Page 331 - DECO403_MATHEMATICS_FOR_ECONOMISTS_PUNJABI
P. 331
VED1
E L-LOVELY-H math24-1 IInd 21-10-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12
fJekJh^24 L nkrs^fBors ftPb/PD
24H4H1 fb:'AfNc d/ rshPhb nkdoP T[Zs/ ;zy/g fNZgDh B'N
(Short note on Leontief’s Dynamic Model)
;fEse nkdoP ftZu noEftt;Ek d/ ftfGzB y/soK d/ seBheh r[DKeK dh ;jkfJsk Bkb go;go
fBoGosk dk nfXnB eod/ jB. gozs{ fJj r[DKe noEftt;Ek ftZu ;Nke (Stock) dh n;b
io{os T[Zs/ gqekP BjhA gkT[Ad/ jB. fJj, fJj th dZ;D ftZu n;woZE ofjzd/ jB fe ;kXB dh T[j
wksok fijVh fe T[d:'r d[nkok ygs ehsh iKdh j?, d/ bJh fezBh g{zih dh io{os j't/rh. fJ;
g{zih dh wzr ;fEo g{zih ftfB:'r fit/A fBowkD, wPhB nkfd iK T[sgkdB d/ bJh eZu/ wkb dk
;Nke pDkJ/ oZyD d/ bJh ehsh iKdh j?. i/eo ;fEoe nkrs^fBors nkdoP (y[Zbk nkdoP) d/
nzsors g{zih dk gqGkt Pkfwb eo fbnk ikt/, T[d'A fJj ftt;Ek rshPhb j' iKdh j?. fJ; bJh
g{zih fBt/P fJ; rshPhb nkrs^fBors nkdoP dk fJZe nGhBt bZSD j?.
fJ; soQK nkrs^fBors ;fEse nkdoP (y[Zbk nkdoP) ftZu fiBQK ;zouBkswe ;wheoDK dk
;jkok fbnk iKdk j?, T[; ftZu jo y/so d/ bJh io{oh g{zih ;w/A nzsokb ;fjs Pkfwb eo fbnk
iKdk j?. fJ; soQK fJj nkdoP ;fEse nkrs^fBors nkdoP (fb:'AfNc y[Zbk nkdoP) dk
ft;Eko jh j?.
wkBsktK (Assumptions)
nkrs^fBors rshPhb nkdoP ;fEse nkdoP dk ;XkoD o{g j?. fJ; soQK fJ;dhnK wkBsktK
nkdoP d/ nB[;ko j'DrhnK. fit/A^(1) jo/e T[d:'r e/tb fJZe jh ;wo{g t;s{ dk T[sgkdB
eodk j? ns/ (2) jo/e t;s{ d/ T[sgkdB d/ bJh e/tb fJZe jh seBheh T[gbpX j?, fiZE/ T[sgsh
d/ ;kXBK dk ;z:'r ;fEo j?.
wzfBnk C i (t) ukb{ ;kb dk T[gG'r j? fijVk it/A T[d:'r d[nkok T[sgkds j[zdk j?. X i (t) it/A T[d:'r
t ;w/A ntXh ftZu e[ZbQ T[sgkdB j? fijVk fszB T[d/PK d/ o{g ftZu ezw ftZu nkT[Adk j?^(i) nrbh
ntXh d/ T[gG'r {C i (t + 1)}, (ii) n T[d:'rK ftZu g{zih t;s{nK dk P[ZX ;Nke S i (t + 1) – S i (t)
ns/ (iii) noEftt;Ek ftZu T[d:'fre T[sgkdB dk ukb{ gqtkj. fJBQK ;fEshnK ftZu ;zs[bB
;wheoD j't/rk^
X i (t) = C i (t + 1) + S i (t + 1) – S i (t) + x 11 (t) + x 12 (t)
(fJZE/ i = 1, 2)
j[D ;tkb fJj T[Zmdk j? fe ukb{ T[sgkdB X 1 (t) ns/ X 2 (t) fet/A T[sgkdB j[zdk j?< fb:'AfNc
T[sgkdB cbB ftZu e[ZbQ T[sgkdB d' soQK d/ ;kXBK dk cbB j't/rk^(i) ukb{ ;kb d/ bJh eZuk wkb
ns/ (ii) g{zih ;zpzXh t;s{nK dk ;Nke^
X 1 (t) = f[x 11 (t), x 21 (t), S 11 (t), S 21 (t)]
X 2 (t) = f[x 12 (t), x 22 (t), S 12 (t), S 22 (t)]
noEftt;Ek ftZu e[ZbQ g{zih ;Nke ;ko/ T[d:'rK d/ g{zih ;Nke dk i'VQ j't/rk^
S i (t) = S i1 (t) + S i2 (t)
ns/ g{zih ;Nke ftZu gfotosB do gqkgs j't/rh^
• S i (t) = S i (t + 1) – S i (t)
g{zih ;Nke r[DKe B{z j/m nB[;ko t:{j T[sgzB ehsk ik ;edk j?^
S
b = ij
ij
X
j
fJZE/ b ij = g{zih ;Nke r[DKe, x i = jt/A T[d:'r dk e[ZbQ T[sgkdB ns/ S ij = jt/A T[d:'r d/ T[sgkdB B{z
it/A T[d:'r d[nkok ehsk frnk P'X.
LOVELY PROFESSIONAL UNIVERSITY 325
