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aupBogqw sMquln
(CONSUMER’s EQUILIBRIUM)
pySkrqw;
bldyv isMG
lYkcrwr ieknwimks
s.s.s.s.huiSAwrpur
swihbzwdw AjIq isMG ngr[
1
aupBogqw dy sMquln dw ArQ
sImq Awmdn, v`D qoN v`D sMquStI,
siQqI nMU nw bdlxw[
pirBwSw;
“ie`k aupBogqw aus smyN sMquln iv`c huMdw hY jdoN
auh AwpxI Awmdn Aqy bwzwr kImqW qo pRwpq
sMquStI nMU AiDkqm kr lYNdw hY”[
sYimaUlsn(Samuleson)
do mu`K ivcwrDwrwvW ;
(A)quStIgux ivSlySx (Utility Analysis)
(B) audwsIn vkr ivSlySx (Indifference Curve Analysis)
2
(A)aupBogI dy sMquln dw quStIgux
ivSlySx
(Utility Analysis of Consumer’s Equilibrium)
quStIgux /aupXoigqw dw ArQ;
vsqU jW syvw dw auh gux, ijhVw aupBogI dI
loV nMU sMquSt krn dI SkqI r`Kdw [
“quStIgux iksy vsqU dI auh SkqI hY jo loVW dI
sMquStI krdI hY”[ ihbfn
“quStIgux auh sMquStI hY ijs nMU koeI
ivAkqI aupBog dy PlsrUp pRwpq krdw hY”[
ilpsI
3
iPSr ny quStIgux dy mwp dI iekweI vjoN
Xuitl (Util) Sbd dw pRXog kIqw[
4
quStIgux dIAW
iksmW
sImWq
quStIgux
ku`l
quStIgux
sImWq quStIgux (Marginal Utility)
iksy vsqU dI ie`k hor iekweI dy aupBog
nwl ku`l quStIgux iv`c jo pirvrqn AwauNdw
hY [
∆TU
sImWq quStIgux = -----
∆Q
sImWq quStIgux= TUn - TUn-1
(i)Dnwqmk (ii) isPr(iii) irxwqmk
5
ku`l quStIgux (Total Utility)
iksy vsqU dIAW swrIAW iekweIAW qoN imlx
vwly quStIgux dw joV [
ku`l quStIgux= TU =
MU1st+ MU2nd+ MU3rd+ MU4th+ MU5th
6
mwnqwvW (Asumptions)
1. ivcwrSIl aupBogqw (Rational consumer)
2.igxqIvwck aupXoigqw (Cardinal Utility)
3.suqMqr aupXoigqw (Independent Utility)
4.mudrw dI sImWq aupXoigqw siQr hY[
5.rucIAW siQr[
6.kImq Aqy Awmdn siQr[
7.pUrn igAwn[
8.vsqUAW vMfxSIl [
7
8
ku`l quStIgux Aqy sImWq quStIgux
iv`c sbMD
nvpRMprwvwdI ArQSwsqrI jYvns(Jevnos)ny
ivAwiKAw kIqI[
ku`l quStIgux iksy vsqU dIAW iviBMn iekweIAW
qoN pRwpq sImWq quStIgux dw joV ;
TU= ∑MU
ku`l quStIgux= TU5th =
MU1st+ MU2nd+ MU3rd+ MU4th+ MU5th
9
mwqrw ku`l
quStIgux
sImWq
quuStIguxW
vrxn
0 0 0
Dnwqmk
1 8 8-0 = 8
2 14 14-8 = 6
3 18 18-14 = 4
4 20 20-18 = 2
5 20 20- 20 = 0 isPr
6 18 18-20 = - 2 irxwqmk
ku`l quStIgux Aqy sImWq quStIgux iv`c sbMD
10
8
14
18
20
Utility
1 2 3 4 5
Quantity
F G
TU
Y
XO
6
TOTAL UTILITY
