American Prices Embedded in European Prices

(1)

HAL Id: inria-00072860

https://hal.inria.fr/inria-00072860

Submitted on 24 May 2006

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

American Prices Embedded in European Prices

Benjamin Jourdain, Claude Martini

To cite this version:

Benjamin Jourdain, Claude Martini. American Prices Embedded in European Prices. [Research Report] RR-3799, INRIA. 1999. �inria-00072860�

(2)

ISSN 0249-6399 ISRN INRIA/RR--3799--FR+ENG

a p p o r t

d e r e c h e r c h e

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

American prices embedded in European prices

B.Jourdain and C.Martini

No 3799

November 20th, 1999

TH `EME 4

(3)

(4)

$%'&)(+*,.-0/)1324/)2-65%'78/),.9:13213;

<>=@?BADCFEG HJIKALNMPORQSIUTWVXCBQYTWZNQSIKA[IU\]ORQSIUTWV

^ C\S_)\Q?BADC`\a`TWA[ZNMUC:b+C`\

cdTReSCBQ"fhg<!iYjk

lYORZNZTWdSQ ^ CmdC`a=@CBda]=@CnVpoJqsrWtutvGxwYTzysCBA{CBd}|u~RQS=tututG BEDZORsC`\

Nuu kVQS=NIU\ZORZCBdWC!ORdCIKVQCBdC`\SQC ^ IKVg"ADCBdSIUaORV[TWZNQSIUTWVZNdSIUa`C`\IKVpQS=@CMPOWaJH)a=@TWMUC`\ADT ^ CBM

j@TWdO>MPORdSsCaBMPOW\\TRNZO`_sTR0\zC\S=@TzQS=ORQIKVFQS=@CdCBuIUTWVp!=@CBdCQS=@CLNdTWZCORVZNdSIUa`CIKV@aBdCOW\C`\!IKQS=QS=@C

QSIKADCQTAORQSLNdSIKQ _s¡QS=NIU\YZNdSIUa`CpIU\YC`¢JLORMQTQS=@CgYADCBdSIUaORV£ZNdSIUa`CTRORV@TWQS=@CBd¤aBMPORIKAv!¥¦CpuIKysCpC:b@ORA[ZNMUC`\

IKV§!=NIUa]=¨C©C:b+ZNMKIUaBIKQQS=@CXa`TWdSdC`\SZ#TWV ^ IKVN8aBMPORIKAD\ª<>=@C©a]=ORd]OWaBQCBdSIK«zORQSIUTWVªTR¤QS=@CXg"ADCBdSIUaORV¬aBMPORIKAD\

TW{NQ]ORIKV@C ^ IKV©QS=NIU\!O_dCBAORIKV@\}ORV©TWZCBVv¢L@C`\SQSIUTWV

®°¯±²³p´ µu TWZNQSIKAORMY\SQTWZNZNIKVN@¶dC`C°{#TWLNV ^ ORdS_·ZNdTW{NMUCBAD\AORdSQSIKVNORMUC`\!MPOWa]H)a]=@TWMUC`\ADT ^ CBM

LNdTWZCORV©TWZNQSIUTWV@\g"ADCBdSIUaORV©TWZNQSIUTWV@\z

¸K¹º »¼½º>¾0¿K»ÀÂÁBÃ

ÄÅÆÇ#È¡É3ÈÅ@ÊË}Ì¶È0ÍsÎJÏ]ÉÑÐ"ÒÓFÔ¡ÕÖÒ]×ÙØÂÚ!ÇNÒ.ØÂÛSÒ]ÕKÎ@È#×ÝÜÞßÚØÂÛSÒ]àÂÜÚáØáÎ+È#âWÒ]ã!äRØØÂåàËmÒàæRÚ:Î)ç:çè`é.émËmÒ]àæÚÕêÒYë¡Ò.ÕÙÕÙÞáÚ!È#ÚáìÚí

î

ÎRïàÒ.æÛáÚ:ÎÚÉPãÒ.×ÙÕNðsñ¶ò:åzàìRÒ]×êæWóÛáÚàã!×ÙÛáØáôÚáæäuÛ:ôõ'à

ö

ÌÑÆÊÌ¶÷[ÇNàò]ñ3ÚÜ¡ËmÒ]Üâzø)Î]ßò.ãÒ.×ÙæRÚ#ìÚ#ëò:ÕÙåÛáÚSÒ.åÎ]Êò`ÛSù`åÚáæRÛáò.åàÂÜSÎ.ÔÇ0úSû:éÎç]ÐzúSé.üýÚ0È#âRÚØÂæWÒáþÈ#ÚSìÚ íÎ.ïàÒ]æRÛáÚ.Î:ÚÉPãÒ]×êÕKð

È#ÕêÒ.åWìzÚ:ôËmÒ]àÂÜ×ÙæR×Öó×Ùæà×êÒôõÖà

Unit´e de recherche INRIA Rocquencourt

Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex (France) T´el´ephone : 01 39 63 55 11 - International : +33 1 39 63 55 11

