100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Solution Manual for Foundations of Mathematical Economics By Michael Carter A+ verified, ISBN: 978-0262531924 $18.99   Add to cart

Exam (elaborations)

Solution Manual for Foundations of Mathematical Economics By Michael Carter A+ verified, ISBN: 978-0262531924

 5 views  0 purchase
  • Course
  • Foundations of Mathematical Economics
  • Institution
  • Foundations Of Mathematical Economics

Solution Manual for Foundations of Mathematical Economics By Michael Carter A+ verified, ISBN: 978-0262531924 Solution Manual for Foundations of Mathematical Economics By Michael Carter A+ verified, ISBN: 978-0262531924 Solution Manual for Foundations of Mathematical Economics By Michael Carte...

[Show more]

Preview 10 out of 265  pages

  • October 16, 2024
  • 265
  • 2024/2025
  • Exam (elaborations)
  • Questions & answers
  • solution manual
book image

Book Title:

Author(s):

  • Edition:
  • ISBN:
  • Edition:
  • Foundations of Mathematical Economics
  • Foundations of Mathematical Economics
avatar-seller
lectmaggie
012345160896392
  



!"




,2345689 6 



36











!"
#

$
%
&'"
36(
)*"
)*"
+

""")*"
,"*"*)*"
)-$"./"
#
360
1
)*"
$
"
"%
)*"
2%%)*"

)*"'
3'
)*"



"

4#"%
56*"76*'
,"8-)*"
9"#"+"*)*"

"./"
#

,12345679





!

"#
$
$$#!
!% !

% $& !'(
) 

* +
1234567,
-./
0

1
./
'(!%) 
0(!%) 
12345672
) 
3'!3 
./4
!
'(!# 4
!
5$
0

$% #!
6!0


 

,


9  







!"#$
1%
&$
'("))!
*+,-./0#12
13
45("605"78(9":;./0#12
1:
45("605"78(9"3;<07=03
:
>4/0
?#0='(0519>0(4@0050@079(;
*+A-.B4@?50("CD7'90(09(4#0
EF 9>050990#("C9>045?>4609GHIHJH
HK!
EF 9>0(09"C="7(L@0#('7470="7"@1
EF 9>0(09"C8"")('7470="7"@1
EF 9>0(09"C?5410#('74
84@0;.B4@?50("CMNDNMOP(09(4#0
EF 9>0#0457L@60#(Q
EF 9>0749L#457L@60#(R
EF 9>0(09"C455?"(('650="5"#(
EF 9>0(09"C?"(('650?#'=0("C="??0#"79>0S"#5)@4#T09
EF 9>0(09"C?"(('65090@?0#49L#0("C5'UL')S490#;
VW
X
Y


Z


[!H\
XY
Z
[!;
*+]-^>0?5410#(09'(%
X_0771
J>#'(!;^>0'#4=9'"7(?4=0(4#0
3`
Xa"=T
b='(("#(
c4?0#! `
X_0771
J>#'(
*+d-^>0(09"C?5410#('(%
X3
Y 
$
; 4^>0(9#49081(?4=0"C04=>?5410#'(9>0(09
"CC04('650"L9?L9(
3`
Xe`
1Qf&e`
gh`
!
S>0#0e`

'(9>0"L9?L9"C)4@`;
*+i-^>0?5410#(09'(%
X
Y

!;^>0#04#0Y
Xj="45'9'"7(H74@051
kl%
mXn
!
Y!

!

Y!


!
Y

!

