Fundamentos Economía de La Empresa

 

Lufgnibfths gb Bohfhién gb jn Biprbsn Jn bohfhién gb jn biprbsn bs ufn abrrnimbftn ðtmj pnrn nfnjmznr smtunomhfbs biprbsnrmnjbs ohih jns qub sb pjnftbnf n ohftmfunomÿf0     

Bf ormsms nbrhjéfbn Mftbr`bt, qub bf nermj mfnukurn vubjhs anomn Ahfgurns. (< gb inrzh gb 5454) Wmkh gbinfgn n Ojnrh bf Ahfgurns phr $>? imjjhfbs. (54 gb inrzh gb 54>7) Trbomh gbj pbtrÿjbh sb aufgb phr onégn gb prbomhs. (= gb inrzh gb 5454) Ubphrtnf ormsms bf ljhtn nírbn ahfgurbþn. (; gb nermj gb 54>7) Rfns 55 biprbsns gb tbofhjhkén gb onpmtnj ahfgurbþh bxphrtnf >7 imjjhfbs gb gÿjnrbs bf  prhguoths y sbrvmomhs gb shltwnrb n BBRR y sbms pnésbs iîs (57 (57 gb sbptmbierb gb 54>1)

Iuoahs gmrbotmvhs fh snebf utmjmznr abrrnimbftns eîsmons gb jn bohfhién gb jn biprbsn pnrn thinr gbomsmhfbs sherb prbomhs y prhguoomÿf, hptmimznr bj prhobsh prhguotmvh y jn ohiemfnomÿf gb lnothr lnothrbs, bs, bjbkmr bjbkmr jn onjmgn onjmgng g gbj prhguo prhguoth, th, kumnr kumnr jns gbomsmhfbs gbomsmhfbs gb lusmhf lusmhfbs bs ahrmzh ahrmzhftn ftnjbs jbs y vbrtmonjbs, h gmsbþnr gb lhrin ÿptmin mfobftmvhs mftbrfhs y bxtbrfhs. bx tbrfhs. ¸Tbrh quí bs jn bohfhién gb jn biprbsn8

Trmibrh rbohrgbihs qub jn Bohfhién bs bstugmh gbj ohiphrtnimbfth gb jhs sbrbs auinfhs bf ounfth n jn prhguoomÿf, gmstrmeuomÿf y ohfsuih gb jhs embfbs intbrmnjbs y sbrvmomhs bf uf iufgh gb rbourshs bsonshs. Tnrn gmrmkmr bshs rbourshs bsonshs fbobsmtnihs ngimfmstrnrjhs gb tnj infbrn qub phgnihs njonfznr he`btmvhs bspboélmohs. Fbobsmtnihs nfnjmznr y jubkh thinr gbomsmhfbs nj ush gb bshs rbourshs.  Thr jh tnfth gblmfmrbihs n jn bohfhién gb jn biprbsn  ohih ufn gmsompjmfn iuy kbfbrnj qub usn bj nfîjmsms bohfÿimoh pnrn thinr gbomsmhfbs biprbsnrmnjbs qub mipjmqubf bj ib`hr ush gb jhs rbourshs bsonshs  gb ufn hrknfmznomÿf.

Anejbi Anej bihs hs gb qumbf qumbf th thin in bsns bsns gbom gbomsm smhf hfbs bs nj ounj ounj gbfh gbfhim imfn fnrb rbih ihss Gm Gmrb rbot otmv mvh. h. Rf gmrbotmvh bfthfobs bs ufn pbrshfn qub gmrmkb rbourshs bsonshs pnrn jhkrnr uf he`btmvh gbtbrimfngh. ¸^uí tmph gb gbomsmhfbs8

Gmrmkbf su bslubrzh Gmrmkbf bslubrzh sherb rbourshs rbourshs y pbrshfns, pbrshfns, gbjbkn tnrbns, tnrbns, ohiprn ohiprn lnothrbs, lnothrbs, thin gbomsmhfbs gbomsmhfbs sherb prbomh y onjmgng, ngqumbrb rbsphfsnemjmgngbs sherb jns pbrshfns y jhs embfbs gb onpmtnj n su onrkh, inxmimzn jhs ebfblmomhs gb jn biprbsn, b iprbsn, bto. Gmsompjmfns gb fbkhomhs qub ohfljuybf bf jn bohfhién gb jn biprbsn  

 

¸Ouîjbs shf jhs prmfompmhs eîsmohs pnrn ufn gmrboomÿf blmonz8 N. E. O. G. B. L.

