk mÌs”;lV~Vk mÌs”;lV~Vk mÌs”;lV~Vk mÌs”; & dsUt ds vuqlkj eqnzk dh lV~Vk ekax bl mÌs”; ds fy, gksrh gS “fd Hkfo’; ds
lEcU/k eas ekfdZV dh rqyuk eas vf/kd tkudkjh }kjk ykHk dek, tk ldsaA lV~Vk mÌs”; ds fy,
j[kh xbZ eqnzk ewY; dk ,d rjy lap; gS tks mi;qDr volj ij ckMksa ;k izfrHkwfr;ksa eas fuos”k dh
tk ldrh gSA”
dsUt ds vuqlkj eqnzk dh lV~Vk ekax C;ktdsUt ds vuqlkj eqnzk dh lV~Vk ekax C;ktdsUt ds vuqlkj eqnzk dh lV~Vk ekax C;ktdsUt ds vuqlkj eqnzk dh lV~Vk ekax C;kt nj dk ?kVrk gqvk Qyu gSA C;kt dh nj ftruh Åaph nj dk ?kVrk gqvk Qyu gSA C;kt dh nj ftruh Åaph nj dk ?kVrk gqvk Qyu gSA C;kt dh nj ftruh Åaph nj dk ?kVrk gqvk Qyu gSA C;kt dh nj ftruh Åaph
gksxhgksxhgksxhgksxh, eqnzk dh lV~Vk ekax mruh gh de gksxheqnzk dh lV~Vk ekax mruh gh de gksxheqnzk dh lV~Vk ekax mruh gh de gksxheqnzk dh lV~Vk ekax mruh gh de gksxh rFkk C;kt nj ftruh de gksxh eqnzk dh lV~Vk
ekax mruh gh vf/kd gksxhA bldks bl izdkj O;Dr fd;k tk ldrk gS &
Ls =f(r)
tgka Ls eqnzk dh lV~Vk ekax gS vkSj r C;kt dh nj gSA js[kkfp= dh lgk;rk ls eqnzk dh lV~Vk
ekax dks Åij n”kkZ;k x;k gSA
Speculative demand for moneyO
Liquidity Trapr1
r2
r3
r4
r5
Ls
js[kkfp= % eqnzk dh lV~Vk ekax
mijksDr js[kkfp= ls Li’V gS fd C;kt dh cgqr Åaph nj r5 ij eqnzk dh lV~Vk ekax “kwU; gS D;ksafd
O;kikjh vius leLr udnh dks ckaMksa esa fuos”k dj nsrs g Sa D;ksafd mUgssa fo”okl gk srk gS fd C;kt nj
C SIR NET, GATE, IIT-JAM, UGC NET , TIFR, IISc , JEST , JNU, BHU , ISM , IBPS, CSAT, SLET, NIMCET, CTET
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Page 6
esa vkSj o`f} ugha gks ldrh ifj.kkeLo:i ckaMksa dh dher vc vkSj ugha ?kVsxh cfYd vc c<+sxh ghA
tSls&tSls C;kt dh nj ?kVsxh eqnzk dh lV~Vk ekax c<+sxh A vr% Ls odz dk vkdkj ;g fn[kkrk gS
fd tc C;kt nj c<+rh gS rks eqnzk dh lV~Vk ekax fxjrh gS rFkk C;kt esa deh ls ;g c<+rh gSA
rjyrk tkyrjyrk tkyrjyrk tkyrjyrk tky (Liquidity trap) & cgqr uhph C;kt nj tSls fd mijksDr js[kkfp= eas r1 ij Ls odz
iw.kZr;k ykspnkj (Perfectly elastic) cu tkrk gS] vkSj eqnzk dh lV~Vk ekax vuUr yksp gksrh gS A
Ls odz dk ;g Hkkx ‘rjyrk tkyrjyrk tkyrjyrk tkyrjyrk tky’ dgykrk gSA bruh uhph C;kt nj ij yksx ckaMksa eas fuos”k djus
ds ctk; eqnzk dks udnh eas j[kus dks vf/keku (Preference) nsrs gS] D;ksafd ckaMksa dks [kjhnus dk
eryc gksxk fuf”pr gkfuA yksx ml le; rd ckaM ugha [kjhnsaxs tc rd C;kt nj bl fuEu
Lrj ij jgrh gSA dsUt ds vuqlkj tc C;kt nj “kwU; ds fudV vkrh gS rks ckaM j[kus eas gkfu dk
tkssf[ke c<+ tkrk gSA vr% C;kt nj ftruh gh de gk sxh udnh j[kus dh ekax mruh gh vf/kd
gksxh A ifj.kkeLo:i] Ls odz iw.kZr;k ykspnkj cu tk,xkA
dsUt ds vuqlkj] eqnzk dh dqy ekax] ysu&nsu rFkk lrdZrk mÌs”;ksa ds fy, eqnzk dh ekax dk ;ksx
gksrh gSA pawfd ysu&nsu vkSj lrdZrk mÌs”;kas ds fy, j[kh xbZ eqnzk eq[;r;k vk; dk Qyu gksrk gS
vkSj lV~Vk ekax C;kt nj dk Qyu gSA bl izdkj eqnzk dh dqy ekax vk; vkSj C;kt nj nksuksa dk
Qyu gksrk gS&
L = Lt + Ls
= f(Y) + f(r)
= f(Y,r)
tgka L eqnzk dh dqy ekax dks O;Dr djrk gSA
eqnzk dh dqy ekax odz ysu&nsu vkSj lrdZrk mÌs”;ksa ds ekax Qyu rFkk lV~Vk mÌs”; ds fy, ekax
Qyu ds ik”oZ ;ksx (lateral summation) }kjk [khapk tk ldrk gSA ftls js[kkfp= esa fn[kk;k x;k
gSA
C SIR NET, GATE, IIT-JAM, UGC NET , TIFR, IISc , JEST , JNU, BHU , ISM , IBPS, CSAT, SLET, NIMCET, CTET
Phone: 0744-2429714 Mobile: 9001297111, 9829567114, 9001297243 Website: www.vpmclasses.com E-Mail: [email protected] /[email protected] Address: 1-C-8, Sheela Chowdhary Road, SFS, TALWANDI, KOTA, RAJASTHAN, 324005
Page 7
T D
L
L = L + Lt s
r1
r2
Demand for Money
Inte
rest
Rat
e
js[kkfp= % eqnzk dh ekax ¼dsUt ds vuqlkj½
mijksDr js[kkfp= esa L eqnzk dh dqy ekax odz gSA tc C;kt nj Or1 gksrk gS rks dqy ekax OD gSA
ftleas rhuksa mÌs”;ksa ds fy, eqnzk dh ekax “kkfey gSA
dsUtksijkUr er dsUtksijkUr er dsUtksijkUr er dsUtksijkUr er (Post Keynesian Approach)
eqnzk dh ekax ds dsUtksijkUr fl)kUr ds vUrxZr cksey (Boumol), Vksfcu (Tobin) rFkk QzhMeSu
(Friedman) ds fopkjksa dks “kkfey fd;k tkrk gSA izks- cksey vius fopkjkssa esa eqnzk dh ysu&nsu ekax
dks C;kt yksp (interest elastic) cryk;kA izks- Vksfcu rjyrk vf/keku (liquidity preference) dks
tksf[ke ds izfr O;ogkj ekurk gSA tcfd QzhMeSu ds vuqlkj eqnzk dh ekax dsoy vk; rFkk C;kt
dh nj dk ugha] cfYd dqy lEifr dk Hkh Qyu gksrk gSA
cksey dk LVkWd lS)kfUrd er cksey dk LVkWd lS)kfUrd er cksey dk LVkWd lS)kfUrd er cksey dk LVkWd lS)kfUrd er (Baumol’s Inventory Theoretic Approach)
pawfd dsUt eqnzk dh ysu&nsu ekax dks vk; ds Lrj dk Qyu ekurk gS vkSj ysu&nsu ekax rFkk
vk; ds chp js[kh; ,oa lekuqikrh] lEcU/k ekurk gSA ysfdu cksey ds vuqlkj eqnzk dh ysu&nsu
ekax rFkk vk; eas lEcU/k u rks js[kh; gS vkSj u gh lekuqikrhd] cfYd gksrk ;g gS fd tc vk; eas
ifjorZu gksrs gSa rks eqnzk dh ysu&nsu ekax eas vkuqikfrd ls de ifjorZu gksrs gSA fQj dsUt ;g Hkh
ekurk Fkk fd ysu&nsu ekax eq[; :i ls C;kt csyksp gksrh gS A ijUrq cksey us eqnzk dh ysu&nsu
ekax dks C;kt yksp ekuk gSA cksey us vius fl)kUr eas bl ckr ij cy fn;k gS fd eqnzk dh ekax
okLrfod “ks’kksaokLrfod “ks’kksaokLrfod “ks’kksaokLrfod “ks’kksa (real balances) ds fy, ekax gksrh gS cksey ds ysu&nsuksa ds fy, okLrfod “ks’kksas
¼eqnzk dh ekax½ dh ekax dks bl izdkj O;Dr fd;k tk ldrk gS &
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Page 8
d1 2hY
M P2 r
= ×
tgka Md eqnzk dh ysu&nsu ekax] P dher Lrj] r C;kt nj] h xSj C;kt ykxrsa rFkk Y vk; Lrj
gSaA
mijksDr mijksDr mijksDr mijksDr lehdj.k ls Li’V gS fd dher Lrj eas ifjorZukas vkSj eqnzk dh ysu&nsu ekax ds chp lehdj.k ls Li’V gS fd dher Lrj eas ifjorZukas vkSj eqnzk dh ysu&nsu ekax ds chp lehdj.k ls Li’V gS fd dher Lrj eas ifjorZukas vkSj eqnzk dh ysu&nsu ekax ds chp lehdj.k ls Li’V gS fd dher Lrj eas ifjorZukas vkSj eqnzk dh ysu&nsu ekax ds chp
izR;{k ,oa lekuqikfrd lEcU/k gksrk gSAizR;{k ,oa lekuqikfrd lEcU/k gksrk gSAizR;{k ,oa lekuqikfrd lEcU/k gksrk gSAizR;{k ,oa lekuqikfrd lEcU/k gksrk gSA bl izdkj cksey }kjk izLrqr okLrfod “ks’kksa dh ekax ds