Y

!!
^>0#04#0Y ="45'9'"7('74907?5410#84@0;
o
psG((L@09>s492

1lW
qr
ms;^>s49'(s2

1t

W
qr
;^>'('@?5'0s(2

s1t

W

47)2

1t

r
H"#2

1sW
47)2
1rs
;J"7(0UL07951H2
1W
ur
;J"7/0#(051H4((L@02
1W
ur
;^>'('@?5'0(9>492
1
W

47)2
1r
;J"7(0UL079512
1t

W

s47)2
1t

r

47)9>0#0C"#0
21t
W
qr
;^>'('@?5'0(9>492
1lW
qr
m;^>0"9>0#')079'91'(?#"/0)('@'54#51;
v
7W
X%

W1w
5W
X n
W1w



, 01344567189 9 
7



!"#
$%
&$#
$

' 7(8 )*
4
564
4 5
4
4
4
4
4
574
4 5 4 5
4
4
4
4
4
4
89:;<=47>7?4@A=4<=5BCD9EF4G4
H5IJKL4?4564M4K64N474O4
4 PQPRS@A=4TCUVB=4TVCW=4EX4C4T9F:B=4WE9F4DETT49T4YI+JZ,J>4@A-=,4T=D4EX4VETT9[B=4E;DWEU=T49F4DA<==4
DETT=T49T4DA=4V<E\;WD4
GYIJZJO]4GYIJZJO]4GYIJZJO4N4HYIJY./IJYLIJHYIJYIJZJLIJHYIJZJIJYLIJ
4


HYIJZJIJZJLIJHZIJYIJYLIJHZIJYIJZJLIJHZIJZIJYLIJHZIJZIJZJL4 ‘/
44
^4D_V9WCB4E;DWEU=49T4DA=4T=`;=FW=4HYIJYIJZJL4EX4DaE4A=C\T4XEBBEa=\4[_4C4DC9B>4
PQPPS
bJc4d0eJN4GRO4
aA=<=4RSN4HfIJfIgggJIJfL49T4DA=4V<E\;WD9EF4VBCF4;T9F:4FE49FV;DT4CF\4V<E\;W9F:4FE4E;DV;DT>4@E4
T==4DA9Th4i<TD4FED=4DACD4ReJS9T4C4X=CT9[B=4V<E\;WD9EF4VBCF>4@A=<=XE<=h4RS14bJ>4^BTEh4
RS14deJ0CF\4DA=<=XE<=4RS14bJc4d >4 0
@E4TAEa4DACD4DA=<=49T4FE4EDA=<4X=CT9[B=4V<E\;WD9EF4VBCF49F44444eJ2, h4a=4CTT;U=4DA=4WEFD<C<_>4@ACD4
9Th4a=4CTT;U=4DA=<=49T4TEU=4X=CT9[B=4V<E\;WD9EF4VBCF4jSSSSSSSS0e1,2,3, JJJJJJRS+,-,
S>44@A9T49UVB9=T4DA=4
=k9TD=FW=4EX4C4VBCF4V<E\;W9F:4C4VET9D9l=4E;DV;D4a9DA4FE49FV;0 DT>4@A9T4D=WAFEBE:9WCB4
9FX=CT9[B=h4TE4DACD4KJ1mJbJ>4
PQPnS 7>44o=D44pS14qJHKL>44@A9T449UVB9=T44DACD44HKIJrpL414bJ>44o=D44ps4t4p>44@A=F44HKIJrpsL4u4
HKIJrpL4CF\4X<==4\9TVETC[9B9D_49UVB9=T44DACD4HKIJrpsL414bJ>4@A=<=XE<=4ps414qJHKL>4
6>44^:C9F44CTT;U=44pSSs14qJHKL>4444@A9T449UVB9=T44DACD44HKIsJrpL4414 bJ>4444v_44X<==44\9TVETCBh4HKsIJ
rpL414bJJXE<4=l=<_4K4u4Kh4aA9WA49UVB9=T44DACD4pS14qJHKL>44qJHKsL4w4qJHKL>4
xyxz{@A=4\EUC9F4EX4|}~49T4G7IJ6O4N4JCF\4DA=4<CF:=49T4G6IJ€O44bJ>4
xyx‚{89:;<=47>7>4
xyxƒ{@A=4<=BCD9EF4|„4TD<9WDB_4A9:A=<4†‡ˆ‰~49T4D<CFT9D9l=h4CFD9T_UU=D<9W4CF\4CT_UU=D<9W>4ŠD49T4
FED4WEUVB=D=h4‹ŒŒŽ„Œ4E<4T_UU=D<9W>4




