Mar 1, 1999 - proaches for differentiated-product discrete-choice models. We exploit the information ... lates closely to the literature using restrictions from economic theory for identification in semi- ..... O ther examples where the presence.
"!#$% &'() *,+.-/ 0(1&2($435 6$798:6$0 * ); < =>@?BACEDGFIH1?KJ L J?NMODPH1Q1?NF +-H? ./(-k!)+)Uml!(n5o.!?61$B!G1(-345+- +-H./+$#01$.p:>#B(./D$B./+0+0(J#BD$3+09!D$0)(-\!8DM:45E*$-3?6)(.!*1$(-R$345)(PD$3+ *!+K? .!-3(-2DM:./+-.;.!*$2#./@!@!(-)@E./+0 #U!UBG94)30+0E? )(0ehB)\!=./+-.G9.!* ?61$#B(#i4).!B:H.!n+0*F+0 D#.!f0+-#? ./+09!
1(#45".!0+-#i4)#B+-#BP+07g./($n))(-U #*45Z? .!*8#*#45(-)+0N4HE#45z-)+0+-#*@E9#i9*!+9i#*./(9#*T1(#45!G0+-.!*./( #*0+0(3$?6*,+-.!\/./(#./D$z?6)+-HRr!(45!(-(-45+-#*@F+-H#*!@!*#+h:I1(-!D$B?./(- *!+#? ?6$#./+0B:T./11#4)./D$B!UvWs*C+-H#1$./1)(v7g )\!B!1O45E*M+0(-E^3*45+-#BE*C./1e 1(-E.!4HNr!(Z#B%')(-*M+-#./+0e1$(-R$345+#-45()+05eh4HE#45K?6)U awK5o1$BE#B+v+-H #*r!(? ./+-#BE*8+-H./+"1(#4545E*M+-.!#*IE*I3$*!D$0)(-\!C?.!*T^.!45+0!()U}9Hz-1'4)#Be y$4)./+-#BE*"./(-ZD$.!0IE*T(-3B+-9=(-E?)+0(#* /!E JG79H>5oR+0*$9Ws?ZD'*$.!* 9)7g): /!E +0F? .!*$80)+0+-#i*@E)G-Hp7#*@+-Hz45E*$#B+-#BE*3*)(79H#4JH85e ? .!*#i[*E*e1$./(J.!?6)+0(#4).!:Z#*M+-#By3-#*@v45E*M+0(-Er3*$45+-#BE*)U
}nHn#*M+-3#B+-#E* 3*)(:R#*@+-Hv45!(-(-45+-#BE*T#*>*E*eh#*./(f0)+0+-#*@EP#f-#? #i./(x+06+-H./+n#*K.6#*./( *,\#B(-E*? *,+)G7H)(-6.F*)7Q45E*M+0(-E\/./(#./D$z#v#i*4)3I#*I+-H6(-)@!(--#BE*C+0 h JP|sg] vP0J¡p¢¤£¥z¡¦]^§¢§¡§¢|¨©£>/-§§Y£]P¢|P¢|P!¨J§h£§n¢|£ªs|¡/«J¬"&¨sª0J^§¢|£¥ Y§] §]g¢|£]«¡]ªY0««sn£/«"&¨[£]YOs£Y¥J®¯iY°PªY¢¤Y£§
±5s]¢|ªs|s¢|[«h0£NP¨Jx²¨J´³r¥©J^¯ ¥J¡]µsµY¤ ¶g¨Jªs¡s£)§g³r¥5^¯i¢¤!Y¶·s^§¢|n§¢|£¥x§Sp¢¤ªYY¸Esª § J£]«P'sB-
¢|P]|¢|ª0§¢|¨©£¨J PY¥©Y0·J£]«Z¡]£]«Y^§h£/«p¢¤£¥Y§]Yx£]YOp¨«¡]ª §¢¤|¤s©«Z§¨s²¯iª0J££]¢|¦/|¢¤µs§¢|¨©£ ¨J §