fo”ys’k.k dk eryc gS fd ysu&nsus ds fy, eqnzk dh ekax eas Hkzkafr (money illusion) ugha gSA
Vksfcu dk fuos”k lwph p;u ekWMy % tksf[ke fuokj.k rjyrk vf/keku fl)kUr Vksfcu dk fuos”k lwph p;u ekWMy % tksf[ke fuokj.k rjyrk vf/keku fl)kUr Vksfcu dk fuos”k lwph p;u ekWMy % tksf[ke fuokj.k rjyrk vf/keku fl)kUr Vksfcu dk fuos”k lwph p;u ekWMy % tksf[ke fuokj.k rjyrk vf/keku fl)kUr (Tobin’s Portfolio
Selection Model : The Risk Aversion theory of liqui dity Preference)
tsEl Vksfcu us vius “Liquidity Preference as Behaviour Tow ards Risk” “kh’kZd izfl} ys[k eas
fuos”k lwph p;u ij vk/kkfjr tksf[ke fuokj.k rjyrk vf/keku fl)kUr (risk aversion theory of
liquidity preference) izLrqr fd;k A
bl fl)kUr esa mlus rjyrk vf/keku (liquidity preference) ds dsUth;u fl)kUr ds nks izeq[k
nks’kkas dks nwj fd;k gSA ,d] dsUt dk rjyrk vf/keku Hkkoh C;kt njksa dh izR;k”kkvksa dh csyksp
(inelasticity) ij fuHkZj djrk gSA nwljk] O;fDr ;k rks eqnzk j[krk gS ;k fQj ckaM (Bond) ghA
Vkschu us vius fl)kUr eas bu nksuksa nks’kkas dks nwj dj fn;k gSA mldk fl)kUr Hkkoh C;kt njksa dh
izR;k”kkvkas dh csykp ij fuHkZj ugha djrk gS cfYd ;g ekU;rk ysdj pyrk gS fd ifjlEifÙk;ka
(interest bearing assets) j[kus ls iwath ykHk vFkok gkfu dk izR;kf”kr ewY; (expected value)
ges”kk “kwU; gksrk gSA fQj ;g bl ckr dks Hkh Li’V djrk gS fd fdlh O;fDr dh fuos”k lwph eas
eqnzk rFkk ckaM (bond) nksuksa gh jgrs gSa] ;g ugha fd ,d le; eas dksbZ ,d gh jgsA
QzhMeSu dk fl)kUr QzhMeSu dk fl)kUr QzhMeSu dk fl)kUr QzhMeSu dk fl)kUr
QzhMeSu }kjk izfrikfnr eqnzk ds ekax fl)kUr dks eqnzk dk vk/kqfud fl)kUr (Modern Theory of
Money) Hkh dgk tkrk gSA QzhMeSu ds vuqlkj eqnzk dh ekax rhu dkjdksa ij fuHkZj djrh gS & (a)
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Page 9
fofHkUu izdkj dh ifjlEifŸk;ksa ds :i eas j[kh xbZ dqy lEifŸk (b) fofHkUu i zdkj dh lEifŸk dh
lEcfU/kr dhersa ;k muds lkisf{kd izfrQy (c) lEifŸk;ksa ds Lokfe;ksa dh :fp;ka ,oa vf/keku A
QzhMeSu us eqnzk dh ekax ;k eqnzk “ks’ kksa dh ekax dks fu/kkZfjr djus okys nks dkjdksa ij cy fn;k gS A
os gSa % (i) fofHkUu izdkj dh oSdfYid ifjlEifŸk;ksa tSls ckaM o “ks;jk sa ij C;kt dh nj (ii) dher
Lrjksa esa ifjorZu dh izR;kf”kr njA okLro esa ;s nksuksa gh dkjd eqnzk “ks’kksa dh j[kus dh ykxr dks
izHkkfor djrs gSA QzhMeSu ;g ekurk gS fd okLrfod vk; eqnzk dh ekax dk izeq[k fu/kkZjd gSA
nh?kZdky eas eqnzk dh ekax dh yksp bdkbZ nh?kZdky eas eqnzk dh ekax dh yksp bdkbZ nh?kZdky eas eqnzk dh ekax dh yksp bdkbZ nh?kZdky eas eqnzk dh ekax dh yksp bdkbZ (unity) ls vf/kd gkrh gSAls vf/kd gkrh gSAls vf/kd gkrh gSAls vf/kd gkrh gSA
QzhMeSu us eqnzk ds ekax Qyu dks fuEu izdkj ls O;Dr fd;k gS &
b e
1 dpM f Y,P, . ,r ,r ,w,u
P dt =
tgak M = ekaxh xbZ eqnzk dk dqy LVWkd
P = dher Lrj
1 dp.
P dt
= oLrqvksa dh dherksa eas gksus okys ifjorZu dh izR;kf”kr nj
w = ekuoh; lEifŸk ls xSj ekuoh; lEifŸk dk vuqikr
u = :fp;ka] vf/kekukas rFkk vU; lEc) pj
rb = ckaMksa ij izfrQy
re = bfDoVh ij izfrQy
bl ekax Qyu ls ;g fu’d’kZ fudyrk gS fd fofHkUu ifjlEifŸk;ksa dh izR;kf”kr ykHk eas o`f} gksus
ls lEifŸk /kkjd dh eqnzk dh ekax jkf”k ?kV tkrh gS vkSj lEifŸk esa o`f} eqnzk dh ekax dks c<+k nsrh
gSA
isfVufdu }kjk fd;k x;k eqnzk rFkk ewY; fl)kUr dk ,dhdj.k % okLrfod “ks’k izHkko isfVufdu }kjk fd;k x;k eqnzk rFkk ewY; fl)kUr dk ,dhdj.k % okLrfod “ks’k izHkko isfVufdu }kjk fd;k x;k eqnzk rFkk ewY; fl)kUr dk ,dhdj.k % okLrfod “ks’k izHkko isfVufdu }kjk fd;k x;k eqnzk rFkk ewY; fl)kUr dk ,dhdj.k % okLrfod “ks’k izHkko (Patinkin’s
integration of m onetary and value theory : The Real Balance Effect)
isfVufdu us uo Dyklhdy vFkZ”kkfL=;ksa dh bl ckr dks ysdj vkykspuk dh gS fd mUgksaus oLrq
cktkj dk f}&foHkktu dj fn;k gSA f}&foHkktu (dichotomizat ion) dk vFkZ gS fd lkis{k dher
Lrj (relative price) dks oLrqvksa dh ekax rFkk iwfrZ fu/kkZfjr djrh gS vkSj fujis{k dher Lrj dks
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Page 10
eqnzk dh ekax rFkk iwfrZ fu/kkZfjr djrh gSA uo Dyklhdy fl)kUr dh f}&foHkktu dh ekU;rk dk
[k.Mu djrs gq, isfVufdu us vFkZO;oLFkk ds eqnzk cktkj rFkk oLrq cktkj dk ,dhdj.k fd;k gSA
mlus okLrfod “ks’k izHkko (real balance effect) ds ek/;e ls nksuksa cktkjksa dk lek/kku fd;k gSA
okLrfod “ks’kk sa dk vFkZ gS& okLrfod “ks’kk sa dk vFkZ gS& okLrfod “ks’kk sa dk vFkZ gS& okLrfod “ks’kk sa dk vFkZ gS& yksxksa ds udnh /kkj.kksa ds LVkWd dh okLrfod dz; “kfDrAyksxksa ds udnh /kkj.kksa ds LVkWd dh okLrfod dz; “kfDrAyksxksa ds udnh /kkj.kksa ds LVkWd dh okLrfod dz; “kfDrAyksxksa ds udnh /kkj.kksa ds LVkWd dh okLrfod dz; “kfDrA
tc dher Lrj cnyrk gS rks og yksxksa ds udnh /kkj.kksa dh dz; “kfDr dks izHkkfor djrk gS tks
fd vkxs oLrqvksa dh ekax vkSj i wfrZ dks izHkkfor djrh gSA ;gh okLrfod “ks ’k izHkko gSA isfVufdu
bl izHkko ds ek/;e ls f}&foHkktu dks udkjrk gSA blds fy, isfVufdu fdlh leqnk; }kjk
/kkfjr okLrfod “ks’kksa ds LVkWd (M/P) dks mldh oLrqvksa ds fy, ekax ij izHkko ds :i eas izLrqr
djrk gSA bl izdkj fdlh oLrq ds fy, ekax] okLrfod “ks’k rFkk lkis{k dherksa ij fuHkZj djrk gSsA
vc ;fn dher Lrj c<+sxk rks blls yksxksa dk okLrfod “ks’k ¼dz; “kfDr½ de gks tk,xk vkSj os
igys ls de [kpZ djasxsA bldk eryc gS fd oLrqvksa dh ekax de gks tk,xh vkSj ifj.kker% dher
Lrj fxj tk,xkA blds foijhr dher Lrj fxjus ls okLrfod “ks’k c<+ tk,axs ftlds ifj.kkeLo:i
oLrqvksa dh dhersa ,oa dher Lrj c<+sxasA isfVufdu ds “kCnksa esa ;gh egRoiw.kZ ckr gS fujis{k dher
Lrj dk vius lUrqyu ewY; dh vksj izkoSfxd lewgu okLrfod “ks’k izHkko ds ek/;e ls& oLrq
cktkjksa dks vkSj fu’d’kZr% lkis{k dherksa dks izHkkfor djsxkA bl izdkj fujis{k dhersa u dsoy eqnzk
cktkj esa cfYd vFkZO;oLFkk ds okLrfod {ks= eas Hkh egŸoiw.kZ dk;Z djrh gSaA
