A Two Country Model of Financial Capital Movements as Stock Adjustments with Emphasis on the Effects of Central Bank Policy

K.7 (#697 in RFD Series)

' INTERNATIONAL FINANCE DISCUSSION PAPERS

: " A Two Country Model of Financial Capital Movements i a as Stock Adjustments with Emphasis on the Effects x J of Central Bank Policy

by

Lance Girton and Dale Henderson

Discussion Paper No. 24, March 23, 1973

Division of International Finance

Board of Governors of the Federal Reserve System

~ The analysis and conclusions of this paper represent the views of the authors and should not be interpreted as reflecting . the views of the Board of Governors of the Federal Reserve >. System or its staff: Discussion papers in many cases are : circulated in preliminary form to stimulate discussion and ; comment and are not to be cited or quoted without the permis- “4 sion of the authors.

tS St ens Steet SS

II.

IIIf.

IV.

TABLE OF CONTENTS

INTRODUCTION

THE MODEL

A. An Overview

B. The Portfolio Balancing Behavior of Ultimate Wealth Holders

C. The Balance Sheets and Behavior of the Central Banks

D. The Market Equilibrium Conditions

E. A Geometric Presentation of the Model Assuming Fixed Exchange Rates

THE OUTSIDE RESERVE REGIME

A. An Overview

B. The Effect of a Shift in Asset Demands for Securities on the Securities Markets

C. Policy Responses by the Central Banks

D. Policy Responses and Target Variables

E, Another Type of Shift in Asset Demands

F, The Reserve Stock Constant Policy Response

G. Policy Responses and Policy Initiatives

THE KEY CURRENCY RESERVE REGIME

A. An Overview

B. Modifications in the Model

C. A Speculative Shift

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TABLE OF CONTENTS continued

V. THE EFFECTS OF A DEVALUATION ON FINANCIAL ASSET HOLDING

VI. FRACTIONAL RESERVE BANKING A. An Overview B, Assumptions and Modifications in the Model C. A Shift in Asset Preferences

D. A Note on "Fractional Reserve Central Banking"

VII. THE DEPENDENCE OF THE EFFECTS OF MONETARY POLICY UPON THE DEGREE OF SUBSTITUTABILITY BETWEEN SECURITIES AND UPON RELATIVE ECONOMIC SIZE

A. An Overview

B. The Effects of Moretary Policy in Some Polar Cases

C. The Impact of Increases in the Degree of Substitutability on the Effects of Monetary Policy in the General Case

D. Relative Economic Size and the Effects of Monetary Policy

VIII. CONCLUSIONS A. An Overview B. The Economic Impact of Policy Actions

C. Some Comments on Balance of Payments Adjustment Mechanisms

D. The Relationship Between Changes in the Demand for and Supply of Money and Net International Movements of Financial Capital

APPENDIX

I. The Comparative Statics Model

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TABLE OF CONTENTS continued

APPENDIX continued II, The Effect of Central Bank Sterilization Behavior on the Changes in International Reserve Holdings Required for Adjustment III, Some Implications of Stability Analysis

IV. The Comparative Statics Model With Fractional Reserve Commercial Banking

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- 6S -

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- 09 -

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- 19 -

a OTIS

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(871) MG), UW = GS + of + HOF od) = NU (®IT) Wt MG T2)U = S+ YO + of = gH (POT) M(2°3),3 + MGI2)F = (od - D US sd Ul (86) M(,2°2) {U4 M (,2°2)d = gf - 38 - 2 = fl

:suotjzenba 3uTMOTTOJ xy UL peZztTieumins o1e SUOTIEI9ITP

- @29 -

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- €9 -

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- 9 -

Jsnu aAIno NN 243 uUoTJeANZTJZUOD sty USATD “OT ain3tiq ut AI pue If se pazeusTsep aie suoT3e1 asay], “19YyIO 94 FO ktddns ssaoxe pue Asuouw jo odfq auo oz puellep ssaoxe JO suoTSei1 ut yooys ay} worz ATIOeITP ZuTJ[NSeI SeAIND NN pue WW 2432 UseEMJeq JOESIeIUT YSN yooys ay} wors A[}0eAITP BuTZ [Nse saaand qq pue qq ay} souRqINySTp 344 jo WIOF Jy WeYA zeq Je ON °S3zOSSP epTs3no uy saBueyo esayi splToy IT FF UeYI SATITANGS ‘s'n ult sa8ueyo aArzasei sprloy gown 947 FT wntaqt,TtInbe Jesse oF syooys UaATZS AOF siow ajenjonTF [TTA sSUTp[oy eAzesel “y'N ‘eatssed