T´el´ecopie : (33) 01 39 63 53 30 - International : +33 1 39 63 53 30

(5)

V£\IKVQBdC`\]\CORL+bhTWZNQSIUTWV@\}gYABdSIUaORIKV@C`\ ^ ORV@\}MUCADT ^ ?BMUC ^ CpMPOWaJH)a=@TWMUC`\z}cTWLNdmLNV@C

yuOW\SQCaBMPOW\\C ^ CZO_sTR\zTWV·ADTWVQSdC°¢JL@C ^ ORV@\MPO©dBuIUTWV§T·MUCZNdSIb6LNdTWZ`CBV§C`\SQaBdTWIU\]\]ORVQDCBV·MPO

AORQSLNdSIKQuNa`CmZNdSIb C`\SQBORM0ORL ZNdSIb°g"ABdSIUaORIKV ^ LNV@CFORLNQSdCmTWZNQSIUTWV V ^ TWVNV@C ^ C`\!C:bNCBA[ZNMUC`\!T MÝTWV

C:b+ZNMKIUaBIKQCMUC`\}TWZNQSIUTWV@\mTW{NQCBVL@C`\OaORd]OWaBQBdSIU\]ORQSIUTWV ^ C`\YTWZNQSIUTWV@\mgYABdSIUaORIKV@C`\¤¢LÝTWVha`TWV@\SQSdSLNIKQFORIKV@\SI

C`\SQ!LNV@C¤¢JL@C`\SQSIUTWV©TWLNysCBdSQCu

´ ² ORdSd!BQFTWZNQSIKAORMZNdTW{NMU?BADC`\"¶dTWVQSIU?BdCDMKIK{NdCu0AORdSQSIKVNORMUC`\ADT ^ ?BMUC ^ C[MPOWaJH)a=@TWMUC`\z

TWZNQSIUTWV@\LNdTWZ#`CBVNV@C`\¡TWZNQSIUTWV@\"gYABdSIUaORIKV@C`\

(6)

& # ¤ ¡]

' TWV@\SI^ CBd"QS=@C¤aBMPOW\\SIUaORMMPOWaJH)a=@TWMUC`\YADT ^ CBM)(

*+-,

. / 0

+-,

.

*132546+7,

.

*98

. :

~+K<;

+-,

= / >7?A@

0BC D 4

?E@

!=@CBdC 8 IU\¤O\SQ]ORV ^ ORd ^ dT!VNIPORV ADTWQSIUTWV

0

QS=@CIKV@\SQ]ORVJQ]ORV@C`TWL@\¤IKVQCBdC`\Q¤d]ORQCORV ^F4 QS=@CpysTWMPORQSIKMKIKQ_

TR + ORV ^v^ CBV@TWQCF{_

GIHKJ

>6LM/

4ON

> N

P

HQQJ

>6L

2

09>

HQ J

>6LSRT0 HKJ

>6L

QS=@CFa`TWdSdC`\Z#TWV ^ IKVNIKVVU@VNIKQC`\SIKAORMsCBV@CBd]ORQTWdXW}IKysCBVXODa`TWVJQSIKVL@TWL@\Y¶LNV@aBQSIUTWV7Y[Z

C

4\^]

C \

\.ORQSIU\á3_)IKVN

\TWADCDudT!QS= OW\\SLNA[ZNQSIUTWV@\QS=@CDZNdSIUa`CTR>QS=@C\TRaORMKMUC ^ gYADCBdSIUaORV6TWZNQSIUTWV6!IKQS=ZO_sTR_YYAORQSLNdSIKQ_

1

?E@

ORV ^ \SZTWQ

>

IU\uIKysCBVv{_QS=@CFC:b+ZNdC`\\SIUTWV

`9ab

c J1

D>6Ld/ efhg

ikjlMm

=n

.porq stu#v

i Y J + ,

i

Lxw

:

~+Ù|;

!=@CBdCFy¨dSLNV@\vOWaBdTu\\QS=@Ch\]CBQTRp\QTWZNZNIKVN8QSIKADC`\°TRpQS=@ChdTz!VNIPORVzU@MKQSd]ORQSIUTWV \SL@a=ªQS=ORQ{y}| 1

ORMKADTu\SQF\LNdCBMK_sb+a`CBZNQmÂTWdF\TWADCysCBdS_hZORdSQSIUaBLNMPORdaBMPOW\\FTRZO`_sTR0\~Y

:

Cu@ZO_sTR\F\.ORQSIU\á3_)IKVN

>5?