dj Hkkj foHkktu ds fofHkUu mikxe dj Hkkj foHkktu ds fofHkUu mikxe dj Hkkj foHkktu ds fofHkUu mikxe dj Hkkj foHkktu ds fofHkUu mikxe (Different approaches to the division of tax burden )
izR;sd dj O;fDr;kas ij ,d Hkkj gksrk gS D;ksasfd djksa ls O;fä;ksa dh vk; de gks tkrh gS rFkk
miHkksx ?kV tkrk gSA vr% ;g vko”;d gS fd lkekftd] vkfFkZd rFkk jktuhfrd nf’Vdks.kksa ls
dj Hkkj dk U;k;iw.kZ forj.k gksA
dj Hkkj ds forj.k eas U;k; ds vkn”kZ dks izkIr djus ds fy, le;≤ ij vFkZ”kkfL=;ksa us vusd
fl)karksa ds izfriknu fd;k gS ftueas fuEu fl)kar izeq[k gSa &
1111---- foŸkh; fl)kar foŸkh; fl)kar foŸkh; fl)kar foŸkh; fl)kar (Financial Theory) : ;g fl)kar dkWycVZ (Colbert) ds bl dFku ls lacaf/kr gS
fd Þ cŸk[k ds ij bl izdkj ls fudkys tk,a fd og de ls de “kksj epk,ß vFkkZr bl fl)kar
dk mÌs”; vf/kdkf/kd vk; izkIr djuk gS rFkk dj bl izdkj ls yxk, tk,a fd turk mudk de
C SIR NET, GATE, IIT-JAM, UGC NET , TIFR, IISc , JEST , JNU, BHU , ISM , IBPS, CSAT, SLET, NIMCET, CTET
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Page 11
ls de fojks/k djsA ;g fl)kar vO;ogkfjd rFkk vuqfpr gSA D;ksafd bl fl)kar ds vuqlkj dj
Hkkj mu O;fä;ksa dks ogu djuk iM+sxk ftueas fojks/k djus ,oa fpYykus dh “kfä ugha g SA
2222---- lerk dk fl)kar lerk dk fl)kar lerk dk fl)kar lerk dk fl)kar (Principle of Equity): vk/kqfud vFkZ”kkfL=;ksa us djk/kku Hkkj ds forj.k ds
ekeys esa U;k; ij Hkkjh tksj fn;k gS vkSj lerk ,oa U;k; ds fl)kar dks viukus dh odkyr dh
gSA lerk ds nks igyw varfuZfgr gSa & leku rFkk vleku ifjfLFkfr;ksa esa yksxksa ls i`Fkd~&i`Fkd~
O;ogkj fd;k tk,A leku ifjfLFkfr;ksa (kide circumstances) dk vfHkizk; ;g gS fd tks yksx
vkfFkZd n`f’Vdks.k ls leku :i ls le`} gSa rFkk leku ifjfLFkfr;ksa esa thou O;rhr dj jgs gSa mUgsa
leku ek=k eas gh dj vnk djuk pkfg,A bls lery U;k; (horizontal equity) Hkh dgk tkrk gSA
vleku ifjfLFkfr;ksa (unlike circumstances) ls vk”k; gS fd vleku ifjfLFkfr;ksa eas jgus okys
yksxksa ls vleku vFkok rn~uqlkj gh O;ogkj fd;k tk, vFkkZr le`} vFkok vPNh gkyr okys O;fä
vU; yksxksa ds eqdkcys vf/kd dj vnk djasA bls vlery U;k; (Vertical equity) dgk tkrk gSA
3333---- lsok dh ykxr dk fl)kar lsok dh ykxr dk fl)kar lsok dh ykxr dk fl)kar lsok dh ykxr dk fl)kar (Cost of Service Theory): bl fl)kar ds vuqlkj] ljdkj O;fäxr
djnkrkvksa ds ykHk ds fy, tks fofHkUu lsok,a laiUu djrh gS mudh ykxr dks gh djk/kku dk
vk/kkj cuk;k tkuk pkfg,A izR;sd djnkrk ls ml ykxr (cost) ds cjkcj dj fy;k tkuk pkfg,
tks fd mldks iznku dh tkus okyh lsok ij yxh gksA bldk vFkZ ;g gS fd ftruh vf/kd ykxr
gksxh] dj dh nj Hkh mruh gh vf/kd Åaph gksxh vkSj blds foijhr ykxr ;fn de gksxh rks dj
dh nj Hkh de gkxhA
4444---- ykHk fl)kaykHk fl)kaykHk fl)kaykHk fl)kar r r r (Benefit Theory) : bl fl)kar ds vuqlkj yksxksa eas djk/kku ds Hkkj dks mu ykHkksa ds
vuqikr eas ckaVk tkuk pkfg, tks fd os jkT; ls izkIr djrs gSaA blds vuqlkj tks yksx jkT; ls
leku ykHk izkIr djrs gSa mUgsa dj Hkh ,d leku gh vnk djuk pkfg, vkSj tks yksx vf/kd ykHk
izkIr djrs gSa mUgsa de ykHk izkIr djus okys yksxksa ds eqdkcys vf/kd dj vnk djuk pkfg,A
5555---- Hkqxrku lkeF;Z dk fl)kar Hkqxrku lkeF;Z dk fl)kar Hkqxrku lkeF;Z dk fl)kar Hkqxrku lkeF;Z dk fl)kar (Ability to Pay Theory ) : ;g ,d loZLohd`fr fl)kar gSA bl fl)kar
ds vuqlkj izR;sd O;fä dks viuh Hkqxrku djus dh lkeF;Z ds vuqikr esa jkT; dks viuk va”knku
nsuk pkfg,A bl izdkj /kuh O;fä dh djnku ;ksX;rk vf/kd gksus mls vf/kd ek=k esa rFkk fu/kZu
dh djnku ;ksX;rk de gksus ls de ek=k eas va”k nku nsuk pkfg,A
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Page 12
Hkqxrku lkeF;Z ds fl)kar ds varxZr ,d ekSfyd leL;k ;g mRiUu gksrh gS fd O;fä dh dj vnk
djus dh lkeF;Z dks dSls ekik tk,\ bl mÌs”; dh iwfrZ ds fy, nks n`f ’Vdks.kksa dk lgkjk fy;k
tkrk gS &
(a) O;fäijd n`f’Vdks.k O;fäijd n`f’Vdks.k O;fäijd n`f’Vdks.k O;fäijd n`f’Vdks.k (Subjective approach)
(b) oLrqijd n`f’Vdks.k oLrqijd n`f’Vdks.k oLrqijd n`f’Vdks.k oLrqijd n`f’Vdks.k (objective approach)
O;fäijd n`f’Vdks.k ds varxZr] djnku lkeF;Z dks ekius ds fy, R;kx fl)kar (sacrif ice theory)
dk mi;ksx fd;k tkrk gS vkSj oLrqijd nf’Vdks.k eas] bl dk;Z ds fy, mRiknd “kfä fl)kar
(faculty theory) vk;] laifÙk dk mi;ksx fd;k tkrk gSA
(a) O;fäijd n`f’Vdks.k O;fäijd n`f’Vdks.k O;fäijd n`f’Vdks.k O;fäijd n`f’Vdks.k (Subjective approach)
O;fäijd n`f’Vdks.k djnkrkvksa dh euksoSKkfud vFkok ekufld izfrfdz;kvksa ij vk/kkfjr gSA bl
n`f’Vdks.k dh ekU;rk gS fd djnkrk dks djksa ds vnk djus eas ekufld vlarks’k] d’V rFkk vU;
izdkj dh vlqfo/kk,a gksrh gSA bl izdkj djnkrk tc dj dk Hkqxrku djrk gS rks mls R;kx djuk
iM+rk gSA ;fn djHkkj dks U;k;iw.kZ jhfr ls ckaVk tk, rks izR;sd djnkrk dks leku R;kx gh djuk
gksxkA
O;fäijd n`f’Vdks.k ls djkjksi.k ds rhu vk/kkj fy, tkrs gSa &
(a) leku fujis{k R;kx (Equal Absolute Sacrif ice)
(b) leku vkuqikfrd R;kx (Equal Proportional Sacrif ice)
(c) lelhekUr R;kx vFkok U;wure dqy R;kx (Equal Marginal Sacrif ice)
leku fujis{k R;kx leku fujis{k R;kx leku fujis{k R;kx leku fujis{k R;kx (Equal Absolute Sacrifice)
bl fl)kar ds vuqlkj djnkrkvkas ij djHkkj dk forj.k bl izdkj ls fd;k tkuk pkfg, fd lc
dj nkrkvkas ij izR;{k okLrfod Hkkj cjkcj gksA
leku vuqikrh R;kx leku vuqikrh R;kx leku vuqikrh R;kx leku vuqikrh R;kx (Equal Proportional Sacrifice)
bl fl)kar ds vuqlkj djnkrkvksa ij dj dk Hkkj leku ugha jgrk gS cfYd mudh vkfFkZd
fLFkfr;ksa ds vuqikr eas fuf”pr gksrk gSA vU; “kCnksa esa] bl fl)kar ds vuqlkj dj yxkus ds
ifj.kkeLo:i gksus okyh mi;ksxhrk dh gkfu djnkrkvksa dh dqy vk; ds vuqikr esa gksuh pkfg,A
C SIR NET, GATE, IIT-JAM, UGC NET , TIFR, IISc , JEST , JNU, BHU , ISM , IBPS, CSAT, SLET, NIMCET, CTET
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Page 13
bl fLFkfr eas vf/kd vk; okys djnkrk fuEu vk; okys djnkrkvksa ds eqdkcys vf/kd dj vnk
djasxsA
leku lhekUr R;kx leku lhekUr R;kx leku lhekUr R;kx leku lhekUr R;kx (Equal Marginal Sacrifice)