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- ¢9 -

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- 99 -

‘os a9uOp jou peYy suot yN{TIsut

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- 19 -

Te,

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- 3o -

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X UT UOTJONpal AS{[eUs e 02 peaT OF aseyoind jeyIeM usdo ue pasned sey AJT[TQEINITISGNS paseatoUT VSO JSATF B42 UT 2eYI BOS aM QBT pur eg] saan3tq Butaedwon *A[Nse1 oJeUTUAaJep B Je BATIIE OF aTqeuN UsEq aAeY 9AM SAQTNSTque vy} OF peeT YOTYM SeToUspusy But [TeAreqUNOD 943 gyno [Teds ued om YBnoYyITY “ITNOTFJTp e10M SF gosn 243 Aq aseyoand qayiew uado ue Jo 93e1 “S*N BY JO TAAST BYQ UO JoOaFFZe OY OJ AVTTTqeanatasqns paseaiout Jo suoyzzeoT{ dwt ayy Zututw193eq *saTaTanoes “yf AOZ JoxAeM YQ UT pouTejzureM eq 03 ST wNTAqT{ Nba Jy ,1J UT aseardep azsZ1eT e Aq peyojeu

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- TIT -

peatnber sf ,1 UT eseetdep JeZ1eT e Jey, suveu But}zejoI are gg pue Jd 42Oq WeYQ YOR y_ °*,1 JO anTea UaATS B AJOJ SaTATANDGS *S'N AOF Jeyiew ay} uy puewep sseoxe jo jJUNOUR UueATS B eAOUaI 03 partnber o1e XJ UT suOTJONpar JaTTeWs Jey ST peoNper ST satnpeyos gq eyy UT IFTUS paeMuMop 394} 3eY} WPF BYR FO uoT}eAeAdIaqUT DTWoUODS SUL ‘aseyoand zoyIewW uado ue 13aqJe STB} I YOTYM Aq Junowe 9Yy} UT UOTZONper B OF SPOT AATTFqQeanqtasqns ut eseetouT ue ey ST IT A[@eATT etow ay} seTNpeyos dq IO @q@ ey. ASYITE Jo UoTIeIOT Jo Junowe ey} AST TUS 9Yy2 STNpoyos €q ey. UT 3FTYS pAeMUMOp USAT & TOF JeYR STeeAaI ‘umoys Jou sAPY 2M yotym ‘ydeis ay 3 YT uoTjequeutiedxg ‘oseyoind Jeyzew uedo ue 1933e STLBJ I YoTyA Aq Qunowe syQ UT UOTJONper B OF SpPPeT A¥TT1TqeynzTAsqns UT aSBaTOUT Ue ZeYI ST IT ATSEATT S10 9yQ seTNpeyos qq oy UT IFTYS PpABMUMOP BY} UT UoTIONper dy} 19ezveAZ ey. SeTNpeyss Ad pue qq eur JO uoT}e}OI JO JUNOWe UsATS B JOZ ATABETO ‘“eQT eanstTyg uy uey 194e813 ST Tglg pue Ogg us0Mjeq BDUEISTP 2UI QgT PANSTY ut 7eYI Jdeoxa [BOT USPT AT ea ,aTdwoo ere Lay, Jey OS QgT pure egT SeAN3Ty uMeip oAeY eM *pegonperz aq o2 gOSN 247 kq aseyoind jayzew uado ue worz BUTI [NSer eTNpeyos qq eyy UT IFTUS pieMuMop ey} sesned JI ,1 ueAT3 eB A0J pue ‘auo aAtjtsod jo adots e& YJIM BUTT & pAePMoj 93B}01 OF Jaq pue gg YIOq sasned AT “erey 3uejzodut aae YOTYM saTnpeyos ay} uo szoezJe Jo sputy om} sey ATT TQeINITISQNsS peseatouT “A UT UOTJONper AaesireyT e OF pReT OF aseyoand jayzew uedo ue

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~ @IL -

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- €IT -

UaAT3 e JOU JO AaYyZeYM yse Ysnw aM ‘3saTqZ ‘“BuTYRZeWos Aes ued aM JNqG Sazea ‘S'p aya JO TeAeT 242 Jo aseyoind yeyrzew usdo Ue Jo Jd9zzO ayy uodn AT{TqeINITASqns UT SasearoUT Jo ZoeRdWT ay} Fo ss8ed 9YI UT

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- VIT -

_ M(o)7m —w(0)74 _ . oMP T= T zp

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oes mea+ mtx Z Sap MTT T T = 3p

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- SIT -

m(o) 2m] < | (mea + mbae|

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- 9IT -

oz aundld4

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- LTT -

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- SIT -

Jo sSUTPTOY ATeY} asePeADUT pue Sat JTAandes Fo sZUTp[OY ATeYy. eonper oF SjuapTsel “7 eoNput TT TM 93k Jse19qIUT PTIOM ay} UT VUTTIEep oU ITWTT ay} UT pue suT[.ep [TeUSs ATaA & *S’f 24} OF GATIPTOA aZaeqT st “w'n

