Principios de Economía: Introducción a la Macroeconomía

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Vck÷c jf Fwzvjkhczfw jf Gkfcgkhw Fgoc÷bkghw

ZFBH 01 Kczyojvggk÷c h lh Bhgyofgocobâh ¿Fgocobkwzhw o Hjk}kcow? Avwzkmkghgk÷c fwzhjâwzkgh woiyf lh jkmkgvlzhj jf pyfjkggk÷c jf lhw }hykhilfw fgoc÷bkghw1 Bvgdhw }hykhilfw fgoc÷bkghw zkfcfc jkwzykivgkocfw co nhvwkhchw, pvfw lh pyoihiklkjhj jf wf pyojvqghc yfhlkqhgkocfw ftzyfbhw pvfjf wfy hlzh1 Low fyyoyfw jf pyfjkggk÷c pvfjfc wfy nyhcjfw# Fgocobkwzhw woc gobo low ftpfyzow fc bfjkgkch1 wf lfw pkjf xvf h+ jkhncowzkxvfc goc yhpkjfq low pyoilfbhw xvf hmfgzhc h vc fgocobâh jfzfybkchjh, o h lh fgocobâh nloihl fc wv gocavczo i+ { xvf pocnhc yfbfjkow fmkghgfw phyh wv goyyfnky fwow pyoilfbhw# •

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Fl Pyojvgzo Kczfykoy Iyvzo $PKI+ ‗ Fl Pyojvgzo Kczfykoy Iyvzo jf vch fgocobâh fw vch fwzkbhgk÷c jf lh hgzk}kjhj fgoc÷bkgh xvf wf yfhlkqh fc wv zfyykzoyko jvyhczf vc pfykojo jf zkfbpo ‗ Fl Pyojvgzo Kczfykoy Iyvzo jf vch fgocobâh fw vch fwzkbhgk÷c fwz kbhgk÷c jfl }hloy jf lh pyojvggk÷c jf ikfcfw { wfy}kgkow xvf wf yfhlkqh fc wv zfyykzoyko jvyhczf vc pfykojo jf zkfbpo ‗ Fl Pyojvgzo Kczfykoy Iyvzo jf vch fgocobâh fw lh wvbh jf low }hloyfw høhjkjow jf zojhw lhw bfyghcgâhw pyojvgkjhw yfbvcfyhjh { lfnhlbfczf fc wv zfyykzoyko jvyhczf vc zykbfwzyf o vc høo Gyfgkbkfczo Fgoc÷bkgo Wowzfckjo Fl gyfgkbkfczo wowzfckjo fw lh ñckgh yvzh dhgkh lh ykxvfqh#

Yfhlkqhjo { Jkwzykivkjo poy QDOVAKF BH


Gyfgkbkfczo Fxvklkiyhjo1 Fl Wfgzoy Pñilkgo N % Q % KCZ 2 Z % JFM ‗ Fbplfow1 fl wfgzoy pñilkgo phnh low wvfljow jf low fbplfhjow pñilkgow { gobpyh bfyghcgâhw jf gocwvbo { jf kc}fywk÷c $N+5 phnh pfcwkocfw { dhgf ozyhw zyhcwmfyfcgkhw h low donhyfw { h lhw fbpyfwhw $Q+5 { mkchcgkh lh jfvjh pñilkgh $KCZ+ ‗ Yfgvywow1 fl wfgzoy pñilkgo goiyh kbpvfwzow, gozkqhgkocfw wogkhlfw { zhwhw $Z+ { fbkzf fbkzf jfvjh $JFM+ gvhcjo gvhcjo wvw yfgvywow pyopkow woc kcwvmkgkfczfw phyh mkchcgkhy wvw fbplfow ‗ Low Jëmkgkzw jfl Wfgzoy Pñilkgo hvbfczhc fl whljo }k}o jf lh Jfvjh Pñilkgh { low Wvpfyè}kzw jfl Wfgzoy Pñilkgo pvfjfc vwhywf phyh yfjvgkylo ‗ Fl fcjfvjhbkfczo ftgfwk}o jfl Wfgzoy Pñilkgo pvfjf co wfy wowzfckilf { pvfjf wfy lh ghvwh jf vch gykwkw gykw kw mkchcgkfyh Gyfgkbkfczo Fxvklkiyhjo1 Fl Wfgzoy Ftzfykoy WIGG 2 T ‗ KB % YFC ‗ Ftpoyzhgkocfw $T+1 kcnyfwow poy }fczhw jf ikfcfw { wfy}kgkow h gobpyhjoyfw co yfwkjfczfw ‗ Kbpoyzhgkocfw $KB+1 phnow poy }fczhw jf ikfcfw { wfy}kgkow h pyojvgzoyfw co yfwkjfczfw ‗ Yfczh Ftzfykoy Ftzfykoy Cfzh $YFC+1 whljo jf ozyow kcnyfwow { jf low phnow goyykfczfw yfgkikjow jfl ftzfykoy o jkyknkjow hl ftzfykoy $yfphzykhgk÷c jf ifcfmkgkow, yfbfwhw jf low fbknyhczfw, h{vjhw hl jfwhyyollo, fzg+ fz g+ ‗ Low Jëmkgkzw fc lh Ihlhcqh poy Gvfczh Goyykfczf wf mkchcgkhc yfjvgkfcjo lhw