bl fl)kar ds vuqlkj fofHkUu djnkrkvksa dk dqy R;kx ugha cfYd lhekUr R;kx ¼ vFkkZr djnkrk
ds vk; dh vfUre bdkb Z }kjk djk;k tkus okyk R;kx½ cjkcj gk suk pkfg, rkfd leqnk; dk
leLr R;kx lEiw.kZ :i ls U;wure gksA
bl fl)kar ds vuqlkj dj dk fu/kkZj.k bl izdkj fd;k tkuk pkfg, fd djnkrkvksa }kjk fd, x,
R;kx dh ek=k de ls de gks rFkk lkekftd ykHk vf/kdre gksA ;g rHkh laHko gS tc lHkh
djnkrkvksa dk lhekUr R;kx cjkcj gksA leku lhekUr R;kx dk fl)kar vR;f/kd vkjksgh
(Progressive) dj <kaps dk fuekZ.k djrk gSA
(b) oLrqijd n`f’Vdks.k oLrqijd n`f’Vdks.k oLrqijd n`f’Vdks.k oLrqijd n`f’Vdks.k (Objective Approach)
R;kx fl)kar vFkok O;fäijd n`f’Vdks.k ds foijhr oLrqijd fl)kar djnkrk dh Hkkoukvksa ,oa
mlds d’Vkas dh vis{kk mldh djns; {kerk (taxable capacity) ds nzkfO;d ewY; (money value)
dks nf’Vxr j[krk gSA bl izdkj R;kx fl)kar dh rjg oLrqijd n`f’Vdks.k djnkrk dh
euksoSKkfud Hkkoukvksa ij vk/kkfjr ugha gS cfYd mldh djns; {kerk ij vk/kkfjr gS tks fd mldh
vk;] lafpr /ku rFkk lEifÙk vkfn ds }kjk ekih tkrk gS oLrqijd n`f’Vdks.k ds varxZr O;fä dh
dj vnk djus dh lkeF;Z dks ekius ds rhu egÙoiw.kZ ekinaM gSa &
(a) djnkrk dh vk;
(b) djnkrk dh lEifÙk
(c) djnkrk dk miHkksx Lrj ;k O;;
djksa dks muds Lo:i] izd`fr rFkk mudks yxkus dh fof/k ds vk/kkj ij dbZ oxkasaZ eas ckaVk tk ldrk
gSA
1- izR;{k ,oa ijks {k dj (Direct and Indirect Taxess)
2- fof”k’V rFkk ewY;uqlkj dj (Specif ic and Advalorem Duties)
3- vkjksgh (Progressive), vuqikrh (Proportional), vojksgh (Regressive) djA
C SIR NET, GATE, IIT-JAM, UGC NET , TIFR, IISc , JEST , JNU, BHU , ISM , IBPS, CSAT, SLET, NIMCET, CTET
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Page 14
izR;{k rFkk ijk s{k dj izR;{k rFkk ijk s{k dj izR;{k rFkk ijk s{k dj izR;{k rFkk ijk s{k dj (Direct and Indirect Taxes)
izR;{k dj og Hkqxrku gS ftleas djk/kku ,oa djHkkj ,d gh O;fä ij iM+rk gSA blds foijhr ;fn
djk/kku (Impact) vkSj djHkkj (Incidence) vyx&vyx O;fä;ksa ij iM+rk gS rks og ijks{k dj
(indirect taxes) dgykrk gSA bl izdkj ijks{k dj rks og gksrk gS ftldk vUrj.k (shif ting) fd;k
tk ldrk gS vFkok ftls fdlh vU; O;fä ij Vkyk tk ldrk gSa] vkSj izR;{k dj og gksrk gSa
ftldk vUrj.k ugha fd;k tk ldrk vFkok ftldh vnk;xh dks vU; fdlh O;fä ij Vkyk ugha
tk ldrkA
vk; dj] lEifÙk dj] fuxe dj vkfn izR;{k dj dh Js.kh eas vkrs gSa tcfd lhek “kqYd] mRiknu
“kqYd] fcdzh dj vkfn vizR;{k dj dh Js.kh eas vkrs g SaA
ewY;kuqlkj dj rFkk fof”k’V dj ewY;kuqlkj dj rFkk fof”k’V dj ewY;kuqlkj dj rFkk fof”k’V dj ewY;kuqlkj dj rFkk fof”k’V dj (Ad-valorem and specific Duties) : ewY;kuqlkj dj og dj gS
tks fd oLrq ds ewY; ds :i eas O;ä fd;k tkrk gS tcfd fof”k’V dj mu djksa dks dgrs gSa tks
fd oLrq dh bdkbZ ,oa ek=k ds vk/kkj ij vnk dh xb Z ,d fuf”pr jde ds :i eas O;ä fd,
tkrs gSaA
vkjksgh ¼izxfr”khy½] vuqikrh rFkvkjksgh ¼izxfr”khy½] vuqikrh rFkvkjksgh ¼izxfr”khy½] vuqikrh rFkvkjksgh ¼izxfr”khy½] vuqikrh rFkk vojksgh dj k vojksgh dj k vojksgh dj k vojksgh dj (Progressive Proportional and Regressive
Taxes): dj i}fr dh jpuk fofHkUu izdkj ds djksa dks feykdj dh tkrh gS ftueas ls dqN dj
vkjksgh gks ldrs gSa rFkk dqN vuqikrh] tcfd dqN vojksghA Hkkjrh; dj&i}fr dk fuekZ.k ;|fi
vkjksgh rFkk vuqikrh nksuksa gh izdkjksa dks feykdj fd;k x;k gS rFkkfi mldh izd`fr] lEiw.kZ :i eas]
vkjksgh gh dgh tk ldrh gSA
vuqikrh] vjksgh rFkk vojksgh djkas dh njas vkxs fn, x, vuqlwfp;ksa dh lgk;rk ls le>kbZ xbZ gSA
vuqikrh dj dh njas vuqikrh dj dh njas vuqikrh dj dh njas vuqikrh dj dh njas (Proportional Tax Rates)
vk; Lrj dj dh nj dj dh jkf”k
10]000 :- 10 izfr”kr 1]000 :-
20]000 :- 10 izfr”kr 2]000 :-
30]000 :- 10 izfr”kr 3]000 :-
40]000 :- 10 izfr”kr 4]000 :-
C SIR NET, GATE, IIT-JAM, UGC NET , TIFR, IISc , JEST , JNU, BHU , ISM , IBPS, CSAT, SLET, NIMCET, CTET
Phone: 0744-2429714 Mobile: 9001297111, 9829567114, 9001297243 Website: www.vpmclasses.com E-Mail: [email protected] /[email protected] Address: 1-C-8, Sheela Chowdhary Road, SFS, TALWANDI, KOTA, RAJASTHAN, 324005
Page 15
bl izdkj Li’V gS fd vuqikrh djksa ds varxZr vk; ds c<+us ds lkFk&lkFk djnkrk }kjk vnk fd,
tkus okyh dj dh dqy jkf”k c<+rh gSaA
izxfr”khy dj dh njas izxfr”khy dj dh njas izxfr”khy dj dh njas izxfr”khy dj dh njas (Progressive Tax Rates)
vk; Lrj dj dh nj dj dh jkf”k
10]000 :- 10 izfr”kr 1]000 :-
20]000 :- 15 izfr”kr 3]000 :-
30]000 :- 25 izfr”kr 7]500 :-
40]000 :- 40 izfr”kr 16]000 :-
Li’V gS fd vkjksgh djksa ds varxZr vk; eas o`f} gksus ij djksa dh njksa eas Hkh rsth ls o`f} gksrh gSA
lkFk gh] djksa ds :i eas vnk dh tkus okyh dqy /kujkf”k Hkh rsth ls c<+rh gSA
vojksgh dj dh njsa vojksgh dj dh njsa vojksgh dj dh njsa vojksgh dj dh njsa (Regressive Tax Rates)
vk; Lrj dj dh nj dj dh jkf”k
10]000 :- 10 izfr”kr 1]000 :-
20]000 :- 7 izfr”kr 1]400 :-
30]000 :- 5 izfr”kr 7]500 :-
40]000 :- 4 izfr”kr 1]600 :-
Li’V gS fd vojksgh djksa ds varxZr] vk; c<+us ij dj dh nj ?kVrh tkrh gS tcfd vk; ds c<+us
ij djksa ds :i esa vnk dh tkus okyh dqy /kujkf”k esa vo”; o`f} gksrh gSA
djk/kku ds izHkko djk/kku ds izHkko djk/kku ds izHkko djk/kku ds izHkko (Effects of Taxation)
vktdy djk/kku dk mi;ksx dsoy jktLo izkfIr ds L=ksr ds :i eas gh ugha fd;k tkrk cfYd
dqN ,sls lkekftd ,oa vkfFkZd y{;ksa dh izkfIr ds ,d egÙoiw.kZ lk/ku ds :i eas Hkh fd;k tkrk gS
tSls fd miHkksx ,oa mRiknu dk fu;eu] rsth ,oa eanh dh fLFkfr;ksa ij fu;a=.k] vkfFkZd izxfr dks
izksRlkgu rFkk vk; dh vlekurkvksas dh lekfIr vkfnA
C SIR NET, GATE, IIT-JAM, UGC NET , TIFR, IISc , JEST , JNU, BHU , ISM , IBPS, CSAT, SLET, NIMCET, CTET
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Page 16
vc ge djk/kku ds izHkkoksa dk fuEu “k h’kZdksa ds varxZr foospu djsxasA
1111---- cpr rFkk fuos”k ij izHkko cpr rFkk fuos”k ij izHkko cpr rFkk fuos”k ij izHkko cpr rFkk fuos”k ij izHkko (Effects on Saving and Investment) : djksa dh vR;f/kd Åaph njas