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- 6IT -

*‘saA1VSa1 aptsyno jo wao0jz ay} UT SeATES9A SIT TTP SpTOY GOAN e432 °3eY4I Vz0Yy powNsse st QI /T

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~ OCT -

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- TéT -

‘41 paxTy & uaATS 9 UT ASTI B JOSJFO 0 peaztnbez 1 ut

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as

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- 671 -

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- OST -

Ped

- 151 -

III. Some Implications of the Application of Stability Analysis .~

In this section we investigate the implications of applying stability analysis of the conventional kind to the important variant of our model in which r, r', and R are the endogenous variables. We have two major points to make, First, we show that the restrictions on the slopes of the BB, FF, MM, and NN schedules employed in the text are consistent with stability under a plausible set of assumptions about how the endogenous variables change in response to disequilibria. Second, we show that certain restrictions must be placed upon the relative speeds of adjustment in the different markets if stability is to be guaranteed under our assumptions and suggest why these restrictions are required.

Let us assume that the way in which the endogenous

variables change in response to disequilibria can be described by

the following set of equations:

r B(x) z tw _ A48 aT = M% n(F-FC') AW > 0, - ( ) R M(x,0,S) R °3BC+OR+S’ 3 (

r rises in response to excess supply of U.S. securities; r' rises

in response to excess supply of U.K. securities; R rises in response

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(Awy-4a(v-1)] gtd + My “gly = Ze

(ZS¥) “(v-1)€d + sta@g 4 2glg = Te

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- LST -

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‘9 > Awitatdzed = %9

(S9v) Bi

(79¥) co Gata - Fwetay Sd + My "8778 = i)

(e9¥) 69 < Awtatg - My7atg = % azeuM

(z9v) ‘Zp 4 Idlp + z'd00 = be - Cele ‘gaey OM T = ,X = YX UOUm AON TS, SY 50 zoy aatatsod st 9F ST = ,X = YX 705 aatatsod st fe - Cele xT snuL "T = ,V = ¥ Jog _sonzea unmyurm ITOUI yoror pue ,\ pue Y ut seseeroUT YITA eUuTT ep Ze pue Te qeyq umoys eq osTe UPD WI ‘T=, = Y veua anp[eA unuTxem s}} seyoret IT 3247 PUL | pue Y ere 12a82eT 89 1OZIeT st 9 20p Edegig - = tO aeyI eARY OM ‘fo pue ‘2m ‘To Sazozereyy pue fg

pue ‘¢q ‘Tg ueat3s *7eUI xTpueddy ey? Jo II 341¥d FO stshTeue oy} wor mouy eM “TL SX SY 50 TT? 403 aATITSOod oq 07 %B - Zele z0jy uot -Ipuoo JueToTygns e& FO uoTIBATIAap BY47 YOReYS OM ajoujoog STYyI UI /Z

"epaeasun st wo sds e

au pue ‘eaTjesou ST fe - tele os ‘antae8eu ST | ‘guo 0} ysnoue

qeou ,¥ pue Y Jo senteA pur ot02 03 y8nous zeeu C0 jo senTeA 10d

(19¥) “fran - 44(,Y-T) ] = + [inv + 7a) 1 + 280 a nglg = Ce

‘sprets Ge jo ZuTz Tamer snogoTeuer uy /T

squsseidex ¢z ean3Tqz 3eYI asoddng ‘AT [BWAOZ SSeT paqTszosep 24 ued

/@

pezTMTT aq ysnw YoTYA FO s}oeFJe 943 soinssead SutZzt{TTqeysep x47 Inq ‘aatqonaqsut Azan Jou ase T > iv SY S50 11® 205 aaTzFsod st fe - Cele Jey} eansut yoTYyA €o pue ‘2a ‘To uo SuUOTATpUuod 3OeXS SUL

‘atqejsun st waqshs ey} pue ‘saT}eZeuU ST fe - Cele

os ‘aaTesau st Ze ‘uo 0} YyYSnoue zeeu ,X pue XY FO sen[eA pue o19Z 03

ysnous ie8U Tp jo senyTeA oz 2eY? IPETO ST 3] ‘°s9u0 yoroidde ,¥ pue XY

Jey pue ‘orzez yoeoadde To eT ‘st 2eYyQ foraz yoroirdde Tg je, pue

(o9v) {tay +

iZa(v- Ty - ta(V\- eg dd fg a(X-D 1 + Fae - “EQOD] 7 + V zat fe2d = Ze

- 8ST -

*azay quewnsie jo suTT Sta ansand jou. op em ang ST S VEX 50 Ile rox aatatTsod aq OF |B - Cele OJ UOFZ}pUodD JuaFoTFINS B Jo woFIeAFAep B YyoReys 07 pesn aq upd JuomnZie jo euTT JBTFOTS V