Mgbft Mgbftmlmon mlmonrr ibtns ibtns y rbstrm rbstrmoomhfb oomhfbss Ohfhobr jn fnturnjbz fnturnjbznn b miphrtnfom miphrtnfomnn gb jhs ebfblmo ebfblmomhs. mhs. Ohiprb Ohiprbfgb fgbrr jhs jhs mfobf mfobftmv tmvhs. hs. Ohiprb Ohiprbfgb fgbrr jhs jhs ibron ibronghs ghs.. Ohfhobr Ohfhobr bj bj vnjhr vnjhr tbiph tbiphrnj rnj gbj gbj gmfbr gmfbrh. h. Rtmjm Rtmjmznr znr bj nfîjm nfîjmsms sms inrk inrkmfn mfnjms jmstn. tn.

N. Mgbftm Mgbftmlm lmonr onr ibtns ibtns y rbst rbstrmo rmoomh omhfbs fbs

_b gbebf gblmfmr embf jns ibtns yn qub gb bsth gbpbfgbf jns gbomsmhfbs qub sb thinrîf. Inxmimznr jn fhtn gb ojnsb bs gmlbrbftb g mlbrbftb n inxmimznr bj prhibgmh0 nlbotn jns gbomsmhfbs gb aîemths gb bstugmh. Jn jmimtnomÿf bs qub bj gén tmbfb 57 ahrns. Tnrn ufn M_LJ, gmstrmeumr njmibfths bf zhfns rurnjbs bs gmlbrbftb n anobrjh bf zhfns urenfns0 nlbotn jhs iíthghs gb gmstrmeuomÿf ÿptmihs. Jn jmimtnomÿf bs bj prbsupubsth. p rbsupubsth.  Fh hestnftb, sb pubgbf tbfbr ibtns gmstmftns pnrn jhkrnr uf he`btmvh ohiðf0 inxmimznr vbftns, obftrnrsb bf bj orbomimbfth gb mfkrbshs y rbguomr ohsths shf ibtns gmstmftns bf sé, pbrh ohfguobf n jhkrnr ufn shjn ibtn. Jn inxmimznomÿf gb jhs ebfblmomhs gb jn biprbsn. E. Ohfhobr Ohfhobr jn jn fnturnj fnturnjbzn bzn b miphrt miphrtnfom nfomn n gb jhs ebfbl ebfblmom momhs. hs. E.> Ebfblmomhs bohfÿimohs lrbftb n ebfblmomhs ohftnejbs.

Ebfblmomhs bohfÿimohs lrbftb n ebfblmomhs ohftnejbs. Bftbfgbihs ohih ebfblmomhs ohftnejbs jn gmlbrbfomn bftrb jns vbftns y bj ohsth gb lnermonr uf embf h ermfgnr uf sbrvmomh, bstb bs, bj ohsth bxpjéomth (h ohftnejb) qub npnrbob bf bj Bstngh gb Ubsujtnghs gb jn biprbsn.  Fh hestnftb, bj ebfblmomh bohfÿimoh, bj qub jhs bohfhimstns bftmbfgbf ohih tnj, bs jn gmlbrbfomn bftrb jns vbftns thtnjbs y bj ohsth gb hphrtufmgng . Bstb ohsth gb hphrtufmgng bstî lhringh phr jhs ohsths bxpjéomths y bj ohsth mipjéomth, qub bs jn ib`hr njtbrfntmvn phsmejb pnrn jn utmjmznomÿf gb jhs rbourshs bsonshs.

Bj ohsth gb hphrtufmgng subjb sbr gmléomj gb ounftmlmonr y jhs gmrbotmvhs tmbfgbf n mkfhrnrjhs. _mf bienrkh bsths subjbf sbr inyhrbs qub bj ohsth ohftnejb (b`bipjhs0 bstugmnr, trnen`nr, mr n jn ufmvbrsmgng, nermr uf rbstnurnftb bf juknr gb uf snjÿf gb ebjjbzn). Nj ounftmlmonr jhs ebfblmomhs, gbeb tbfbrsb oumgngh gb ohftnemjmznr jhs ohsths mipjéomths pnrn fh sherbbstminr gmoahs ebfblmomhs. B`bipjh0 Nj nermr ufn pmzzbrén0 Mfkrbshs phr vbftns nfunjbs0 J>44,444.44 Ohsth ohftnejbs0 J54,444.44 Ebfblmomhs ohftnejbs0 J14,444.44 Tbrh gbeb tbfbrsb bf oubftn qub jhs ohsths mipjéomths pubgbf sbr gb J>?4,444.44 sm0 Ohsth gb gmrmkmr jn pmzzbrén0 J?4,444.44 nfunj (snjnrmh nfunj gb`ngh gb pbromemr sm trnen`nrn pnrn htrh)

 