cprksa ij izfrdwy izHkko Mkyrh gSa D;ksafd cpr vk; ij fuHkZj djrh gS vkSj tc djk/kku }kjk vk;
de gks tkrh gS rks cpr vius vki gh de gksus yxrh gSA pwafd fuos”k cpr ij fuHkZj djrk gS
blfy, tc djk/kku ls cprsa de gks tkrh gSa rks bldk izfrdwy izHkko fuos”k ij Hkh iM+rk gSA
2222---- mRiknu ds xBu rFkk Lo:i ij djk/kku ds izHkko mRiknu ds xBu rFkk Lo:i ij djk/kku ds izHkko mRiknu ds xBu rFkk Lo:i ij djk/kku ds izHkko mRiknu ds xBu rFkk Lo:i ij djk/kku ds izHkko (Effects of Taxation on Composition and
Production) : mRiknu dk xBu rFkk izfr:i bl ckr ij fuHkZj gksrk gS fd fofHkUu m|ksxksa ds
chp rFkk fofHkUu {ks=ksa ds chp lk/kuksa dk c aVokjk fdl izdkj dk gksrk gSA fofHkUu m|ksxksa rFkk {ks=ksa
ds chp lk/kuksa dk varj.k ;k fn”kk ifjorZu (diversion) djus dss fy, djk/kku dks jktdks’kh; uhfr
(f iscal policy) ds ,d vL= ds :i eas iz;qä fd;k tk ldrk gSA
tc dqN m|ksxkas dh mRikfnr oLrqvksa ij dj yxk;k tkrk gS rks mlls mudh dheras c<+ tkrh gSaA
dhersa c<+us ls mu oLrqvksa dh ekax de gks tkrh gS rFkk blds QyLo:i ykHk Hkh ?kV tkrk gSaA
3333---- forj.k ij djk/kku ds izHkko forj.k ij djk/kku ds izHkko forj.k ij djk/kku ds izHkko forj.k ij djk/kku ds izHkko (Effects of Taxation on Distribution): teZu vFkZ”kkL=h oSxuj
(Wagner) dks ,sls loZizFke vFkZ”kkfL=;ksa eas fxuk tkrk gS ftUgksaus bl ckr ij tksj fn;k fd
djk/kku dk mi;ksx vk; dh vlekurkvksa dks de djus ds ,d vL= ds :i eas fd;k tkuk
pkfg,A vR;f/kd vkjksgh dj i z.kkyh vk; rFkk /ku ds forj.k eas ikbZ tkus okyh vlekurkvksa dk s
dkQh de djrh gSSA
4444---- djk/kku rFkk eqnzk LQhfr djk/kku rFkk eqnzk LQhfr djk/kku rFkk eqnzk LQhfr djk/kku rFkk eqnzk LQhfr (Taxation and Inflation): eqnzk LQhfr ds fnuksa eas djk/kku dk mÌs”;
yksxkas dh dz; “kfä (Purchasing Pow er) dks de djuk gksrk gSA u, dj yxkus rFkk izpfyr djksa
dh njksa eas of} djus ls miHkksx ij vadq”k yxrh gS] ftlls izHkkoh ekax (ef fective demand) dk
Lrj fxjrk gS vkSj blls dherksa eas fLFkjrk ykus eas enn feyrh gSA ;gh ugha eqnzkLQhfr ds fnuksa eas
Hkkjh dj yxkus ls rFkk izpfyr djksa dh njksa eas o`f} djus ls dz; “kfä yksxksa ds gkFkksa eas ls
ljdkj dh vksj LFkkukUrfjr gks tkrh gS ftldk ;fn leqfpr :i ls mRiknu dk;kaasZ ds fy,
mi;ksx fd;k tk, rks blls vkfFkZd fdz;kvksa o jkstxkj dk Lrj Åapk mBrk gS vkSj oLrqvksa rFkk
lsokvksa dh iwfrZ eas oakfNr o`f) gksus ls c<+rh gqbZ dheras :dus yxrh gSaA eqnzkLQhfr ds fnuksa eas dqN
C SIR NET, GATE, IIT-JAM, UGC NET , TIFR, IISc , JEST , JNU, BHU , ISM , IBPS, CSAT, SLET, NIMCET, CTET
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Page 17
dj laca/kh NwVas rFkk dj fj;k;rsa nsuk Hkh blfy, t:jh gks tkrk gS rkfd cprksa rFkk fuos”kksa dh
nj eas o`f} djds mRiknu dks c<+k;k tk ldsA
lglEcU/klglEcU/klglEcU/klglEcU/k
lg&lEcU/k dh ifjHkk ’kklg&lEcU/k dh ifjHkk ’kklg&lEcU/k dh ifjHkk ’kklg&lEcU/k dh ifjHkk ’kk (Definition of Correlation)
ifjHkk’kkifjHkk’kkifjHkk’kkifjHkk’kk
izks- cksfMaxVu ds vuqlkj ^^tc dHkh nks ;k vf/kd lewgksa oxkZsa vFkok lead&Jsf.k;ksa esa lqfuf”pr
la;ksx fo|eku gks rks muesa lglEcU/k dk gksuk dgk tkrk gSA MsouiksVZ us vius fopkj O;Dr djrs
gq, fy[kk gS fd ^^lglEcU/k dk lEiw.kZ fo’k; iFkd~ fo”ks’krkvksa ds e/; ik;s tkus okys ml
ikjLifjd lEcU/k dh vksj ladsr djrk gS ftlds vuqlkj os dqN lhek rd lkFk&lkFk ifjofrZr
gksus dh izo` fÙk j[krs gSaA^^
lglEcU/k ds i zdkjlglEcU/k ds i zdkjlglEcU/k ds i zdkjlglEcU/k ds i zdkj
lg&lEcU/k dks lEcfU/kr pjksa ds e/; ifjorZu dh fn”kk] vuqikr rFkk lead] Jsf.k;ks dh la[;k ds
vk/kkj ij fuEu izdkj O;Dr fd;k tk ldrk gS%&
1111---- /kukRed rFkk _.kkRed lglEcU/k /kukRed rFkk _.kkRed lglEcU/k /kukRed rFkk _.kkRed lglEcU/k /kukRed rFkk _.kkRed lglEcU/k (Positive and Negative Correlation) & tc nks pjksa esa
ifjorZu ,d gh fn”kk esa gks vFkkZr~ ,d pj esa o`f) gksus ij nwljs pj esa of) gks rFkk ,d pj esa
deh gksus ij nwljs pj esa Hkh deh gks] rks ,sls lglEcU/k dks /kukRed lglEcU/k (Positive
Correlat ion) dgrs gS a]
/kukRed lglEcU/k ds foijhr tc nks pjksa esa ifjorZu foijhr fn”kk esa gksa] vFkkZr~ ,d pj esa o`f)
gksus ij nwljs esa deh gks vFkok ,d pj esa deh gksus ij nwljs esa o`f) gks] rks ,sls lglEcU/k dk s
_.kkRed lglEcU/k dgrs gSaA
2222---- js[kh; rFkk v&js[kh; oØ&js[kh; lglEcU/k js[kh; rFkk v&js[kh; oØ&js[kh; lglEcU/k js[kh; rFkk v&js[kh; oØ&js[kh; lglEcU/k js[kh; rFkk v&js[kh; oØ&js[kh; lglEcU/k (Linear and Non-Linear or Curvilinear
Correlation) & & & & ;fn nks pjksa ds e/; ifjorZu dk vuqikr fLFkj jgrk gS rks ,slk lglEcU/k js[kh;
dgykrk gSA bls ;fn xzkQ isij ij vafdr fd;k tk; rks ,d lh/kh js[kk cusxhA
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Page 18
;fn nks pj ewY;ksa esa ifjorZu dk vuqikr LFkk;h :Ik ls leku ugha jgrk] rc lglEcU/k oØjs[kh;
;k v&js[kh; (Curvilinear or Non-linear) gksxk A bls ;fn xzkQ isij ij vafdr fd;k tk; rks ,d
oØ js[kk cUksxhA
lglEcU/k ds ifj.kke lglEcU/k ds ifj.kke lglEcU/k ds ifj.kke lglEcU/k ds ifj.kke (Degree of Correlation)
lglEcU/k dk vkaf”kd ifj.kke (Degree) lglEcU/k xq.kkad (Coeff icient of Correlation) ds ek/;e
ls Kkr fd;k tkrk gSA blds vk/kkj ij /kukRed ,oa _.kkRed lglEcU/k ds fuEu of.kZr ifj.kke
gks ldrs g Sa%
1111---- iw.kZ lglEcU/k iw.kZ lglEcU/k iw.kZ lglEcU/k iw.kZ lglEcU/k (Perfect Correlation) & ;fn nks pj&ewY;ksa ds ifjorZu leku vuqikr esa gksa rks
muesa iw.kZ lglecU/k gksrk gSA ;fn leku vuqikr esa ifjorZu ,d gh fn”kk esa gksrk gS rc
lglEcU/k iw.kZ /kukRed (Perfect Positive Correlation) gksrk gSA blds foijhr ;fn leku vuqikr
esa ifjorZu foijhr fn”kkvksa eas gks rks lglEcU/k iw.kZ _.kkRed (Perfect Negative Correlation)
gksrk gSA
2222---- lglEcU/k dh vuqifLFkfr lglEcU/k dh vuqifLFkfr lglEcU/k dh vuqifLFkfr lglEcU/k dh vuqifLFkfr (Absence of Correlation) & ;fn nks pjksa esa vkfJrrk fcYdqy u ikbZ
tk;s vFkkZr~ muds ifjorZuksa esa dksbZ lguqHkwfriw.kZ lecU/k u gks rks ,lh fLFkfr dks lglEcU/k dk
vHkko dgrs gSaA