Oz “Tg (Ge q uey} 1038013 sAeMTe® ST To qeya fem be * _—_

yons uy IFWFT WNoyIFA aseorout €o pure ‘@p ‘ly yey. st eatnbet Ayyree4 am Zeya ‘AT SnosuezUeysut qsn{pe sqoyzew qosse oy TTP qeyq supunsse aie eM aouTg ‘eATITSOd st €e . Zele uay ‘quemgsn{pe Fo speeds

om} z2yz0 ay JO J9YyITe UT aseorouy ue 4zTM aNTPA UT SsaseeroUT YOTYM syoyIeW OM} 12YyIO 94} UT quowjsn{pe jo speeds ey3 Jo uot }ounj e OF ATI -B] a1 ,y8noue e32eT,, St soTaqzanoes *S*f oF 2exIeW eyA UT jue snl pe yo poeds ay3 JI TS ,Y SX 50 TIP 405 aatztTsod 9q 03 te - Zele za0z uoT}Tpuod quetoTszgns e St pue | = 1X = Y 103 aat3ztsod aq 02 *B - Zele

93 ZOJ UOTITpuod eToOTFINS pue kzesseoeu e st ld (Se-a) uey 1038013 To * eo)

2. (22\% Qn z V 2 fe (99¥) e9 lis) t | +IgT- = 18 *%

fo19z 03 [enbe Ep - Zele sayem yotym Ig zo anreA sAzjFsod ay} TOF BATOS urd om ‘szoqowered z9y}O 842 TTB UeATO

(a8ed snopAeid worz penuyjuos a@30U3003)

¢2 aYNOIA

7)

+

‘NN MoTeq saTT ated oer Jso187UT Sut{TeAeaid ay JT JseeyzNos pue NN 9ACKP SOTT ated 0381 3Ss9109UT Zut[Teaeid ay} Jt ysemMyjiou sAoW qq pue ad *cosv) 4q (64”V) aoeTdaz om JI /T

ues ssaooad ay} pue ‘uotse1 SsTYy} UT ,,peddezj,, ewooeq ued ated

ajei yseraquT ButT{TeAead aya ‘fo pue ‘Go ‘Ip uo peoetd ere suot3 -oT1}Saq awos ssaTuUQ ‘“SeATeSeT eSOT OF sanutquoo *S'f ay3 pue ‘STTeF a ‘sesti ,21 ‘aq pue WW eAoge uoTZe1 pepeys ey} UT suTPeuwlet ated oa3e1 qserequtT But[TeAeid oy} se Buoy sy ‘3seeyzNos ay} OF sAOU aq jue gg qeyq soattdut sesso, aAraset “S*f) FO uoT}eZT[T193s ayz pue ‘Aeuow “S*f jo Ajddns ssaoxe ue st o1eyy Satduexe oJ ‘Oe ay _*squeq yearque. OM} aya Jo suoTjerzado uoTIBZTTTA9IS OF anp sat jtanoes cam jo Atddns 94} ut (asearsep) eseeroUT uP pue satatanoas *s'n jo Atddns ay ut (aseaiout) aseaioep B OF pPeT (suoTzeTNuND.e) SessoyT eSe4L *saAtesol (So eT -nunooe) sesotT “§ ‘N 243 pue ‘fauow *s*p (103 pueuep) Fo Atddns sseoxe ue ST o294} eTNpeyos WW 94 (MoTeq) eAoge sited 9381 JsaerejUT [Te 10g *sartnpeyos qq pure gq 947 UO suotzeiado uoTzeZT{T1eIs Fo sJoeFyze UA quaseidexz ysemyzaou pue JsPeyRNoS Zutjutod smoize TeuoseTq “1 uo aanssead piemMuMop pue ,Ji uo aainssead paeadn st erzey} os Sat zTAnoes “S'N 4Aoj pueuep ssaoxo ue pue set zTanoes *y'n jo Atddns ssooxe ue st er9y4 atTdwexsa 10; ‘Oe ay ‘suoT8a1 anoy sues 947 FO yore ut 1 uo aainsseid 3y3 queseidea umop pue dn 3utjutod smoizze [POTIIEA *sartnpeyos qa pue aa ayy Aq Jjo payrew suotse1 InoFz 9Yy3 FO yore ut ,1 uo aansseid 343 quasesidaz WYysTAI JO 2FeT Zutqutod smoiie [eUOZTIOH «Te 3e st qutod wntiqiTrTnbs meu ey ey? OS T = ,t = ¥ zeYy pue Oe 3e sem yOous ay}

