Elasticity of Demand Analysis
Elasticity of Demand Analysis
Elasticity 8
f‚wgKv
BDwbU 5 I 6 Avgiv h_vµ‡g Pvwn`v I †hvMvb m¤ú‡K© †R‡bwQ| †hLv‡b Wvbw`‡K wbgœMvgx Pvwn`v †iLvi gva¨‡g
†µZvi AvPiY Ges Wvbw`‡K DaŸ©Mvgx †hvMvb †iLvi gva¨‡g we‡µZvi AvPiY wb‡q Av‡jvPbv Kiv n‡q‡Q| Avevi
BDwbU 7 G Pvwn`v I †hvMv‡bi fvimv‡g¨i gva¨‡g `ª‡e¨i fvimvg¨ `vg I cwigvY wba©viY Kiv n‡q‡Q| GB BDwb‡U
Avgiv †`Le `v‡gi cwieZ©‡bi mv‡_ mv‡_ wKfv‡e †µZv I we‡µZvi `ªe¨ µq I weµ‡qi cwigvY mvov †`q| GB
aviYvwU we‡køl‡Yi Rb¨ †h nvwZqviwU cÖ‡qvRb †mwU n‡”Q w¯’wZ¯’vcKZv|
GB BDwb‡Ui cvVmg~n
cvV 8.1: Pvwn`vi w¯’wZ¯’vcKZv
cvV 8.2: †hvMv‡bi w¯’wZ¯’vcKZv
GBP.Gm.wm †cÖvMÖvg
D‡Ïk¨
GB cvV †k‡l wkÿv_©xiv-
w¯’wZ¯’vcKZv m¤ú‡K© aviYv Ki‡Z cvi‡eb;
Pvwn`vi w¯’wZ¯’vcKZvi aviYv e¨vL¨v Ki‡Z cvi‡eb;
Pvwn`vi `vg, Avq I AvovAvwo w¯’wZ¯’vcKZvi cwigvc e¨vL¨v Ki‡Z cvi‡eb|
g~jcvV-
w¯’wZ¯’vcKZv (Elasticity)
f‚wgKv
Avgiv Rvwb, `ª‡e¨i `vg evo‡j H `ª‡e¨i Pvwn`v K‡g| A_©vr Pvwn`v wewa‡Z `ª‡e¨i `vg I Pvwn`vi cwigv‡Yi g‡a¨
wecixZ m¤úK© we`¨gvb| wKš‘y wK cwigvY `vg evo‡j ev Kg‡j wK cwigvY Pvwn`v Kg‡e ev evo‡e Zv Pvwn`v wewa
Øviv cÖKvk K‡i| GKBfv‡e †hvMvb wewa †hvMv‡bi cwigvY I `v‡gi g‡a¨ mggyLx m¤úK© cÖKvk K‡i| A_©vr `ª‡e¨i
`vg evo‡j †hvMv‡bi cwigvY ev‡o Ges `vg Kg‡j †hvMv‡bi cwigvY K‡g| wKš‘y wK cwigvY `vg evo‡j ev Kg‡j
wK cwigvY `ª‡e¨i †hvMvb evo‡e ev Kg‡e Zv †hvMvb wewa Øviv cÖKvk K‡i bv| Pvwn`v ev †hvMv‡bi `vg
w¯’wZ¯’vcKZv Øviv `v‡gi kZvswkK cwieZ©‡bi d‡j Pvwn`vi ev †hvMv‡bi kZvswkK cwieZ©b cwigvc Kiv hvq| G
Aa¨v‡q Pvwn`v I †hvMv‡bi w¯’wZ¯’vcKZv wb‡q Av‡jvPbv Kiv n‡jv|
w¯’wZ¯’vcKZv (Elasticity)
mvaviY A‡_© w¯’wZ¯’vcKZv ej‡Z cwieZ©‡bi nvi‡K eySvq| MvwYwZKfv‡e ejv hvq †Kvb A‡cÿ‡Ki ¯^vaxb Pj‡Ki
cwieZ©‡bi d‡j Aaxb Pj‡Ki †h cwieZ©b nq, ‡mB cwieZ©‡bi gvÎv ev AbycvZ‡K w¯’wZ¯’vcKZv e‡j| A_©bxwZ‡Z
w¯’wZ¯’vcKZv wewfbœ iKg n‡Z cv‡i| †hgb Pvwn`vi `vg w¯’wZ¯’vcKZv †hvMv‡bi `vg w¯’wZ¯’vcKZv, Avq
w¯’wZ¯’vcKZv, cwieZ©K, AvovAvwo w¯’wZ¯’vcKZv cÖf…wZ|
Pvwn`vi cwieZ©b (
g~j Pvwn`v (
=
`v‡gi cwieZ©b (
g~j `vg (
Q
Q Q P
.