3333---- lglEcU/k dk lhfer ifj.kke lglEcU/k dk lhfer ifj.kke lglEcU/k dk lhfer ifj.kke lglEcU/k dk lhfer ifj.kke (Limited Degree of Correlation) &tc nks pj&ewY;ksa esa u rks
iw.kZ lglEcU/k gksrk gS u lglEcU/k dk vHkko gh gksrk gS vFkkZr~ nksuksa ds chp dh fLFkfr gksrh gS]
rc lglEcU/k lhfer ifj.kke esa gksrk gSA lhfer ifjek.k esa lglEcU/k xq.kkad “kwU; ¼0½ ls vf/kd
fdUrq 1 ls de ¼>0 but < 1 ½ gksrk gSA ;g /kukRed ;k _.kkRed gks ldrk gSA
> = Greater than; < = Less than
lhfer lglEcU/k izeq[kr% fuEufyf[kr rhu izdkj dk gks ldrk gS %&
¼d½ mPp Lrj dk lglEcU/k¼d½ mPp Lrj dk lglEcU/k¼d½ mPp Lrj dk lglEcU/k¼d½ mPp Lrj dk lglEcU/k (High Degree of Correlation) - tc nks pj&ewY;ksa esa lglEcU/k
iw.kZ (Perfect) rks u gks] ij dkQh vf/kd ek=k esa gks rks ogk¡ mPp&Lrj dk lglEcU/k gksrk gSA
mPp&Lrjh; lglEcU/k dh fLFkfr esa lglEcU/k xq.kkad 0-75 ;k blls vf/kd ysfdu 1 ls de gksrk
gSA
C SIR NET, GATE, IIT-JAM, UGC NET , TIFR, IISc , JEST , JNU, BHU , ISM , IBPS, CSAT, SLET, NIMCET, CTET
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Page 19
¼[k½ e/; Lrj dk lglEcU/k¼[k½ e/; Lrj dk lglEcU/k¼[k½ e/; Lrj dk lglEcU/k¼[k½ e/; Lrj dk lglEcU/k (Moderate Degree of Correlation) - ,slh fLFkfr esa lglEcU/k
xq.kkad 0-25 ls 0-75 ds e/; gksrk gSA ;g /kukRed rFkk _.kkRed gks ldrk gSA
¼x½ fuEu&Lrj dk lglEcU/k¼x½ fuEu&Lrj dk lglEcU/k¼x½ fuEu&Lrj dk lglEcU/k¼x½ fuEu&Lrj dk lglEcU/k (Low Degree of Correlation) - tc nks pj&ewY;ksa esa lglEcU/k rks
gks ysfdu cgqr gh de ek=k esa gks rks ogk¡ fuEu&Lrj dk lglEcU/k gksrk gSA ,slh fLFkfr esa
lglEcU/k xq. kkad “kwU; ¼0½ o 0-25 ds e/; gksrk gSA ;g Hkh /kukRed rFkk _.kkRed gks ldrk gSA
lglEcU/k Kkr djus dh jhflglEcU/k Kkr djus dh jhflglEcU/k Kkr djus dh jhflglEcU/k Kkr djus dh jhfr;k ¡ r;k ¡ r;k ¡ r;k ¡ (Method of Determ ining Correlation)
lglEcU/k Kkr djus dh izeq[k jhfr;ksa dks vxzkafdr pkVZ }kjk ljyrk ls le>k tk ldrk gS %&
lglEcU/k Kkr djus dh jhfr;k¡
fcUnq&js[kh; jhfr;k¡ xf.krh; jhfr;k¡(Graphic Methods) (Mathematical Methods)
fo{ksi fp= lk/kkj.k fcUnq j s[kh; jhfr(Scatter diagram) (Simple Graphic Method)
dkyZ fi;lZudk lglEcU/k xq.kkad(Karl Pearspn’s)
fLi;jeSudh dzekUrj jhfr(Speaman’s)
laxkeh fopyu jhfr(ConcurrentDeviation)
vU; jhfr;k¡(Others)
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Page 20
dkyZ fi;lZu ds lglEcU/k xq.kkad dk ifjdyu dkyZ fi;lZu ds lglEcU/k xq.kkad dk ifjdyu dkyZ fi;lZu ds lglEcU/k xq.kkad dk ifjdyu dkyZ fi;lZu ds lglEcU/k xq.kkad dk ifjdyu (Calculation of Coefficient of Correlation by Karl
Pearson’s Method)
izR;{k jhfr izR;{k jhfr izR;{k jhfr izR;{k jhfr (Direct Method) & izR;{k jhfr ls lglEcU/k xqa.kkd Kkr djus dh fuEu izfdz;k gS %
1- nksuksa Jsf.k;ksa dk lekUrj ek/; ¼ X rFkk Y ½ Kkr dj ysrs gSaA
2- nksuksa Jsf.k;kas ds rRlEcU/kh lekUrj ek/; ls fofHkUu ds fopyu dx rFkk dy fudky ysrs g SaA ;gk ¡
( )dx X X= − rFkk ( )dy Y Y= − gSaSA
3- nksuksa lead Jsf.k;kas ds ijLij lEcfU/kr fopyuksa (Corresponding Deviations) dks xq.kk djds mu
xq.kkvksa ds ;ksx (Σdx dy) Kkr dj ysrs gSaA
4- nksuksa Jsf.k;ksa ds fopyuksa ds oxZ (Square) i`Fkd~&iFkd~ Kkr dj muds izeki fopyu fuEu lw=ksa
}kjk Kkr dj ysrs gSa %
2 2
x y
d x d y,
N NΣ Σσ = σ =
5- vUr eas lglEc/k xq.kkad Kkkr djus gsrq fuEu lw++= dk iz;ksx fd;k tkrk gSa %&
x y
dx,dyr
N.Σ=
σ σ ¼ izFke lw=½
;gk¡ r = dkyZ fi;lZu dk lglEcU/k xq.kkad (Coeff icient of Correlation) Σdxdy = X rFkk Y
Jsf.k;ksa ds okLrfod lekUrj ek/;ksa (Means) ls rRlEcU/kh (Corresponding) fopyuksa ds xq.kuQy
dk ;ksx(
σx o σy = X rFkk Y Jsf.k;ksa ds izeki fopyu (S.D.); N = in&;qXeksa dh la[;k (Mumber of pairs
of Items)
2 2
dx.dyr
d x d yN.
N N
Σ=
Σ Σ× ¼ f}rh; lw=½ or
2 2x y
dx.dyr
d dN.
N N
Σ=Σ ×Σ
×
or 2 2
x y
dx.dyr
Nd d
N
Σ=Σ × Σ
or
2 2
x y
dx.dy
d d
ΣΣ × Σ
¼ rrh; lw=½
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Page 21
mi;qZDr lHkh lw=ksa eas rrh; lw= lcls ljy gS] vr% O;ogkj esa blh lw= dk iz;ksx djuk pkfg,A
y?kq jhfr y?kq jhfr y?kq jhfr y?kq jhfr (Short-cut Method) & y?kq jhfr ls lglEcU/k xq.kkad Kkr djus dh izfdz;k fuEu
izdkj gS&
1- X rFkk Y Jsf.k;kas eas ls lcls lqfo/kktud ,oa mi;qDr ewY; dks dfYir ek/; Ax eku fy;k tkrk
gSA ,sls ewY;ksa dks dfYir ek/; ekuuk lqfo/kktud jgrk gS ftlls fopyuksa dk ;ksx de ls de
vk;sA dHkh & dHkh lead Js.kh eas ,d ewY; dbZ ckj vkrk gS] ,slh fLFkfr eas ml ewY; dks dfYir
ek/; ekuuk lqfo/kktud jgrk gSA
2- nksuksa Jsf.k;ksa ds dfYir ek/;ksa ls ewY;ksa ds fopyu vFkkZr~ dx ,oa dy Kkr dj fy;s tkrs gSaA ;gk¡
dx ls rkRi;Z X – Ax rFkk dy ls rkRi;Z Y – Ay ls gSA
3- mi;qZDr fopyuksa ds ;ksx vFkkZr~ Σdx ,oa Σdy Kkr dj ysrs gSaA
4- fopyuksa ds vkil eas xq.kk djds mudk ;ksx vFkkZr~ Σdxdy Kkr dj fy;k tkrk gSA
5- fopyuksa ds oxZ djds mudk ;ksx vFkkZr~ Σd2x rFkk Σd2y Kkr dj fy;s tkrs gSaA
6- vUr eas lglEcU/k xq.kkad Kkr djus ds fy;s fuEu lw= dk iz;ksx fd;k tkrk gSA izFke lw= fuEu
izdkj gS %
( )( )x y
dxdy N X Ax Y Ayr
N
Σ − − −=
σ σ lw= eas iz;qDr]
X o Y = Actual means of X and Y series
Az o Ay = Assumed means of X and Y serie s
Σdxdy = sim of the products of deviations from assumed means ¼ dfYir ek/;ksa ls foypuksa
ds xq.kuQyksa dk ;k sx½
σx o σy = Standard deviat ions of X and Y Series
N = Number of pairs of items ¼ in;qXeksa dh la[;k½
lw= ds fofHkUu izdkj gksaxs % &
f}rh; lw= %
C SIR NET, GATE, IIT-JAM, UGC NET , TIFR, IISc , JEST , JNU, BHU , ISM , IBPS, CSAT, SLET, NIMCET, CTET
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Page 22
2 22 2
dx dydxdy N
N Nr
d x dx d y dyN N N N
Σ Σ Σ − × =
Σ Σ Σ Σ − −
pw¡fd xdx
X AN
Σ= = rFkk 22
xd x dxN N
Σ Σ σ = −
bl lw= dks vkSj Hkh ljy :i eas O;Dr fd;k tk ldrk gS %
rrh; lw= % ( ) ( )2 2
2 2
dx. dydxdy
Nrdx dy
d x d yN N
Σ ΣΣ −=
Σ ΣΣ − Σ −
prqFkZ lw= % ( )( ) ( )
× Σ − Σ × Σ=
× Σ − Σ × Σ − Σ
2 22 2
N dxdy dx dyr
N d x dx N d y dy
f}rh;] rrh; rFkk prqFkZ lw= eas iz;qDr % Σdx, Σdy = Sum of deviations from assumed means
of X and Y series.