aztoyeq qutod wntaqt{Inbe ayy ey SUNsse sn jay ‘*‘aourqanjstp [eT Tut

ue Jazze SsaTNpeyos NN pue ‘WH ‘dd ‘Gd 947 FO uoTjeangstTjuod ey}

- O9T -

“gcq a8ed uo [ aqouz003 Peg =/Z

*gcT a8ed uo [ a20u}00F 98g /T

YoTYM uT esAT}eZeU fe - Cele aney ues am ,Usnousa TTeUs, ST YoTYyA Tp Jo onyTeA e& pue T = ,Y = Y TOF eYF SAOGE UsBS ZAPY 2M ‘ZIWIT JNOYIIA seATeSaI sazerTNuNd.e “S*f 84} pue ‘sasTi 1 ‘s[[e} ,1 eseo sty UT ‘Ad pue ‘gq ‘WW MoTeq uoTse1 pepeys ayq ut ,,pedderz3,, 3utwodeq ated a}e1 3se193UT Zut[teaeid ay} ut 3[Nser ued [Tews 003,, ST YoTYyA Ip yo anzTeA e MOY 3sa3Bns 07 pesn aq UBD SUOTZEOTJTpow JoUTW YIM JusUNSIe Jo BUTT oes STYL ‘atqeqsun st woqshs ay} pue ‘ated a}ei JseteqUT Sut[Teaesid ay} sutez -uod sABMTe 2T 2eY OS YBnoue ATptde1r spuedxe qq pue WW eAcge uotTser pepeys 343 to pue 2p 03 eatqeTeEI _uITBUS 003,, ST To JI ‘aq pue aq JO JueWeAOW przePAJSseey NOS nua’ caenquesse Avuow jo ATddns ssaoxe AITey. JO pTa 303 03 szdwazje suezTITO “g'N OF eNp yx UT SesPetIag ‘dq pue gq Jo JUaWeAOU pieMJSPayzNos ay. eJeNQU|DDe Set ITAN.esS “AA OJ JoyAeM ay o2eAqT[INbe 07 BuTpue} eTTYM ,1I UT SesBaeToUT Inq ‘dA pue gq Jo JUawWeAOW pieAJseayINoOS 9Y} piejeI pue set ITanoses *§*n IO Jayrew 9yQ oqeAiqT{Inbe 07 pus} AI UT SaseatoUT “syUeq TPAUSD omy 943 4q suotjezedo uotjezT[T193s pue SessoyT eATaSeT “*S*f jo azts ay. seuTWAsjJep YOTYA *€o ‘kauow Jo ATddns ssaoxe ATeYy] 03 sueZzTqTo ‘s'g Jo asuodsea oy} pue ‘2d ‘seTzTanoes “YN IOFZ 4tddns ssvoxe 0} ,1 jo asuodsarz ay} OF VATIETII T[eUS ST ‘Ip ‘satqqzanoes ‘g'f] 103 puewep ssaoxe 02 1 Jo asuodsez oy. JT Jaq pue WW ePAoge uoTZe1 pepeYys 24) uI UTPWeT [TTA ated aje1 JsaroqUT B3uT{TeAeId ay 2eY epNtToUOD UFO

aA astoeid aq 02 BuTqdmaqje 3NOYUIIM “JTWTT JnNoYy_TA snuTjUODS

/T

- I19T -

*AVITTqeqs vsansut 0} qUaToTZgNs uoTITpuoo e 10J QST eased UO T 3}0UJ0OJ 99S /T

suoTJTpuod wNTaqt{tInbe ey *SuTyueq [TBTOTeuMIOD sATESeIT [ePUOTIOBAF Jo qunoose yToT{Tdxe sexe YOTYM TeEpou & uo peseq suoTsny{su0d 0} [BOTIUapPT eae ‘pszeIdiz9zUT A[aadoid uaym ‘xtpueddy ey? Fo I 31eqg JO [@epow ayy uo peseq suoTSNTIUODS Suotjdunsse ute}1ea0 Jepun

“yey) moys 03 ST xTpueddy ey Jo qaed sty} jo asodand oul

sutyueg [eTorsmmoy eAzesey TeuOTIOeIZ UTM TPPOW soTjeIS aATJeIeduoD eyL “AT

ts ivSY 5 0 10OF PTqEIS ST wajsks oy} 2eYQ eAInsse OF fo pue Cn 03 tn aeqer ,U8noue 231eT,, ST To yey SuNnsse am ‘aouRqInjsTp TeFIFUT ue zaqzje wntaqt{tinbe meu e suteq7e we sks ay} ueym [nzJ3uyTueem ATuUo ST stsh[eue soT}eIS aATIeARdWOD BUTS “7 epow ay Jo satziedoad sot}e3s aAtjzeiedwod 3y3 yaTA pauasouos st Aesse sTyq * T@AeMOH ‘asTie prlnoo AIT TqeysuT Jou Jo JaYyVeYA BuTutw1s ap ut queziodwt eq prTnom fo pue Zo jo azTs 243 0} eaTIeTAI Tp yo azts ayy ‘eAoge sy “eased payeottdwos eiow sty Jo unoooe 2x2] 03 peTsJTpow eq pTNos eAocqe uoTSSNOSTp 94E “YAM qe are sa010y BuTZzT{TqeIsSep AeTFWTS “T > VY 5 0 eum *suot3so2 pepeys om} ay} JO auO UT ,peddezj,, semooeq A[yTenquaae ated a3e1 qsazequtT Suy{qeaead ay} ¢€z eansT_ Jo sw19e7 UT ‘atTqeqsun st weshs ayy pue ‘31ed [Pe7 aatztsod e YIM S}OO1 xatTdmos yo ated @ 10 3007