@VD G Y J

>OLE@

TWd3

>7?E@VD G Y J

>OL

| @

;:WIKVsCBV@CBd]ORMWQS=@CBdCIU\V@T}aBMUTu\C

^

ÂÂTWdSA C:b)ZNdC`\\IUTWV@\ÂTWd

` ab

c J1 D>OL

<>=@CFa`TWA[ZNLNQ]ORQSIUTWV£TR

` ab

c J1 D>6L

L@\SLORMKMK_ dCBMKIUC`\YCBIKQS=@CBd"TWV{U@VNIKQC: ^ I0CBdCBV@a`CQ _JZC¤ADCBQS=@T ^ \"TWd"f£ORdSsTyJ

a]=ORIKV°ORZNZNdTb)IKAORQSIUTWV°ADCBQS=@T ^ \>QT\TWMKysC"QS=@C}a`TWdSdC`\SZTWV ^ IKVNDTWZNQSIKAORM0\SQTWZNZNIKVNZNdTW{NMUCBA IKV°O ^ IU\aBdCBQC

QSIKADC:\SZOWa`C¶d]ORADCBTWdS<>=@CBdCIU\ORMU\TYO"=LNsCMKIKQCBd]ORQSLNdC>TWV\SZC`aBIPORM)ORZNZNdTb)IKAORQSIUTWV[ADCBQS=@T ^ \ ^ C`\SIKuV@C ^

ÂTWd\]TWADC"ZORdSQSIUaBLNMPORd!ZO_sTR\NORADTWVN[!=NIUa]=QS=@CmaOW\C}TRQS=@CmcLNQ!TWZNQSIUTWV)uIKysCBV°{_Y

J

>6L/

J

RT>6L

\

!=@CBdC IU\!\TWADCFZ#Tu\SIKQSIKysC¤a`TWV@\Q]ORVQ

:

QS=@C\SQSdSIKsCFTRQS=@C¤TWZNQSIUTWV%;>=OW\!dC`a`CBIKysC ^ ApL@a=£ORQSQCBVQSIUTWV

<>=@CZNLNdSZTu\C>TR¡QS=NIU\ZORZCBdIU\QT¤C:b+=NIK{NIKQOYV@CB§aBMPOW\\TRZO`_sTR0\KY ÂTWd!=NIUa=O}aBMUTu\C ^ ÂÂTWdSA C:b+ZNdC`\\SIUTWV

ÂTWd

` ab

c J1 D>6L

IU\YO`yuORIKMPOR{NMUCu<>=@C¤I^ CODTWdSIKuIKVORQC`\!¶dTWA QS=@CORVORMK_)QSIUa¤ZNdTWZ#CBdSQSIUC`\}TRQS=@Cm3LNV@aBQSIUTWV

` ab

c (

QS=NIU\¶LNV@aBQSIUTWV[IU\udCORQCBdQS=ORVIY¦{_

:

@V

P ;ORV ^ Q_)ZNIUaORMKMK_QS=@C\ZOWa`C

@VD[C

4\

\SZNMKIKQ\IKVJQT¤QTmdCBuIUTWV@\

QS=@C¤\TRaORMKMUC ^ b+CBdaBIU\]CmdCBuIUTWVv!=@CBdC¤{_ ^ CU@VNIKQSIUTWV

`

ab

c /

YªORV ^ IKQ\"a`TWA[ZNMUCBADCBVQ"QS=@C ' TWVQSIKVLORQSIUTWV

dCBuIUTWVv!=@CBdC

` ab

c ?

YYkQ!IU\>)V@T!VvQS=ORQ

` ab

c

\TWMKysC`\!QS=@C¤CBysTWMKLNQSIUTWVhC`¢LORQSIUTWVhOW\\T)aBIPORQC

^

!IKQS=

:

@V

;

.` ab

c / G ` ab

c

IKV QS=@C ' TWVJQSIKVLORQSIUTWV¬dCBuIUTWV

:

ORQDMUCOW\SQ[IKV QS=@C ^ IU\QSdSIK{NLNQSIUTWV \CBV@\C<;: fhTWdC`TysCBd!OW\¶dTWA

:

@V

P ; 1]

` ab

c J1 D>6L

IU\V@TWV+ ^ C`aBdCOW\SIKVN@ .` ab

c @

=@TWM^ \·k V·ÂOWaBQ\SIKV@a`C

` ab

c

IU\O£a`TWVJQSIKVL@TWL@\3LNV@aBQSIUTWVIKQ

AO_h{C[dCBAORdSsC ^ QS=ORQQS=@CJV@Tz!MUC ^ sCTR

`

ab

c

IKV6QS=@C

'

TWVJQSIKVLORQSIUTWV·dCBuIUTWVIU\pCBV@TWLNu=QTvsCBQ

`

ab

c

CBysCBdS_)!=@CBdCu

<>=NIU\MUCO ^ \QT}QS=@C>VORQSLNd]ORM@I^ CO}QT}{NLNIKM^ gYADCBdSIUaORV[ZNdSIUa`C`\

:

IÝCu¶LNV@aBQSIUTWV@\

`

ab

c

¶TWd\]TWADCY;{_ZNIUa)IKVN

LNZ°QS=@CFaBMPOW\]\SIUaORM\TWMKLNQSIUTWV

`

J 1

D>6L

TRQS=@C¤CBysTWMKLNQSIUTWVXC`¢JLORQSIUTWV(

1

D>7?E@VD

.

