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vUrjkZ"Vªh; O;kikj ,oa foÙk
uksV B = Y – A ...(2)
lehdj.k (2) ;g O;Dr djrk gS fd Hkqxrku 'ks"k jk"Vªh; vk; (Y) rFkk oqQy vo'kks"k.k (A) dk vUrj gSA Hkqxrku
'ks"k dks ?kjsyw vk; c<+kdj vFkok vo'kks"k.k (mi;ksx rFkk fuos'k O;;) dks de djosQ lq/kjk tk ldrk gSA
,ysDtSaMj blosQ fy, voewY;u djus dk lq>ko nsrk gSA mldk roZQ Øe bl izdkj gSμvoewY;u ls fu;kZr c<+rs
gSa rFkk vk;krksa esa deh vkrh gS ftlls jk"Vªh; vk; esa o`f¼ gksrh gSA bl rjg c<+h gqbZ vfrfjDr vk; xq.kd izHkko
ls vk; dks vkSj vf/d c<+k,xh blls ?kjsyw miHkksx esa o`f¼ gksxhA bl rjg jk"Vªh; vk; esa o`f¼ dk Hkqxrku&'ks"k
ij 'kq¼ izHkko jk"Vªh; vk; esa oqQy o`f¼ rFkk vo'kks"k.k esa izsfjr o`f¼ dk vUrj gS ftls fuEu lehdj.k }kjk O;Dr
fd;k tk ldrk gSμ
ΔB = ΔY – ΔA ...(3)
voewY;u gksus ij oqQy vo'kks"k.k dh lhekUr izo`fÙk (vo'kks"k.k dh lhekUr izo`fÙk (a) miHkksx dh lhekUr izo`fÙk
rFkk fuos'k dh lhekUr izo`fÙk dk ;ksx gksrh gS) ij fuHkZj djrk gSA ;gka vo'kks"k.k dh lhekUr izo`fÙk dks a }kjk
O;Dr fd;k x;k gSA bl rjg]
ΔA = a . ΔY ...(4)
lehdj.k (4) ls ΔA dk eku lehdj.k (3) esa j[kus ij gesa izkIr gksrk gSμ
ΔB = ΔY – (a . ΔY)
ΔB = ΔY – a . ΔY
ΔB = (1 – a) ΔY
voewY;u Hkh vk; esa ifjorZu osQ }kjk vo'kks"k.k dks izR;{k :i ls izHkkfor djrk gS ftls ;gka D ls izn£'kr fd;k
x;k gSA bl rjg]
ΔB = (1 – a) ΔY + ΔD ...(5)
mijksDr lehdj.k mu rhu ?kVdksa dh vksj laosQr djrk gS tks Hkqxrku 'ks"k ij voewY;u osQ izHkkoksa dh foospuk
djrs gSaA ;s rhu ?kVd gSaμ(i) vo'kks"k.k dh lhekUr izo`fÙk (a), (ii) vk; esa ifjorZu (ΔY) rFkk (iii) izR;{k vo'kks"k.k
esa ifjorZu (ΔD)A
1- vo'kks"k.k dh lhekUr izo`fÙkμ;fn vo'kks"k.k dh lhekUr izo`fÙk bdkbZ ls de (a < 1) gS rks voewY;u
fu;kZr dks c<+k,xk vkSj vk;kr esa deh yk,xkA mRiknu vkSj vk; esa o`f¼ gksxh rFkk pkyw [kkrs ij Hkqxrku
'ks"k esa lq/kj gksxkA nwljh vksj ;fn a > 1 gks rks Hkqxrku 'ks"k ij foijhr izHkko iM+sxkA vU; 'kCnksa esa] yksx
vf/d vo'kks"k.k dj jgs gSa vFkkZr~ miHkksx ij vf/d O;; dj jgs gSa rFkk vfèkd fuos'k dj jgs gSaA ,slh
n'kk esa voewY;u u rks fu;kZr gh c<+k,xk vkSj u gh vk;kr dks de djsxkA Hkqxrku 'ks"k dh fLFkfr [kjkc
jgsxhA
iw.kZ jkstxkj dh n'kkvksa osQ vUrxZr ;fn a > 1 gks rks ljdkj dks voewY;u osQ lkFk&lkFk O;; ?kVkus okyh
uhfr mik;ksa dks viukuk gksxk rkfd vFkZO;oLFkk osQ lalk/uksa dk iqu% vkc.Vu bl rjg gks fd fu;kZr
c<+s vkSj vk;kr esa deh vk,A varr% Hkqxrku 'ks"k dh fLFkfr esa lq/kj vk,xkA
2- vk; esa ifjorZuμ;fn vFkZO;oLFkk esa fuf"Ø; lalk/u fo|eku gSa rks voewY;u ls fu;kZr c<+sxk vkSj
vk;kr de gksxkA fu;kZr rFkk vk;kr izfr;ksxh m|ksxksa osQ foLrkj ls vk; esa o`f¼ gksrh gSA blls vFkZO;oLFkk
esa vfrfjDr vk; dk l`tu gksxk tks xq.kd izHkko ls vkxs Hkh vk; dks c<+k nsxhA blls Hkqxrku 'ks"k dh
fLFkfr esa lq/kj gksxkA ;fn vFkZO;oLFkk esa iw.kZ jkstxkj dh fLFkfr gS rks voewY;u izfrowQy jk"Vªh; 'ks"k dks
Bhd ugha dj ik,xk D;ksafd jk"Vªh; vk; vc bl Lrj ls vkxs ugha c<+ losQxhA voewY;u ls dhersa c<+saxh
ftlls fu;kZr ?kVsxk rFkk vk;kr c<+sxk iQyLo:i Hkqxrku 'ks"k dh fLFkfr vkSj vf/d [kjkc gksxhA
3- O;kikj 'krZ izHkkoμvoewY;u ls ns'k dh O;kikj 'krs± izfrowQy gksrh gSa D;ksafd blls fons'kh eqnzk esa fu;kZr
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