P P Q
P
GLv‡b D‡jøL¨ †h, `v‡gi mv‡_ Pvwn`vi †h‡nZz FYvZ¥K m¤úK© we`¨gvb †m‡nZz Pvwn`vi `vg w¯’wZ¯’vcKZvi wPý
me©`v FYvZ¥K (-) n‡e|
D`vniY t g‡b Kwi, †Kvb `ª‡e¨i `vg 10 UvKv †_‡K 8 UvKv n‡j `ª‡e¨i Pvwn`v e„w× †c‡q 100 GKK †_‡K 120
GKK n‡jv| Pvwn`vi `vg w¯’wZ¯’vcKZv †ei Kiæb|
GLv‡b,
`ª‡e¨i cÖv_wgK `vg, 10UvKv
cÖv_wgK Pvwn`v, 100 GKK
`v‡gi cwieZ©b, 8 - 10 = - 2 UvKv
Pvwn`vi cwieZ©b, 120 - 100 = 20 UvKv
Q P 20 10
myZivs Pvwn`vi `vg w¯’wZ¯’vcKZv, EP = .
P Q 2 100
1
1
GLv‡b D‡jøL¨ †h, Pvwn`vi `vg w¯’wZ¯’vcKZvi †ÿ‡Î we‡qvM/FYvZ¥K (-) wPý‡K D‡cÿv Kiv nq|
wkÿv_©xi KvR
GKwU `ª‡e¨i `vg 40 UvKv †_‡K K‡g 30 UvKv n‡j hw` Zvi Pvwn`v 50 GKK †_‡K e„w× †c‡q 70
GKK nq, Z‡e †m‡ÿ‡Î H `ª‡e¨i `vg w¯’wZ¯’vcKZv KZ?
Pvwn`vi cwieZ©b (
g~j Pvwn`v (
=
Av‡qi cwieZ©b (
g~j Avq (
Q
Q Q Y
.
Y Y Q
Y
D`vniY : mvaviY `ª‡e¨i †ÿ‡Î t g‡b Kwi †Kvb †fv³vi Avq e„w× †c‡q 5000 UvKv †_‡K
e„w× †c‡q 7000 UvKv n‡jv| d‡j `ª‡e¨i Pvwn`vI e„w× †c‡q 100 GKK †_‡K 200 GKK n‡jv| Pvwn`vi Avq
w¯’wZ¯’vcKZv wnmve Ki Ges `ª‡e¨i cÖK…wZ m¤ú‡K© gšÍe¨ Kiæb|
GLv‡b,
g~j Avq, 5000 UvKv
Av‡qi cwieZ©b, 7000 - 5000 = 2000 UvKv
g~j Pvwn`v, 100 GKK
Pvwn`vi cwieZ©b, 200 - 100 = 100 GKK
GLv‡b,
g~j Avq, 5000 UvKv
Av‡qi cwieZ©b, 7000 - 5000 = 2000UvKv
g~j Pvwn`v, 200 GKK
Pvwn`vi cwieZ©b, 100 - 200 = - 100 GKK
Q Y
myZivs Pvwn`vi Avq w¯’wZ¯’vcKZv, EY .
Y Q
- 100 5000 5
1.25
2000 200 4
‡h‡nZz Pvwn`vi Avq w¯’wZ¯’vcKZv FYvZ¥K, myZivs `ªe¨wU wbK…ó cÖK…wZi|
wkÿv_©xi KvR
†Kvb e¨w³i gvwmK Avq 10,000 UvKv †_‡K e„w× †c‡q 12,000 UvKv n‡jv| Gi d‡j Zvi `ª‡e¨i
Pvwn`v e„w× †c‡q 500 GKK †_‡K 600 GKK n‡jv|
(K) Pvwn`vi Avq w¯’wZ¯’vcKZv cwigvc Kiæb Ges `ªe¨wUi cÖK…wZ m¤ú‡K© gšÍe¨ Kiæb|
(L) hw` H e¨w³i Avq 10,000 UvKv †_‡K e„w× †c‡q 12,000 UvKv nq Ges H `ª‡e¨i Pvwn`v 500
GK‡KB w¯’i _v‡K| G‡ÿ‡Î Avq w¯’wZ¯’vcKZv KZ? G‡ÿ‡Î `ªe¨wUi cÖK…wZ wK iƒc?
D`vniY
cwieZ©K `ªe¨ ( t g‡b Kwi wPwbi `vg hLb †KwR cÖwZ 40 UvKv ZLb ¸‡oi
Pvwn`v 20 GKK| wPwbi `vg e„w× †c‡q 50 UvKv n‡j ¸‡oi Pvwn`v †e‡o 30 GKK nq| Pvwn`vi
AvovAvwo w¯’wZ¯’vcKZv †ei Kiæb I `ªe¨wUi cÖK…wZ m¤ú‡K© gšÍe¨ Kiæb|
GLv‡b,
¸‡oi cÖv_wgK Pvwn`v Q X = 20 GKK
¸‡oi Pvwn`vi cwieZ©b, Q X 30 - 20 = 10 GKK
wPwbi cÖv_wgK `vg, PY = 40UvKv
wPwbi `v‡gi cwieZ©b, PY 50 - 40 = 10 UvKv
Qx PY
myZivs Pvwn`vi AvovAvwo w¯’wZ¯’vcKZv, EC .