yfwfy}hw ftzfykoyfw, }fcjkfcjo phzykbocko $kc}fywk÷c ftzyhcafyh jkyfgzh+ o fcjfvjècjowf goc co yfwkjfczfw $jfvjh ftzfych+ ‗ Fl gyfgkbkfczo ftgfwk}o jf lh jfvjh ftzfykoy pvfjf co wfy wowzfckilf { pvfjf wfy lh ghvwh jf vch gykwkw mkchcgkfyh Fl Fbplfo { Fl Phyo Fl fbplfo yfbvcfyhjo fw lh pykcgkphl mvfczf jf yfczhw jf lh bh{oyâh jf low donhyfw# Poy fwo lh gyfhgk÷c gyfhgk÷c jf vc cñbfyo wvmkgkfczf jf fbplfow jf ghlkjhj ghlkjhj fw vch jf lhw pyfogvphgkocfw mvcjhbfczhlfw jf lh polâzkgh fgoc÷bkgh ‗ Vc ogvphjo fw vch pfywoch xvf zkfcf vc fbplfo yfbvcfyhjo $poy gvfczh hafch o pyopkh, h zkfbpo gobplfzo o phygkhl, fzg+ ‗ Vc phyhjo fw bèw jkmâgkl jf jfmkcky poyxvf fl phyo co fw vch hgzk}kjhj wkco lh mhlzh jf vch hgzk}kjhj $co zfcno vch ogvphgk÷c yfbvcfyhjh+, { vc jfwfo $pfyo bf nvwzhyâh zfcfylh+ ‗ Co zojow low jfwogvphjow woc phyhjow Pyfgkow Fwzhilfw Lh kcmlhgk÷c fw lh zhwh jf }hykhgk÷c jf low pyfgkow o, bèw zëgckghbfczf, jf vc âcjkgf jf pyfgkow ‗ Lh kcmlhgk÷c pvfjf gocmvcjkywf goc low ghbikow fc low pyfgkow yflhzk}ow ‗ Low ghbikow ghbikow fc low pyfgkow yflhzk}ow cow fbpoiyfgfc# Poy fafbplo, fafbplo, wk wvif fl pyfgko jfl pfzy÷lfo, fl }hloy jf cvfwzyo wvfljo bfjkjo fc ihyyklfw jf pfzy÷lfo jkwbkcv{f fc lh bkwbh pyopoygk÷c ‗ Pfyo lh kcmlhgk÷c co cow fbpoiyfgf poyxvf cvfwzyow whlhykow cobkchlfw, xvf woc vc pyfgko bèw, wvflfc gyfgfy bèw jfpykwh xvf lh kcmlhgk÷c ‗ Lh kcmlhgk÷c fw vc kbpvfwzo xvf nyh}h hl jkcfyo { dhgf xvf jkwbkcv{h wv }hloy ‗ Low gowzfw jf lhw zhwhw jf kcmlhgk÷c bojfyhjhw { pyf}kwkilfw woc pfxvføow, pfyo low gowzfw jf lhw dkpfykcmlhgkocfw d kpfykcmlhgkocfw woc jf}hwzhjoyfw ‗ Lh kcmlhgk÷c fw wkfbpyf { fc zojhw phyzfw vc mfc÷bfco bocfzhyko { fc gvhlxvkfy ghwo co cow nvwzh# Jfwknvhljhjfw Hgfpzhilfw Lh wvfyzf nfcëzkgh cow dhgf jfwknvhlfw, low bfyghjow hbplkmkghc lh jfwknvhljhj, { lh dfyfcgkh lh pfypfzñh ‗ Lh jfwknvhljhj zkfcf bvgdhw jkbfcwkocfw1 yfczh, ykxvfqh, opoyzvckjhjfw, fjvghgk÷c, fjhj, mflkgkjhj,… ‗ Lh wolkjhykjhj cow llf}h h yfgdhqhy lh jfwknvhljhj ftgfwk}h ‗ Lh bo}klkjhj fw ozyh ghyhgzfyâwzkgh jf lhw jkwzykivgkocfw yflhgkochjh goc lh

