-* *-

                                  

              ,  
  30-  40-  .  XX  .,        
 .            
   .        
   .
                       
               
         .
     ,       
.
                    
,          .  
               ,
 ,      
.
             
  .   :       
;            ;
  ,          ;
   ..
                          .
      epea oapa oaae eee poya ao-o  p  
aax opeee o ocax poyo aoo  acca.  epea
pecae coo opy eeoo oype p. aopa  poyoo
epea oy c a ypeee aeco  oapa    ee
eo ypex xapaepc,  a    eee  aeco  -  e,  paep,
yaoa, ycy, oope copooa eo poay.
      epea poya ee eco o ex op, oa ca  opee
pacea pae oape ap  aece ecoepex  aeee.  B
opeeeo   cce   poyoa   epea   pecae   coo
cyey xapaepcy oee oyaee.
   poyoa epea oe  a peao,  ae    ce
pa    aece  oapo,  ooeoc    pyx  yoax
xapaepcax, a  aoo.  B  ocee  cyae  pa  oapx
apo oc cyyo e  xapaep,  a    ce  ee  ea,
yao, eeo a. K aoo epea oo oec  pa
  aaax  ca  oapa,  apep,  oa  poae  oae-ceoo
poya coye pece aa  poa coeo oapa.
   epea poya ee  y a ocec  p.  Bo-
epx, poyooe paoopae coae poy  ac  p,  ocoy
cea axoc  oyae,  oope  oaac  pepe  poyy
eo  ao  oapo  ap    ao  p.  Cooeceo,   ec
oyae   paccapa   pae   oape   ap   a   ecoepee
cycy, pa oe o ey a co  ocoe  oap  e  ypo
e  oypeo    e   oep   oyaee.   Bo-opx,   poyoa
epea oa  oyae. Koa pa xo a  po  c  oo
oapo apo, opee oya ee oee poyooe  paoopae,
oopoe  cocoo    ye  cee  cooecoa   x   peoe.
poyoa epea pac  oooc opeecoo opa.


                      

      pee ceo, ae  cee poyoo epea poc
 ce oapx apo, peaaex pa a pe, a ae  oeaype
ycaex oapo oo po  o pepe ao-o  opac.
e oee co oapx apo peaaec opee    paax  ooo
poyooo acca  e oee co oapo ycaec po  ao
opac, e e cee poyoo epea peeo  aoy-
o poyooy accy.
   Cee  poyoo  epea  oe    epea  a   ocoe
epepeco  acoc  cpoca.  epepeca  aoc  oaae
pea cpoca a a poy p ee e  pyoo  poya  
pyo oapo  ap.  e  e  epepeca  acoc,  e  oee
 cycya c  aax opeee pae oape  ap
  e  e  cee  poyoo  epea.    aoopo,   cee
poyoo epea ye e e, e e  aee  epepeco
acoc cpoca.
      Ee o oaaee cee poyoo epea cy ec
po.
                     E = Z [qiln(1/qi)], i = 1, ..., n,
e  qi  co aao,  oopx opee oyae i- oap;
   n  co oyaex oapo.
      Ec E = 1, opee  oya  ce  poy    oo    o  e
aae.  poe  epea  ec  aca.  p   E   =   0
opee pacpee co oy  paoepo  ey  ce  aaa.
poe epea ec a.
     ,     
       Ha pax c epepoa poyo pa oaae opeeeo
 cee oooo ac, ooy ee yaa pa cpoca ye
 e opae ao. Bea aoa yao po  cpoca
 - eoa a-coc  cpoca  oeo  p  -  ac  o  cee
 poo  ac,  oopo  oaae  pa.  Ha  o  ocpoe  o  
 eco,  oeax  cee  oooo   ac   p   a   pe
 oooceco oype, - ec Poa.
    ec Poa  cpoc  a  ocoe  coocae  aeco  yo
 aoa po  pooo  cpoca  aoo  poyooo  acca    po
 yaoo cpoca p,  ycae  ay-o  oapy  apy  
 oo acca:
                      R = tga/tgb,
   e  R  ec Poa;
      tga  aec ya aoa po yaoo cpoca;
      tgb  aec ya aoa po cooyo cpoca.
      Ec pa e oaae poo ac, o ee ya cpoc e
oaec o cooyoo pooo cpoca, oa ec Poa pae  1.
e oe poa ac p, e oe paa aeco,  e  oe
ya- cpoc ooec o pooo,  a  a  a  ya
cpoc cea oee ace, o ce eca paec   y,  ,
ceoaeo, aee eca ae ye pac  y.
    C pyo copo,  ec  apep  xoa    opac  ocycy,  o  
oocpoo epoe  ooeca  p  p,  ecyx  a  pe
oooceco oype, a oaa .eep, ye  paa  y.
Ec p oya oo-ey p, oe p xo    opac,
yca  ee  oy  paooc  oapa,    yeeec   cooyoe
peoee ee  ae e a oap. Ec p  ecy  y,  ac
p paopc  ye   opac,  yeeec  cooyoe  peoee
oe  e  o  eyooo   ypo.   Ta   opao,   a   pe
oooceco oype oocpooe paoece, oe   p,
ocaec a, e  ea  oapa  oaaec  pao  cpe  epa
yca.
      ocoy cpee ep yca e U-opay  opy,  o  oa
paeca  e  (aoo  po  yaoo   cpoca)      cpex
oocpox epe  pec  a  yc  e  ao  eoo,
paoo yy cpex oocpox  epe.  Ceoaeo,    pa
oooceco oype xapaepo ee X-eeoc -  yc
oapa e c ae epa.