11
2
4
6
8
Utility
1 2 3 4 5
Quantity
M
Y
XO
-2
6
U
Marginal Utility
Zero
+ve
- ve
12
8
14
18
20
Utility
1 2 3 4 5
Quantity
G
TU
Y
A
O
6
F
Quantity
Utility
MU
2
4
6
8
O
1 2 3 4 5 6
-2
X
X
B
mwqrw ku`l
quStI
gux
sImWq
quuStIguxW
vrxn
0 0 0
Dnwqm
k
1 8 8-0 = 8
2 14 14-8 = 6
3 18 18-14 = 4
4 20 20-18 = 2
5 20 20- 20 = 0 isPr
6 18 18-20 = - 2 irxwqm
k
ku`l quStIgux (TU) Aqy sImWq quStIgux
(MU) iv`c sbMD
(i)jdoN MU G`tdI hY qW TU G`tdI dr qy v`DdI hY[
(ii)jdoN MU isPr huMdI hY qW TU AiDkqm huMdI hY[
(iii)jdoN MU irxwqmk huMdI hY qW TU G`txw SurU
krdI hY[
do inXm;
(i) G`tdy sImWq quStIgux dw inXm
(Law of Diminishing Marginal Utility)
(ii) sm-sImWq quStIgux dw inXm
(Law of Equi-Marginal Utility)
13
14
(A) G`tdy sImWq quStIgux dw inXm
(Law of Diminishing Marginal Utility)
gosn dw pihlw inXm
lgwqwr iekweIAW dw aupBog krn nwl
hryk vwDU iekweI qoN pRwpq quStIgux G`tdw
jWdw hY[
aupBogI aunIAW iekweIAW KrIddw jdoN
vsqU dI sImWq iekweI dw quStIgux, kImq
dy brwbr huMdw hY[
MU= Price
ieQy sMquln iv`c Aqy sMqStI AiDkqm huMdI
15
(B) sm-sImWq quStIgux dw inXm
(Law of Equi- Marginal Utility)
jy aupBogI v`D qoN v`D sMquStI pRwpq krnw
cwhuMdw hY ,auh AwpxI mudrw nMU v`KrIAW
vsqW qy ies qrHW Krc krnw cwhIdw hY ik
hr vsqu qy mudrw-Krc dw sImWq quStIgux
brwbr hovy[
 v`D qoN v`D sMquStI dw inXm[
 pRqIsQwpn dw inXm[
( Law of Substitution)
16
G`tdy sImWq quStIgux dw inXm dI mh`qqw
(Significance of Law of Diminishing Marginal Utility)
(i) aupBog dy inXmW dw AwDwr; mMg dw inXm,
sm-sImWq aupXoigqw Aqy aupBogqw vwDw
(Consumer surplus)[
(ii) aupBog Aqy auqpwdn iv`c iviBMnqw;
auqpwdk vsqUAW dy ifzweIn, gux pYikMg iv`c
pirvrqn leI mzbUr huMdy[
(iii) kr dw AwDwr; Awmdn vwDy nwl AmIrW
iv`c Dn dI sImWq aupXoigqw Gtx lgdI [
17
G`tdy sImWq quStIgux dw inXm dI mh`qqw
(Significance of Law of Diminishing Marginal Utility)
(iv)smwjvwd dw AwDwr; AmIr lokW pwsoN Dn
grIb lokW pws pirvrqn krn dw suJwA[
(v)mu`l inrDwrx; jy auqpwdk AiDk vsqUAW
vycxw cwhuMdw qW kImq G`t krnI pvygI[
(vi)aupBogqw leI mh`qv: auh ie`k hI vsqU qy
AiDk Krc nhIN krdw[
(vii)aupXoigqw mu`l Aqy vtWdrw mu`l iv`c
AMqr; pwxI qy hIry dw AMqr[
aupBogqw dy sMquln dw inrDwrx
