Page 184 - DECO403_MATHEMATICS_FOR_ECONOMISTS_PUNJABI

VED1
E L-LOVELY-H math11-1 IInd 6-8-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

noEPk;soh dk rfDs

B'N (2) fJ; cbB ns/ g?okwhNo v (;wo{gsk e'fN) g?wkB/ dh gqfefonk (Scale of Operation) ns/
seBheh gfotosBK s'A gqGkfts j[zdk j?. fJj d'B'A PeshnK g?wkB/ d/ gqfscb dh e'fN B{z
gqGkfts eo ;ed/ jB, gozs{ fJBQK dk tZyo/ o{g ftZu gsk BjhA ehsk frnk j?.

(3) fJ; ftZu fJj wkBsk b? e/ uZbd/ jK fe gqfs;EkgB dh b'u e/tb seBheh d/ gfotosB s'A
gqGkfts j[zdh j? ns/ ;kXBK d/ nB[gks fJ;B{z gqGkfts BjhA eod/ jB, gozs{ fttjkfoe nfXnB
s'A gsk uZbdk j? fe gqfs;EkgB b'u ;kXBK d/ nB[gksK s'A th gqGkfts j[zdh j?. fJ; soQK fJj
cbB fJZe pj[s wjZstg{oD sZE B{z SZv fdzdk j?.

(4) nzs, fJ; cbB dk g?okwhNo δ wkfgnk BjhA ik ;edk. fJ;d/ fJbktk fJ; cbB ftZu
nzefVnK B{z iKuD ftZu th pj[s w[PfebK dk ;kjwDk eoBk g?Adk j?.
α
β
T[dkjoD 4L fJZe T[sgkdB P = AL C fiZE/ A, α ns/ β ;fEo jB. do;kU fe i/eo
L ns/ C ekoeK B{z ;wkB nB[gks ftZu tXkfJnk ikt/ ns/ α O β fJekJh d[nkok ;wkB
j'D s/ T[sgkdB tZX, xZN iK ;wkB nB[gks ftZu tX/rk.
β
α
(The production function is P = AL C where A, α and β are constant. Show that if the
factors L, C are increased in the same proportion, the product increases in greater, equal or
less proportion, according as α + β is greater than, equal to, or less than unity).
jZbL T[sgkdB cbB j?^
β
α
P = AL C
wzfBnk ;kXB L ns/ C ftZu r[Dk ψ r[Dk tkXk eo fdZsh ikt/ sK
β
α
= A (ψL) (ψ C) (fJZE/ ψ > 0 j?)
β
α
= ψ α+β AL C
β
α
= ψ α + β P (∴ P = AL C )
i/eo α O β = 1 j't/ sK
= ψP
fJ; soQK T[sgkdB mhe T[;h nB[gks ftZu tZX ikt/rk fi; nB[gks ftZu ;kXBK ftZu tkXk ehsk
frnk j?. fJ; ;fEsh ftZu T[sgkdB g?wkB/ d/ ;fEo gqfscb d/ fB:w d/ nzsors j't/rk^

i/eo α O β < 12-3 i.e. wzfBnk α O β T[d'A

1/2
= ψ P
fJ; ;fEsh d/ T[sgkdB ;kXBK ftZu tkXk eoB Bkb nB[gks s'A xZN tX/rk. fJj ;fEsh g?wkB
d/ xNd/ j'J/ gqfscb d/ fB:w dh j't/rh.
i/eo α O β > 1 i.e. wzfBnk α O β & 2 T[d'A
2
= ψ P

eh s[;hA ikDd/ j' T[sgkdB ;kXBK ftZu tkXk d/ nB[gks s'A tZX j't/rk ns/ T[sgkdB g?wkB d/
tXd/ j'J/ gqfscb d/ fB:w d/ nzsors fefonkPhb j't/rk.

ns/
fJj ;ko/ w[Zb Io{oh ft;Eko gE dk f;oiB eoBr/.

178 LOVELY PROFESSIONAL UNIVERSITY