                     

      peoo,      opac   ecy    e    p,    ycae
epepoa poy. Cpoc ao p ocaec a:
                        Qdi(Pi, Pj) = a - bPi + dPj,
e Pi  ea a oap ao p;
       Pj  ea a oap p-oypea;
    a, b, d  - ooee apaep pa.
      Ta    a    poy     p     peca     coo     oap-
cycy, o epepeca acoc cpoca ooea.
p o:
    d < b - poc e oox oapo  ee    copae  cpoca  a  oap
    epo p;
    a > c(b - d) -  ec  pa  ycaaae  ey  a  ypoe  peex
epe c, o ee yc ooee.
      yc  peee  ep  p  pa    oco.  Kaa  pa
cpec acpoa p:
                              i = Qi(Pi - c).
      epe yco aca p  ao p  ay  ceye
 y pea:
                        Ri = Pi = [a + dPj + bc]/2b.
      B ycox paoec e yx p yy pa:
                           P* = (a + bc)/(2b - d).
      Oya oyae p ao p:
      * = P* - C = [a + c(b - d)]/(2b - d) > 0.
      Ta opao,  oyae, o  ycox poyoo  epea
eoa oype ey pa po   ooeo  p  ao
p.
      :     
                                   
      Toap oo paccapa c o pe cooyoc  opeecx
coc, oope  e  axo  opee.  Ta,  aoo    ox
opeee pecae epec c o pe  ooc  eo  ae,
pye oea  e  epy oepe  e  ,    pex  ao
yoco  ypae  .. Cooeceo  peoe  opeee  o
ooe  oapy oy  pae  e ap px epa, e
op ocyecec ey y ( ec pe e o  pocpace  -  N)
eo xapaepca. y, poee  aaa oopa, a  epecee
c   ao-o   po   epa   oaae   ecoc   ao
xapaepc  oape. e oy ecoc o ao xapaepce
ee oap, e e eo oeoc.
      peoo, epoaao a  pe  pcycy  e  paooc
oapa,  A    B,  oeoc  oopx  oao    aax   opeee.
opya pa ycae oap D c a  xapaepca,  o  eo
oeoc peocxoa oeoc peyx apo oapa:
                                U(D) > U(A);
                                U(D) > U(B).
      opee epeac a oap opye p, ocae p
ep cpoc.
      Paccop  eep  pyo  cya.  opya   pa   aao
pcycoaa a  pe    ycaa  oap  B.  B  peye  oe  
peoaa, o apa px  epa  oaoa      opye
p,   pox p pa, o ec opee o    e  e  y  cex
p pa. Teep ee oee coy peocy o o, o  peoe
opeee  paac.  peoe  opeee  o-pye  p
eee ac,  e  peoe  opeee  p-aycaepo.  aaa
opye   p   aaec      o,   o   ye    poyoo
epea epea opeee p-aycaepo,  o  oca  a
coo   cex   cox   peyx    eo    (e    oyc    ea
caoopa).  a  e  ocaec,  ec  oa  apa   oapa   M,
ycaea opye po,  aae    cooec  co  co  xa-
paepca poeyooe eco a poyoo  pa, a o:
                                U(M) > U(A);
                                U(M) < U(B).
      B o cyae  opee,  paee  pepee  opye  pe,
ocac e o, ocoy oeoc ooo oapa  x  e,  e
oeoc capoo poya; a  opee  p-aycaepo  epexo  
opee poya o-pye p, a a oeoc oeeo 
x e.