(i)ie`k vsqU nwl (Single Commodity Case)
(ii) do vsqUAW nwl (Two Commodity Case)
(i)ie`k vsqU nwl ;
KrIdx leI kImq Adw krnI ,
iqAwg bdly kuJ aupXoigqw pRwpq
G`tdI sImWq aupXoigqw inXm Anuswr hryk
vwDU iekweI dy aupBog qoN pRwpq hox vwlI sMquStI
G`tdI jWdI hY[
pr mudrw dI aupXoigqw siQr rihMdI hY[
18
aupBogqw dy sMquln dw inrDwrx
isAwxw aupBogI vsqU dw aupBog aus sImw
q`k vDweygw, ijQy
AwKrI iekweI qoN pRwpq sImWq aupXoigqw,
mudrw(kImq) dI sImWq aupXoigqw dy brwbr hovy[
ieh sMquln dI AvsQw hovygI[
MU= Price
19
aupBogqw dy sMquln dw inrDwrx
20
vsqU A
dIAW
iekweIAW
vsqU A
qoN pRwpq
quStIgux
Adw kIqI
kImq vjoN
iqAwgI
aupXoigqw
quStIgux pRwpqI -
iqAwgI aupXoigqw
iv`c AMqr
1 50 20 +30
2 40 20 +20
3 30 20 +10
4 20
(MUA)
20
=(PA)
0
5 10 20 -10
21
10
20
30
50Utility
1 2 3 4 5
Quantity A
Y
XO 6
40
U
P
MU=Price
E
M
aupBogqw dy sMquln dw inrDwrx
(ii) do vsqU nwl (Two Commodity Case)
 sImq Awmdn nMU ie`k qoN v`D vsqW qy Krc
krdw hY[
do vsqW qoN pRwpq sImWq aupXoigqw dI qulnw
krdw hY[
aus qy Krc krdw jo v`D aupXoigqw idMdI hY[
sm-sImWq quStIgux dy inXm Anuswr sMquln
iv`c hovygw jdoN dohW vsqW qoN pRwpq sImWq
quStIgux brwbr hovygw[ 22
aupBogqw dy sMquln dw inrDwrx
(ii) do vsqU nwl (Two Commodity Case)
G`tdI sImWq aupXoigqw dy inXm Anuswr AiDk
mwqrw iv`c vsqU dw aupBog krn nwl sImWq
aupXoigqw G`tdI jWdI hyY [
aupBogqw vsqU dI KrId bMd kr idMdw hyY jdoN
dUjI vsqU qoN sImWq aupXogqw G`t ho jWdI hY[
 G`t sImWq aupXoigqw vwlI dI QW v`D sImWq
aupXoigqw vwlI vsqU dw pRqIsQwpn krdw hY[
23
aupBogqw dy sMquln dw inrDwrx
24
Krc kIqy
rupey
vsqU A qoN
pRwpq sImWq
quStIgux
MUA
vsqU B
qoN pRwpq sImWq
quStIgux
MUB
1 14 12
2 12 10
3 10 8
4 8 6
5 6 4
25
1 2 4 5
Commodity
A
UtilityMU
2
4
6
8
O12345 X
Commodity
B
14
10
12
3
M U of
A M U of
B
K
J ME H
F
G
L
X1
vsqU A dI sImWq aupXoigqw= vsqU B dI
sImWq aupXoigqw =10 iekweI
MUA = MUB = 10 Units
MUA = MUB = MU of Money
MUA MUB
---- = ----- = MU of Money
PA PB
26
pRIiKAw dy nzrIey qoN pRSn
Q 1.ku`l aupXoigqw iks nMU ikhw jWdw hY?
Q 2.sImWq aupXoigqw iks nMU ikhw jWdw hY?
Q 3.ku`l aupXoigqw Aqy sImWq aupXoigqw iv`c
sbMD dw vrnx kro[
Q4.aupBogqw dy sMquln qoN kI Bwv hY?