PY QY
10 40
2
10 20
GLv‡b Pvwn`vi AvovAvwo Avq w¯’wZ¯’vcKZvi wPý abvZ¥K, myZivs `ªe¨wU cwieZ©K (subbsitute goods)|
cwic~iK `ªe¨ t g‡b Kwi, Pv‡qi †KwR hLb 80 UvKv ZLb wPwbi
Pvwn`v 150 GKK| Pv‡qi `vg e„w× †c‡q 120 UvKv †KwR n‡j wPwbi Pvwn`v n«vm †c‡q 50 GKK
nq| Pvwn`vi AvovAvwo w¯’wZ¯’vcKZv wnmve Kiæb I `ªe¨wU m¤ú‡K© gšÍe¨ Kiæb|
GLv‡b,
Pv‡qi cÖv_wgK `vg, PY = 80 UvKv
Pv‡qi `v‡gi cwieZ©b, PY 150 - 80 = 70UvKv
wPwbi cÖv_wgK Pvwn`v, QX = 150 GKK
wPwbi Pvwn`vi cwieZ©b, Q X 50 - 150 = - 100 GKK
Qx PY
myZivs Pvwn`vi AvovAvwo w¯’wZ¯’vcKZv, EC .
PY Q X
100 80 2 16
70 150 21 21
m¤cK©nxb `ªe¨
Pvwn`vi AvovAvwo w¯’wZ¯’vcKZv EC k~Y¨ A_©vr EC=0 n‡j we‡eP¨ `ªe¨wU‡K m¤úK©nxb ev ci¯úi †_‡K ¯^vaxb
nq|
BDwbU AvU c„ôv-102
A_©bxwZ 1g cÎ
D`vniY
‡gvevBj †dvb Ges AvUv ci¯úi m¤úK©nxb `ªe¨|
g‡b Kwi †gvevBj †dv‡bi `vg PY e„w× ‡c‡q 4000 UvKv †_‡K 6000 UvKv n‡jv Ges G‡ÿ‡Î AvUvi Pvwn`v 50
†KwR‡ZB w¯’i _vK‡jv| Pvwn`vi AvovAvwo w¯’wZ¯’vcKZv wnmve Kiæb I `ª‡e¨i cÖK…wZ wbY©q Kiæb|
GLv‡b,
AvUvi cÖv_wgK Pvwn`v, QX = 50 ‡KwR
AvUvi Pvwn`vi cwieZ©b, QX= 50 - 50 = 0 ‡KwR
‡gvevBj †dv‡bi cÖv_wgK `vg, PY = 4000 UvKv
‡gvevBj †dv‡bi `v‡gi cwieZ©b, PY= 6000 - 4000 = 2000 UvKv
Qx PY 0 4000
myZivs Pvwn`vi AvovAvwo w¯’wZ¯’vcKZv, EC . 0
PY Q X 2000 50
GLv‡b Pvwn`vi AvovAvwo w¯’wZ¯’vcKZv k~Y¨| myZivs `ªe¨ `ywU ci¯úi ¯^vaxb ev m¤úK©nxb|
wkÿv_©xi KvR
hw` Kgjv‡jeyi cÖwZ nvwji `vg e„w× †c‡q 70 UvKv †_‡K 80 UvKv nq Z‡e Av‡c‡ji Pvwn`v e„w× 3.50
†KwR †_‡K 4.50 †KwR nq| G‡ÿ‡Î Pvwn`vi AvovAvwo w¯’wZ¯’vcKZv wbY©q Kiæb| G‡ÿ‡Î `ªe¨ `ywU
ci¯ú‡ii cwic~iK bv cwieZ©K? gšÍe¨ Kiæb|
`vg
Pvwn`vi cwigvb
wPÎ 8.1.1: GKK w¯’wZ¯’vcK
wP‡Î A‡ÿ Pvwn`vi cwigvY Ges A‡ÿ `v‡gi cwigvY wb‡`©wkZ| `ª‡e¨i `vg e„w× †c‡q ‡_‡K n‡j
`ª‡e¨i Pvwn`v †_‡K n«vm †c‡q nq| G‡ÿ‡Î `v‡gi cwieZ©b I Pvwn`vi cwieZ©b ci¯úi
mgvb nq| A_©vr | ZvB G‡ÿ‡Î Pvwn`vi w¯’wZ¯’vcK GKK n‡e|
D
P1
দাম`vg
P2
D
O Q1 Q2 X
Pvwn`vi cwigvb
চািহদার পিরমান
wPÎ 8.1.2: GKK A‡cÿv †ekx Pvwn`v w¯’wZ¯’vcKZv
GLv‡b `ª‡e¨i `vg n«v‡mi cwigvb A‡cÿv `ª‡e¨i Pvwn`v e„w×i cwigvY †ekx|
A_©vr