¹]"º J|s»¨J¢|§¨§]Y»¨«p¡]ªY§s¼ ½Y¾r£P§]¢|ª0§]S¦]¢¤J'ªs¨©¡¿«n¦!!¨J¢§¢¤±©
¨J £s¥5-§¢|±5©·«s!Y£/«¢|£¥m¡!¨©£n]¨0¢|ªsY
§ ¢§"p¨©P¨§¢¤¨J£/RªY§¢|±p¢§¢|ss¼
54 E*#B+-#BE*CE3++-H61$./(-+N!m+-H)(-(-!(+-H./+#i45!(-(-./+0A79#B+-HC+-H6*$!@!*E3 (-)@!(--0!( 0)+-H#i.!n#4)3-0`#*F}S0)( JG'79H#i4HF./(-?6!(=!(J? .!B: )\!B!1?'J£]«n¦¢|£/®f¨©¦¢§ ¦)®@»¢¤±©YJ£]«BA¡¨©£¥B587:9;>? ¼
+-#4))GE.!*Z79H)(-g+-H)(-f? .p:N*!+D'f? .!*M:1(-345+-»!D$0)(-\!#*z.-#*@EBg? ./(-k!)+)U 14)#By$4).!B:!GR7g".!iBp7X45E*3?6)(g+0 H.p\!N##BE-:R*45(J./+-#4/GR3$*!D$0)(-\!K1(R3$45+se 014)#By$4+-.!0+0)G0 r!(g5o.!?61$[+-H79#iB: 30KB!@E#B+P.!*>1(-!D#B+m?6f./(- *!+n(3`E3+)G.!*F7gN.!B7X+-H-311$B:#v+0.]%45+9LR3##D(#3? 1(#45)U t*C.!B+0)(J*./+-#B\!./11(-E.!4JH8#*I#&%)(-*M+-#./+081(-345+9? ./(k!)+-#i9+0`#*4)3$ 1(-345+seh? ./(-k!)+»yoRe5%'45+-)U
}nH#i ./11(-E.!4JH.!B79 r!(»##BE-:R*45(J./+-#4»1$(-R$345+se 45E*-3?6)()(-(-!(J)G/D$3+»(LM3#(-»+-H$./+S+-H-m)(-(!(»+-./k!n.1$./(-+-#i4)3./(»r!(?z3./+-#BE*U }nH +s+-.!0+0 ,)(-(-!(»*,+0)(#i*@93+-#i#B+h:+-H./+»#*!+»#*)1**,+'!1(#45[?z30+D[.!e #B+-#B\!B:0)1$./(J./D$Bnr(-E? !+-H)(x!D$0)(\!1(R3$45+[4H./(.!45+0)(J#0+-#4)m!(x1(J#45+-H./+ *,+0)(z3+-##B+ :!U l!(z+-H06(-.!0E*$)GS7g 4).!*AHp7 +-H./+D!+-Hw#*O*E*e1$./(.!?6)+0(#i4 .!*c0+-.!*./(J;1./(.!?6)+0(#4 (.!*$E? 45M >4)#B*,+Jz? Ri)G[*#B+-H)(+-H45E*M+0(-E r3*$45+-#BE*T./11$(-E.!4HC*!(+-HN1$(-R$345+seh? ./(-k!)+yoR85%45+"./1$1(-E.!4HI./(-*0+0 #*`E*N.!*!+-H)(U }nH[1$(-R$345+seh? ./(-k!)+»./1$1(-E.!4HeD#*@n.Pyoe5%45+»+ :M1x./11$(-E.!4He$(.!#0 +-H>33.!
yoe5%'45+z# 4)3$B+h: -#m+-H>*M3?ZD)(!f!D$0)(-\/./+-#BE*NE*w+-H>yoR 5%'45+-Z#v*!+v#*45(-.!#*@F./+.F-3 4)#*,+-B:T(./1$#I(./+0!G+-H #*4)#*M+-.!1$./(.!?65e +0)(n1(!D$B? ):R?.!*T.!* 45!+0+ 04).!309+-HN0+-#i? ./+0!(9r!(9+-HNyoR 5%'45+-Z+0TD6#*45E*#0+0*M+)GS.!*O#i*w.*E*eh#i*./(0)+0+-#*@F+-H D$#.!#+v@!*)(./+0 #v+0(.!*? #B+0+0O+0I.!