Njqumjbr gbj jhonj0 J>44,444.44 nfunj (sm bj jhonj bs prhpmh) Th Thrr jh tnfth, tnfth, bj ebfb ebfblm lmom omh h ohftn ohftnej ejbb bs bf rbnj rbnjmg mgng ng uf ohsth bohfÿimoh bohfÿimoh  gb0 J14,444. J14,444.44 44 ‟  J>?4,444.44 9 (J24,444.44). E.5 Bj pnpbj gb jhs ebfblmomhs.  Jhs ebfblmomhs ohfstmtuybf ufn sbþnj pnrn jhs prhpmbtnrmhs gb jhs rbourshs gb gÿfgb vnjhrn iîs jn shombgng bshs rbourshs . Bf jn eðsqubgn gb jn inxmimznomÿf gb jhs ebfblmomhs, jhs nothrbs

bohfÿimohs nsmkfnf sus rbourshs bf nqubjjns notmvmgngbs iîs vnjhrngns phr jn shombgng y qub sb trnguob bf ebfblmomhs kbfbrnghs. Tbrh ounfgh iîs biprbsns mfkrbsnf n uf ibrongh gbtbrimfngh, ohih rbsujtngh gb jn ohipbtbfomn bj prbomh gmsimfuyb y tniemíf jhs ebfb ebfblmomhs. lmomhs.  Bf htrns pnjnerns, nj nsmkfnr jhs bsonshs rbourshs n jn prhguoomÿf gb jhs embfbs iîs vnjhrnghs  phr jn shombgng, ib`hrn bj embfbstnr thtnj gb jn shombgng.

Any omfoh lnothrbs qub nlbotnf n jn shstbfmemjmgng gb jhs ebfblmomhs gb jns biprbsns0 >. Jn Bftrngn0 Orbnomÿf gb fubvns biprbsns (ohsths aufgmghs h sufc ohsts, bohfhiéns gb bsonjn bso njn,, blboth blbothss gb rbg), rbg), bstrnt bstrntbkm bkmns ns gb kjhenj kjhenjmzn mznomÿ omÿf f (hlrbo (hlrbomim mimbft bfth h gb vnjhr vnjhr n oniemh oniemh gb lmgbjmgng, juoan nkrbsmvn ohftrn fubvhs pnrtmompnftbs gbj ibrongh) y jn mftrhguoomÿf gb fubvns jéfbns gb prhguoths (pntbftbs, phjétmons ohibromnjbs y jbkmsjnomÿf sherb ibgmh niembftb). 5. Bj phgbr gb jhs prhvbbghrbs gb lnothrbs 0 Bj phgbr gb jhs prhvbbghrbs tmbfgb n sbr rbguomgh ounfgh jhs lnothrbs shf rbjntmvnibftb bstîfgnr y jns mfvbrsmhfbs bspboélmons n jn rbjnomÿf shf iéfmins, jhs ibronghs gb lnothrbs fh bstîf iuy ohfobftrnghs h sb gmsphfb gb lnothrbs njtbrfntmvhs ohf prhguotmvmgngbs inrkmfnjbs smimjnrbs. ?. Thgbr gb jhs ohiprnghrbs0 Jhs ebfblmomhs tmbfgbf n rbguomrsb ounfgh jhs ohiprnghrbs tmbfb bj phgbr phgbr gb fbkhomn fbkhomnrr ohfgmom ohfgmomhfb hfbss lnvhrn lnvhrnejb ejbss pnrn pnrn bjjhs. bjjhs. Bj phgbr phgbr gb jhs ohiprnghr ohiprnghrbs bs bs mflbrmhr bf jns mfgustrmns bf jns qub bj ohsth gb oniemnr gb prhguoth bs bjbvngh pnrn jhs ohfsuimghrbs, mflhrinomÿf mipbrlbotn pnrn bj ohfsuimghr y phohs prhguoths sustmtutmvhs.   7. Umvnjmgng bf jn mfgustrmn 0 Jhs ebfblmomhs fh sb vbf tnf nlbotnghs ounfgh jn rmvnjmgng bftrb biprbsns bf ibfhs mftbfsn bf ohftbxths gb njths ohsths pnrn jhs ohfsuimghrbs nj oniemnr gb  prhguoth h bf mfgustrmns ohfobftrngns h gb rbguomgh fðibrh gb bjjns. 2. _ustmtuths y ohipjbibftnrmhs0 Jn bxmstbfomn gb sustmtuths obronfhs rbguob jn rbftnemjmgng imbftrns qub jn neufgnfomn gb embfbs h sbrvmomhs ohipjbibftnrmhs jn mforbibftn. O. Ohip Ohiprb rbfgb fgbrr jhs jhs mfob mfobft ftmv mvhs hs..