 3

, 01344567189 9 
7



!"#
$%
&$#
$

' 7(8 )*
3
4546789:3;<==<>?@A3BCD=:3=?EBE3B9:?F3F:EG:HB?I:3GF<G:FB?:EJ3
KL N3 M33 M
OBFPCQ@PER?BS?TIP:33 U3 3
M M33M3
EVWW:BF?H3 U3 M 3M33M3
CCE@VB?WW:
XEVWW: BF?H3BF?H3 M33U3 M3UM3
H<WG=:B:3 M3M3U3
Y<B:3B9CB3B9:3GF<G:FB?:E3<;3EVWW:BFV3C@Z3C@B?XEVWW:BFV3CF:3@<B3W[B[C==V3:\H=[E?I:J3
454]7^:B3,- D:3C@3:_[?IC=:@H:3F:=CB?<@3<;3C3E:B3`/L-a0- 3J389CB3?Eb3B9:3F:=CB?<@,- 3ScdOPQPRSTPe3
cfggPhOSidjkldhOjkcShSTPmdnPdoOchdcpqrdhpjhdPTPOfdsL`LD.- :=<@AE3B<3E<W:3:_[?IC=:@H:3H=CEEJ3
^:B3tLD:3C@V3:=:W:@B3?@3`LC@Z3=:B3utv3D:3B9,- :3H=CEE3<;3:=:W:@BE3:_[?IC=:@B3B<3
tb3B9CB3?E3
,utv3w3x3sL.3̀Ly3sL,3tLz3
{?@H:3,-?E3OPQPRSTPe3tL,-tLC@Z3E<3tL.-,-utvJ3|I:FV3tL.-`LD:=<@AE3B<3E<W:3:_[?IC=:@H:3
H=CEE3C@Z3B9:F:;<F:3
`La3t1 .`L
2,utv3
Y:\Bb3>:3E9<>3B9CB3B9:3:_[?IC=:@H:3H=CEE:E3CF:3:?B9:F3Z?E}<?@B3<F3?Z:@B?HC=b33B9CB3?E3
,utv3~a3,uv3?;3C@Z3<@=V3?;3;,utv3€3 ,uv3a3J3
‚?FEBb3CEE[W:3,utv3€3,uv3a3J389:@3tL.3,utv3D[B33t.,uƒL vJ389:F:;<F:3,utv3~a3,uvJ3
„<@I:FE:=Vb33CEE[W:33,utv3€3,uv33~a333C@Z33=:B33sLL.3,utv3€3,uvJ33389:@33sLL,3tLLC@Z33DV3EVWW:BFV3
tL,3sJ333=E<3sL,3LC@Z3E<3DV3BFC@E?B?I?BV3tL,3J333^:B3†LD:3C@V3:=:W:@B3?@33,utv33E<33B9CB33†LL
,3tJ333AC?@33DV33BFC@E?B?I?BV33†LL,3LLC@Z33B9:F:;<F:33†LL.3,uvJ333‡:@H:3
,utv3ˆ3,uvJ3{?W?=CF33F:CE<@?@A3?WG=?:E33B9CB3,uv3ˆ3,utvJ389:F:;<F:3,utv3a3,uvJ3
‰:3H<@H=[Z:3B9CB3B9:3:_[?IC=:@H:3H=CEE:E3GCFB?B?<@3`J3
454Š789:3E:B3<;3GF<G:F3H<C=?B?<@E3?E3@<B3C3GCFB?B?<@3<;3B9:3E:B3<;3G=CV:FEb3E?@H:3C@V3G=CV:F3
HC@3D:=<@A3B<3W<F:3B9C@3<@:3H<C=?B?<@J3‚<F3:\CWG=:b3G=CV:F3‹3D:=<@AE3B<3B9:3H<C=?B?<@E3
x‹zb3x‹ŒLz3C@Z3E<3<@J3
454Ž7 3
sL3†La3sL‘3†LC@Z3†L~‘3sL
†L,3’La3†L‘3’LC@Z3’L‘3†L
8CFECE[@W:
E?B?I3?’BLV‘3
3<;s3L‘3 ?E3?W=?:GE=3?s:EL‘3
89?WG 3’’L,3
J3‰: B?I?BB9VC3B†3’LL,3
sLC3@@Z:3:DZV33B<BF3CE9@<E?>3 ~‘s3s
J3J“3[BE3EB[9W:
?E3?3W<GB9=?::FE>?
3B9E:CbB33B9CB3?E3
†L‘3sL>9?H93H<@BFCZ?HBE3B9:3CEE[WGB?<@3B9CB3sL3†J389:F:;<F:3>:3H<@H=[Z:3B9CB3’L~‘3sL
C@Z3B9:F:;<F:3sL3’J389:3<B9:F3F:E[=B3?E3GF<I:Z3?@3E?W?=CF3;CE9?<@J3
45”•7–—˜™™š›œžŸEE[W:3sL3†J3
3 sL3†La3†L~‘3sL
3
3
>9?=:3 L †L3sLa3†L‘3sL
3
89:F:;<F:3 L sL3†La3†L~3sL