!P+-H 1./(.!?6)+0)(ND'#i*@F0+-#? ./+0UKt#B+-#E*.!B:!G +-H !D s45+-#\!^3*45+-#BE*#[*#B+-H)(m#*./(x#*61$./(J.!?6)+0)(g*!(x@!*)(J.!B:z@EB!D$.!B:45E*e 4).\!Z#i*>+-H?FGB.!#*@Z+0 .64)3(J0"!#i?6*-#BE*$.!#B+h: .!f+-H)(-./(-v!r+0*0)\!)(.! HM3*$(-`5o+0(.61$./(.!? )+0)(P+0-+-#? ./+0!U g)(-(-: v.!* m)((-:!G )\#*0EH$* G'.!*$I
./k! GSH*45)r!(-+-H "»g 1(-p\!F+-HK5o#0+0*$45.!*_3*#LR3*-Z!.C0)+61$(-R$345+seh? ./(-k!)+645E*M+0(-E+-H./+ ? ./+-4H_!D$-)(-\!d+0I1$(-#45+0d? ./(-k!)+6-H./(z3$*)(N+-H`./r!(-?6*M+-#BE*_.!e #B+-#B\!T-)1$./(./D$#i#B+h:c.!--3$?61+-#BE* Uu}nH):_.!i0A1(p\#T.;?6)+-H2r!(>B4)./+-#*@ +-H?FUQa H#I3-)r3#* ? .!*M:q0)+0+-#i*@E)G+-H#`./11(-E.!4JHu4).!*u5o.!45)(-D$./+0O+-H +syoRe5%'45+-seh#i*eh.]eh*E*eh#i*./(0eh0)+0+-#* @ , 1(-!DB?FGD4).!30+-HN1(-345+P? ./(-k!)+ 45E*,+0(-EiF./(-w45E*45*,+0(J./+0XE3+KDM:b? ./+-4H$#*@_!D$0)(-\!b+0c1(#45+0b-H./(-)G B.!#*@-.!?61#*@z!(n-#?z3./+-#BE*K)(-(!(n#*K+-H0-H./(f+06*,+0)(n+-H-+-#? ./+-#*@ LM3./+-#E*#*C.H#@EHB:*E*ehi#*./(v? .!**)(pU g)(-(:!G »#*M+0E* G».!*$w./k! /!E 7m!(-kE3+m+-H95o.!45+n45E0/+ -+-H-+-#? ./+0!(P#g45E*-#0+0*M+f.!*.!0:?61+0!+-#i4).!B: *!(0e ? .!# +-H*R3?ZD')(g! !D$0)(\!>13(4H$.!0)( !(P-#i?Z3i./+-#BE*(J.79J[#*45(-.!-m./+
Ì
Ì
Ì
.!*5o1'E**,+-#.!(J./+0(-./+-#B\!N+0 +-H*R3?ND)(P!
1(-345+-U }P7g8!+-H)(#-34).!*_./(#079#B+-HO+-H$#N./11$(-E.!4H Ul
#B(J0+)G#g+-H "» 45E*e +0(.!45+-#BE*A.!@!!(#B+-H? #"+0FD 3-C+0BR4)./+0+-H61(-345+seh? ./(k!)+45E*,+0(-Ei)GS.!* #*)1**M+S.!*$z#i*,+-#i4).!B:v#0+0(J#BD$3+0 #U|#U| U¿NB!@E#B+)(-(-!(?z30+
Dg./11* +0+-Hn3+-#i#B+h:^3*45+-#E* U }nH$#
.!--3?61$+-#BE*#
1(-!D$? ./+-#4g#*6? .!*M:z0)+0+-#i*@E)G,.! *!+06#*zS)+0(J#* /!E JG g)(-(-:Z.!*./k! /!E JG RE0D)f.!*)+0(#* /! JG .!* E*@ /!E JU 45E*$ GM+-H945E?61$3+-./+-#E*.!D$3(*6!+-H./11(-E.!4JH>4).!*>D 0)\!)(-!G