aAT3TSod auo savy ysnu wazshs BY} FO uot zenbe oT9STaOPABYD B42 ESP

- 29T -

Sg0uaTUaAUOD

AO} ay UOTITUTJap sy Jeadez am ‘aAoqe se pauTyJap st Xk Ys8noyITY

(ZV) "0 = (8°, 0°%)y (ELV) ‘Oo = (s‘0°X)W (ZL¥) ‘Oo = (*)g (TLV) ‘o = (Og :Wx0J

SUTMOT[OJF 9Y2 UT waqzsdks dy} 9ITIMeI UBD aM SasuReYyD LL ssaTuN paexT}# o1e ,M pue mM 2eYyQ pue fo19z 3e queqsuod play ere W pue oH ‘ 5a 7243

4 ‘ ‘ SpexTy ere ,O pue ‘oO ‘y ‘gq ‘gq Wey fuoTJeAepTsuod Aspun waTqoad ayy

[Ty ay}

Io} ajetidoidde ete san[ea TeAae eYA Je Jue ISUOD PTey sie s, yey} pownsse st 3I JI ‘xtpueddy ay} Jo I leg UT se uot eJeIdIA3UT ewes 34} sAPY YOTYM SAdJowered AFTYsS are YOTYA s,efty ey. 105

qdaoxe 32x93) a4) Jo 7g a8ed uo asoy. se owes dy} aie sUOoTJeNba assay]

(O4v) O= [as +( oH + jo + oz +

rom (a - Wl + cab Pp - M(efeys a2) pun ( _ 0 €Tiy« ‘ 69¥) O= EE: - (S + ,oH - YO+ OF | - M(eo ys ,az%2t)u

vod ahs - ,m(etZy!, 262), su + m(etly *,262)3

(49v) 0 = [(S + oH - YO + of) (sr) vod = of - a) - m(et@y *,3°3),qu + m(etly ‘2 ‘a)q :SMOT[OF se Ud}97TIM aq UReD SaTAQUNOD YI0q UT padNporzjqUT ATITOTTdxe st Zuryurq

@AIVSII [euOTIOeAZ uaym ABssa STYJ UT paTpNzs szayxIeW Aanoz ay} AOZ

- £91 -

-fauom paremod y8TYy AOZ UOTJeZT{TAIsS Jo sZUSTOFFFZ90OO OA

aie ix pue ¥ *SOTITATIOe UOTIEZTTTA9eIsS OF pazeTeauN soseyoind Jay1eu

uado squasaider ,o4P pue ‘yo03s Aauow *y*f 943 UO SMOTZ BATaSEI FO

qoedmy ey} eZT{TT12Is 02 Gon y4I kq uayeqzepun saseyoind Jex1eU uado

sjusseidei ‘Ts ¥ S 0 a194M “UP. ‘AT seT TIS “sat aTAy Joe uoTIeZTTFA9IS

0} pazeTeaun saseyoind yoyzeu uedo sjuaseidel o€P aTTym Avuow peremod

usty “s' UO SMOTJUT eATBSeI Jo QORdWT |Yy. aZTT 193s 03 AISN PUA

fq uayeqiepun seyes yeyzew uado ayy squaseidax Is \ S 0 219yM “apy - (62¥) * ogP + UP X= dP (82) 'o9p + EP Y- = oP

:SMO[T[OJ SB pauTjyep o1P vol pue .@ uy sesueyo ayy

*suoT}9TA}SeI OM} BuTsodwT pue suOTITUTJZep oMZ Jo osn BuTyeu (¥/¥) y8no1y (1ZY) JO STeTUeATeTFTP [2307 YZ UTeIGO Mou eM

vs f¥y queadato1

ay} Jo anyea dy} uodn spuadep yesse usaTs e I0F puBulap ssedxe oY47 UO

B UT a8ueyo eB JO JOazZO SYL ‘eAoge se peUTJep s1e YA PUP Vd a194a

u

u (LLY) ‘yi T 7 yit+ Md = 9

‘atdwexa aozy ‘os sa8ueyo u ueyA o8ueyd ,M PUP M ‘xt pueddy ayy Jo I W1eg UT Sy °X 1039aA ay} Jo JuoauleTe Aue sT Fx a10ym (9L¥) ‘os Mua Pit Mat "Kg ‘aaey aM OS ‘SqUapuadapuT oie SUOTITpUOD unTaqT[Inbsa JoyIeU AnoJ ay} Jo very, ATUO 3x} eyR Jo 78 ased uo pansie sAey eM SY