Q5.ie`k vsqU dy sbMD iv`c aupBogqw dy sMquln dI
ivAwiKAw kro[
Q6.do vsqW dy sbMD iv`c aupBogqw dy sMquln dI
ivAwiKAw kro[
Q7.G`tdI sImWq aupXoigqw dy inXm dI
ivAwiKAw kro[
27
pRIiKAw dy nzrIey qoN pRSn
28
vrqIAW
iekweIAW
ku`l
aupXoigqw
sImWq
aupXoigqw
0 0
1 10
2 25
3 38
4 48
5 55
Q8.rwkyS dI
ku`l aupXoigqw
sUcI hyTW id`qI
geI hY[aus dI
sImWq aupBogqw
pqw kro[
pRIiKAw dy nzrIey qoN pRSn
au`qr;
29
vrqIAW
iekweIAW
ku`l aupXogqw sImWq aupXogqw
0 0 0
1 10 10-0= 10
2 25 25-10= 15
3 38 38-25= 13
4 48 48-38= 10
5 55 55-48= 7
DMnvwd
pySkS ; bldyv isMG
lYkcrwr ieknwimks
s.s.s.s. huiSAwrpur
swihbzwdw AjIq isMG ngr[
84270-04513
30

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L 3 Consumer's behaviour

  • 1. aupBogqw sMquln (CONSUMER’s EQUILIBRIUM) pySkrqw; bldyv isMG lYkcrwr ieknwimks s.s.s.s.huiSAwrpur swihbzwdw AjIq isMG ngr[ 1
  • 2. aupBogqw dy sMquln dw ArQ sImq Awmdn, v`D qoN v`D sMquStI, siQqI nMU nw bdlxw[ pirBwSw; “ie`k aupBogqw aus smyN sMquln iv`c huMdw hY jdoN auh AwpxI Awmdn Aqy bwzwr kImqW qo pRwpq sMquStI nMU AiDkqm kr lYNdw hY”[ sYimaUlsn(Samuleson) do mu`K ivcwrDwrwvW ; (A)quStIgux ivSlySx (Utility Analysis) (B) audwsIn vkr ivSlySx (Indifference Curve Analysis) 2
  • 3. (A)aupBogI dy sMquln dw quStIgux ivSlySx (Utility Analysis of Consumer’s Equilibrium) quStIgux /aupXoigqw dw ArQ; vsqU jW syvw dw auh gux, ijhVw aupBogI dI loV nMU sMquSt krn dI SkqI r`Kdw [ “quStIgux iksy vsqU dI auh SkqI hY jo loVW dI sMquStI krdI hY”[ ihbfn “quStIgux auh sMquStI hY ijs nMU koeI ivAkqI aupBog dy PlsrUp pRwpq krdw hY”[ ilpsI 3
  • 4. iPSr ny quStIgux dy mwp dI iekweI vjoN Xuitl (Util) Sbd dw pRXog kIqw[ 4 quStIgux dIAW iksmW sImWq quStIgux ku`l quStIgux
  • 5. sImWq quStIgux (Marginal Utility) iksy vsqU dI ie`k hor iekweI dy aupBog nwl ku`l quStIgux iv`c jo pirvrqn AwauNdw hY [ ∆TU sImWq quStIgux = ----- ∆Q sImWq quStIgux= TUn - TUn-1 (i)Dnwqmk (ii) isPr(iii) irxwqmk 5
  • 6. ku`l quStIgux (Total Utility) iksy vsqU dIAW swrIAW iekweIAW qoN imlx vwly quStIgux dw joV [ ku`l quStIgux= TU = MU1st+ MU2nd+ MU3rd+ MU4th+ MU5th 6
  • 7. mwnqwvW (Asumptions) 1. ivcwrSIl aupBogqw (Rational consumer) 2.igxqIvwck aupXoigqw (Cardinal Utility) 3.suqMqr aupXoigqw (Independent Utility) 4.mudrw dI sImWq aupXoigqw siQr hY[ 5.rucIAW siQr[ 6.kImq Aqy Awmdn siQr[ 7.pUrn igAwn[ 8.vsqUAW vMfxSIl [ 7
  • 8. 8 ku`l quStIgux Aqy sImWq quStIgux iv`c sbMD nvpRMprwvwdI ArQSwsqrI jYvns(Jevnos)ny ivAwiKAw kIqI[ ku`l quStIgux iksy vsqU dIAW iviBMn iekweIAW qoN pRwpq sImWq quStIgux dw joV ; TU= ∑MU ku`l quStIgux= TU5th = MU1st+ MU2nd+ MU3rd+ MU4th+ MU5th