 +

, 01344567189 9 
7



!"#
$%
&$#
$

' 7(8 )*
0
12345616789:;;<=>?@0A?B0CDE?B0A?FG?
@0A?B0HI?@0J?B0CDE?B0 @0
B0A?F00HI?B0J?F00CDE?F0JK??B0
LMDN>?J?M;?OPCD;MOMQ>R?S>?NTDNU<E>?OVCO?@0J?FG?
WOOV?CP>O?=C
@0J? PCDOV;MCOMOQ?MFOZ0?J?
MD;B?0OTC?D;EV?TOS? M=[@GU?M>:;;?;O<V=>
CO??FT0OJ?
V>BPSM C;?;<F=[
R?N;T>DR?OOPVCCPZO??MO;T??CO;V;><?=> OM@TDG??X>?YDTS?
0J?
OVCO?B0A?FG?X>?NTDNU<E>?OVCO?F0 @0CDE?
@0J?F0CDE?F0KJ?@0HI?@0A?F0
\VM;?;VTS;?OVCO?A?M;?OPCD;MOMQ>G?
]^_]`abcbdefb9LMDN>?J?M;?ghihjklhm?@0J?@0SVMNV?M=[UM>;?@0n?@G?
12345616789:;;<=>?@0n?B0CDE?B0n?FG?oTS?
@0n?B0pI?@0J?B0CDE?B0J?@0
B0n?F0pI?B0J?F0CDE?F0J?B0
?
\PCD;MOMQMOZ?Tq?J?M=[UM>;? 9 @0J?B0CDE?B0J?F0HI?@0J?F0
?
? rT=sMDMDt? 0 F0J?B0CDE?B0J?@0HI?F0J?@0
?
??
5uvv8126w9 0 @0J?F0CDE?F0J?@0HI?@0n?F0

@0n?B0pI?@0J?B0CDE?B0J?@0
pI?B0J?@0CDE?@0J?B0
pI?B0n?@0
]^__`abcbdefb9xQ>PZ?MDO>t>P?M;?C?=<UOM[U>?Tq?MO;>UqR?OVCO?M;?y0H?zyG?
123456167899:;;<=>?y0H?{|0CDE?|0H?}~0SV>P>?{0}0 ,-€0G?\V>D?y0H?{}~0;T?OVCO?y0M;?C?
=<UOM[U>?Tq?~G?
41995uvv8126w99Wq??y00H??{|R??{00,?€0R??OV>D??|00H??z./?y00CDE??{00,‚00€0G???ƒTP??>„C=[U>R????M;??C?
? ]^_†`??=<UOM[U>?Tq?ˆ?s<O?ˆ?M;?DTO?C?=<UOM[U>?Tq?G?
9 ? ‰Š0‹Œ?H?? Š0B0‹0F0Ž?
9
9 ]^_‡`?  Š ‹
0 ?H ?
 B?0Ž?
? J?B ?H?‹0B0F0Ž?
‘?B?H?‹0F0Ž?
’?B ?H?Š0@0B0Ž?
“?B ?H?Š0@0Ž?