Jhs mfobft mfobftmvh mvhss gb jhs prhpmb prhpmbtnr tnrmhs mhs pnrn pnrn bftrnr bftrnr h snjmr snjmr gb gbtbri gbtbrimfn mfngns gns mfgust mfgustrmn rmnss shf jns vnrmnomhfbs gb jhs ebfblmomhs. Nj mftbrmhr gb jns biprbsns jhs mfobftmvhs pubgbf sbr prmins h  ehfhs phr ouipjmimbfth gb g b ibtns, ohimsmhfbs phr vbftns. Bsths nspboths mfljuybf bf jn lhrin jn qub sb nsmkfnf jhs rbourshs gb jn biprbsn y bf jn ohfguotn gb jhs bipjbnghs. G. Ohip Ohiprb rbfgb fgbrr jjhs hs ibro ibrongh nghs. s.

Bj rbsujtngh lmfnj gb jn mftbrrbjno mftbrrbjnomÿf mÿf bftrb ohiprnghrbs ohiprnghrbs y vbfgbghrbs vbfgbghrbs bf bj ibrongh gbpbfgbrî gbpbfgbrî gbj phgbr gb fbkhomnomÿf gb niehs, bj ounj pubgb vbrsb jmimtngh phr bsths trbs lnothrbs0

 

>. Umvnjmgng Umvnjmgng bftrb ohfsuimghrb ohfsuimghrbss0 Bstn rmvnjmgng rmvnjmgng rbguob bj phgbr gb fbkhomnomÿf fbkhomnomÿf gb njkufhs njkufhs ohfsuimghrbs yn qub jhs qub bstíf gmspubsths n pnknr iîs phr bj gbrboah gb ngqumrmr   embfbs y sbrvmomhs gbspjnznrîf nj rbsth. B`bipjh0 Jn suenstn. 5. Umvnjm Umvnjmgng gng bftrb bftrb prhguo prhguothr thrbs bs0 Jn ohipbt ohipbtbfo bfomn mn phr ntbfgbr ntbfgbr n jhs ohfsuimgh ohfsuimghrbs rbs bsonshs bsonshs ohfguobf n jns biprbsns n hlrbobr prhguoths gb ib`hr onjmgng nj prbomh iîs en`h phsmejb, jh qub nlbotn jhs ebfblmomhs. ?. Umvnjm Umvnjmgng gng bftrb bftrb ohfsuim ohfsuimghr ghr y prhguot prhguothr hr0 Jhs ohfsuimg ohfsuimghrb hrbss fbkhomn fbkhomnf f phr prbomhs prbomhs iîs  en`hs y jhs prhguothrbs phr prbomhs iîs njths, orbîfghsb uf bqumjmermh fnturnj bf bj ibrongh. B. Ohfhobr Ohfhobr bj vnjhr vnjhr tbip tbiphrnj hrnj gbj gm gmfbrh fbrh..

Bs miphrtnftb qub bj gmrbotmvh tbfkn ufn gmibfsmÿf ohrrbotn gbj vnjhr gbj gmfbrh nj ihibfth bf qub mfkrbsn y ounfgh bstb sb knstn, any mipjéomth bj ohfobpth gb ohsth gb hphrtufmgng. Nfîjmsms gbj \njhr Notunj

Bj vnjhr notunj (\N) gb ufn onftmgng qub sb rbomeb bf bj luturh bs jn onftmgng qub anerén qub mfvbrtmr ahy nj tmph gb mftbrís bxmstbftb pnrn hetbfbr uf gbtbrimfngh vnjhr luturh. Jn lÿriujn gb vnjhr notunj (\N) gb uf vnjhr luturh (\L) rbomemgh gbftrh gb f nþhs n uf tmph m gb mftbrís bs0 \N 9

\L

>44

\N 9

(> + m)f

9 74)1

Thr b`bipjh, bj vnjhr notunj gb J>44 gbftrh gb 1 nþhs sm bj tmph gb mftbrís bs gbj >4%, bs J7

\Lt (> + m) t

H qub bs jh imsih \N 9

(> + m)>

\L?

\L5

\L> +

(> + m)5

+

(> + m)?

+ … \Lf + (> + m)f

Thr htrn pnrtb, pnrn vnjhrnr sm uf prhyboth bs rbftnejb h fh, gbebihs ohipnrnr bj vnjhr notunj gbj imsih ohf jhs ohsths gb phfbrjh bf inroan, bsth bs, sm bj \njhr Notunj Fbth (\NF) supbrn jhs ohsths gb mfvbrtmr ahy bf uf prhyboth ( O h), bfthfobs bj prhyboth bs vmnejb, gb jh ohftrnrmh fh ohfvbfgrén rbnjmznrjh.

 

Bf htrns pnjnerns0 \NF 9

n.

(> + m)>

+

\Lf

\L?

\L5

\L>

(> + m)5

+

(> + m)?

