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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/:
7H2 :{bo; gqw/: (Euler’s Theorem) B'N
:{bo; gqw/: dZ;dh j? fe id'A ;ko/ T[sgZsh d/ ;kXB fJZe fdZs/ j'J/ nB[gks ftZu tXkJ/ iKd/ jB
sK Bshi/ ti'A T[sgkdB th T[;h nB[gks ftZu tZX ikJ/rk, i/eo jo/e T[sgZsh d/ ;kXB B{z T[;dh
;hwKs T[sgkdesk d/ w{b d/ pokpo g[o;eko fdZsk iKdk j? ns/ e[ZbQ T[sgkdB g{oD o{g s'A ysw
1
j' iKdk j?. rfDse o{g ftZu :{bo; gqw/: B{z j/mb/ o{g ftZu do;kfJnk ik ;edk j?. i/eo
T[sgkdB cbB, p = f (L, K) fJZe o/yh ;wo{g cbB (Linear Homogenous Function) j[zdh j?^
∂ P ∂ P
P = L + K , d{i/ PpdK ftZu P = LMP L + KMP K
∂ L ∂ K
fiZE/ P = e[ZbQ T[sgkdB L = fwjBs ;kXB dhnK fJekJhnK, K = g{zih ;kXB dhnK fJekJhnK,
∂ P iK MP L & fwjBs dh ;hwKs T[sgkdesk ns/ ∂ P iK MP K = g{zih dh ;hwKs T[sgkdesk
∂ L ∂ K
B{z do;kT[Ad/ jB.
wkBsktK (Assumptions)
gqw/: fBwBfbys wjZstg{oD wkBsktK T[Zs/ nXkfos j?^
1H g?wkB/ d/ ;fEo gqfscb dk fB:w (The Law of Constant Returns of Scale) fefonkPhb
j[zdk j?. fJj sK jh ;zGt j[zdk j? id'A fe T[sgkdB cbB o/yh ;wo{g ns/ fJZe e'fN
(Degree) dh j[zdh j?.
2H pkIko ftZu g{oD gqfs:'frsk dh ;fEsh gkJh iKdh j?.
3H fJj T[sgZsh d/ ;kXB dh tzv dh wkBsk B{z b? e/ uZbdh j?.
4H fdZs/ j'J/ ;w/A d/ bJh seBheh ;fEo j[zdh j?.
7H2H1 :{bo; gqw/: dk fusoe gqdoPB
(Diagramatical Presentation of Euler’s Theorem)
:{bo; gqw/: B{z T[go'es wkBsktK B{z fXnkB ftZu oZye/ fuZso d[nkok gqdofPs ehsk ik ;edk j?.
wzB fbU T[sgkdB cbB P = f (L, K) j? sK d'B'A ;kXB L ns/ K dk e[ZbQ T[sgkdB P T[Zs/ gqGkt
g?Adk j?. gfjbk, n;hA L ;kXB dk eqw T[sgkdB P T[Zs/ gqGkt d/yKr/ id'A fe K ;kXB ;fEo
ofjzdk j?. fJ;d/ pknd K ;kXB dk P T[Zs/ gqGkt d/yKr/ id'A fe L ;kXb ;fEo ofjzdk j?.
o/ykfuZso 7H1
o/ykfuZso 7H1 ftZu L ;kXB dhnK fJekJhnK X-neP T[Zs/ ns/ e[ZbQ T[sgkdB B{z Y-neP T[Zs/
wkfgnk frnk j?. TP e[ZbQ T[sgkdB B{z do;kT[Ad/ jB. M fpzd{ T[Zs/ e[ZbQ T[sgkdB tZX s'A tZX j[zdk
j?. wzb fbU e[ZbQ T[sgkdB teo TP T[Zs/ N fpzd{ TI ;goP o/yk fyZuh rJh j?. N fpzd{ s'A X-
neP T[Zs/ bzpts o/yk fyZuh rJh j? fijVh X-neP T[Zs/ Q fpzd{ T[Zs/ fwbdh j?.
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