014)#.!B:I79H*A30A#i*O0)+0+-#*@EN79#B+-HO?#45(-/ehB)\!m./+-.T.!* !(N(.!*e E? 45R 4)#B*M+-)G
79H)(#*M+0)@!(./+-#BE*d31A+08+-H1(R3$45+seh? ./(-k!)+ZH./(-N?z30+ D'ZE*NDR:F-#?z3./+-#BE*U T}nH#in45E?61$3+-./+-#E*.!D$3(*F! "» H.!95%'45+-#B\!: 1(-4)3F#B+-P30DR:`? .!*,:K1(.!45+-#+-#BE*)(n.!*$`1'Ei#45:,eh?./k!)()U aw1$(-0*M+x+-H(-)?61$#B(J#4).!? .!*$./11$i#4)./+-#BE*+-H$./+x(-)1$i#4)./+09014)#By$4).]e +-#BE*fr(-E? ./(#B)(f7g!(-kRge[.!'!S79H#4JH>3-1$(-R$345+seh? ./(-k!)+P45E*M+0(-Ege[#*4)3$e #*! @ g)(-(:!G »)\R#i*0EH* GM.!*>
./k! JG7HZBR!k./+f.!3+0E?6!D$#iB)G "ME-D') .!*S)+0(J#* /! JGM79H"BR!k./+
4)./DBm+0)\R##BE* G!.!* fH#*M+-./@E3*M+-.G 3D'!G!.!* EH /!E JG79HBR!k`./+? ./(-@E./(#i*!Ug}9H0N./11#4)./+-#BE*9./(-Z4JHE0*8+0>01$.!*
Ì
¾=§£p¡g¦!Y¨J¨«p¡]ªY§¢|¢|£/« s«¦)® ·]§]Y£§]£¡g¦!Y ¨]¡pª ]JYSJ£]«¢|g¡p¯ ¤-§¢¤¨J£«phsg¡^§¥J¨08§§]h-§ ½ ¼ 1]¢|Y¨s£]¡ps'§/-§'§s¢J|¥©¨¢§]_¢|[ªs¨©£)§hJª §¢¤¨J£n]]¢|£¥¼ ¨¥©Y£]Yh¤®)·§] |¥©¨J¢§_¢||¢ ©s®f§¨¨J f's|/¢§£9¢B¼ ¢B¼ «,¼$Y¨J'§/§«¨)s£]¨§«s]§'¢¤¥J£]¢¹/ªsJ£)§®f²¨J §'|¨©¥J¢§'«p¢|^§¢¤¦¡§¢|¨©£,(¼ 1]'J|¥©¨¢§]w¦!sªs¨JPsp¨©¦]|sn-§¢|ª']s£[§]Y¨J¦!Y¥©¢|£m§¨»ªs¨-±©-® ¢|¥J£]¢¹/ª0£)§|®gJª ¨©§] ªh]¨©¢|ªsYs·)J$!¨J§Y£§¢¤¤®x¢§Pg¡§¢¤±J¢¤-§£]¨nJ!sªs¢¹/ªs§¢|¨©£ 5Bs ¨)¨J|¦!sg£/« Y§¢|£ 5 /? ¼ 4'sª0¡]g ¨J¢|£§]x¢¤m¡]¤§s«¢|£)§s¥hJs£)§Y§mY^§¢¤n-§¢|¨©£ )¡/-§¢¤¨J£]
£¨©£p¯=|¢|£]s®)· §¢|m¡]¤§0«¢|£)§s¥Jh|g¡^§R¦!$s±JJ|¡/-§0«
&¨JnJ£)®
P¨¢|g¡¤§¢|¨©£x«phsR§]J£¢|R§=®¢|ª0J|® «p¨©£ 5B©¼ ¥¼9§]¨©¡J£]« ? ¼ ]¡§YP¨JJ·M²¨JgJ£)®Nª0J£]«¢¤«]-§P±©¤¡P¨J ]hPY§Ys·s±JJ|¡]§¢|¨©£ ¨[§]v¨©¦ ^YªY§¢|±5v&¡]£ªY§¢|¨©£` )¡¢|Y9§vª0J|ªs¡¿-§¢|¨©£¨J[§]Yv¢¤m¡]¤§s«`¢¤£)§s¥hJ|9!¨©¢|¦]® ¡£/«ps«
¨ §¢¤PY¦!sª0J¡f§]f ¨J[snJ¢|£¢¤£¥²¨J §]fªY¨©£)§hJªY§¢|¨J£¨)ªss«¡Pm¡]^§¦! ¡p°Pªs¢|s£)§®n|·!J¥5¢|£v¦!sª0J¡§]¢|S ¨JSs£)§Y §]s^§¢|n§¨£¨©£p¯=|¢|£]s®)¼ ¨JJ§Y£/-¯ §¢|±5[]p¨5Jªh]Y§]§»«p¨f£]¨§S¡