`

J1

D>OLd/

G

`

J1

D>OL

>7?A@VD

` J

@VD>6L/

J

>OL

IKV°QS=@C¤dCBuIUTWVX!=@CBdCFIKQ!IKV@aBdCOW\C`\Y!IKQS=vQSIKADCujNdTWA OU@VORV@aBIPORMZ#TWIKVJQYTRyJIUCBF

`

J1

D>6L

IU\!QS=@CFMPOWaJ

H)a]=@TWMUC`\ZNdSIUa`CTRQS=@CLNdTWZCORVTWZNQSIUTWVD!IKQS=DZO_sTR

ORV ^ AORQSLNdSIKQ_ 1 IÝCu

`

J1

D>6L/

q s t u#v

. J+ ,

. L w

<>=NIU\>CBA{C ^N^ IKVNDI^ COp=OW\>{C`CBVTWdSsC ^ TWLNQ>IKVFÙ|#IKV°aOW\C

0/z@V

g \SIKA[IKMPORd"ORZNZNdTsOWa=°=OW\ORMU\]Tp{C`CBV

^ CBysCBMUTWZNZC ^ IKVQS=@C ^ I0CBdCBVQa`TWVJQC:b)Q!TRQS=@C"¶dC`CY{TWLNV ^ ORdS_ORdSIU\IKVNIKVvOQTRZN=OW\C`\!ZNdTW{NMUCBA

:

\C`CK

ÊÊ æBüBç

(7)

;:<dS_)IKVNQT¤sCBV@CBd]ORMKIK«CYQS=NIKVNs\QTFQS=@C"aOW\C

0/z@

sCd]ORVOWaBdTu\]\OmZNdTW{OR{NIKMKIU\SQSIUaYZNdT)TR!=NIUa]=ORMKMUTz\

OysCBdS_ a`TWA[ZOWaBQY\SQ]ORQCBADCBVJQYTRQS=@C¤CBA{C ^N^ IKVNdC`\SLNMKQ

<>=@CU@d\SQp\]C`aBQSIUTWV8TR"QS=@CZORZCBdIU\ ^ CBysTWQC ^ QTh\TWADC{OW\SIUaZNdTWZ#CBdSQSIUC`\TR"LNdTWZCORV§ORV ^ gYADCBdSIUaORV

ZNdSIUa`C`\!IKQS=NIKVQS=@CMPOWaJH)a=@TWMUC`\ADT ^ CBMwYC:b+QCY\SQ]ORQC"ORV ^ ZNdTysC"TWLNdCBA{C ^N^ IKVNpQS=@C`TWdCBA

:

\C`aBQSIUTWV

|;:6<>=@CBV C uIKysC \TWADC°C:b@ORA[ZNMUC`\

:

\C`aBQSIUTWV q;: OW\QSMK_sC ^ IU\]aBL@\\[\TWADCZNdTWZ#CBdSQSIUC`\TRYQS=@CAORZ

!=NIUa]=Q]ORsC`\!OZO`_sTR

QTQS=@C"ZO_sTR

QS=@C}gYADCBdSIUaORV ZNdSIUa`CYTR!=NIUa= IU\>CBA{C ^N^ C ^ IKVIKQ\>LNdTWZCORV

ZNdSIUa`C

:

\]C`aBQSIUTWV¦E9;:<>=@CDa]=ORd]OWaBQCBdSIK«zORQSIUTWV TR>QS=@CDZO`_sTR0\

TW{NQ]ORIKV@C ^ IKVQS=NIU\FO_£dCBAORIKV@\ORVTWZCBV

¢JL@C`\SQSIUTWV

¦ ! "# ] " ¤ ¤

k VQS=NIU\!\]C`aBQSIUTWV°CmdC`aORMKM0QS=@C}ysCBdS_DÂCBªZNdTWZ#CBdSQSIUC`\TRLNdTWZCORV©ORV ^ g"ADCBdSIUaORVvMPOWaJH)a=@TWMUC`\"ZNdSIUa`C`\

CF\S=ORMKM0V@C`C ^ IKVvQS=@CmV@C:b+Q"\C`aBQSIUTWV

CBQ

/ N v

!#"

F<>=@CIKVyuORdSIPORVQ¤¶LNV@aBQSIUTWV@\¤TRQS=@C[\CBA[IKudTWLNZ¦OW\\T)aBIPORQC ^ !IKQS=

:

~+K<;}ORdCCOW\IKMK_X\C`CBV£QT

{CmQS=@CmysC`aBQTWdY\SZOWa`CmsCBV@CBd]ORQC ^ {_

>

ORV ^ >

u%$

¥¦CF\S=ORMKMa`TWV@\SI^ CBd"ZO`_sTR0\

\SL@a]=vQS=ORQ

>7B7C

4\ ] J

>6LB7C

\

IU\a`TWVQSIKVJL@TWL@\}ORV ^

efhg

,'&

= J

>6L

> 2 >

u%$)(

:+*

@ ;