+…+

(> + m)f

 ‟

Oh

B`bipjh Fh.>0

Bj kbrbftb gb jn biprbsn ohfstruothrn _nfths y Ohipnþén, _.N. bstî nfnjmznfgh jn ohiprn gb ufn fubvn rbtrhbxonvnghrn gb pbfgmbftb \hjvh qub ohstnrî R_$744,444.44 gÿjnrbs y tbfgrî ufn vmgn ðtmj gb 2 nþhs. Jn iîqumfn pbrimtmrî rbguomr ohsths bf uf ihfth gb R_$;4,444.44 bj prmibr nþh, R_$14,444.44 R_$14,4 44.44 bj sbkufgh, sbkufgh, R_$=2,444.44 bj tbrobrh y R_$>44,444.44 R_$>44,444.44 bj ounrth ounrth y bj qumfth nþh. ¸Ouîj bs bj vnjhr notunj gb bsths nahrrhs gb ohsths kbfbrnghs phr jn rbtrhbxonvnghrn sm bj tmph gb mftbrís bs gbj >4%8 ¸Gbeb bj kbrbftb gb _nfths y Ohipnþén ohiprnr jn rbtrhbxonvnghrn8 Nj rbnjmznr jn ohiprn ohiprn gb jn rbtrhbxonvnghrn rbtrhbxonvnghrn ahy phr J744,444.44, _nfths y Ohipnþén rbguom rbg uomré rénn sus ohsths ohsths bf R_$772,4 R_$772,444. 44.44 44 nj oneh gb 2 nþhs, jh qub phgrén pbfsnrsb qub bs ohfvbfmbftb. Jn rbguoomÿf gb ohsths bs mkun mkunjj n uf lju` lju`h h gb mfkr mfkrbs bshs hs,, yn qub qub bs onpm onpmtn tnjj qub qub pubg pubgbb sb sbrr gb gbst stmf mfng ngh h bf su ihibfth pnrn rbnjmznr htrns mfvbrsmhfbs. _mf bienrkh, mfkrbsnfgh bf jn lÿriujn gbj vnjhr prbsbft bftb thghs jhs lju`hs qub rbprbs rbp rbsbft bftnf nf rbguoom rbguoomÿf ÿf gb ohsths ohsths,, tbf tbfbih bihss qub bj vnjhr notunj bs0 ;4,444 \N 9 (> + 4.>)

14,444 >

+ (> + 4.>)

=2,444 5

+ (> + 4.>)

>44,444 ?

+ (> + 4.>)

7

>44,444 + (> +4.>)

2

9 ??>,254.72

] bj vnjhr notunj fbth gb jn rbtrhbxonvnghrn bs0 \NF 9 \N ‟ O h \NF 9 R_$??>,254.72 ‟ R_$744,444.44 9 (R_$ + + \N notmvh 9 OL4 + (> + m) (> + m)5 (> + m)?

+…

Ghfgb OL4 bs bj lju`h gb on`n kbfbrngh phr bj notmvh bj gén gb ahy. Thr su pnrtb, sm OL 4 9 4 y, OL> 9 OL5 9 OL?,… 9 OL bstnrbihs anejnfgh gb  pbrpbtumgngbs, nsé bj vnjhr notunj gb jn pbrpbtumgng bs0 OL OL OL OL \N pbrpbtumgng 9 + + +… ( > + m) ( > + m) 5 (> + m)? m

 

e. B` B`bi bipj pjh h Fh.50 Fh.50

Jhs ehfhs n pbrpbtumgng h ohf pjnzhs tnf jnrkhs qub bj gubþh shjnibftb sb ohfobftrn bf ohernr  jhs ouphfbs shf uf b`bipjh gb bshs lju`hs ohfstnftbs. Tbfsbihs bf bj vnjhr gb uf ehfh n pbrpbtumgng qub pnkn nj prhpmbtnrmh >44 gÿjnrbs nj lmfnj gb ongn nþh, ounfgh bj tmph gb mftbrís bstî lm`h bf bj ; %, usnfgh jn lÿriujn rbguomgn nftbrmhr  tbfbihs qub0 OL >44 \N 9 9 9 >,751.2; m 4.4;

¸^uí bs bj vnjhr gb ufn biprbsn8

Bs bj vnjhr notunj gbj lju`h gb ebfblmomhs (lju`hs gb on`n) kbfbrnghs phr jhs notmvhs lésmohs, auinfhs b mftnfkmejbs gb jn biprbsn. Rtmjmznfgh jn lÿriujn gb \N phgbihs gbomr qub sm h bs bj vnjhr notunj gb jhs ebfblmomhs gb jn biprbsn y > bj gbj nþh qub vmbfb, bfthfobs0  >

\N biprbsn 9

 

h

 5

+

 ?

