Page 167 - DECO401_MICROECONOMIC_THEORY_HINDI

bdkbZ 7 % ek¡x fl¼kar esa uwru fodkl

tgk¡ X =i oLrqvksa dk miHkksx caMy uksV

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U = miHkksx caMy ls izkIr gqbZ mi;ksfxrk
P =i oLrqvksa dh dhersa
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Y = miHkksDrk dh oqQy vk;A

eku yhft, fd vkSj λ = Pi/Y vkSj vc mi;ksfxrk vfèkdredj.k leL;k dks bl izdkj fy[kk tk ldrk
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gS]
Max U (X)

Subject to ∑ λ X ≤ l ...(2)
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tgk¡] λ lkekU;Ñr (Normalised) dhersaA
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bl :Ik esa] mi;ksfxrk vfèkdredj.k leL;k osQ n pjksa osQ nks lSV gksrs gSaµ(i) X ewY;ksa osQ lkFk miHkksx
ek=kk,¡] vkSj (ii) lkekU;Ñr dhersa λ = λ ,...., λ ewY;ksa osQ lkFkA
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b"Vre ek¡x caMy ek¡x iQyu osQ flLVe }kjk bl izdkj fn;k tkrk gSA
X = D (λ) i = 1, ........ n ...(3)
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vfèkdre mi;ksfxrk Lrj lehdj.k (3) osQ b"Ve miHkksx caMy dks lehdj.k (1) osQ mi;ksfxrk iQyu esa
LFkkukiUu djosQ izkIr fd;k tkrk gSA vkxs] ;g b"Vre miHkksx caMy vk; Lrj vkSj dherksa osQ lfn'k
(Vector) ij fuHkZj djrk gS] tks lehdj.k (3) esa ek¡x iQyu osQ flLVe esa izfr¯cfcr gksrk gSA blls izkIr
gksrk gS ijks{k mi;ksfxrk iQyu]
V (λ) = U (d), (λ), ......... d (λ) ...(4)
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V ijks{k mi;ksfxrk iQyu dgykrk gS] D;ksafd ;g ijks{k :i ls vk; Lrj vkSj dher lfn'k ;k lkekU;hÑr
dherksa osQ ,d lSV λ ij fuHkZj djrh gSA

ijks{k mi;kssfxrk iQyu dh fo'ks"krk,¡ (Properties of Indirect Utility Function)

ijks{k mi;ksfxrk iQyu dh fuEu fo'ks"krk,¡ gSaµ
1- ;fn U fujarj gS] rks V Hkh λ osQ lHkh èkukRed lSVksa ij fujarj gSaA
2- U ugha c<+rk D;ksafd ;fn dher c<+kbZ tkrh gS ;k vk; de dh tkrh gS] rks ;g vfèkdre mi;ksfxrk
dks ugha c<+k ldrh gSA ;g lgh gS ;|fi U miHkksx caMy ith esa c<+ jgh gksA
3- U t:jru~ ?kVrh ugha gS tc ith lkekU;Ñr dher gks] ;|fi U miHkksx caMy ith esa c<+ jgh gksA
4- ;fn ,d dks.kkRed gy (Corner solution) gks] vFkkZr~ X = 0, rks P dks c<+kus ls miHkksDrk dh
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mi;ksfxrk ij dksbZ izHkko ugha gksrkA mnkgj.kkFkZ] ;fn ek#fr tsu dh dher c<+k nh tkrh gS rks bldk
vfèkdrj miHkksDrkvksa osQ mi;kssfxrk Lrjksa ij izHkko ugha iM+rk gSA

xzkiQh; izLrqrhdj.k (Graphic Presentation)
ijks{k mi;kssfxrk iQyu dks ijks{k mnklhurk oØksa }kjk fpf=kr fd;k tkrk gSA eku yhft, fd osQoy nks
miHkksDrk oLrq,¡ 1 vkSj 2 gSa ftudh lkekU;Ñr dhersa λ vkSj λ gSa ftUgsa Øe'k% lekukarj vkSj vuqyac v{kksa
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ij fy;k x;k gS] tSlk fd fp=k 7-3 esa gSA ,d ijks{k mnklhurk oØ tSls IIC lkekU;hÑr dherkas osQ la;ksxksa
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dks λ n'kkZrk gS] tks vfèkdre mi;ksfxrk Lrj dks vifjofrZr NksM+ nsrs gSaA ;fn miHkksDrk IIC oØ ij nksuksa
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esa ls fdlh ,d oLrq ls larq"V ugha gS vkSj mQ¡ps oØ IIC ij pyk tkrk gS] rks nksuksa oLrqvksa dh lkekU;hÑr
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dhersa c<+rh gSa vkSj mi;ksfxrk ?kV tkrh gSA blosQ foijhr ;fn miHkksDrk uhps osQ oØ IIC ij pyk tkrk
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