 +

, 01344567189 9 
7



!"#
$%
&$#
$

' 7(8 )*
2
3456789:2;<=92>?@9?9@2=A2BC2D<,2;<EF2G2HEIEHGJ29J9H9I:2:K9?92EF2I>29J9H9I:2LKEMK2F:?EM:JA2
N?9M9@9F2E:O2:KG:2EF2:K9?92EF2I>29J9H9I:2P<,2;<FQMK2:KG:2P<R2DC2D<,2;<EF2:K92S?F:29J9H9I:2ET2E:2
N?9M9@9F29U9?A2>:K9?29J9H9I:O2:KG:2EF2D<V2P<T>?2GJJ2P<,2;C2
345W7XK92HGYEHGJ29J9H9I:F2>T2;<G?92Z<GI@2[C2XK92HEIEHGJ29J9H9I:2>T2;<EF2DC2XK9F92G?92
GJF>2=9F:2GI@2L>?F:29J9H9I:F2?9FN9M:EU9JAC2
345\7]FFQH92:KG:2D<EF2G2=9F:29J9H9I:2EI2;<>?@9?9@2=A2BC2XKG:2EFO2D<B2P<T>?2GJJ2P<<<<<;,- C2XKEF2
EHNJE9F2:KG:2:K9?92EF2I>2P<<<<;<,- LKEMK2F:?EM:JA2@>HEIG:9F2DC2XK9?9T>?9O2D<EF2HGYEHGJ2EI2;C2^I2
_=Y9GF:HN29JJ99H9 2`CIa:bC2O2:K92IQH=9?F2cd<ed<fd<gd<h2G?92GJJ2HGYEHGJ29J9H9I:FO2=Q:2I>I92>T2:K9H2EF2G2
345i7]FFQH92:KG:2:K929J9H9I:F2G?92@9I>:9@2D`d<Dadjjjd<DkC2l92MGI2E@9I:ETA2:K92HGYEHGJ2
2
9J9H9I:2=A2M>IF:?QM:EIm2GI>:K9?2JEF:2QFEIm2:K92T>JJ>LEIm2?9MQ?FEU92GJm>?E:KH2
n`2o2D. `2
/p< ET2Dp<q2npr`2
2 D
np<o2npr`2 >:K9?LEF92
2
sA2M>IF:?QM:E>IO2:K9?92EF2I>2Dp<LKEMK2F:?EM:JA2FQMM9@9F2nkC2nk<EF2G2HGYEHGJ29J9H9I:C2
345t7 2
u
u :KG:2EF2 2
Dv2EF2HGYEHGJ2wx2:K9?92@>9F2I>:29YEF:2D<q2 Dv2
qyDvz2o2{D2<|2D<q2Dv2}2o2~2
Dv2EF2=9F:22wx2Dv2B2D<T>?29U9?A2D<,2;<
wx2D<V2Dv2T>?29U9?A2D<,2;<
XKG:2EFO29U9?A2D<,2;<=9J>ImF2:>2VyDvz2>?2VyDvz2o2;C2
34€789:2<=92G2I>I9HN:A2F9:2>T2G2F9:2;<>?@9?9@2=A2BC2D<,-;<EF2G2J>L9?2=>QI@2T>?2
=><EQTI2@E:22NET?29E:M29@@>9HE
F2I9GU:99?FA2929UJ99?H9 2EI?22=O>2:QKIG@:O22E:FK2GD:<2V2
A2JI>:L9 EF2nD<<TB2
>?P2G<TJJ>2?n2<9U9,-
?A2J>C2L9
^:2?E2F2=G>2QmI@?92GP:<9>FT:22J>C2L9?2
3437]IA2HQJ:ENJ922>T2e‚2EF22GI2QNN9?2=>QI@2T>?2C22XKQFO2:K922F9:2>T2QNN9?22=>QI@F2>T2<EF2
e‚0d<-`a‚d<aƒ‚djjj<C2X1K-92J9GF:2QNN9?2=>QI@2>T2<EF2e‚C2XK92>IJA2J>L9?2=>QI@2EF2`O2K9IM92
E:2EF2:K92m?9G:9F:2J>L9?2=>QI@C2
3457XK92J9GF:2QNN9?2=>QI@F2>T2EI:9?UGJ2„nd<Z2G?92Z<GI@2[C2XK92J9GF:2QNN9?2=>QI@2>T2ynd<
Zz2EF2PC2
347 2
u
u
u
D<EF2GI2QNN9?2=>QI@2>T2<wx2D<B2n<T>?29U9?A2n<,2<
u wx2n<V2D<T>?29U9?A2n<,2<
wx2<‡2VyDz2
u
†EHEJG?JA2
2 D<EF2G2J>L9?2=>QI@2>T2<wx2D<V2n<T>?29U9?A2n<,2<
wx2n<B2D<T>?29U9?A2n<,2<
wx2<‡2ByDz2