                   

      opee oy oea oap,  poaaee  pa  pa,  c
o pe pee, eoxooo  oca poya, yoeopeo x
ocoe peoa. e e poy   ecoooe  oyae  
e e eo coca pac  eae xapaepca opee,
e  e  p  pox   pax   ycox   oeoc   aoo   oapa.
Cooeceo e e a poya pacooe py  pyy  e  oee
cxo c x coca, e oee  cycya o  yy  
aax  opeee.  Ta  opao,  oap  oy   paccapac   
pocpaceo     poyoo   pocpace.   C   pyo   copo,
opee ae o-y paccapac  pocpaceo  poyoo
pocpace: ec opee pacooe aeo o eca  poa  oapa,
o ece ooee pacope  apa  a  oyy  poya;  ec
opee oyae  oap  c  eee  eae  coca,  o  oyae
ey oeoc o  eo  opee.  Ha  ocoe  x  yx  po
ocpoe e ae oe  pocpaceo  epea  poya  
oe Xoea  oe Caoa. Paccop opoee  .

                               

   peoo, o oape ap oac py o  pya  oo  o
oaaee -yaeoc o  opee.  yc  opee  pacooe
paoepo  o  eceo  y      opoe.   Ka   opee
pee cpoc a oy ey oapa. e p poa o   o  e
oap. Oa pa pacooea a pacco  a  o  ooo  oa  y,
pya a pacco  o pyoo ee oa (pc. 1). opee pa
py, cxo  pacopx epe: a oyae oap y o  p,
oopa pacooea e  eo oy.
   yc opee N e a pacco x o p A (pacooeo a
pacco a o ooo oa  y)    a  pacco  y  o  p  
(pacooeo a pacco  o pyoo oa y). Ec  x  >  y,  o
opee ye peoa py . Ec x <  y,  o  opee  ye
peoa py A. opee cea ye pa y py,  oxo  o
oopo ye copooac oee  pacop epa.
      peoo, o e a oap  oao  y  oox  p.  Toa  p
yco o pa  ye pacooea a pacco  o ooo oa y
 e oe cpo e coe ecopacooee, pa  A  epe  aoe
ecopacooee, p oopo ee p  ye  acao.    oo
pa A oa  ae   ooo  oeo  ca  .
pa A ye pacooea eee p ,  a  pacco  a1  o  pyoo
oa y. Bce opee, ye a o oe y,  yy  oya
oap y p A, a x oco. B co oepe pa  ,  ocoy  oa
ye ec oep o pacooe p A, epeecc  cey epo
eoo eee p A, a o epexa opeee, yx a  o
oe y. o poecc ye pooac o ex op, oa oe p  e
oayc  epe y: oa y x ye  oaooe  co  oyaee,
poo ooa o oeo x oeca. aoe paoece ye  ca
paoece, ocoy p ao pacooe  y  oo  p  e  ye
cyo epeac  ay-o copoy, e coe  pacooee  -
apaep coe eeoc.

      . 1.   
       

                                   x                      N               y
              a1             

      a, p eoooc ee ypo e, ecopacooee  yx
p ye  cy  cpaeeco  epeeo    ooao  opeec
epo  oac  ocya.  Ta,  cceoa  oape  p   pyx
opoo,   aeae,  o  aoa  ooc  aao  eceo
pxoc a ep opoo.
      Ta opao,  p  cpoao  ee  ecopacooee  poao
ooo    oo  e  oapa  oaaec  cpoo   eeppoa.   o
pocpaceoe paoece ec paoece o Hy: a oo  p
opee  coe  paoecoe  ecopacooee,    y  oo  p  e
cyo e eo, ocoy o e pee  pocy ca oyaee.
      Booa  pya eppea ao oe. Ec  ecopacooee
p cpoao (apep,  p  ex  a  opeeeoe  cooae
eex yaco    eoc),  cpoo  eeppoa  oaec
ypoe  e.      ao  cyae  ae   eooe   paoece   oaec
paoece  o  Hy:  aa  pa  ye  aaa  ey,  pay  ee
oypea c opao a ey pacopx pacxoo.
      caoee  pox  e  p  cpoao  ecoooe   p
opeeec eo pacopx pacxoo.
      Ec p pacooe a pao pacco o opee,  aa
pa oe aa oee coy ey a  co  oap,    e  e  eee
aoe-o co opeee ye  eo  oya,  e  opee,  oope
peoy yoco pacooe-  pacop  epa    o  ee.
ooy yoo pacooea pa oaae opeeeo  poo  ac,
o  ooe e aaa y oee coe e.
      Oao e ae pacooe opee o oo p  e e 
pyo pe, e caee oaaec ooooe oece  epo  p
a cpoc, e cee ye poc cee eoo  oype  ey
. Ee oa  yaeoc  opee  o  epo  p  yeae
aoc pac pacxoo  oc pyo p  eo, a  o
o epe  oo,  a  opee  yaec  o  epo  p,  opacae
oooa ac opo p.
      Ta  opao,  pocpacea  epea   oapa   aoap
a pacopx epe ee  paee  pa  a  p  ceea:
cee oooo ac epo  p,  cee  eoo  oype  
cee oooo ac opo p (pc. 2).
      Ta a e cea epooc poa  oapa    yaeo  pe,
aa pa ye peca coo e ooo, a opyy py a
cox ceeax pa  py-oceoae a yx ceeax c ceopo
oypex aoec  poeye.