vU; ladsrk{kjksa dk ogh vFkZ gS tks izFke lw= esa gSA
xq. kk ifj?kkr lg lEc/k jhfr xq. kk ifj?kkr lg lEc/k jhfr xq. kk ifj?kkr lg lEc/k jhfr xq. kk ifj?kkr lg lEc/k jhfr (Product Moment Method of Correlation)
;g jhfr “kwU; (Zero) dkYifud ek/; ij vk/kkfjr gSA tc “kwU; ls fopyu fy;s tk;saxsa rks fopyu
X rFkk Y ds ewY;ksa ds led{k dh gksaxsA bl jhfr dh x.kuk izfdz;k fuEu izdkj gS&
1- izR;sd Js.kh ds ewY;ksa dk ;ksx Kkr djrs gSaA (ΣX ,oa ΣY)
2- izR;sd Js.kh ds in ewY;ksa ds oxZ Kkr dj mudk ;ksx djrs gSaA (ΣX2 ,oa ΣY2)
3- nksuksa Jsf.k;ksa ds ikjLifjd in ewY;ksa dks xq.kk djds (X), (Y) xq.kuQyksa dk ;ksx djrs gSaA (ΣXY)
4- rRi”pkr fuEu lw= dks iz;qDr dj lg lEcU/k xq.kkad Kkr djrs gSa %
( ) ( )( )( ) ( ) ( ) ( )2 22 2
N. XY X Yr
N. X X N. Y Y
Σ − Σ Σ=
Σ − Σ × Σ − Σ
fLi;jeSu dh dksfV & vUrj jhfr (Spearman’s Rank Dif ference Method)
C SIR NET, GATE, IIT-JAM, UGC NET , TIFR, IISc , JEST , JNU, BHU , ISM , IBPS, CSAT, SLET, NIMCET, CTET
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Page 23
izksQslj pkYlZ fLi;jeSu us O;fäxr Js.kh eas lglEcU/k Kkr djus dh ,d ljy jhfr dk izfriknu
fd;kA bl jhfr dks fLi;jeSu dh dksfV vUrj jhfr (Spearman’s Rank Dif ferences Method) ;k
dzekUrj jhfr (Ranking Method) dgrs gSaA
lglEcU/k xq.kkad Kkr djus dh jhfr
1- dksfV&dze iznku djuk (Assigning Ranks)
2- dksfV vUrj ;k dzekUrj Kkr djuk (Calculating Rank Dif ferences)
3- dzekUrjksa (D) dk chtxf.krh; tksM+ lnSo “kwU; (ΣD = 0) gksrk gSA
dzekUrjksa oxZ Kkr djuk (Calculating Squares of Rank Dif ferences) & dzekUrjksa (D) ds oxZ
Kkr djds mu oxkasZ dk tksM+ (ΣD2) Kkr fd;k tkrk gSA
lw= (Formula) & vUr eas fuEu lw= ds ek/;e ls dksfV&lglEcU/k Kkr fd;k tkrk gS %
( ) ( )
2
R 2
6 Dr 1
N N 1Σ= −
−
lw= esa iz;qä&
r(R) = dksfV&vUrj lglEcU/k xq.kkad (Rank Correlat ion Doeff icient)
ΣD2 = dzekUrjksa ds oxkssa Z dk ;ksx (Total of squares of rank dif ferences)
N = in&;qXeksa dh la[;k (Number of pairs of items)
lekUrj dze ds fy, la”kks/ku (Correction for tied ranks) & lead Js.kh eas tc nks ;k nks ls
vf/kd in ewY;ksa dk vkdkj leku gks rks mUgsa leku dze iznku fd;s tkrs gSaA ,slh fLFkfr eas
dksfV& vUrj lglEc/k fudkyus ds lw= eas la”kks/ku djuk iM+rk gSA la”kksf/kr lw= fuEu i zdkj gS %
( )
( )( )
2 3
R 2
16 D m m
12r 1N N 1
Σ + −= −
−
lw= eas iz;qä m = mu in ewY;ksa dh la[;k ftuds dze leku gSaA
(Number of items whose ranks are equal)
C SIR NET, GATE, IIT-JAM, UGC NET , TIFR, IISc , JEST , JNU, BHU , ISM , IBPS, CSAT, SLET, NIMCET, CTET
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Page 24
;gk¡ ;g /;ku j[kk tkuk pkfg, fd mijksä la”kksf/kr lw= esa ( )31m m
12+ − dk la”kks/ku mruh ckj
djuk gksxk ftruh ckj nksuksa Js f.k;ksa esa leku dze vk;s gSaA
laxkeh fopyu jhfr laxkeh fopyu jhfr laxkeh fopyu jhfr laxkeh fopyu jhfr (Concurrent Deviation Method)
fcUnq js[kh; jhfr ls ;fn lEc} laed Jsf.k;ksa ds odz ,d gh fn”kk eas lkFk&lkFk xeu djrs gSa ;k
laxkeh gSa rks mueas /kukRed lglEcU/k gksrk gSaA ;fn odz foijhr fn”kk esa xeu djrs gSa vFkkZr~
izfrxkeh gSa rks mueas _.kkRed lglEcU/k ik;k tkrk gSA blh izdkj laxkeh fopyu jhfr ds
vuqlkj Hkh ;fn lead Jsf.k;ksa ds vf/kdkj fopyu laxkeh (Concurrent) gksrs gSa rks mueas /kukRed
lglEcU/k gksrk gS rFkk ;fn ;s fopyu izfrxkeh (Divergent) gksrs gSa rks mueas _.kkRed lglEcg
gksrk gSA
x.ku fØ;k%x.ku fØ;k%x.ku fØ;k%x.ku fØ;k%
1. izR;sd Js.kh esa vxys in ewY; dh mlls fcYdqy iwoZ (Previous) ds in ewY; ls rqyuk dh tkrh
gSA ;fn ewY; fiNys ewY; ls vfèkd gSa rks mldk fopyu (+) gksxk] ;fn ewY; xr ewY; ls de gS
rks mldk fopyu (–) rFkk ;fn cjkcj gS rks fopyu (=) gksxk ;g è;ku j[k tkuk pkfg, fd bl
jhfr esa fopyu dk dsoy fpUg gh fy[kk tkrk gS] fopyu dh ek=k ughaA fopyu ;qXeksa dh la[;k fopyu ;qXeksa dh la[;k fopyu ;qXeksa dh la[;k fopyu ;qXeksa dh la[;k
Js.kh esa fn;s x;s in&;qXeksa dh la[;k ls ,d de Js.kh esa fn;s x;s in&;qXeksa dh la[;k ls ,d de Js.kh esa fn;s x;s in&;qXeksa dh la[;k ls ,d de Js.kh esa fn;s x;s in&;qXeksa dh la[;k ls ,d de gksrh gSAgksrh gSAgksrh gSAgksrh gSA
2. X rFkk Y Jsf.k;ksa ds fopyu fpUgksa ds vkèkkj ij laxkeh izofr Kkr dh tkrh gSA ftu in&;qXeksa esa
,d lkFk o`f)] deh ;k cjkcjh jgh gS] muds lkeus (+) dk fpUg yxkrs gSA ,sls enksa ds ;ksx dh
ladsrk{kj ‘c’ }kjk O;ä fd;k tkrk gSA
3. fQj fuEulw= dk iz;ksx fd;k tkrk gS%
c
2c Nr
N−
= ±
lw= esa iz;qä ladsrk{kj ls vk”k;] rc = coefficient of concurrent deviation,
c = Number of concurrent deviations, N = Number of pairs of observation
[ksy fl)kar[ksy fl)kar[ksy fl)kar[ksy fl)kar
C SIR NET, GATE, IIT-JAM, UGC NET , TIFR, IISc , JEST , JNU, BHU , ISM , IBPS, CSAT, SLET, NIMCET, CTET
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Page 25
jSf[kd izksxkfeax ds foospu esa vlekurkvksa (inequalities) ds lekos”k ls vfèkdredj.k vFkok
U;wuredj.k dh n”kk,¡ “kkfey gksrh gSa] ysfdu ,d lkFk nksuksa dk feJ.k “kkfey ugha fd;k tk
ldrkA [ksy&fl)kar esa vfèkdredj.k o U;wuredj.k dh izfØ;k,¡ lkFk&lkFk py ldrh gSa] vkSj
bldk <k¡pk fHkUu fdLe dk gksrk gSA
[ksy&fl)kar dh vkèkkjHkwr voèkkj.kk, ¡ [ksy&fl)kar dh vkèkkjHkwr voèkkj.kk, ¡ [ksy&fl)kar dh vkèkkjHkwr voèkkj.kk, ¡ [ksy&fl)kar dh vkèkkjHkwr voèkkj.kk, ¡ (Basic Concepts of Game Theory)
[ksy esa nks ;k vfèkd Hkkx ysus okys ny ysrs gSaA f[kykfM;ksa ds y{;ksa esa ijLij fojksèk dh fLFkfr
ik;h tkrh gS] blfy, ,d lkFk lHkh ds y{;ksa dks izkIr djuk dfBu gksrk gSA dqN f[kykM+h thrrs
gSa ftlls mudks èkukRed is&vkWQ dk Hkqxrku* (positive pay–off) feyrk gS] vFkkZr~ mudh izkfIr;k¡
(+) ls lwfpr dh tkrh gSaA vU; dks gkfu mBkuh iMrh gS ftldks _.kkRed is&vkWQ ;k izkfIr;k¡
(+) ls lwfpr dh tkrh gSA vU; dks gkfu mBkuh iM+rh gS ftldks _.kkRed is&vkWQ ;k Hkqxrku
(negative pay–off) ls lwfpr fd;k tkrk gSA blds fy, (–) dk fu”kku i z;qDr fd;k tkrk gSA
[ksy nks izdkj ds gksrs gSa % (1) volj&[ksy (games of chance), (2) j.kuhfr ;k O;wgjpuk ij
vkèkkfjr [ksy (games of strategy) volj&[ksy ds fy, rk”k ds [ksy dk mnkgj.k ys ldrs gSa
ftlesa mÙke rk”k ds iÙkksa okyk f[kykM+h thrrk gSA mlesa mldh n{krk dke ugha djrhA j.kuhfr
okys [ksy esa izR;sd f[kykM+h viuh n{krk o prqjkbZ dk mi;ksx djds viuk ykHk vfèkdredj.k
djus dk iz;kl djrk gSA