<>=@CYudT!QS=vOW\\SLNA[ZNQSIUTWVIU\TWVNMK_DQS=@CBdC"QTpud]ORVQ>QS=@C}C:b)IU\QCBV@a`CYTRQS=@CYyWORdSIUTWL@\>C:b+Z#C`aBQ]ORQSIUTWV@\IKVJysTWMKysC ^

k Q¤\C`CBAD\¤QS=ORQ¤QS=@CDa`TWVJQSIKVLNIKQ_OW\]\SLNA[ZNQSIUTWVa`TWLNM^ {CdCBADTysC ^ {NLNQFQS=@C[a`TWVNV@C`aBQSIUTWV¦!IKQS=gYADCBdSIUaORV

TWZNQSIUTWV@\!TWLNM^ {CmADTWdC¤IKVQSdSIUaORQCu¡\TCFsC`CBZvQS=NIU\=J_JZTWQS=@C`\SIU\

, ´%-´ /.Ñ/.´021436587:9 % J *

@L

<;V% !>=?<;V 9!h ! ! A@K<<;B <+C 1

E@

%h'C!>D

FE<GkHC

`

J1

D>OLd/

q st u#v . J+ ,

. L w

I V KJ

` J

@VD>OLd/[

J

>6L%

L ;VM=9%N !

`

!% #h!M=!

@VD[#{C 4\ %)!

C %F= ! OC 1

?E@VD

<;h "!r

Jt u#v8P

`

J1

RRQ D + , P LL

=HS P S .

$! #h!9 T VHUx% VE"9HJIH WEBJ

CBQ"L@\!V@T QSLNdSV©QT[g"ADCBdSIUaORV©TWZNQSIUTWV@\<(

, ´%-´ /.Ñ/.´0XY36587ZI

= Y B \[ J *

@L

]<;VK% !>=F<;V ! !:@K+<;IB 9++C

1

E@

%

VBC !^D Y E \Gk TC

` ab

c J1

D>OLd/ efhg

ikjklKm

=n.po q st u#v i Y J+ ,

i L w

@_;V y 9# "!`<;V~ !>= H)!WE: ~!>= <;V "!'@K a[MJb "c !7hH;A<; B y | 1 'JI!H

9HJdC

eI

V WJ

` ab

c J

@VD>6Ld/

Y J

>OL

L

;V?= %f !

`

ab

c

p{!% #h!?="!

@VD3TC

4\ %)!

C D

%g= !{OC

> BC

4\

<;h

1]

`

ab

c J1 D>6L

!OU 9 kWE

hji

ÚÜâWÒ]æ#kÊÞml:×ÙØË}ò:æRæÚSÒ.åanPÈÅÊË}ÌÂÈ0Ípo¡õò.àrqà×Ùæpl:×Ùæ#l>ò.åÜ0Üâ×êØts#ò.àVkÜò>ò:åzàÒ]ÜÂÜÚáæ`Ü×Ùò:æô

ÌÑÆÊÌ¶÷

(8)

#] ¦p !p

LNdpAORIKV6dC`\SLNMKQ\dCBMPORQC`\QS=@CDZNdSIUa`C

`

J 1

D>6L

TRQS=@CLNdTWZCORV TWZNQSIUTWV6!IKQS=8ZO`_sTR

QT©QS=@CZNdSIUa`C

`

ab

J1

D>6L

TRQS=@CFgYADCBdSIUaORV©TWZNQSIUTWVv!IKQS=©ZO`_sTR4

J

>6Ld/

. = ` J1

D>OL

(

¯J´ ¯ 9

% J

J

>6L/

. =

`

J1

D>OL

L ;V J1

D>6LB @VD

2

_L {C

4\ D efhg

ikjlMm

=n.po q st u#v

i

J +7,

i

Lxw

|

`

J1

D>6L

:

|+K<;

@_;V <;V<%9 p )$!BGk 'J<JK<;VH)!WE` y !>= <;Vt[MJb "B !!^= <;V !'@K#!B !

IBJ\J`<;

1

! !BGk =?<;hIp !% #V! M=9f ! 1 Z C 4\ ] @VD

2 VH; <; c

>7?A@VD

. =

`

J1

D>OLd/

`

1 J

>6LD>"!

@_;V

`

J

zD>6L

p <[ k$#

%&' .'(

\*)

`

J1

D>6L

<<;V ,+

>?E@VD 1 J

>OL

( 2

!-+

./

?E@VD

> D10$?E@VD32 J

>OLMR J 0#L,2

| / J 2>$R4052 2 2>

u%$

R60 u%$

2L

<;V <;V =9f !

B \[ 7

J1

D>6LB @VD

2

_L {C 4\ D ` ab

J 1

D>OLd/

` 158

1 J

>6LD>"!