  • 9. 9 mwqrw ku`l quStIgux sImWq quuStIguxW vrxn 0 0 0 Dnwqmk 1 8 8-0 = 8 2 14 14-8 = 6 3 18 18-14 = 4 4 20 20-18 = 2 5 20 20- 20 = 0 isPr 6 18 18-20 = - 2 irxwqmk ku`l quStIgux Aqy sImWq quStIgux iv`c sbMD
  • 10. 10 8 14 18 20 Utility 1 2 3 4 5 Quantity F G TU Y XO 6 TOTAL UTILITY
  • 11. 11 2 4 6 8 Utility 1 2 3 4 5 Quantity M Y XO -2 6 U Marginal Utility Zero +ve - ve
  • 12. 12 8 14 18 20 Utility 1 2 3 4 5 Quantity G TU Y A O 6 F Quantity Utility MU 2 4 6 8 O 1 2 3 4 5 6 -2 X X B mwqrw ku`l quStI gux sImWq quuStIguxW vrxn 0 0 0 Dnwqm k 1 8 8-0 = 8 2 14 14-8 = 6 3 18 18-14 = 4 4 20 20-18 = 2 5 20 20- 20 = 0 isPr 6 18 18-20 = - 2 irxwqm k
  • 13. ku`l quStIgux (TU) Aqy sImWq quStIgux (MU) iv`c sbMD (i)jdoN MU G`tdI hY qW TU G`tdI dr qy v`DdI hY[ (ii)jdoN MU isPr huMdI hY qW TU AiDkqm huMdI hY[ (iii)jdoN MU irxwqmk huMdI hY qW TU G`txw SurU krdI hY[ do inXm; (i) G`tdy sImWq quStIgux dw inXm (Law of Diminishing Marginal Utility) (ii) sm-sImWq quStIgux dw inXm (Law of Equi-Marginal Utility) 13
  • 14. 14 (A) G`tdy sImWq quStIgux dw inXm (Law of Diminishing Marginal Utility) gosn dw pihlw inXm lgwqwr iekweIAW dw aupBog krn nwl hryk vwDU iekweI qoN pRwpq quStIgux G`tdw jWdw hY[ aupBogI aunIAW iekweIAW KrIddw jdoN vsqU dI sImWq iekweI dw quStIgux, kImq dy brwbr huMdw hY[ MU= Price ieQy sMquln iv`c Aqy sMqStI AiDkqm huMdI
  • 15. 15 (B) sm-sImWq quStIgux dw inXm (Law of Equi- Marginal Utility) jy aupBogI v`D qoN v`D sMquStI pRwpq krnw cwhuMdw hY ,auh AwpxI mudrw nMU v`KrIAW vsqW qy ies qrHW Krc krnw cwhIdw hY ik hr vsqu qy mudrw-Krc dw sImWq quStIgux brwbr hovy[  v`D qoN v`D sMquStI dw inXm[  pRqIsQwpn dw inXm[ ( Law of Substitution)
  • 16. 16 G`tdy sImWq quStIgux dw inXm dI mh`qqw (Significance of Law of Diminishing Marginal Utility) (i) aupBog dy inXmW dw AwDwr; mMg dw inXm, sm-sImWq aupXoigqw Aqy aupBogqw vwDw (Consumer surplus)[ (ii) aupBog Aqy auqpwdn iv`c iviBMnqw; auqpwdk vsqUAW dy ifzweIn, gux pYikMg iv`c pirvrqn leI mzbUr huMdy[ (iii) kr dw AwDwr; Awmdn vwDy nwl AmIrW iv`c Dn dI sImWq aupXoigqw Gtx lgdI [
  • 17. 17 G`tdy sImWq quStIgux dw inXm dI mh`qqw (Significance of Law of Diminishing Marginal Utility) (iv)smwjvwd dw AwDwr; AmIr lokW pwsoN Dn grIb lokW pws pirvrqn krn dw suJwA[ (v)mu`l inrDwrx; jy auqpwdk AiDk vsqUAW vycxw cwhuMdw qW kImq G`t krnI pvygI[ (vi)aupBogqw leI mh`qv: auh ie`k hI vsqU qy AiDk Krc nhIN krdw[ (vii)aupXoigqw mu`l Aqy vtWdrw mu`l iv`c AMqr; pwxI qy hIry dw AMqr[
  • 18. aupBogqw dy sMquln dw inrDwrx (i)ie`k vsqU nwl (Single Commodity Case) (ii) do vsqUAW nwl (Two Commodity Case) (i)ie`k vsqU nwl ; KrIdx leI kImq Adw krnI , iqAwg bdly kuJ aupXoigqw pRwpq G`tdI sImWq aupXoigqw inXm Anuswr hryk vwDU iekweI dy aupBog qoN pRwpq hox vwlI sMquStI G`tdI jWdI hY[ pr mudrw dI aupXoigqw siQr rihMdI hY[ 18