nks&O;fDr fLFkj&;ksx [ksy nks&O;fDr fLFkj&;ksx [ksy nks&O;fDr fLFkj&;ksx [ksy nks&O;fDr fLFkj&;ksx [ksy (Two persons constant games)
[ksy esa nks&O;fDr] rhu O;fDr] ;k n–O;fDr gks ldrs gSA ^^O;fDr** (person) dk vFkZ Hkkx ysus
okyh ikVhZ (participating party) ls fy;k tkrk gS tSls ekfydksa dk laxBu ,d rjQ o etnwjksa dh
;wfu;u nwljh rjQA tc nks ny ;k nks O;fDr;ksa dk [ksy gksrk gS rks mls nks&O;fDr [ksy (Tw o-
person game) dgk tkrk gSA Lej.k jgs fd O;fDr dk vFkZ O;fDr ;k O;fDr&Lewg ls fy;k tk
ldrk gSA
Hkqxrku ;k ^is&vkWQ* ds vkèkkj ij [ksy dks fLFkj&;ksx (Constant–sum) vFkok xSj&fLFkj ;ksx ;k
vfLFkj ;ksx (nonconstant-sum) esa foHkkftr fd;k tk ldrk gSA fLFkj&;ksx [ksy esa [ksy ds var
esa ifj.kke ,d fLFkj jkf”k gksrk gS] pkgs fofHkUu f[kykM+h dqN Hkh j.kuhfr viuk,¡A eku yhft,]
C SIR NET, GATE, IIT-JAM, UGC NET , TIFR, IISc , JEST , JNU, BHU , ISM , IBPS, CSAT, SLET, NIMCET, CTET
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Page 26
fdlh txg nks isVªksy iEi gS vkSj mudh dqy fcØh 1000 bdkb;ksa ds cjkcj gksuh gS] pkgs ijLij
fcØh dk va”k cny tk;A ;g fLFkj&;ksx [ksy dk –‘Vkar ekuk tk ldrk gS] gkykafd blesa fcØh
esa nksuks ds ijLij va”k cny ldrs gSaA
“kwU;&;ksx [ksy “kwU;&;ksx [ksy “kwU;&;ksx [ksy “kwU;&;ksx [ksy (Zero-games)
“kwU;&;ksx [ksy fLFkj&;ksx [ksy dh ,d fo”ks’k fLFkfr dks dgrs gSa tgk¡ [ksy dk ifj.kke “kwU; ds
cjkcj gksrk gSA ;fn “kwU;&;ksx [ksy esa nks f[kykM+h gksa rks ,d f[kykM+h dk is&vkWQ èkukRed
(positive) gksus ij nwljs f[kykM+h dk is&vkWQ _.kkRed (negative) gksxk] rkfd [ksy ds ifj.kke dk
;ksx “kwU; gksA vr % ,d f[kykM+h ftruk thrrk gS] nwljk mruk gh gkjrk gSA
};kfèkdkj (duopoly) esa nks QesZ gksrh gSA ,d QeZ nwljh QeZ ds xzkgd ^rksM+us* dk iz;kl djrh gSA
eku yhft, QeZ A, QeZ B ds 50 xzkgd rksM+ ysrh gS rks A dk is&vkWQ +50 gksxk vkSj lkFk esa B dk
–50 gksxk rFkk dqy ;ksx “kwU; gksxkA
vk;rkdkj [ksyksa esa lSMy&fcanq gy vk;rkdkj [ksyksa esa lSMy&fcanq gy vk;rkdkj [ksyksa esa lSMy&fcanq gy vk;rkdkj [ksyksa esa lSMy&fcanq gy (Saddle–point solution)
nks O;fDr “kwU;&;ksx [ksyksa esa ^lSMy fcUnq* dk cM+k egRo gksrk gSA ;fn izR;sd f[kykM+h ,d “kq)
j.kuhfr (pure strategy) iz;ksx esa ykrk gS vkSj [ksy esa lSMy fcanq gksrk gS rks mls [ksy dk gy
(solution of the game) dgk tkrk gSA tc iafDr;ksa ds U;wure ewY;ksa dh vfèkdre jkf”k (maximin)
dkWyeksa ds vfèkdre ewY;ksa dh U;wure jkf”k (minimax) ds cjkcj gksrh gS rks og fcanq lSMy fcanq
ekuk tkrk gSA bls fuEu mnkgj.kksa dh lgk;rk ls le>k tk ldrk gS %
mnkgj.k 1mnkgj.k 1mnkgj.k 1mnkgj.k 1---- uhps f[kykM+h 1 dk i s&vkWQ eSfVªDl fn;k gqvk gS
f[kykM+h 1 dk is&vkWQ eSfVªDlf[kykM+h 1 dk is&vkWQ eSfVªDlf[kykM+h 1 dk is&vkWQ eSfVªDlf[kykM+h 1 dk is&vkWQ eSfVªDl
izFke f[kykM+h
dh j.kuhfr
nwljs f[kykM+h dh j.kuhfr
j.kuhfr (1)
iafDr dk
U;wure
j.kuhfr 1 (11)
8
15
13
11
8
eSfDlfeu
C SIR NET, GATE, IIT-JAM, UGC NET , TIFR, IISc , JEST , JNU, BHU , ISM , IBPS, CSAT, SLET, NIMCET, CTET
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Page 27
j.kuhfr 2 (maximin)
dkWye dk vfèkdre 11 15
feuheSDl (minimax)
izLrqr mnkgj.k esa lSMy ikbaV 11 gS] D;ksafd ;g i afDr;ksa ds U;wure ewY;ksa esa vfèkdre gS] ,oa lkFk
esa dkWyeksa ds vfèkdre ewY;ksa esa U;wure gSA bl izdkj iafDr;ksa dk ^eSfDlfeu* dkWyeksa ds
^feuheSDl* ds leku gksus ls ;g ^lSMy fcanq* gSA ;gk¡ f[kykM+h 1 izFke “kq) j.kuhfr (pure
strategy) dke esa ysxk vkSj f[kykM+h 2 Hkh viuh izFke “kq) j.kuhfr gh iz;qDr djsxkA blfy, 11
ij larqyu izkIr gk srk gS vkSj ;gh [ksy dk gy gSA 11 gh bl [ksy dk loksZÙke ifj.kke gSA
fefJr j.kuhfr;k¡ % “kwU;&;ksx&[ksy fefJr j.kuhfr;k¡ % “kwU;&;ksx&[ksy fefJr j.kuhfr;k¡ % “kwU;&;ksx&[ksy fefJr j.kuhfr;k¡ % “kwU;&;ksx&[ksy (Mixed Strategies : A Zero-sum game)
eku yhft, fiNyh rkfydk ifjofrZr :I esa bl izdkj gksrh %
;wfu;u dh is&vkWQ;wfu;u dh is&vkWQ;wfu;u dh is&vkWQ;wfu;u dh is&vkWQ
dEiuh dh j.kuhfr;k¡
;wfu;u dh
j.kuhfr;k¡
C1 C2 C3 C4 iafDr dk U;wure
¼fefuee½
U1 25 120 17 40 17 eSfDlfeu
U2 30 19 13 15 13
U3 45 7 24 10 7
U4 0 9 16 5 0
dkWye dk 45 20 24 40
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Page 28
vfèkdre
¼eSfDlee½
;gk¡ feuheSDl dk ewY; 20 gS tks eSfDlfeu ds ewY; 17 ls fHkUu gSA vr% ;gk¡ l SMy fcUnq ugha gksus
ls fefJr j.kuhfr;ksa dk ekxZ viuk;k tk;xkA ge fefJr j.kuhfr dk irk yxkus ds fy, bl
izdkj c<+ ldrs gSaA
igys mu j.kuhfr;ksa dks NksM+rs tkrs gSa ftu ij nwljh j.kuhfr;k¡ Nk;h gqbZ gSa] tSls ;wfu;u dh U1
j.kuhfr bldh U4 j.kuhfr ij Nk;h gqbZ gS] D;kasfd U1 iafDr esa izR;sd jkf”k U4 dh izR;sd jkf”k ls
vfèkd gksus ls ge U4 j.kuhfr dks NksM+ ldrs gS (U4 may be dropped)A blds i”pkr~ iqu% ns[kus
ij] dEiuh ds fy, C1 dh j.kuhfr ij C2 ;k C3 Nk;h gqbZ gSa] D;ksafd dEiuh dks C2 ;k C3 j.kuhfr
ds varxZr C1 rqyuk esa vis{kkÑr de etnwjh&o`f) nsuh gksrh gSA blfy, C1 dks Hkh NksM+ ldrs gSaA
mlds ckn iqu% ns[kus ij ;wfu;u ds fy, U1 j.kuhfr U2 ij Nk;h gqbZ gS D;ksafd ;wfu;u dks U1 esa
izR;sd dks’Bd esa U2 ls T;knk jkf”k feyrh gSA blfy, U2 Hkh NksM+ nsrs gSaA ;wfu;u dks U1 esa izR;sd
dks’Bd esa U2 ls T;knk jkf”k feyrh gSA blfy, U2 Hkh NksM+ nsrs gSaA
vc fLFkfr bl izdkj curh gSA
2 3 4
1
3
C C C
U 20 17 40
U 7 24 10
;gk¡ dEiuh ds fy, C2 j.kuhfr C4 j.kuhfr C4 ij Nk;h gqbZ gSa] ¼izR;sd dks’Bd esa C2 dh jkf”k C4 ls de½
blfy, ge C4 dks Hkh gVk nsrs gS] ftlls var esa fLFkfr bl izdkj jg tkrh gS %
;wfu;u dk is&vkWQ;wfu;u dk is&vkWQ;wfu;u dk is&vkWQ;wfu;u dk is&vkWQ
;wfu;u dh j.kuhfr;k¡
dEiuh dh j.kuhfr;k¡
C2
(q)
C4
(1 – q)
C SIR NET, GATE, IIT-JAM, UGC NET , TIFR, IISc , JEST , JNU, BHU , ISM , IBPS, CSAT, SLET, NIMCET, CTET
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Page 29
U1(p)
U3(1 – p)
20
7
17
24
vc gesa fefJr j.kuhfr (mixed strategy) dh ekU;rk ds vkèkkj ij fu.kZ; djuk gSA blds fy,
chtxf.kr dh fofèk ;k xzkQ dh fofèk dk iz;ksx djds vklkuh ls ifj.kke fudkyk tk ldrk gSA
eq[; fcanqeq[; fcanqeq[; fcanqeq[; fcanq
1111---- fQ”kj dk fofue; dk lehdj.k Mv = PT
2- dsUt ds vuqlkj eqæk dh lêk ekax C;kt nj dk ?kVrk gqvk Qyu gSA
3- ewY;kuqlkj dj og dj gS tks fd oLrq ds ewY; ds :i esa O;Dr fd;k tkrk gSA
4- Hkkjrh; dj&i)fr vkjksgh gSA
5- ;fn izR;sd f[kykM+h ,d “kq) j.kuhfr iz;k sx esa ykrk vkSj [ksy esa lSMy fcanq gS rks mls [ksy gy
dgk tkrk gSA