:

|+Ù|;

, ´0´:9 CBQ J1

D>OLBC

\

C

4\ g!a`a`TWd ^ IKVNFQTmcdTWZTu\SIKQSIUTWV©usQS=@C>ZNdTJa`C`\\ Jt u#v8P

` J1 R Q D + ,

P LL

P

j<;

=n.>=

IU\OAORdSQSIKVNORMUCukMy{| 1 IU\"O\SQTWZNZNIKVNDQSIKADCu@{_@?mTJTW{vTWZNQSIUTWVORM\.ORA[ZNMKIKVNQS=@C`TWdCBA

`

J 1

D>6L/

q st u#v

i

`

J 1 R y D + ,

i L w q st u#v i

J+ ,

i L w

HJIKV@a`C y IU\YORdS{NIKQSd]ORdS_s@C ^ C ^ L@a`C¤QS=ORQ

:

|+K<;=@TWM^ \

<T ZNdTysC[QS=@C[TWQS=@CBd\Q]ORQCBADCBVQ\CD\SLNZNZTu\CQS=@C[C:b+IU\SQCBV@a`CDTR

1 Z C 4\ ] @VD

2

a`TWVQSIKVJL@TWL@\p\SL@a]=

QS=ORQ

>7?E@VD

J

>6L/

` 1 J

>6LD>A!

k

>E? @VD 1 J

>6L

( 2

QS=@CBV8QS=@Ca`TWVJQSIKVLNIKQ _8TRa

IU\Ova`TWV@\C`¢JL@CBV@a`CTR>QS=@Ca`TWVQSIKVJLNIKQ_·TR J1

D>6LIB

@VD

2

EL {C

4\ ] ` J1

D>6L

k > D10$?E@VD32 J

>6LSR J 0#L,2

| / J 2>RB0*2 2 2>

u%$

R40 u%$

2L

@QS=@CBV

1

E@VDC2

`

J1

D>6LSR

`

J1

D10#L*2

| q stu#v . 2 J+ ,

. L R J+ED . L,2w

| / 2>R4052

q st u#v . +BF

.9w 2 2>

u%$

R40 u%$

2q s t u#v . J +4F

. L u%$

w,!

| / J 2>R4052 2 2>

u%$

R40 u%$

2L

ÊÊ æBüBç

(9)

i}CBV@a`ChQS=@Ch3LNV@aBQSIUTWV@\

> ] ` J1 D>OL

IKV ^ C:b+C ^ {J_ 1 @

ORdC C`¢JLNIUa`TWVQSIKVJL@TWL@\m!=NIUa=CBV@\SLNdC`\°QS=@C

a`TWVJQSIKVLNIKQ_vTR

> ]

. =

`

J1

D>OLd/

J

>6L

<TD\S=@T

:

|+Ù|;:NC¤AORsCpO ^ IU\SQSIKV@aBQSIUTWV©{CBQC`CBV©QS=@CmQT[ÂTWMKMUT!IKVN\SIKQSLORQSIUTWV@\ (

aOW\C 1 J

>6L/

2

(\SIKV@a`C ] `

ab

J

D>OL

IU\!IKV@aBdCOW\SIKVN@+ÂTWd

Q-

1

J

>OLd/

`

ab

J

@VD>OL

| `

ab

J1

D>6L

| `

ab

JQ D>6L

|

`

J Q D>6L

{_

:

|+K<;

CBQSQSIKVN

Q ] 2

+C ^ C ^ L@a`CFQS=ORQ

1

E@VD

` ab

J1

D>OLd/

J

>OLK/

` J

^D>6L/

` 158

1 J

>OLD> !

aOW\]C 1 J

>6L

( 2

(FMUCBQ 1 1 J

>OL

ORV ^ y = / NQ

Z 1 R QR

1 J+ ,

P L |

@

°HJIKV@a`C 1 J+ ,

. L @

QS=@C

\SQTWZNZNIKVNQSIKADC y =

IU\\SAORMKMUCBdQS=ORV

1

_a`TWVJQSIKVLNIKQ _©TR

Q ] 1 R QR

1 J+ ,

P L 1 R y = / 1 J+ ,

i

L

i}CBV@a`C

`

J1

D>OLd/

q st u#v i

` 1 R y = D + ,

i

! w / q st u#v i

`

1 J+ ,

i LD

+ ,

i

!rw

/ q st

u#v

i

J+-,

i Lxw

| ` ab

J1

D>OL

<>=@Cpa`TWVysCBd\CIKV@C`¢LORMKIKQ _

:

|+K<;>IU\mORMKdCO ^ _°ZNdTysC ^ !i}CBV@a`C 1 1 J

>6L

`

ab

J1

D>OL/

`

J 1

D>6L

ORV ^ y = IU\

ORVTWZNQSIKAORM\SQTWZNZNIKVN©QSIKADCu°HJIKV@a`C 1 ] `

ab

J1

D>6L

IU\FIKV@aBdCOW\SIKVN@ÂTWd 1 | 1 J

>6L

J

>6L

| `

ab

J1

D>OL

|

`

ab

J1 J

>6LD>OL/

` 1 J

>OLD> ! /

J

>6L

N!=NIUa]=©CBV ^ \QS=@C¤ZNdT)TRS

¯

N

L

;hX! % 9++C!>=<;VjE %K!>=<;V N[ ME " <;V = !BJ\J!'@KWE~ #jT h

< hB !A+-rh!k <; B

> ? @VD .