 +

, 01344567189 9 
7



!"#
$%
&$#
$

' 7(8 )*
0
1234567809:98;0<=,0>?@0
0
<=A0B=CD0<E0F=BE0780<E0G0BE0HIJ0<?0F=B?0
KCIL90HMM09M9N9IOP0<=,0>?0H890L7NQH8HRM9@0A0CP0L7NQM9O9S0CO0CP0H0O7OHM078J98T0
1G
23U 0E5\V=?P\P^W^N90
^=\=_0@X09Y=C=OC[P9008L07<NQ M9O900D78009:98;00YT0000Z[
Y=XY=BY=780BY=XY=<Y=780R7O [9 I0O0[D79880009:98;00<\=B= ,-]==HIJ00D7800HMM00Y==
T0̀C
<Y=aY=BY=bcdefggeY=Z[9I0hijki0<=a0BT0
<Y=laY=BYl=ab0BctdTe0msu7
cnoeY=p9O0q=R90O[90j8PO0CIJC:CJWHM0rCO[0H0PO8CLO0Q89D989IL9@0O[HO0CP0q=G0
NQM9O9I9PP007D0XY==9IPW89P0O[HO0q=CP00hijkihvT0Z[9I0hijki0
NCIYs<Y=
Y
<=A0B=CD0<q=AY=Bq=
B=A0 <=7O[98rCP90
123w5p9O0x@0y=HIJ0z=R90PWRP9OP07D0H0jICO90P9O0]T0K9O0CILMWPC7I0{0CP0
|}~}€}ePCIL90x={0xT0
‚dfƒm„‚„oePCIL90x={0y=HIJ0y={0z=CNQMC9P0x={0z=T0
fƒ‚„†m‡nno‚d„ˆePCIL90x={0y=HIJ0y={0x=CNQMC9P0x=G0y=
Z[989D7890{0CP0H0QH8OCHM078J98T0
1X0
23‰‹5 =DV7P8P0WHN9
MM0 ‹ <=HŠITJ006BW8=OH[9898@00RCD70O<[=0CPM90HH0PM9O0HWPQO0QW9Q8Q09R870WRI7JWPI0J7@D00BŠ=X0
0== T0Z<[HT0OŒ0DC0P0B<==CPX0
0H‹0M=9DH7P8O00HWQMM0Q‹9=80ŠR=H7I,-
WJI0JB@0=
<=X0BT0;0HIOCŽP;NN9O8;@0<=G0BT0 ,-
1235 0
<=a0B=G0<=X0B=HIJ0B=X0<=
0
r[CL[0CNQMC9P0O[HO0<=G0B=R;0HIOCP;NN9O8;T0̀HL[09‘WC:HM9IL90LMHPP0
a0s<t0G0’B0=,0]=“0B=a0<=”0
L7NQ8CP9P0•WPO0H0PCI–M909M9N9IO0<T0
—˜™šeeNH›0œs]t0G0]==HIJ0NCI0œs]t 0G0T0
124ž5Z[90PWRP9O0’?\?=Ÿ\=¢”0D78NP0H0L[HCIT0¡7890–9I98HMM;@0O[90P9O07D0CIO9–980Q7r98P07D0H0
–C:9I0IWNR980’_0\=_\=_ \^^^=”0D78NP0H0L[HCIT0
£¤¥£¦VPPWN90<=HIJ0B=H890NH›CNHM09M9N9IOP07D0O[90L[HCI0ŠT0Z[9I0<=X0‹=D780HMM0‹= ,-Š=
HIJ0CI0QH8OCLWMH80<=X0BT0KCNCMH8M;@0B=X0‹=D780HMM0‹= ,-Š=HIJ0CI0QH8OCLWMH80B=X0<T0KCIL90
X0CP0HIOCŽP;NN9O8CL@0<=G0BT0
124§50ET00;0HPPWNQOC7I@0D7809:98;0̈===,-.- ==y====©=@00/- 000s̈t0CP0H0I7I9NQO;0jICO90L[HCIT0ª9IL9@0CO0
[HP0H0WIC‘W90NH›CNHM09M9N9IO@0«s̈tT0
?T00p9O0̈=R90HI;0I7J9T00`CO[980̈=CP00HI0CICOCHM0I7J90780̈=[HP0H00WIC‘W90Q89J9L9PP780«s̈tT0
`C O[9800«s̈t00CP00HI00CICOCHM0I7J9@007800CO00[HP00H00WIC‘W90Q89J9L9PP780«s«s̈ttT00u7IOCIWCI–0CI0
O[CP0rH;@0r90O8HL907WO0H0WIC‘W90QHO[0D87N0¨=RHL¬0O70HI0CICOCHM0I7J9T0­90LHI0R90
PW8907D09:9IOWHMM;089HL[CI–0HI0CICOCHM0I7J90PCIL90y=CP0jICO9T0
e
12435 0
sE\=?t0®0s¢\=Et0G0s¢\=?t0HIJ00sE\=?t0̄0s¢\=?t0G0sE\=?t0