§]
ªY¨©£)§hJªY§¢|¨J£ 5B|¢ ©
§]
ªs¨J£)§¨©M²¡]£ªY§¢|¨©£"]p¨5Jªh ?¨J£]® ¨J£]s±JJ|¡]§¢|¨©£"¨§]¢| ¢|£)§s¥JhR¢|£]sªsY®)·p¢|§!¨©¢|¦]®"n£)®P&Y'Y»¢¤m¡]¤§¢|¨J£v«phss¼ Y¾r£N¨©¡[±¢|Yw§¢¤¦¡h«ps£Z¢|
)®§] 4 8J]p¨5ª Z/J
®5Y§
§¨¦!m¢¿«ps®Z©«¨J§0«N¦)® Y¥©¡]¤-§¨J®NJ¥Js£]ªY¢¤Ys·,¨-m¨²§s£N¡]£]«Y»§¢|PY¯iªs¨©£^§hJ¢|£)§S¢|£NJ£)§¢§¡]^§ -PY¥©
ª0ss¼ £ ªY¨©P]¡p§h§¢|¨©£]J/¦¡h«ps£M·5J|!¨J,§]] Y§¨J²¨JªY¢|§s«f/J! §/-§¡Sp¨«¡]ª §¯=n- 5Y§ªs¨J£)§¨©| -gªs¨«p0«v¢|£NY¢|§Y "-§¤J¦N¨J ¡]s·MJ£]«"nJ£)®"¨§sqªsJ| ¨J¡§¢|£]sS§¨9!Y0«v¡]"§] ªY¨©P]¡p§h§¢|¨©£]JpJ|¥J¨J¢§]C§]§|¨)ª0-§s§]¹p0«Y¸EsªY§§¨»0«¡ªs¡£¯§¢|PsM§¨SnJ£]J¥J0J¦¤ |s±©sB¼
!
"
$#
!
%"
&
%'(
*)
,+
-
.
. (.!*@!9!»? ./(k!)+-g.!*$1!+0*M+-#.!$45E?61)+-#B+-#\!91(#i4)#*@DH.p\R#B!(J)GM.!*>#*4)3$ N +-H(-)+h:R1'g!»$#&%')(*,+f./+-.[./@!@!(-)@E./+0 ?./(-k!)+sehB)\!=m./+-.GHE3$0HEeh)\! 45(-E-seh045+-#E*.!S$./+-.G'.!*8HE30HEehB)\! 1.!*./+-.UPawz30N+-H?~+0>Hp7 #*K1(.!45+-#45vH7uE*v#?61$B? *,+-g+-Hv45E*M+0(-Er3$*45+-#BE*`./11(-E.!4JH`=!(P+-H0v#B=e =)(-*M+n+ :M1n!1(-345+-P.!*$./@!@!(-)@E./+-#BE*IB)\!)U 3(-#?61$0+f=!(?z3./+-#E*Pr!(+-HZ45E*,+0(-ES^3*45+-#BE*8./11(-E.!4JHT30N(-)@!(-se -#BE*w#*I+-H6y(J0+v0+-./@!.!*C+-H*w?.]o#?#B)6.Ki#Bk!#HR8#*I+-H -45E*w0+-./@!!G .!*64).!*6+-HR3
Dg(J3*#*0+-.!*./(1$(-!@!(.!? ? #i*@1.!4-k/./@!)U[l!(m#?61$Bg? .!* 014)#By$4)./+-#BE*9+-H+-HZ.!0+-#4)#+-#B9./(-z.!?6E0+#*M+-#4).!».!45(-E9+-HZ+-HZ45E*M+0(-E r3*$45+-#BE*./11$(-E.!4H`.!*>+-H "Sc./11(-E.!4JH GR.!*$+-H):>#&%)(m-#B@E*$#By$4).!*M+-B:=(-E? +-HN3*45!((-45+0F.!0+-#i4)#B+h:`0+-#?./+0)G79H#i4HF./(-D#.!0F79*#*`)\!)(-:F4).!0!U }nH"1$./1)(f1(-45)f.!f=EiBp79U 45+-#BE* -45(#BDm+-H"D$#.!f./(##*@z=(-E? 3*!D$0)(\!? .!*>./+ V .!* 45E*#B+-#BE*$.! U p7g)\!)(G#B #*1$./(-+x( 45+-f3*!D$0)(\!^.!45+0!( E* V V +0Z-+-#? ./+0 J2 +-H./+ ./(-F*!+6?6.!-3(_DM:;+-H`45E*E?6)+0(#4)#i.!* Gx.!*c#Bn-B)(4H$./(-@!F1(#45 D$.!0>E* +-H0"3*!D0)(-\! ^.!45+0!()GR+-H* .!* 79#*!+mD9#*)1**,+)UWY* +-H#n4).!0NE*(-45\!)(