      . 2.      
        1                            2



                                   

                          
                                 
           1                
                     2

      eee pacopx pacxoo ee  cy  cpoca  e  
eca pacooe p, a o oac eoo  oype  copaaec,
a oac ooooo  ao   p  opaca,  xo  p  o
ypoe e, oopy opee oo a a oap, copaaec.
      a oe oaae ooe e poca  pacopx  apo  a
ooee  p:  c  oo  copo,  yeee  apo  ee    cye
oax pa pa  pocy  poo  ac  poaa  a  peoao
pe, a c pyo copo, copaaec aeecoco cpoc.
      Moe  Xoea  oaae  ae  coca  eoo  oype
oooco. Ec a pe oae eoa  oype,  o  paoece
eppaa ooo oo p oopooc oapa.  B  cyae  eoopooc
oapa, apep, pocpaceo  epea,  p  oy  aaa
pae e, pe  ce e yy e peex epe.
      co p, ecyx a pe c epepoa poyo, po
poopoao pacop pacxoa    opao  poopoao  ee
ocox epe. ea oapa opacae p poce pacopx  pacxoo
 yee ocox epe.
      Paccop eep oee coy cya, oa p pa aae
ecopacooee,  a  oo   oopeeo   aaa   e   -   oe
'Acpeoa aea  - Tcce.
      peoo, a pe ecy e p, aa  oopx ycae
o  epepoaoo oapa. Kaa pa  pae  o  ae,
a opao op ecooe ee aaa oae e e  oo  a
ee y cpoca, o  a cee eoo oype ey pa.
      ecoooee poaa p pocpaceo epea  oaae
ooe oece a p p. C  oo  copo,  ecye  e
cpoca - poe e ecoooe a oe cpoca. C  pyo  copo,
oae cpaeec  e  -  oceoe  oece  ecoooe
ooo poaa a ey, oopy ycaaae pyo poae.
      Kaa pa cpec epeecc  eo,  ec  oa  epoaao
a pacooea cea o pyo p,  pao,  ec  oa  epoaao
a pacooea cpaa  o  pyo  p.  ooy  paoece    oe
'Acpeoa    aea  -  Tcce  oaae   acay   yaeoc
poao py o pya - acay cee poyoo epea.
      Ta opao, poca, cxoa oe opoao  epea
oapa ae coeo poa  acoe  paoece    eo  opoe.  Ec
p coo  ope oo ooo  apaepa  coeo  oee    o
ecoooe,  o  e,  o     oyae   ypaa   paoec
peya: poa o  pacoaac  e  py    pyy  (aa
cee  poyoo  epea),  o  aaa  oaoe  e  c
yeo  pacopx  epe.  Ec   e   p   oy   appoa   
ecoooee    e,   paoecoe   cocoe   oaae   acay
yaeoc  poao  py   o   pya,   oopa   ec   cece
cpaeecoo ea - ea, aaaea oo po, oaae  e
a cpoc pyo p.


                     

                     
  .       
     . ,   
       .     
        .
            , 
:
                               dC(U)/dU >> 0,
 C(U)    ;
   U   ;
   d    ,
                
.              ,
  ,       ,    
,               
,    .
      ,     .     
   ,    ,    
   ,       .
            
  .     .
               (      
    )         
           .
   ,  ,      .  
         ,    
        ,        ,
     .        
         ,    
  .         
    ,      
  .         .         
  -  ,      
     .