 +

,  01344567189 9 
7



!"#
$%
&$#
$

' 7(8 )*
1
23445 6718/9:;<1=>1?@@AB1CD?>E1FDB1G18H:9:IJ1KL=K1;<1M/NOP18:=>E1M/NOP1971Q;R;S=BSTJ1
8:/19:;<1=1SDUAB1CD?>E1FDB1G81H:9:I71
3VWX<<?RA18:P1971YLA>18:;<1=>1?@@AB1CD?>E1FDB1G18H:9:IJ1KL=K1;<18:P18:/1971ZF1[:;<1=>T1?@@AB1
CD?>E1FDB1G18H:9:IJ1KLA>1[:P1871YLABAFDBAJ18:;<1KLA1SA=<K1?@@AB1CD?>E1FDB1G18H:9:I71
Q];DR;>^S=ABBS<TAJ1ST9J:1;=<1<=<?1SRA
DUA
18B:1/1C9D:?_>1E81F7D1YB1LAG18>1H:89::;I<J11==>>1E?1@;<@1A\BB1AC=DK?A>BE11KLFD=B>11=>T1DKLAB1SDUAB1CD?>E71
G81H:9:IJ1KL=K1;<18:P1971
`VWa<;>\1KLA1@BAbAE;>\1Ac?;^=SA>bA1
8:P18:-19::_d18:/1e8:-19f1_18:
8:/19:P18::_d1e8:/19f1-18:_18:
234g5X1bL=;>1h:;<1=1bDR@SAKA1@=BK;=SST1DBEABAE1<AK71iDB1A^ABT18H:9:01h:U;KL18:j_19J1
A;KLAB18:k19:DB19:k1871YLABAFDBAJ1lmnom1KLA1RAAK1=>E1pD;>1CT1
8:, -
.9:_19:;F18:k1
8:;F19:k1
9:
8:
, . 8:;F18:k1
8:/ 9:_19:;F19:k198::
:
h:;<1=1S=KK;bA1U;KL1KLA<A1D@AB=K;D><71
234q5X<<?RA1h61=>E1hr1=BA1S=KK;bA<J1=>E1SAK1h:_1h61s1hr71]D><;EAB1=>T1KUD1ASARA>K<1MO
_11e86H:8rf11=>E11NOO_1e96H:9rf11;>11h711Q;>bA11h611=>E11hr11=BA11S=KK;bA<J11[611_1861/1961101h61
=>E11[r11_118/. r1 11110. 19r1111111hrJ11<D11KL=K11tOO_11e[6H:[r/. f1_11e86/. 111111960.
H:8r1111119rf111111h7111
i
C ?
D B
?K>L EAB
1 FRD
D B B
1 AK
L1At 1O P1 M O = >
E1 t O P1 N O ;> 1KL A 1 > = K ? B= S1 @ BD E ? bK1 D BE A BJ1 <D1 K
L =K1tO;<1=>1?@@AB1
GMH:NI7111v u^ABT11?@@AB11CD?>E11t v11_11e[v6H:[vrf11DF11GMH:NI1R?<K11L=^A11[w::Pw::8w::=>E11[w::Pw::9wJ1
<QD;R;
11KLS==BKS 1tJ111MP1
1T O-N t