GLv‡b Pvwn`vi kZvswkK cwieZ©b `v‡gi kZvswkK cwieZ©b †_‡K †ekx nq| Pvwn`vi GKK w¯’wZ¯’vcKZvi
gvb me©`v 1 †_‡K †ekx nq| G‡K w¯’wZ¯’vcK Pvwn`vI ejv nq|
দাম
P2
`vg
D
O Q1 Q2 X
Pvwn`vi
চািহদার cwigvb
পিরমান
wPÎ 8.1.3: GKK A‡cÿv Kg w¯’wZ¯’vcKZv
GLv‡b `ª‡e¨i `v‡gi n«v‡mi cwigvb A‡cÿv Pvwn`vi e„w×i cwigvb Kg nq|
A_©vr | GLv‡b `v‡gi kZvswkK cwieZ©b Pvwn`vi kZvswkK cwieZ©b A‡cÿv †ekx nq| G‡ÿ‡Î
Pvwn`vi `vg w¯’wZ¯’vcKZv 1 Gi †_‡K Kg nq [EP < 1] |
P1
দাম`vg
P2
D
O Q X
Pvwn`vi cwigvY
চািহদার পিরমান
wPÎ 8.1.4: k~Y¨ w¯’wZ¯’vcKZv
wPÎ 8.1.4 G †`Lv hvq, `ª‡e¨i `vg †_‡K K‡g n‡jI `ª‡e¨i Pvwn`vi †Kvb cwieZ©b nqwb| A_©vr
Pvwn`vi cwigvb GKB _v‡K| A_©vr Pvwn`v w¯’i _v‡K| G‡K m¤ú~Y© Aw¯’wZ¯’vcK Pvwn`vI ejv nq| G‡ÿ‡Î
Pvwn`v w¯’wZ¯’vcK [EP = 0] k~Y¨ nq|
দাম
`vg
P D
O Q1 Q2 X
Pvwn`vi
চািহদার cwigvY
পিরমান
wPÎ 8.1.5 G †`Lv hvq, †Kvb `ª‡e¨i `vg w¯’i _vK‡jI Pvwn`vi n«vm-e„w× ev cwieZ©b N‡U| G‡ÿ‡Î
Pvwn`v †iLv f‚wg A‡ÿi mgvšÍivj| G‡K Avevi Pvwn`vi Amxg w¯’wZ¯’vcKZvI e‡j|
wkÿv_©xi KvR
Pvwn`vi w¯’wZ¯’vcKZvi gvb GK‡Ki †P‡q †ewk Ges GK‡Ki †P‡q Kg Pvwn`v †iLv AsKb Kiæb|
w¯’wZ¯’vcK Ges Aw¯’wZ¯’vcK Pvwn`vi g‡a¨ cv_©K¨ (Difference between elastic and Inelastic demand)
w¯’wZ¯’vcK I Aw¯’wZ¯’vcK Pvwn`vi g‡a¨ cv_©K¨mg~n wb‡¤œ †`qv n‡jv:
w¯’wZ¯’vcK Pvwn`v Aw¯’wZ¯’vcK Pvwn`v
1| `v‡gi cwieZ©‡bi nvi A‡cÿv Pvwn`vi cwieZ©‡bi 1| `v‡gi cwieZ©‡bi nvi A‡cÿv Pvwn`vi cwieZ©‡bi
nvi †ekx n‡j Zv‡K w¯’wZ¯’vcK Pvwn`v e‡j| nvi Kg n‡j Zv‡K Aw¯’wZ¯’vcK Pvwn`v e‡j|
2| w¯’wZ¯’vcK Pvwn`vi gvb GK‡Ki †_‡K †ekx nq 2&| Aw¯’wZ¯’vcK Pvwn`vi gvb GK‡Ki †_‡K Kg nq|
A_©vr EP 1 A_©vr EP 1
3| w¯’wZ¯’vcK Pvwn`v †iLvi †ÿ‡Î Pvwn`v †iLvi Xvj 3| Aw¯’wZ¯’vcK Pvwn`v †iLvi †ÿ‡Î Pvwn`v †iLvi Xvj
Kg e‡j Pvwn`v †iLv wKQzUv P¨vcUv AvK…wZi nq| GKUz †ekx e‡j Pvwn`v †iLv wKQzUv Lvov AvK…wZi nq|
4| w¯’wZ¯’vcK Pvwn`vi †ÿ‡Î `v‡gi cÖfve †ekx nq| 4| Aw¯’wZ¯’vcK Pvwn`vi †ÿ‡Î mvaviYZ: `v‡gi cÖfve
Kg nq|
5| mvaviYZ: wejvm I Avivg RvZxq `ª‡e¨i †ÿ‡Î 5| mvaviYZ: wbZ¨ cÖ‡qvRbxq `ª‡e¨i †ÿ‡Î Pvwn`v
Pvwn`v w¯’wZ¯’vcK nq| †hgb- Mvwo, wd«R, iwOb wUwf Aw¯’wZ¯’vcK nq| †hgb- Pvj, AvUv, wPwb BZ¨vw`|