                             
      o cx op  paccapa poyoy epea c o  pe
opee - co oapx apo, oope ec  a  pe    ocy
oyae. Teep cae  opoc,  oo    yca  ooe  co
oapx  aeoa  cao  pe.  C  o   pe   p   poea
poyoo epea popeae  epca pooca.
      epca oaae  poee  p    oe  aocae
oac  pooca  -  pacpee  poyoo  ,  o     pye
eopaece  p  -  pacpee  pocpaceo  cep  p.  Ec
epca pocxo  e cae  c  oco  pooco  cep
eeoc, o oa oc aae ooeppoa, a caa pa  ao
cyae  ye  aac  ooepao.   Ka   pao,   ooepae
pacpe eeoc p xapaep  epex, caoxc  po.
Haoee aco cpeac eoa  pex  po  c  ce
epcaoe ee pooca  ca p.
      epca ee  pocy ca  poyox  ,  ocyaex
oo  po,  o  epe  ypeee  pacpee    pooco  ox
oapx apo  ox oapo, o  o-cpeco  c    ooe.
Boae  opoc,  oey    ox  cyax  peoaae  epx   coco
epca, a  pyx  opo? cceoa  oa  oaa,  o
op p ca c ao  eoo  a  opac.  B  oo  pacye
opac p oea epce  poca  ooeo  (ocec),
ooy o cpec   yee  poocex  ooce.  o  epe
poca opac   yee  ca  oapx  apo,  peaaex  po,
pepaaec pacpee cpoca, ooeoe co aeoa oapa e
ee  cyeceoy yee o p a pe, copaaec  o
p ooceo eecoopaoc  ypeeo  poca.  Ha  ae  peoc
opac   pye   acoo   pee   p   yy   epcpoa
pooco ye c  ooe c  e  pooe  a  pye
p. ec e epca oe paccapac a coco  yxoa
c pa , o pae epe, oecee ao a  epoo
ea.
        epe  cee   epca   p   coy   ec
epca, opaoa a ocoe eca Xep-aXpaa:
                         d = 1/[Szi2], i=1, ..., n,
e zi - o oea poa p, pxoac a i-  eeoc;
    n - oee co o eeoc,  oopx aa pa.
      Ec pa ecye oo  oo  cepe,  o  d  =  1.  Ec  pa
ecye  10 poyox x,  a  ay    oopx  pxoc  10%
oea poa, o  ec  epca  cocae  10.  Co  oa
o,  pxoac  a  o    eeoc,  p  o  o  a  pye
pxoc eaea  ac  yca,  ye  aa  ae  eca
epca, e  ee.
                                 
      poy oe xapaepoac epe aop eo  coc,  ax  a:
aeco, ecoooee poaa ooceo opeee, pe  poa,
ooeoc, opaoa  ocyoc  eo  coc    opeee,
ooee ycy, peocaee o  pe    oce  poa    ..
Kaoe  x  coc  oe  cya    aece  aopa  poyoo
epea.
      B ycox coepeo oypeoo pa poy  oopo,  aa
pa poae oap  e  oapy,  oop  peaae  a  pya
pa pa. eoc oypex oapo ae  ce  oaooc
cex ca poyoo  eo,  o  pooca  o  yco  poa  
ocepoaoo ocya. ooy y p  e  cyo    oy,  o
pepa ae-o ocoe yc  ca oapa, oype  po
peocae ao pe oooc poaa oe oeco oapa  o
oypeo  ee  e  ooex  pacxoo    yc.  Oe   ca
yao p ac  oo  o  ee  exooecx  apaepo  -
coooe px cpex    peex  epe.    oo    ycox
ecoepeo oype pa eecoopao pepa yc a  poc
oea poa. Koa po e ec ooco oype,  pa  oe
pe ocoe  cpae    ycaoe  ee  oooo  ac  a
oyae.
      B ooe cyecy p, a oopx p ocaoo oo  ce
poao  oyaee p oaa ce e opeeeo ac   cepe
ycaoe  e.  Tae  p   aac   pa   oooceco
oype, a a o oe ep a oype -  e ooo
ca oyaee  poao, coooo xoa  xoa p    opac,
a  ooo -  e opeeeoo oec a ey oapa, a  o
cpoc a poy ao p pecae  coo  py  c  opae
aoo. Poy ac a oapo ae pe epea poya.
      cceoa   poyoo   epea    oaa    cooc
opeee  oapa      aax   opeee.   Paoec   a   pax
ooocecoo poya oy po o  co oo, o  
e ao cee epea oapa.   o  e  oee  a,  ec
pa o ae, o  pea  poy  oe    epepoa
cpay  ecox    opoao, epao.


                         


      1)  .,    .,      ,  ,
         1998.
      2)  .,    .,      ,  ,
         2000.
      3)  .,  .,   , , 1997.



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