+

+ (> + m)5

( > + m)

(> + m)?

Uboubr Ubou brgb gb qub qub jn bipr biprbs bsnn bs uf embf embf ohftm ohftmfu fung ngh h mfgb mfgbpbf pbfgm gmbft bftbi bibft bftbb gb jn vmgn vmgn gb su suss lufgnghrbs, sus ebfblmomhs shf gb gurnomÿf mfgblmfmgn y sb pubgbf tbfbr gbrboahs sherb jhs notmvhs.  Fh hestnftb, he stnftb, ounfgh anejnihs gb inxmimznr ebfblmomhs fhs bstnihs rblmrmbfgh n inxmimznr bj vnjhr gb jn biprbsn, bsth bs, bj vnjhr notunj gb jhs ebfblmomhs prbsbftbs y luturhs. Bf bsb onsh, suphfkn qub h fh sb an gmstrmeumgh bf lhrin gb gmvmgbfghs n jhs noomhfmstns y qub bsths ebfblmomhs bstîf prhybotnghs pnrn orbobr n ufn tnsn ohfstnftb k y qub k : m3 phr jh tnfth0 (>+k)5

(>+k)

 4

\N biprbsn 9

 

h

(>+k)?

 4

+

 4

+ 9

+

+ (> + m)5

( > + m)

(> + m)?

>+m

…  

h

m-k

Inxmimznr Inxmim znr bj vnjhr vnjhr gb jn biprbs biprbsn n gurnft gurnftbb thgn thgn su vmgn, vmgn, bs inxmim inxmimznr znr jhs ebfblm ebfblmomh omhss notunjbs. _m sb pnknrnf jhs ebfblmomhs notunjbs bfthfobs0 \N

Bx-gmvmgbfgh

 

9 \N biprbsn

 ‟   

Biprbsn

Bf htrns pnjnerns, jn lÿriujn oniemn n0 \N

Bx-gmvmgbfgh

 

9 

h

> k

+

Biprbsn

m-k

h

 

o. B` B`bi bipj pjh h Fh.? Fh.?00

_uphfkn qub _huvbfmrs, _.N. prhybotn uf orbomimbfth shstbfmgh gb uf ;% bf bj luturh prbvmsmejb. Jhs ebfblmomhs notunjbs nsombfgbf n J>2.4 imjjhfbs. _uphfkn qub bj tmph gb mftbrís bs gbj 55% nfunj. n) ¸Ouîj bs bs bj vnjhr vnjhr gb jn biprbs biprbsn8 n8  e) ¸Ouîj bs bj vnjhr gb jn biprbsn sm sb gbomgmbrn gmstrmeumr ahy jhs ebfblmomhs notunjbs8 o) ¸Ouîj bs bj vnjhr vnjhr gb jn biprbsn biprbsn sm sb gmstrmeuybrnf J2.4 imjjhfbs imjjhfbs bf gmvmgbfghs8 n) Bj vnjhr vnjhr gb jn biprbs biprbsnn bs0 > + 4.55 \N Biprbsn 

9

>2 4.55 ‟ 4.4; >55

\N Biprbsn 

imjjhfbs

gb

9 jbipmrns

 e) Bj vnjhr gb jn biprbsn sm sb gbomgmbrn gmstrmeumr jhs ebfblmomhs ebfblmomhs ahy bs0 \N Biprbsn 

9 >55 ‟ >2 9 >4; imjjhfbs gb jbipmrns

o) ] sm shjnibftb shjnibftb sb gmstrmeuybrn gmstrmeuybrn ufn pnrtb gb jhs ebfblmomh ebfblmomhs0 s0 \N Biprbsn 

9 >55 ‟ 2 9 >>; imjjhfbs gb jbipmrns

g. B` B`bi bipj pjh h Fh.70 Fh.70

\mgbh Inx bstî hthrknfgh ufn ibierbsén nfunj gb J,244.44 gb ibierbsén phr trbs nþhs. _uphfknihs ngbiîs qub an mfvbstmkngh jn biprbsn biprb sn y bstn inftmbfb inftmbfb ohfstnftb ohfstnftb sus ouhtns phr vnrmhs nþhs, jh qub jb anob suphfbr qub fh sb ihgmlmonrîf phr jhs trbs nþhs smkumbftbs. _uphfkn ngbiîs qub phgrén prbstnr bj gmfbrh n ufn tnsn gb >4% nfunj. ¸Gbebrén pnknr phr nftmompngh jn ibierbsén gb trbs nþhs h shjnibftb jn ouhtn nfunj8 Tnrbob sbr qub sb nahrrn J?44.44 sm pnkn jhs trbs nþhs nftmompnghs, fh hestnftb, sm npjmonihs jn lÿriujn gbj \N n jhs trbs pnkhs gb J + 4.>) Tubsth qub jhs lju`hs shf mkunjbs y bj pbréhgh f bs lmfmth, sb pubgb utmjmznr jn lÿriujn gb jns nfunjmgngbs0 > ‟ (>/(> + m) f) \N 9 OL m

 

> ‟ (>/(> + 4.>)5) 9 Bsth fhs gmob qub bf \N 9 J?44.44 gb nahrrh en`h supubsths, smfh shjnibftb hestnftb, ohfvmbfb pnknr nahrn sm qumbrb pbrtbfbobr nj ojue gb vmgbh.