(SZv) "(@ fu oa So SH ‘,2°9) = x

- 791 -

yo yoo3Ss oy} asneoeq YP ou (X-T) Aq s{tez OfTqnd eyQ 09 eTqQeTTeAe satjtanoas jo Atddns ayy *Xauow pozemod ysty uo yp Jo 359zze OUI FO qaed aZzT[ 1199s 03 Aepio ut usyYeJaepun goSsN e437 hq seztes yayrew uado jo asneseq uPY kq sasta ot qnd ayz 02 aTqeTTeae sat Tanoes Jo 4 tddns aul ‘“aoSN eu2 sq play saAreser [eUCTJeUIIIUT UT SSPETSUT 949 jo uotjzodoid e se ploy 07 oTTQnd ayW A0F ST QeTTeAe saTqtanoes “S'n jo Atddns ay} ut a8ueyos 243 squeseidai let (¥-1) - \) wid} su ‘soTqeTieA awes ay} 02 Joodser YITM J 31eq WOIT N pue ‘W ‘a ‘q@ JO SeATIeATIOP yetqaed ay? 03 Tenboa are epue fu ‘,1 ‘4 03 3oadsel YIM N pue ‘W “a “g Jo SeATJeATIep TeTII1ed ayI Wey S]T Buty} ewes oy} Buthes jo AemM AaYyJoUy “STPTUETSFFTP JO 10299A ayQ ut oP pue ogP + SdTIqUe OM oY} pure XTAWeW JUaTOTJJZaI09 9yy Jo uunj{oo paty. ey} 10z Ydeoxe J eTqGeL Jo wa3shs ay} 02 TeoOTIUAapPT ST III eTqGeL Jo weysks ey “III eTqeL UT uMoYys se WtOF xXTAQeW UT (yL¥) U8n0zya (TLV) JO STeTIWUeTeFFTP [PIO SY GITAM UBD OM ydeai3 -ered JseyT ay} JO SUOTIOTAWSeA pue SUOTITUTFEp 94 UBATH (Z8¥) [2 rs - op | ‘ = up ‘fq uaAT3 ST ,Op pue ‘op Sup Suowe drysuotjze[er ay as19ym (T8¥) ‘,oP (a - H) - = SP (O8v) opy - = SP ‘u ut aBueyo e 03 anp ArqUNOD QUeAaTAI 9Y UT Sjasse GAIVSe1 apts no Jo anyea Aduerzind oy} uT seBueyd 0} UBTS UT a3tsoddo 3nq ezts ut [Tenbe aq 02 pazoTAWSeA sie ‘JeaYys souPTeq yueq [e1WUaD

ay? uo swat ButToueTeq ey? ‘,S pue § UT saZuRYyd aI0jZeq SY

- SOT -

Table III

da

lo

- 991

ue atqtssod sayeu oP Jo suotzeredo uoTzeZT{T199S YIM pazeTIOSSe Jou g9sn ey3 Aq JexIeW uado ue Tepom JuerINdS 9yj UT

*san[ PA dATIeSOU

apny[out 03 pepuedxe useq evry ,\ pure XY jo senTea atqtsstwied ay} ey

qdaoxa J 21g JO XTAJeW JUSETOTFZO09 9YQ OF [ROTIUSPT Ajazetduood st

[@pow Juezino ay} Jo XT1A}ZeU JUaTOTFJZa09 aya Ts Vv SY > - areye

LGD - YI =X . ” Lgaz¥-D) -V¥le=%

‘227 OM JT MON *uoTzeJeAidiaqut snogo[eue ue sey ‘SGY-1) 7eya pue g9sn aya 4q pley seAreser [euoTIeUIaUT UT eseeTOUT UP OF SNP otTqnd ay} Jo spuey ay} ut ATddns Aouow “g* OY} UT sSveTOUT BYR ST

uP lez(Y-1) -\J-1T= ap-(Y-T)

v v TY

‘yey. azPeeTO aq PINnoys JI ‘uoTIeZeAdAazUT snoSoTeUuR ue sey Oa GX-T)-¥] wie} sy “oTTQnd ayq oF eTqeTTeAe SeTRTAnses "S*f FO Atddns ay] UT [[eF JO asT1z e zsyWTe eq Aew wajsks SuTyUeG TeToreuMlod *$*f ay} Jo uotsuedxa ay} pue seTes Jayrew uedo ay} jo JoaFze JOU SUL ‘oTITqnd ay 07 eTqeTTeAe saTjTAnoss *s'n Fo AtTddns ay} uo suoTt} -ezlado uoTJeZT{[TAIIS JO ZOeFFOe VY JOSFJO 0} SHIOM wo3sks suTyueq [eTolewuod *s'p ey Jo uotTsuedxe ay “YP a (X-1) fq satqtanses Jo sS8uIp[Toy sq asearouT 07 a Tqe ST waqshs BuTyueG TeTISUMIOD