1 J

>6L

|

J

>6LD

J

>6L/

` 1 J

>6LD> !

@_;V

Z C

4\]

C \

! % V!9 aL ;V-Cg<;h !% # <+CI!>= %

`

S+ C )! <; B

J

>6Ld/

.

j<;

=n m, o>=

`

J1

D>6L

!% #h!

?

!!'Gk

1 J

>OL/

1

z@

Z

J

>OL/

`

J1

D>OL ))

1 J

>6L/ efhg

1 |

J

>6L

Z

J

>6L/

`

J1

D>OL /

1 J!'@ r\U"!% #h!9)) <h ~ <U ! % V!9 1 !% #h!

E -a;V!'J

IU\}VNIKM)(!IKV aOW\C

#

%_efhg

, ( = > $ J

>OL / @

ORV ^ #

'%_efhg

, (

\*)

J

>6L >/z@

NCFCOW\SIKMK_ a=@C`a°QS=ORQ

>-?E@VD

#

%

.'(

\*)

` J1

D>6L/z@V

k V§\SL@a=¬O \SIKQSLORQSIUTWV>QS=@C ÂTWMKMUT!IKVN6MUTJaORMKIK«C ^ ysCBd\SIUTWV TRFTWLNdDAORIKV§dC`\SLNMKQIU\ORdDADTWdC°IKVQCBdC`\QSIKVN

QS=ORVª<>=@C`TWdCBA q+kQIU\ZNdTysC ^ {_ QS=@Ch\]ORADC£ORdSuLNADCBVQ\}O3QCBdV@TWQSIUaBIKVN6QS=ORQQS=@Cha`TWVQSIKVLNIKQ _¬TR

J1

D>6LB @VD

2

_L$C 4\A]

`

J 1

D>OL

IKA[ZNMKIUC`\!QS=@C¤a`TWVQSIKVJLNIKQ_vTR

> ]

J

>6Ld/

=HS

.

S

`

J1

D>OL

!=@CBdC

?A@

¯J´ ¯

?E@

L

;VM=9%N !

J

>6L/

=HS . S

`

J 1

D>6L

B \[ 7%

J 1

D>OLB @VD

C 4\ D ` ab

J 1

D>6L

|

`

J1

D>6L6

! !BGk =?<;hIp!% #V! M=9f ! 1 Z C 4\ ] @VD

hH; <; c

>-?E@VD

=HS .S

`

J 1

D>6L/

`

1 J

>6LD>A!dD

<;V J1

D>OLB @VD

{C 4\ D ` ab

J1

D>6Ld/

` 1*8

1 J

>6LD> !

ÌÑÆÊÌ¶÷

(10)

¯ N L

;h !%JCe=rB !^=`<;V J /UH; !'J !r9HJ @_;H; p 8T 9 <;V!BGkKJd

HUV; ! I! E++C I = N<!V!k< !h % L ;V! 5 % F A )! <;V

!'U BJ\J E6"BJ< J /UH; !'JI!<HJ +

+ ,

. /^>Vg

4O8

. 2 J0 RR

4 N P L1 !

` J1

D>6L/

q

stu#v . J+ ,

. Lxw

`9ab

c J1

D>6L/ efhg

i jlMm

=n

.porq stu#v

i Y J+ ,

i

LxwMD

!`)!:<;V !E9'Jr HUV;V!!8E!!rHJ +

+7,

= /A> D

*+-,

.{/

+7,

. J4 J +-, .OL

*8

. 2 J0 J+7,

.6LSR J+7,

.6LL

*1

L

`

J1

D>6LK/

q

tu

v m

o

J+ , . L

%

` ab

c J1

D>6L/ efhg

ikjklMm

=n.po q tu

v m!"

o

Y J+ ,

i

L

'J !:)!:<;V KJb h !'JtGk!h !>=`<;V !rHJ

a`TWLNd\]CIKQ}TWLNM^ {#CTRudCORQ}IKVJQCBdC`\SQ¤QT uIKysCa`TWV ^ IKQSIUTWV@\FTWV

!=NIUa=¦CBV@\SLNdCQS=@C[C:b+IU\SQCBV@a`CTR>O

a`TWVJQSIKVL@TWL@\aBLNdSysCmIKV QS=@C¤ORdSuLNADCBVQ"TRQS=@CYIKVVU@ApLNAv V@C}O_IU\QTZCBdá¶TWdSA C:b+ZNMKIUaBIKQ>a`TWA[ZNLNQ]ORQSIUTWV@\z

\SIKV@a`C}QS=@CmMPOWaJH)a=@TWMUC`\Y\CBA[IKudTWLNZ°IU\!C:b)ZNMKIUaBIKQwYCBysCBdSQS=@CBMUC`\\>QS=NIU\>IU\>V@TWQ>ysCBdS_IKMKMKLNA[IKVORQSIKVN@¥¦Cmd]ORV

OWaBdTu\\mQS=@C[¶TWMKMUTz!IKVN©\SQ]ORQCBADCBVQÂTWd¤QS=@CMUTJaORMCBAp{#C ^N^ IKVNXdC`\SLNMKQ0!=NIUa=IU\¤AO`_){#CQS=@C\SIKA[ZNMUC`\SQ¤IKV

QS=NIU\

^

IKdC`aBQSIUTWV3(

,

´%-´

/.Ñ/.