BZ¨vw`|
6| w¯’wZ¯’vcK Pvwn`vi †ÿ‡Î `ª‡e¨i `vg evo‡j †gvU 6| Aw¯’wZ¯’vcK Pvwn`vi †ÿ‡Î `ª‡e¨i `vg evo‡j †gvU
e¨q n«vm cvq Ges `vg Kg‡j †gvU e¨q e„w× cvq| e¨q e„w× cvq Ges `vg Kg‡j †gvU e¨q n«vm cvq|
wkÿv_©xi KvR
w¯’wZ¯’vcK I Aw¯’wZ¯’vcK Pvwn`vi g‡a¨ cv_©K¨¸‡jv D‡jøL Kiæb|
wkÿv_©xi KvR
wb‡¤œi `ªe¨¸‡jvi Pvwn`v w¯’wZ¯’vcK D‡jøL Kiæb|
Pv, †mvbv, wn‡ivBb, Pvj, jeb, cvwb, Kjg, †gvUiMvox, iwOb wUwf|
mvims‡¶c
†Kvb A‡cÿ‡Ki ¯^vaxb Pj‡Ki cwieZ©‡bi d‡j Aaxb Pj‡Ki †h cwieZ©b N‡U Zvi cwieZ©‡bi
gvÎv‡K w¯’wZ¯’vcKZv e‡j| A_©bxwZ‡Z Pvwn`vi mv‡_ m¤úK©hy³ w¯’wZ¯’vcKZv n‡jv: Pvwn`vi `vg
w¯’wZ¯’vcKZv, Avq w¯’wZ¯’vcKZv, cwieZ©K I AvovAvwo w¯’wZ¯’vcKZv|
Pvwn`vi w¯’wZ¯’vcKZvi gvb GK‡Ki mgvb n‡j Zv‡K GKK w¯’wZ¯’vcKZv, GK‡Ki †_‡K Kg n‡j
Aw¯’wZ¯’vcKZv, GK‡Ki †ewk n‡j w¯’wZ¯’vcK, k~Y¨ n‡j k~Y¨ w¯’wZ¯’vcK Ges Amxg n‡j Amxg
w¯’wZ¯’vcKZv e‡j|
Avq w¯’wZ¯’vcKZvi gvb abvZœK n‡j Zv‡K mvaviY `ªe¨ Ges FYvZ¥K n‡j wbK…ó `ªe¨ e‡j|
AvovAvwo w¯’wZ¯’vcKZvi gvb abvZ¥K n‡j Zv‡K cwieZ©K Ges FYvZ¥K n‡j cwic~iK `ªe¨ e‡j
we‡ewPZ nq|
cv‡VvËi g~j¨vqb-8.1
eûwbe©vPwb cÖkœ
1| AvovAvwo w¯’wZ¯’vcKZvi m~Î †KvbwU?
Q P S P Q X PY Q Y
(K) . (L) . (M) . (N) .
P Q P S PY Q X Y Q
2| ‡Kvb `ª‡e¨i `v‡gi cwieZ©‡bi nvi hw` Pvwn`vi cwieZ©‡bi nvi A‡cÿv †ekx nq, Zv‡K wK e‡j?
(K) Aw¯’wZ¯’vcK Pvwn`v (L) w¯’wZ¯’vcK Pvwn`v (M) k~Y¨ w¯’wZ¯’vcK (N) Amxg w¯’wZ¯’vcK
3| †Kvb `ª‡e¨i `v‡gi cwieZ©‡bi d‡jI hw` Pvwn`vi †Kvb cwieZ©b bv nq Zv‡K wK e‡j?
(K) w¯’wZ¯’vcK Pvwn`v (L) Aw¯’wZ¯’vcK Pvwn`v
(M) Amxg Pvwn`v w¯’wZ¯’vcK (N) k~Y¨ w¯’wZ¯’vcK Pvwn`v
4| †Kvb `ª‡e¨i cÖwZ GK‡Ki `vg 20 UvKv ‡_‡K K‡g 16 UvKv n‡j †µZvi Pvwn`v 40 GKK †_‡K e„w× †c‡q 44
GKK nq| G‡ÿ‡Î `ª‡e¨i Pvwn`v n‡e-
(K) GKK w¯’wZ¯’vcK (L) Aw¯’wZ¯’vcK (M) w¯’wZ¯’vcK (N) k~Y¨ w¯’wZ¯’vcK
D‡Ïk¨
GB cvV †k‡l wkÿv_©xiv-
†hvMv‡bi w¯’wZ¯’vcKZv m¤ú‡K© aviYv w`‡Z cvi‡eb;
†hvMv‡bi w¯’wZ¯’vcKZvi cwigvc I cÖKvi‡f` eY©bv Ki‡Z cvi‡eb|
g~jcvV-
wkÿv_©xi KvR
†Kvb `ª‡e¨i evRvi `vg e„w× †c‡q 100 UvKv †_‡K 120 UvKv n‡jv| GgZve¯’vq H `ª‡e¨i †hvMvb e„w×
†c‡q 200 †KwR †_‡K 280 †KwR n‡j `ª‡e¨i †hvMvb w¯’wZ¯’vcK KZ?
