Page 117 - DECO403_MATHEMATICS_FOR_ECONOMISTS_PUNJABI

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/:

d' uoK s'A tZX d/ bJh ;XkoBheoD eoB s/ B'N
u ∂ u ∂ u ∂
=
x
y
z
x + y + + ... ku ( , , ,....)
x ∂ y ∂ z ∂
fiZE/ k ;hwoD dh e'fN j?.
f (x, y, z) = 3x + 2y – 4z
fJZe ;wo{g o/yh cbB j?
sK w{b d/ nB[;ko
xf x + yf y + zf z = 1 × (3x + 2y – 4z)
f x = 3, f y = 2, f z = –4
fJ; soQK yZpk gZy j/mbk j't/rkl
L.H.S. = 3x + 2y – 4z = R.H.S.

7H2H3 :{bo; gqw/: dk wjZst (Importance of Euler’s Theorem)

:{bo; gqw/: dk nkofEe y/so ftZu, ftP/P eoe/ tzv y/so ftZu ftP/P wjZstg{oD ;EkB j?.
T[sgkdB ftfGzB ;kXBK d/ ;z:[es ;zi'r Bkb j[zdk j?. j[D ;tkb T[Zmdk j? fe e[ZbQ T[sgkdB B{z
T[sgZsh d/ ftfGzB ;kXBK ftZu fe; soQK tzfvnk ikt/. i/eo T[sgkdB cbB ;wo{g j[zdh j? sK ;kB{z
fJj dZ;dk j? fe jo/e ;kXB B{z T[;dh ;hwKs T[sgkdesk d/ pokpo g[o;eko gqkgs j'Dk ukjhdk
j? sK fe e[ZbQ T[sgkdB g{oD o{g s'A ysw j' ikJ/rk. fJ;d/ fJbktk fJj gqw/: T[sgkde dh
ngbekbhB ;wZf;nktK B{z jZb eoB ftZu wdd eodh j?^T[sgkdB dk jo/e ;kXB ftZu pNtkok
ns/ e[ZbQ T[sgkdB B{z ftfGzB ;kXBK d/ ftukb/ tzv nkfd ;wZf;nktK B{z jZB eodh j?. gqw/: coe
B{z fJj th dZ;dh j? fe ;kXBK dk fe; soQK Bkb gq:'r eoBk ukjhdk j?. T[sgZsh d/ ;kXB B{z T[;
;hwk sZe gq:'r eoBk ukjhdk j? fiZE/ T[;dk w[Zb T[;dh ;hwKs nkrw T[sgkdesk d/ pokpo j'
ikt/. fJ; soQK fJj T[sgZsh d/ ;kXB dh ehws fBoXkoD ftZu th ;jkfJsk eodh j?.

;t?^w[bKeD (Self Assessment)

1H ykbh ;EkBK dh g{osh eo' (Fill in the blanks)^

1H noEPk;so ftZu finkdkso gq:'r j'D tkb/ fJZe ftP/P soQK d/ cbB B{z HHHHHHHHH cbB
efjzd/ jB.

2H HHHHHHHHHHH gqw/: ;wo{g cbB dh ;jkfJsk Bkb ;hwKs T[sgkdesk d/ f;XKs ftZu fJZe
ftP/P ;zpzX B{z dZ;dhnK jB.
3H :{bo; gqw/: dk HHHHHHHHHHH y/so ftZu ftP/P wjZstg{oD ;EkB j?.

4H HHHHHHHHHHH ftfGzB ;kXBK d/ ;z:[es ;zi'r Bkb j[zdk j?.
5H i/eo T[sgkdB cbB HHHHHHHHHHH j[zdh j? sK ;kB{z fJj dZ;dk j? fe jo/e ;kXB B{z T[;dh
;hwKs T[sgkdesk d/ pokpo g[o;eko gqkgs j'Dk ukjhdk j? sK fe e[ZbQ T[sgkdB g{oD
o{g s'A ysw j' ikJ/rk.

7H3 e'p^v'rb; T[sgkdB cbB (Cobb-Douglas Production Function)

e'p^v'rb; T[sgkdB cbB dk nkofEe y/so ftZu ftnkge o{g s'A gq:'r ehsk iKdk j?. fJ;
T[sgkdB cbB d/ ;{soheoD dk ;fjok ;hHvpfb:{H e'p (C.W. Cobb) ns/ vhH n?uH v'rb; B{z
fdZsk iKdk j?. T[jBK B/ fJ; cbB dk nB[wkB brkT[D d/ bJh ftPg d/ ftfGzB T[d:'rK dk
nfXnB ehsk. fJ; soQK fJ;dk gq:'r T[sgkdB d/ ;XkoD fB:w (Universal law) d/ o{g ftZu
ehsk iKdk j?.

LOVELY PROFESSIONAL UNIVERSITY 111