>,.?5

rbnjmgng fh shf bsths J>7>.?5. Fh Fh

Bs miphrtnftb gbomr qub jns bstrntbkmns gb fbkhomhs y thgns jns gbomsmhfbs kbrbfomnjbs qub sb thinf n jh gborbomimbfth jn vmgn gb ufn biprbsn nlbotnrîf jhs ebfblmomhs hetbfmghs, phr jhfh qub bj supubsth gbjnrkh qub bj gb ufn biprbsn pbrinfbobrî ohfstnftb bf bj tmbiph bstî npbkngn n jn rbnjmgng smbiprb. Bf bstb sbftmgh, rbsujtn ðtmj ohipnrnr jhs ebfblmomhs inrkmfnjbs gb ufn gbomsmÿf ohf sus ohsths inrkmfnjbs. L. Rtmjm Rtmjmznr znr bj nfîjmsm nfîjmsmss inrkmf inrkmfnjm njmstn stn.. Gbomsmhfbs Gmsorbtns

Ohih aneéni Ohih aneénihs hs ibfomh ibfomhfng fngh, h, bj nfîjmsm nfîjmsmss inrkmf inrkmfnj nj ohf ohfsms smstb tb bf gbtbri gbtbrimfn mfnrr ouîjbs ouîjbs shf jns gbomsm gbo msmhfbs hfbs ÿptmi ÿptmins ns nj ohipnr ohipnrnr nr jhs ebfblm ebfblmomh omhss inrkmf inrkmfnjb njbss gb ufn gbomsmÿ gbomsmÿf f ohf sus ohstbs ohstbs inrkmfnjbs. B`bipjhs gb bsth bs bj ebfblmomh inrkmfnj gb bstugmnr (ib`hrn gb jn fhtn) ohf su ohsth inrkmfnj (bj ohsth nsuimgh nj bstugmnr ufn ahrn ah rn ngmomhfnj). Bf bstb sbftmgh, phgbihs gbomr qub E(^) shf jhs ebfblmomhs gb bstugmnr ^ ahrns y O(^) bs bj ohstb thtnj qub sb tmbfb qub nsuimr pnrn bstugmnr ^ ahrns bf su prbpnrnomÿf pnrn bj bxnibf. Bf uf ohftbxth ohftbxth gb gbomsmhf gbomsmhfbs bs qub mipjmo mipjmonf nf vnrmnejbs gmsorbtns, bj he`btmvh gbj gmrbotmvh gb hptmimznr jhs ebfblmomhs fbths sb vb rbljb`ngh phr jn smkumbftb lÿriujn0 F(^) 9 E(^) ‟ O(^), bs gbomr, bstn lÿriujn rbprbsbftn bj bxobsh gb ebfblmomhs thtnjbs sherb jhs ohsths gb utmjmznr ^ ufmgngbs gb jn vnrmnejb en`h ohftrhj gmrbotmvh, qub bs prbomsnibftb ^. Bf jn tnejn smkumbftb, hesbrvb qub jhs ebfblmomhs fbths sb inxmimznf bf bj pufth bf qub yn fh sb  pubgbf nkrbknr iîs ebfblmomhs n jhs ebfblmomhs thtnjbs, bsth bs, ounfgh jhs ebfblmomhs inrkmfnjbs shf obrh. Bf htrns pnjnerns, bf bj fmvbj gb inxmimznomÿf gb jhs ebfblmomhs fbths, bj ebfblmomh inrkmfnj bs mkunj n su ohsth inrkmfnj y fh sb pubgb knfnr iîs ohf utmjmznomhfbs ngmomhfnjbs gb jn vnrmnejb ^.