Ì
$ ! " # V V V V V V V V
l!(5o.!?61$B!Gm#B45E*3?6)(79#i#*@E*-+0w1$.p:d#i*45(-.!06#*d+-H3$*!D$0)(-\! r.!45+0!(GR.!*61(R3$45)(
4H./(-@!?6!(-Pr!(1(-345+-
79#B+-H?6!(P!+-Hn3$*!D$0)(-\! r.!45+0!(GM+-H* #@!*)(.!iB:ND$#i.!0z+0p7f./())(-GM.!45E*-3?6)(JBM!kZB-
1(#i45 0*-#B+-#\!+-H.!*d+-H):O.!45+-3.!iB:A./(-KD4).!30+-H):A./(-K@!)+0+-#*@C?6!(-K=!(z1$.:#*@ +-H1(#i45+-H):K1.:`+-H.!*F+-Hv45E*E?6)+0(#4)#.!*8H.!P+-./k!*8#*,+0>.!4)45E3*,+)U #*45v}S(.0+0*,D)(-@ *.!?6. =)7U
Ì
Ì
Ì
2- ['
´ [[
P9
aw =4)3E*C+-H6)+0)(?#*./+-#BE*I!g1(#45z=!(vD!+-HC-#*@EB5e1(-345+0B)(".!* ?Z3+-#&e1(-345+-B)()G979#B+-Hb.!*q? 1$H.!-#>E* #*M\!)(-+-#*@d1(#45>+0_(-45p\!)( G 79H#4JH87g )y$*z.!.KE*5e+0/eE* r3$*45+-#BE*I!x+-H6(345I=!(J?)(-(-!( =(-E? +-HN-31$1$B: LR3./+-#BE* U
AAP¨«s|s·MP¢s«|¨J¥©¢§mJ£/«N¨J¦]¢§ 5B©¼ ¥¼|· 4¨0£]^§¨©£nJ£]! « 1Mh¢|£ 587:99>? ?[|¤¨0O§] ªY¨±J¢¤£]ªsn¨J'§]f¡£]¨©¦Y±50«Nªs¨©P!¨J£]s£)§
§¨"«s!s£]«N¨J£¨©¦Y±50«N±©-¢¤J¦]|s¨0s±5 0·R§] PsJ£¢|»J¡P0«9§¨g¦!ªs¨©£^§hJ£)§0·¢|ª "psªs|¡/«ps ªs¨s¤§¢|¨©£v¢§"¢|ªs 5&²¨J»YJP| ? ¼
a 90+-./(-+7#B+-Hz+-Hn-#*@E5e1(-345+»y$(?FU »)+ DP."\!45+0!(x!$1$(-R$345+4JH./(0e w .!45+0)(#0+-#4)G7H)(-4JH./(.!45+0)(#-+-#4)Z./(D(-E.!$B:w)y$*w+0C#*4)i36.!*,:w^.!45+0!( +-H./+.]%45+-"? .!*8.!*I-H#Br+-n45E0+- !U@U.>1$HM:R#4).!1(R3$45+n4H./(.!45+0)(J#0+-#4 !(n.!\!)(-+-#-#i*@MJU )+ D'!+-H)(f1!+0*,+-#i.!'? .!*K.!*`45E0+P-H#Br+0)()G D'v+-HN? ./(-@E#*$.! 45E0+9!1(-345+-#BE*G.!*$ PDLM3.!*M+-#B+ :`? .!*F./+ 1(#45 @E#\!* JUmab#+-HF1(-!y+-9*!+0
+-H!1+-#?.! 0+-./+-#4pf1$(#45v0EB\!
? ? .
