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VED1
E L-LOVELY-H math7-1 IInd 6-8-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

fJekJh^7 L ;wo{g cbB ns/ :{bo; gqw/:

fJ; soQK fi; nB[gks ftZu ;kXBK B{z tXkfJnk iKdk j? T[;h nB[gks ftZu T[gkdB th tZX iKdk B'N
j?. fJ;B{z o/ykfuZso 7H2 dh ;jkfJsk Bkb th ;gPN ehsk ik ;edk j?. X-neP T[Zs/ ;kXB L
(fwjBs) ns/ Y-neP T[Zs/ ;kXB K (g{zih) B{z fbnk frnk j?. T[sgkdB dhnK 100 fJekJhnK
T[sgkfds eoB d/ bJh ;kXB L dh OA 1 fJekJhnK ns/ ;kXB K dh OB 1 fJekJhnK ezw ftZu
bJhnK iKdhnK jB. i/eo T[sgkdB dhnK 200 fJekJhnK T[sgkfds eod/ jB sK ;kXB L ns/
;kXB R B{}z th d[ZrDh io{oh gJ/rh. fJZE/ OA 2 fpbe[b OA 1 dk d[ZrDk j?. fJ;h soQK OB 2
fpbe[b OB 1 dk d[Zrdk j?. fJ;h soQK T[sgkdB dhnK 300 fJekJhnK d/ bJh ;kXB A ns/ B B{z
fszB r[Dk fJekJhnK dh io{os j't/rh. fit/A fe o/ykfuZso 7H2 ftZu ;gPN ehsk frnk j?.
fJ;B{z d{i/ sohe/ Bkb th ;gPN ehsk ik ;edk j?. OM T[sgkdB dk ft;sko gE j? fijVk P,
Q ns/ R ;zs[bB fpzd{nK B{z fwbkT[Adh j?. fJj ;ko/ ;zs[bB fpzd{ ;wkB nzso s/ j'Dr/ Gkt OP =
PQ = QR, fijVk fJj dZ;dk j? fe T[sgkdB T[;h nB[gks ftZu tX/rk fi; nB[gks ftZu ;kXB
tXkJ/ iKd/ jB.
2H T[sgkdB cbB ;wo{g ns/ fJZe e'fN dk j[zdk j?L i/eo T[sgkdB cbB ;wo{g ns/ fJZe
e'fN (Degree) dk j[zdk j? sK T[;dk Gkt fJj j? fe T[sgkdB ;fEo g?wkB d/ gqfscb d/ nzsors
nkT[Adk j?, Gkt
α
β
T[sgkdB cbB, P = AL K u
d'jK gk;/ log b?D s/
log P = log A + αlog L + βlog K + log u
tZy^tZy o{g ftZu L ns/ K d/ ;zdoG ftZu nzPe fBy/VB (Differentiate) eoB s/
∂
1 P α
= HHHHH(i)
∂
P L L
∂
1 P β
ns/ = HHHHH(ii)
∂
P K K
(i) ns/ (ii) B{z d[pkok fbyD s/
∂ P
L =α P HHHHH(iii)
∂
L
∂ P
K =β P HHHHH(iv)
∂
L
;wheoD (iii) ns/ (iv) B{z i'VB s/
∂ P ∂ P
L + K = Pα+ β ( P +P )α+β
∂ L ∂ L
= P [∴ α +β = ]
1
3H i/eo T[sgkdB cbB ;wo{g ns/ fJZe e'fN dk j[zdk j? sK gqfs;EkgB dh b'u (Elasticity of
α
β
Substitution) jw/PK fJekJh d/ pokpo jzdh j?. i/eo T[sgkdB cbB P = AL K u fiE/
α O β &1 n;hA ikDd/ jK fe
;kXB dh wksok nB[gks ftZu gfogosB
gqfs;EkgB dh b'u & σ &
;kXB dh ehws nB[gks ftZu gqshPs gfogosB
∂ ( )K / (/L )K /L ∂ ( )K /L / K /L
σ
∴ = =
∂
∂ (P /P )/ P /P R /R
L K L K
fiZE/ K /L & ;kXB wksok nB[gks
R= P P & ;kXB ehws nB[gks
K
L

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