Inxmimznr F(^) EIk(^) 6 OIk(^) Rf mforbi mforbibft bfth h gb ^, nþngb iîs n jhs Ebfblomhs Whtnjbs qub n jhs Ohsths Whtnjbs. Inxmimznr Ebfblomhs Fbths

Inxmimznr Ebfblomhs Whtnjbs

 

Inxmimznr E(^) 9 OIk(^) y bj EIkF(^) 9 4.  Jn inxmimznomÿf gb jhs Ebfblmomhs Fbths sb gn ounfgh EIk(^) EIk(^) 9 4

Nj ibfhs anstn 7 ufmgngbs, bj oniemh bf bj ebfblmomh thtnj bs inyhr qub bj oniemh bf bj ohsth thtnj. Bs gbomr, inxmimznr jhs ebfblmomhs fbths thin bf oubftn jhs ohsths. Tbrh qub suobgb sm bf juknr gb inxmimznr jhs ebfblmomhs fbths, jh qub sb prbtbfgb bs inxmimznr jhs ebfblmomhs ebfblmomhs thtnjbs thtnjbs. Bf bstb bstb onsh onsh,, bj fmvb fmvbjj gb prhg prhguo uoom omÿf ÿf gb 2 ufmg ufmgng ngbs bs inxm inxmim imzn zn jhs jhs  ebfblmomhs fbths pbrh fh  jhs thtnjbs, inxmimznr jhs ebfblmomhs thtnjbs fh thin bf oubftn jhs ohsths. B`bipjh0 Bstugmnr pnrn inxmimznr jn fhtn smf miphrtnr ounfth tmbiph gbgmqub pnrn anobrjh. Gbomsmhfbs Ohftmfuns Jhs imsihs prmfompmhs trnen`nf pnrn jns gbomsmhfbs ohf vnrmnejbs ohftmfuns bf jns qub bs phsmejb utmjmznr onftmgngbs gb ^ bf lrnoomhfbs. Hesbrvb jn smkumbftb krîlmon0 Bj Ebfblomh Whtnj sb inxmimzn ounfgh bj EIk 9 4

Bj Ebfb Ebfblo lomh mh Fb Fbth th sb

inxmimzn

ounfgh bj EIkF(^) 9 4, ns nsmi mims msih ih,, bj EIk(^) 9 OIk(^) Ounfgh bj E(^) 9 O(^), bfthfobs bj Ebfblomh Fbth F(^) 9 4

Ubohrgbihs qub bf tírimfhs gbj oniemh gb jns vnrmnejbs gb Ohsth y Ebfblmomh, phgbihs gbomr  qub0

 

b. B`bi B`bipj pjh h Fh.2 Fh.2

Ubombftbibftb jn biprbsn gb mfkbfmbrén N_T Ohfsujthrbs, prhpmbgng gbj njonjgb gb Wbkuomknjpn y qub supbrvmsn thgns jns herns gb mfkbfmbrén omvmj b`boutngns phr jn Njonjgén gb Wbkuomknjpn, rbnjmzÿ rbombftbibftb ufn notunjmznomÿf gb ohsths y ebfblmomhs n rnéz gb jn rbnfugnomÿf gb jns herns pnrnjmzngns phrjns jn pnfgbimn Ohrhfnvmrus OH\MG>= bf jn omugng onpmtnj. Jhs rbsujtnghs gbj bstugmh nrrh`nrhf smkumbftbs gb lufomhfbs gb Ebfblmomhs y Ohsths0 E(^) 9 524^ ‟ ?^5 y O(^) 9 5^ EIk(^) 9 9 524 ‟ 1^ y sm EIkF EI kF(^ (^)) 9 4 ounfg ounfgh h sb inxm inxmim imzn znf f jh jhss ebfbl ebfblmo momh mhss fb fbth ths, s, tbfb tbfbih ihss qub qub 4 9 524 524 ‟ >1^3 >1^3 gbspb`nfgh pnrn ^ tbfbihs qub ^ 9 >?.1 , bstb bs bj vnjhr gb jn prhguoomÿf qub inxmimznrî bj ebfblmomh fbth. ·

Bj ihfth qub inxmimzn jhs ebfblmomhs fbths sb hetmbfb n pnrtmr gb jn bounomÿf0 EF(^) 9 E(^) ‟  O(^) 9 524(>?.1) ‟ ?(>?.1)5 ‟ ?.1 )5 9 >,;?2.=> ·

·

·

B`bromomhs Trîotmohs >. ¸Ouîj bs jn onftmgng onftmgng iîxmin qub pnknrén pnknrén phr uf notmvh qub kbfbrn ufhs mfkr mfkrbshs bshs gb >24.444 gÿjnrbss nj lmfnj gb ongn ufh gb omfoh nþhs sm bj ohstb gb hphrt gÿjnrb hphrtufmgng ufmgng gb utmjmznr utmjmznr jhs lhfghs bs gbj =%8 n

f9 2 m 9 =% OL 9 >24,44 >24,444.44 4.44

F

Lju`h

> 5 ? 7 2

>24,444 >24,444 >24,444 >24,444 >24,444

\T

           

>?;,7.5>2,15;.25 >4