1O_1e861-196H:8r1-O;<
7 11 1Y L A B AFDBA J1 1t O 191r1KfL71A11SA=<K11?@@AB11CD?>E11DF11GMH:NIJ11KL=K11;<11tOO_11MO/1N71
234x5yAK1z:CA1=1<?C<AK1DF1h:=>E1SAK1
z{1_1G18:01h:|18:P1}:FDB1A^ABT1}:01z:I1
CA1KLA1<AK1DF1?@@AB1CD?>E<1DF1z71YLA>18{101z{1 ~7 1T1=<<?R@K;D>J1z{1L=<1=1\BA=KA<K1
SDUAB1CD?>E1[71Q;>bA1A^ABT1}:z:;<0. 1=1SDUAB1CD?>E1DF1z{J1[:P1}:FDB1A^ABT1}:z71YLABAFDBA0. 1[:;<1
=>1?@{@AB1CD?>E1DF1z71i?BKLABRDBAJ1[:;<1KLA1SA=<K1?@@AB1CD?>E1DF1zJ1<;>bA1[:€18:FDB1A^ABT111
8:z71Y=L;B;<11DAF<1K=ASCASRA ;<LA<1KL=0. K1A^ABT1<?C<AK1DF1h:=S<D1L=<1=1SA=<K1?@@AB1CD?>E71Z>1@=BK;b?S=BJ1
A;<^1A=B1Tb1D@R@ SAKA1S=KK;bA71 <1=1SA=<K1?@@AB1=>E1=1\BA=KA<K1SDUAB1CD?>E71]D><Ac?A>KST1h:
> K<1L=
2345‚;KLD?K1SD<<1DF1\A>AB=S;KTJ1UA1U;SS1@BD^A1KLA1bSD<AE1;>KAB^=S1b=<A71yAK1ƒ„H:[1CA1=>1
;>KAB^=S1;>1=1S=KK;bA1†71‡Ab=SS1KL=K1„:_1;>Fƒ„H:[1=>E1[:_1<?@ƒ„H:[71]LDD<A1=>T18H:9:;>1ƒ„H:[1
ˆ1†71Q;>bA1†:;<1=1S=KK;bAJ18:/19:01†:=>E1
8:/19:_1<?@G18H:9:I1€1[:
YLABAFDBA18:/19:01ƒ„H:[71Q;R;S=BSTJ18:-19:01ƒ„H:[71ƒ„H:[1;<1=1S=KK;bA71Q;R;S=BSTJ1FDB1=>T1<?C<AK1z:ˆ1ƒ„H:[1
01ƒ„†HJ1:[<?1@1<Dz1:KL01
=K†1:ƒ;„F1H†:[:;<11;b<D1bR@S 71<DJ1<?@1z:€1[:_1<?@ƒ„H:[71YLABAFDBA1<?@1z:01ƒ„H:[71Q;R;S=BST1;>F1z:
ˆ1 AKAA7K1AXS
DR@S




 +

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller lectmaggie. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for $18.99. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

82191 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling
$18.99
  • (0)
  Add to cart