0
#
Ì
(-./+0P1$(#45n.!*F4JH./(.!45+0)(#i0+-#4))U
5 9A 5' &
$ $!#"$&%'(')#"+*&-,/.0"1,23465'7.-.-83*9&:@? 9&=>? ½9 A 9CB ? 9CB .-, &VU 'W*YXZ: $#!#"S[\-8 D , ' '], &&C*C'.&*^ -,2-*_, `a"E%*YC*_,Z.b' &c, &&C*C'7.#*b, & 465d% $ 'e, &VU ' ' ']* 'f.&*g $&h.0"L ' &"LK
id:$$j`
}»!+-.!n$#&%')(*,+-#./+-#E*_!9+-HFy(J0+se!()( 45E*$#B+-#BE*d79#B+-Hd(-0145+6+0 .!*$ 4 45E31$B`79#+-H`+-H#?61$i#4)#B+x^3*45+-#E*>+-H)!(-?~B.!n+06+-H45E?61$./(./+-#\!N0+-./+-#4
C9 B 9&= >
k k
9 j½ lSm 7B njo 9CB9CB&prqts 9 ½jlSm B7njo 9CB9CB&prqts
V 9 ½ulSm Bvn(o
9CB9#= > t 9 ½ A 9&= >xw 9CB&9 = >
V bk 9#A
9&:; 9#A 9&= > C9 B!q
#
9 j½ lSm vB njo #P1E-#+-#B\!v=(E?~1(-!y$+9? .]o#? #B./+-#BE*Ux}nH+-H(-)+0)(? 9+-H./+?z3B+-#Be 9CBy9CB#p
1$B:F+-H#1E-#B+-#B\!Z+0)(?#* ./(-6.!S*E*eh*)@E./+-#\!!G 79#B+-HI./+".!0+E*z0+0(J#45+-B: 1'E#B+-#B\!!x U z g:T+-Hy(-+.!-3?61+-#BE*G'? ./(@E#*.!
45E0+-"!x1$(-R$345+-#BE*I./(-6#*45(-.!-#i*@>#* +-Hn.!?6E3*M+!$+-Hn4JH./(.!45+0)(#i0+-#4/U g:Z+-Hn-45E*6.!--3? 1+-#BE* G!? .!*$=!(+-H @!M`#m#i*45(-.!-#*@Z#*>+-H".!?6E3*M+g!»+-H4JH./(.!45+0)(#i0+-#4 45E*-3? )( .|g\].!3+-H 4H./(.!45+0)(J#0+-#4pJUx}9H+-H$#B(.!-3?61+-#E*(-LR3#B(m?.!*+0D45E?6"B-g1(#i45 .!0+-#4F.!6+-H`4JH./(.!45+0)(#i0+-#4F#*45(.!0)UdW +-H045E*#+-#BE*HE G ? ? .
Ì
- Hp7m+-H$./+g1$(#4597#D"?6E*!+0E*#i4).!B: #*45(.!-#*@z#*>.!*`3*!D$0)(-\!K? .!* r.!45+0!(U }nH#z#?61$i#BvD!+-Hd+-H./+1(#45`4).!*dD'K7n(#+0+0*d.!6.N`0 &#"1, $ &C!9+-H 3*!D$0)(\!Fr.!45+0!(pG$.!*F+-H./+91(#45#P#i*,\!)(-+-#D$Bv#*`+-H#f^.!45+0!(U awZ*7 45E*#)(9. ?z3B+-#Be1(-345+P0)+0+-#*@UmawNrR4)3$PE*T0+-./+-#i4 g)(-+0(.!*e .!-H 1(J#45A45E?61)+-#B+-#BE*G79H#4JH#81)(H./1$T+-H;? E0+81!1$3$./(T? .!#*M+-.!#* 45E?61)+-#B+-#B\!.!--3$?61+-#BE*c#*_+-H./11$#B_#i-45(-)+0F4HE#i45T#B+0)(./+-3(-!Ucl!(+-H m)(+0(.!*eh.!-HN-)+-31G)y$* .! +-H[1(!y+-=!(»y( ? G 6G 79H#4JH61(-345[.N-3D$0)+! +-Hn@!M N.!* 4HME0m1(#i45+0Z? .]o#? #) 0+-./+-#4"1(-!y$+-) U )+ *M+0)(9.!f+-Hvy(J0+C./(-@E3$?6*,+-9.!* *M+0)(9.!f+-Hi.!0+ F [*!+0 ./(-@E3?6*M+-f#* )\!)(-:1(-!y+[^3*45+-#E* Ul!(gyoR GMB)+ V .6\!45+0!(+-H$./+9-./+-#0y$
Ì###
# # #
Ì####