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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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