´0$#

/&% = %f ! @_;H; B \[ J *

@L

% .

>('BC

4\ hH; <; B

J*)

L G J> ' Ld/z@

% <<;h

>-?E@VD

J

>$RT> ' L G J

>OL E@

!

>7?E@VD

J

>RT> ' L G J

>6L

| @

J*)+)

L G N J

>,'L?E@

% G , J

>,'L/z@

L

;V <;V 1H$!#H)%

?E@

hH; <; B <;Vk9 !h !>=

L

;h!- B \[

, ´0´:9 HJIKV@a`C

IU\ / %u#QS=@C¶LNV@aBQSIUTWV

`

J1

D>OL

{CBMUTWVNs\}QT / N n% JC \

-C

4\ L : / NFIKV 1 / %IKV

>

;YORV ^

\]ORQSIU\UC`\>QS=@CFMPOWaJH)a=@TWMUC`\YZORdSQSIPORM ^ ICBdCBVJQSIPORMC`¢JLORQSIUTWV

.

`

/ G

`

¶TWd 1

E@

ORV ^ V@TWQTWVNMK_ 1

?E@

' TWV@\SI^ CBd>QS=@C¤C`¢JLORQSIUTWV .` J1

D>6Ld/[@

IKVvOpV@CBIKu={TWLNdS=@T)T ^ TR

J

@VD> ' L IKV

J1 D>6LD

1

E@

_ ^ CBdSIKyuO

., ` J

@VD>('L{/

G , J

>,'L / @

iYCBV@a`Cu!{J_§QS=@C

IKA[ZNMKIUaBIKQ!¶LNV@aBQSIUTWV@\QS=@C`TWdCBAv@QS=@CBdC¤IU\>ÂTWd"\TWADC&.

?E@

O[aBLNdSysC

> (

> Z @VD

.r ] C 4\

a`TWVJQSIKVL@TWL@\}TWV

@VD . D

!IKQS=A

> J

@Ld/z>(' D

\SL@a]=vQS=ORQ .` J1 D > J1

LLK/[@VD

ORV ^ / F TWV

@VD .

!IKQS=

N

."

`

J1 D > J1

LL 2 N

., ` J 1 D > J1 LL

> Q J1

LK/z@

fhTWdC`TysCBd{J_Q]ORJIKVN/.}\SAORMKM@CBV@TWLNu=CaORVOW\\SLNADC>QS=ORQ > Q J1 L ^ T)C`\V@TWQyuORVNIU\S=ORV ^ sC`CBZ@\QS=@C\]ORADC

\SIKuV£OW\

> Q J@ \

L/ R10

" m

,32

o

054 m, 2 o

"¥¦C

^ C ^

L@a`CQS=ORQYQS=@CBdCC:b)IU\Q\}Oa`TWVQSIKVJL@TWL@\m3LNV@aBQSIUTWV

1 Z >,' D > J. L ]

@VD

> 1 J

>OL1!/^>

g}\\SLNADC > Q J@ \ L ? @

F<>=@CBV QS=@Cp3LNV@aBQSIUTWV

1

IU\mIKV@aBdCOW\IKVN@fhTWdC`TysCBd

G , J

>6L

( @

!=NIUa]=¦CBV@\SLNdC`\

> (

>,'D G J

>6L }@

ORV ^ > ? >('D G J

>OL

| @

¥¦CD\CBQ /

.ORV ^ C:b+QCBV ^ 1 QT

C 4\

{_£\CBQSQSIKVN

1 J

>6L /

ÂTWd

>?[>('

2 .DORV ^ 1 J

>6L / @

ÂTWd

> (

>,'

<>=@CTW{NQ]ORIKV@C ^ 3LNV@aBQSIUTWVhIU\Ya`TWVJQSIKVL@TWL@\ORV ^ QS=@C

!=@TWMUCZ#TWIKVJQpIU\pQTh\S=@T QS=ORQÂTWdpCBysCBdS_

> D

QS=@CIKVVU@ApLNA TR

1

R ] ` J1 D>6L

TWV

@VD

>IU\dCOWa=@C

^

ORQ

1 J

>6L%

<>=NIU\ORADTWLNVQ\QTv\S=@TnQS=ORQ

.

`

J1

D>6L / G

`

J1

D>OL

IU\FV@TWV+ZTu\SIKQSIKysCÂTWd J1

D>6L

OR{TysC > : IÝCu

ÊÊ æBüBç