  • 19. aupBogqw dy sMquln dw inrDwrx isAwxw aupBogI vsqU dw aupBog aus sImw q`k vDweygw, ijQy AwKrI iekweI qoN pRwpq sImWq aupXoigqw, mudrw(kImq) dI sImWq aupXoigqw dy brwbr hovy[ ieh sMquln dI AvsQw hovygI[ MU= Price 19
  • 20. aupBogqw dy sMquln dw inrDwrx 20 vsqU A dIAW iekweIAW vsqU A qoN pRwpq quStIgux Adw kIqI kImq vjoN iqAwgI aupXoigqw quStIgux pRwpqI - iqAwgI aupXoigqw iv`c AMqr 1 50 20 +30 2 40 20 +20 3 30 20 +10 4 20 (MUA) 20 =(PA) 0 5 10 20 -10
  • 21. 21 10 20 30 50Utility 1 2 3 4 5 Quantity A Y XO 6 40 U P MU=Price E M
  • 22. aupBogqw dy sMquln dw inrDwrx (ii) do vsqU nwl (Two Commodity Case)  sImq Awmdn nMU ie`k qoN v`D vsqW qy Krc krdw hY[ do vsqW qoN pRwpq sImWq aupXoigqw dI qulnw krdw hY[ aus qy Krc krdw jo v`D aupXoigqw idMdI hY[ sm-sImWq quStIgux dy inXm Anuswr sMquln iv`c hovygw jdoN dohW vsqW qoN pRwpq sImWq quStIgux brwbr hovygw[ 22
  • 23. aupBogqw dy sMquln dw inrDwrx (ii) do vsqU nwl (Two Commodity Case) G`tdI sImWq aupXoigqw dy inXm Anuswr AiDk mwqrw iv`c vsqU dw aupBog krn nwl sImWq aupXoigqw G`tdI jWdI hyY [ aupBogqw vsqU dI KrId bMd kr idMdw hyY jdoN dUjI vsqU qoN sImWq aupXogqw G`t ho jWdI hY[  G`t sImWq aupXoigqw vwlI dI QW v`D sImWq aupXoigqw vwlI vsqU dw pRqIsQwpn krdw hY[ 23
  • 24. aupBogqw dy sMquln dw inrDwrx 24 Krc kIqy rupey vsqU A qoN pRwpq sImWq quStIgux MUA vsqU B qoN pRwpq sImWq quStIgux MUB 1 14 12 2 12 10 3 10 8 4 8 6 5 6 4
  • 25. 25 1 2 4 5 Commodity A UtilityMU 2 4 6 8 O12345 X Commodity B 14 10 12 3 M U of A M U of B K J ME H F G L X1
  • 26. vsqU A dI sImWq aupXoigqw= vsqU B dI sImWq aupXoigqw =10 iekweI MUA = MUB = 10 Units MUA = MUB = MU of Money MUA MUB ---- = ----- = MU of Money PA PB 26
  • 27. pRIiKAw dy nzrIey qoN pRSn Q 1.ku`l aupXoigqw iks nMU ikhw jWdw hY? Q 2.sImWq aupXoigqw iks nMU ikhw jWdw hY? Q 3.ku`l aupXoigqw Aqy sImWq aupXoigqw iv`c sbMD dw vrnx kro[ Q4.aupBogqw dy sMquln qoN kI Bwv hY? Q5.ie`k vsqU dy sbMD iv`c aupBogqw dy sMquln dI ivAwiKAw kro[ Q6.do vsqW dy sbMD iv`c aupBogqw dy sMquln dI ivAwiKAw kro[ Q7.G`tdI sImWq aupXoigqw dy inXm dI ivAwiKAw kro[ 27
  • 28. pRIiKAw dy nzrIey qoN pRSn 28 vrqIAW iekweIAW ku`l aupXoigqw sImWq aupXoigqw 0 0 1 10 2 25 3 38 4 48 5 55 Q8.rwkyS dI ku`l aupXoigqw sUcI hyTW id`qI geI hY[aus dI sImWq aupBogqw pqw kro[
  • 29. pRIiKAw dy nzrIey qoN pRSn au`qr; 29 vrqIAW iekweIAW ku`l aupXogqw sImWq aupXogqw 0 0 0 1 10 10-0= 10 2 25 25-10= 15 3 38 38-25= 13 4 48 48-38= 10 5 55 55-48= 7
  • 30. DMnvwd pySkS ; bldyv isMG lYkcrwr ieknwimks s.s.s.s. huiSAwrpur swihbzwdw AjIq isMG ngr[ 84270-04513 30