P1
`ª‡েবর
S
O Q1 Q2 X
†hvMv‡bi cwigvY
যাগােনর পিরমান
S
P2
e¨i `vgদাম
P1
`ª‡েবর
O Q1 Q2 X
†hvMv‡bi cwigvY
যাগােনর পিরমান
wPÎ 8.2.2: GK‡Ki †P‡q †ekx w¯’wZ¯’vcKZv
P2
দাম
`ª‡e¨i `vg
P1
েবর
O Q1 Q2 X
†hvMv‡bi
যাগােনর cwigvY
পিরমান
wPÎ 8.2.3: GK‡Ki A‡cÿv Kg w¯’wZ¯’vcK
wPÎ 8.2.3 G †`Lv hvq, `v‡gi Av‡cwÿK cwieZ©b Δ †hvMv‡bi Av‡cwÿK cwieZ©b A‡cÿv †ekx|
A_©vr Δ | G‡ÿ‡Î †hvMv‡bi w¯’wZ¯’vcKZv GK‡Ki †P‡q Kg [Es < 1] n‡e| G‡ÿ‡Î `vg †h nv‡i
cwiewZ©Z nq, †hvMvb Zvi †P‡q Kg nv‡i cwiewZ©Z nq| Bnv‡K Aw¯’wZ¯’vcK †hvMvbI ejv nq|
(4) k~Y¨ w¯’wZ¯’vcKZv [ES = 0]
†Kvb `ª‡e¨i `v‡gi cwieZ©b n‡jI hw` †hvMv‡bi †Kvb cwieZ©b bv nq Z‡e Zv‡K k~Y¨ w¯’wZ¯’vcK e‡j| A_©vr
`v‡gi cwieZ©b n‡jI †hvMvb w¯’i _v‡K| Bnv‡K m¤ú~Y© Aw¯’wZ¯’vcK †hvMvbI ejv nq|
Y
S
P1
`vg
দাম
P2
S
O Q X
†hvMv‡bi
যাগােনর cwigvY
পিরমান
wPÎ 8.2.4: k~Y¨ w¯’wZ¯’vcKZv
wPÎ 8.2.4 G †`Lv hvq, `ª‡e¨i `vg n‡Z e„w× †c‡q n‡jI `ª‡e¨i †hvMv‡bi †Kvb cwieZ©b nq bv|
A_©vr †hvMvb w¯’i _v‡K| G‡ÿ‡Î †hvMvb †iLv `vg A‡ÿi mgvšÍivj n‡e Ges †hvMvb w¯’wZ¯’vcKZv k~Y¨ [Es
= 0] n‡e|
`vgদাম
P S
O Q1 Q2 X
†hvMv‡bi
যাগােনর cwigvY
পিরমান
wPÎ 8.2.5: Amxg w¯’wZ¯’vcK
wPÎ 8.2.5 G †`Lv hvq, `ª‡e¨i `v‡gi †Kvb cwieZ©b QvovB †hvMv‡bi cwieZ©b nq| `ª‡e¨i `vg ‡Z w¯’i
_vK‡jI `ª‡e¨i †hvMvb ‡_‡K e„w× †c‡q nq| G‡ÿ‡Î †hvMvb †iLv f‚wg A‡ÿi mgvšÍivj nq|
wkÿv_©xi KvR
av‡bi `vg cÖwZ †KwR 25 UvKv w¯’i _vKv m‡Ë¡I av‡bi ev¤úvi djb nIqvi Kvi‡Y av‡bi †hvMvb 50
gb †_‡K 70 gb n‡jv| G‡ÿ‡Î av‡bi †hvMvb †iLv AsKb K‡i †hvMvb w¯’wZ¯’vcKZv wbY©q Kiæb|
mgvavb
GLv‡b `ª‡e¨i cÖv_wgK `vg 10 UvKv
`v‡gi cwieZ©b Δ = 15 - 10 = 5 UvKv
cÖv_wgK †hvMv‡bi cwigvY 60GKK
‡hvMv‡bi cwigv‡Yi cwieZ©b 80 - 60 = 20 GKK
Q P 20 10 2
myZivs †hvMvb w¯’wZ¯’vcKZv, E S . 0.67
P Q 5 60 3
D`vniYt †Kvb `ª‡e¨i `vg 40 UvKv e„w× †c‡q 60 UvKv n‡j `ª‡e¨i †hvMvb e„w× †c‡q 100 GKK †_‡K 120 nq,
†hvMvb w¯’wZ¯’vcKZv KZ?