"s'n aya ‘3[Nsez e se ‘pue ‘yp(Y-T) 4q spuedxe Aauow peremod ysty v

- LOT -

‘pazeptsuod eq ysnu ,\ pue Y Jo senTeA @ATIeSoU 7eYI uotzerepTsuos s0uTu AT@ATIETII BYR TOF Ydooxe SuTyueg [eyIIewMMOD VATeSeI TPUOTIIETF FO aoussead ayQ Aq paqooz ze jou o1e [ 34eq JO Tepow ay} uo peseq suotsnTIU0S xtpueddy ey} jo AI 248g JO Sutuuyz3eq ay} 7e peuUTT INO suUOTIOTAIZSeA [TPUOTITPPe aya zepun pue IA reqdeyg ut ATINJZ pezeas ore YyoTYym (4/y) Ysnozy? (TAY) fq pettduy suotzdunsse oy} tepun ey} sure STU IlV “] 3aeg JO T@epow sy} UT STeTWUEIeTFTP JO 10ZD9A BY OF TBOTIVSPT

Aja a TdwWoo Sf [epow JuazzNd 9Yy} AOZ STeTWUSTSFFTP JO 109A OUR

fo]

‘ pre _ og T= 08?

Pal os

“@P = o€P Fe) ‘JaT aM JI ‘“UoTZeJeIdIeRUT SNoZoTeuUe Ue Sey oP! v

"GP 2 fq ot Tqnd ay} 03 aTqeTteAe seTzTanses Jo Atddns ey} ut

Fe) uoTjONper [e307 B OF SpeeT pue o8PT kq A{ddns fsuow ay} Fo uotTsuedxe

- 89T -

Ys

“961-SLT “dd ‘(q0261 SEW) AIXXXT “1OA ‘SO}MOUCDy JO

[euanop ATaejaeng oul ,,‘UeWZSaAUT UZTa10g OT[OFRAOd Wra]-Buo] sazeIs peatug jo sts euy soueyiej-ueoW y,, ‘UeWITYM “N‘A°W pue °O'N ‘121 LIN

*(eOL6T

‘oamyu) [eITdepg Jo QuawaAOW pue AITTTGOW TeUOTJeUAaQUT UO BdUsSTazZUOD Ae peraatted aededg ,,°Ssmo[Tq pue sy909g FO squeujsnfpy :seq7eqg pejtun ey a world spung w1ay-2IOYS Jo MOTFINO ay, ‘uUeWITYM “N°A°W pue “O'N *I2TLIN

* (696T *ssaig o8eoTyQ Jo ARTSAVATUN ayy sUOpuoT pue o8eotyud) epogqoms “°yx°y pue Ttepuny °y Aq paatpe ‘Xwouoogq TeuoT zeursquyl ey 2 JO sweTqoid Aire au

{queugsn{py squemfeg [euoTzeureqU] pue soueT eg OT[OF310d4,, S°L°yY ‘SuouuTyoH

(9961 ‘UOTQ9ag adoUPUTY

TeuoTzeurIsqUL suoq@OUTAd) OT “ON S‘soueuTy TeuoTJeUASQUT UT SseTpNyAS uoqeaoutag ,,‘AoF[od aqey-eBueyoxg pue ‘TeosTy ‘A1eQeUOW 103Z U0 7 PAZ9RUT DTMOUDT [eUOTIeEUIEIUI JO suoFIeoT{dmM] ay, *se7eO “AM pue “LY ‘uouuT yon

"(ZL61T ‘oomfm) unpueiowa,_ QUewjiedeq puny AreJoUoW TeuoT}eUISIUT 4 UNTAQT TINby OT[OJ}A0g pue sMoT_ TeIFdeD TeuUoTZeUIaAUI,, £49}310g °)°W pue “A'Lr’d ‘Fanoy

"1 *d *(zZ61 Sy Tt4dy) 22972 “ON ‘ZTE TOA ‘aoreumIoD Jo Teuinor

"(2261 YWIeN) LIA “1OA ‘StsATeuy eATJeRTIUeENH puy TeTOUeUTA JO Teuanor ,, ‘St0ay] squauhed-jo-aoueTeg OF yoroaddy Azeqouow ayL, ‘°D°H ‘uosuyor

; “IET-66z1 “dd “(9961 aequaced) IIIAI “10A ‘MeFASY OTWOUODY uedtaouy ,,‘SsmoTd TeITdeD pue SUTE) 2APJTAM :SOTTOFRAOd patsFTsSasAtd ATT euoTtT 7 eur9jIUYI,, S*o°eH STaeqnay

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