mgvavbt
`ª‡e¨i cÖv_wgK `vg, 40 UvKv
`v‡gi cwieZ©b, Δ = 60 - 40 = 20 UvKv
cÖv_wgK †hvMvb, 100 GKK
†hvMv‡bi cwigv‡Yi cwieZ©b 120 - 100 = 20 GKK
P 20
myZivs `v‡gi kZKiv cwieZ©b, 100 100 50%
P 40
Q 20
†hvMv‡bi kZKiv cwieZ©b, 100 100 20% =
Q 100
20% 2
†hvMvb w¯’wZ¯’vcKZv, E S 0.4
50% 5
mvims‡¶c
†Kvb `ª‡e¨i `v‡gi kZvswkK ev Av‡cwÿK cwieZ©‡bi d‡j †hvMv‡bi †h kZvswkK ev Av‡cwÿK
cwieZ©b nq Zvi AbycvZ‡K †hvMvb w¯’wZ¯’vcKZv e‡j| Bnv‡K ‡hvMv‡bi `vg w¯’wZ¯’vcKZvI e‡j|
†hvMv‡bi w¯’wZ¯’vcKZvi gvb GK‡Ki mgvb n‡j Zv‡K GKK w¯’wZ¯’vcKZv, GK‡Ki †_‡K Kg n‡j
Aw¯’wZ¯’vcKZv, GK‡Ki ‡_‡K †ewk n‡j w¯’wZ¯’vcKZv, k~Y¨ n‡j k~Y¨ w¯’wZ¯’vcKZv Ges Amxg n‡j
Amxg w¯’wZ¯’vcKZv e‡j|
†hvMv‡bi w¯’wZ¯’cKZv mvaviYZ: `yB fv‡e cwigvc Kiv nq| (1) MvwYwZK ev msL¨vMZ c×wZ I (2)
kZKiv c×wZ|
cv‡VvËi g~j¨vqb-8.2
eûwbe©vPwb cÖkœ
1| m¤ú~Y© w¯’wZ¯’vcK †hvMv‡bi †ÿ‡Î †Kvb `ª‡e¨i †hvMvb †iLvi AvK…wZ n‡e-
(K) evg †_‡K Wvb w`‡K DaŸ©Mvgx
(L) j¤^ A‡ÿi mgvšÍivj
(M) f‚wg A‡ÿi mgvšÍivj
(N) Wvb †_‡K evg w`‡K DaŸ©Mvgx
wb‡Pi DÏxcKwU jÿ¨ Kiæb Ges 2bs Ges 3bs cÖ‡kœi DËi w`b|
Y
S
P2
`vgদাম
b
P1 a
`ª‡e¨i
েবর
O Q1 Q2 X
†hvMv‡bi
যাগােনর cwigvY
পিরমান
2| wP‡Î SS †iLvwU †Kvb ai‡bi †hvMvb wb‡`©k K‡i-
(K) GKK A‡cÿv †ewk w¯’wZ¯’vcK (L) Aw¯’wZ¯’vcK
(M) k~Y¨ w¯’wZ¯’vcK (N) Amxg w¯’wZ¯’vcK
3| i. ‡hvMv‡bi cwieZ©b < `v‡gi cwieZ©b
ii. `v‡gi cwieZ©b = †hvMv‡bi cwieZ©b
iii. ‡hvMv‡bi cwieZ©b > `v‡gi cwieZ©b
wb‡Pi †KvbwU mwVK?
(K) i I ii (L) ii I iii (M) iii (N) i, ii I iii
P~ovšÍ g~j¨vqb
m„Rbkxj cÖkœ
5| iwng mv‡ne cÖwZgv‡m GKvwaKevi Pvj µq K‡ib| †KwR cÖwZ wewfbœ `v‡g Zvi Pvj µ‡qi Pvwn`v wb‡¤œ †`Iqv
n‡jv:
Pv‡ji cÖwZ †KwRi `vg (UvKvq) µ‡qi cwigvY (‡KwR)
30 25
35 20
40 15
4| Mwb wgqv GKRb `ÿ Avjy Pvlx| wZwb cÖwZ †KwR Avjy 10 UvKv `‡i 100 †KwR Avjy evRv‡i wewµ K‡ib|
evvRv‡i Avjyi `vg e„w× †c‡q 12 UvKv Ges 15 UvKv n‡j h_vµ‡g 200 †KwR I 250 †KwR Avjy evRv‡i
wewµ K‡ib|
(K) DÏxc‡Ki Z_¨wU †hvMvb wewa mg_©b K‡i?
(L) Avjyi `vg cÖwZ †KwR 10 UvKv †_‡K e„w× †c‡q 12 UvKv n‡j Avjyi †hvMvb w¯’wZ¯’vcKZv KZ
n‡e?
(M) fwel¨‡Z Avjyi `vg e„w×I m¤¢vebv _vKv m‡Z¡I Avjy wewµ m¤ú~Y© eÜ K‡i w`‡jb| GgZve¯’vq
Avjyi †hvMvb †iLvi w¯’wZ¯’vcKZv †Kgb n‡e?
(N) fwel¨‡Z Avjyi †Kvb `vg e„w×i m¤¢vebv †bB| GgZve¯’vq Avjyi †hvMvb ‡iLvi w¯’wZ¯’vcKZv
†Kgb n‡e?
5| wb‡¤œ Zviv wgqvi `ªe¨ †hvMvb m~wP †`qv n‡jvt
`vg cÖwZ GKK (UvKv) ‡hvMv‡bi cwigvY
100 200 GKK
150 400 GKK
200 600 GKK
250 800 GKK
(K) †hvMvb wewa wK?
(L) cÖ`Ë †hvMvb m~wPi wfwˇZ GKwU †hvMvb †iLv AsKb Kiæb|
(M) `ªe¨wUi †hvMvb w¯’wZ¯’vcKZv †ie Kiæb hLb `ªe¨wUi `vg 100 UvKv †_‡K e„w× †c‡q 200 UvKv nq|
(N) †hvMvb mgxKiYwU †ei Kiæb|
MvwYwZK D`vniY
Avgiv Rvwb,
QY PX - 20 10
Pvwn`vi AvovAvwo w¯’wZ¯’vcKZv, EC . 1 0
PX QY - 2 100
2| I `ywU ci¯úi m¤úwK©Z `ªe¨| `ª‡e¨i `vg 20 UvKv †_‡K K‡g 16 UvKv n‡j `ª‡e¨i Pvwn`v 200
GKK †_‡K e„w× †c‡q 220 GKK nq| AvovAvwo w¯’wZ¯’vcKZv †ei Kiæb| `ªe¨ `yÕwUi g‡a¨ wK ai‡Yi m¤úK©
we`¨gvb?
mgvavb:
GLv‡b,
`ª‡e¨i cÖv_wgK `vg, 20 UvKv
`ª‡e¨i cÖv_wgK Pvwn`v, 200 GKK
`ª‡e¨i `v‡gi cwieZ©b, Δ = 16 - 20 = - 4 UvKv
`ª‡e¨i Pvwn`vi cwieZ©b, Δ 220 - 200 = 20 GKK
Avgiv Rvwb,
Q A PB 20 20 2
Pvwn`vi AvovAvwo w¯’wZ¯’vcKZv, EC . 0.5
PB Q A - 4 200 2
GLv‡b Pvwn`vi AvovAvwo w¯’wZ¯’vcKZv n‡jv - 0.5 hv FYvZ¥K| myZivs `ªe¨ `ywU ci¯úi cwic~iK|
D`vniY:
GKwU `ª‡e¨i `vg 40 UvKv ‡_‡K K‡g 32 UvKv n‡j hw` Zvi Pvwn`v 40 GKK ‡_‡K †e‡o 96 GKK nq
Z‡e †m‡ÿ‡Î Pvwn`vi `vg w¯’wZ¯’vcKZv KZ? gšÍe¨ Kiæb|
GLv‡b,
`ª‡e¨i cÖv_wgK `vg, 40 UvKv
Avgiv Rvwb,
Q P 16 40
Pvwn`vi `vg w¯’wZ¯’vcKZv, E P . 1
P Q - 8 80
myZivs `ªe¨wUi GKK Pvwn`v w¯’wZ¯’vcK| KviY `ªe¨wUi Pvwn`v `vg w¯’wZ¯’vcKZv n‡jv - 1 |
D`vniY: †Kvb e¨w³i gvwmK Avq 5000 UvKv †_‡K e„w× †c‡q 8000 UvKv n‡jv| Gi d‡j Zvi `ª‡e¨i Pvwn`v
50 GKK †_‡K e„w× †c‡q 80 GKK n‡jv| `ª‡e¨i Avq w¯’wZ¯’vcKZv cwigvc Ki I `ª‡e¨i cÖK…wZi
Dci gšÍe¨ Kiæb|
mgvavb: GLv‡b,
cÖv_wgK Avq, 5000UvKv
cÖv_wgK Pvwn`v, 50 GKK
Av‡qi cwieZ©b, Δ = 8000 - 5000 = 3000 UvKv
Pvwn`vi cwieZ©b, Δ 80 - 50 = 30 GKK
Avgiv Rvwb,
Q Y 30 5000
Pvwn`vi Avq w¯’wZ¯’vcKZv, EY . 1
Y Q 3000 50
DËigvjv
cvV 8.1: 1| M 2| K 3| N 4| L 5| K 6| L
7| M 8| M 9| M 10| M 11| K 12| L
cvV 8.2: 1| M 2| K 3| M