jfwknvhljhj# Lh bo}klkjhj dhgf xvf lh jfwknvhljhj wfh bèw hgfpzhilf#



¿Xvë pvfjf dhgfy lh Polâzkgh Fgoc÷bkgh phyh Bfaoyhy lhw Gowhw? ]kwk÷c lkifyhl1 Jfmkcky { dhgfy gvbplky low jfyfgdow jf pyopkfjhj { jfahy mvcgkochy h low bfyghjow ]kwk÷c hgzk}kwzh1 Kczfy}fcky lh fgocobâh bfjkhczf polâzkghw { yfnvlhgkocfw fgoc÷bkghw Polâzkghw mkwghlfw { jkwzykivzk}hw $kbpvfwzow, wfnvykjhj wogkhl { zyhcwmfyfcgkhw+ Polâzkghw bocfzhykhw { ghbikhykhw $kczfy}fcgk÷c { yfnvlhgk÷c jf low bfyghjow bocfzhykow { ghbikhykow+ Yfnvlhgk÷c jf low bfyghjow jf zyhihao Ozyhw yfnvlhgkocfw $goczyolfw jf pyfgkow, yfnvlhgkocfw hbikfczhlfw, fzg+ •

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Fl Gowzf jf Opoyzvckjhj Fl gowzf jf opoyzvckjhj jf jfjkghy vc yfgvywo h vwo jfzfybkchjo fw fl }hloy jfl bfaoy vwo hlzfychzk}o yfgdhqhjo# Gèlgvlo jfl Gowzf jf Opoyzvckjhj 8# Wf kjfczkmkgh fl yfgvywo fwghwo 9# Wf kjfczkmkghc lhw hlzfychzk}hw 7# Wf }hloyhc lhw hlzfychzk}hw :# Wf vwh lh jfmkckgk÷c Low Mlvaow { low Mocjow Jfmkckgk÷c1 Mlvao Vc mlvao fw vch }hykhilf fgoc÷bkgh xvf yfpyfwfczh vc pyogfwo xvf wf pyojvgf fc vc pfykojo jf zkfbpo, { gv{h jfmkckgk÷c ftknf xvf wf fwpfgkmkxvf lh jvyhgk÷c jf fwf pfykojo# Jfmkckgk÷c1 Mocjo Vc mocjo fw vch }hykhilf fgoc÷bkgh gv{h gvhczâh wf jfzfybkch fc vc bobfczo jfl zkfbpo { co h lo lhyno jf vc pfykojo# Lh yflhgk÷c fczyf low mlvaow { low mocjow



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ZFBH 81 Fl bojflo bhgyofgoc÷bkgo ièwkgo

Fl bojflo ièwkgo fw vc bojflo gfyyhjo { ftdhvwzk}o jf lh fgocobâh nloihl1 Kcglv{f h zojhw lhw pfywochw, h zojhw lhw fbpyfwhw, { h zojhw lhw kcwzkzvgkocfw Vch Phyèiolh jfl Bvcjo1 Fl Bojflo Ièwkgo Low bhgyofgocobkwzhw wf kc}fczhc vch phyèiolh jfl bvcjo $vch hchlonâh+ ihwhjh fc lh wkbplkmkghgk÷c { lh hnyfnhgk÷c Flknfc vch fgocobâh jf yfmfyfcgkh phyh fwzvjkhylh goc jfzhllf1 fl wfgzoy kczfykoy Gocwolkjhc h zojhw lhw jfbèw fgocobâhw fc fl wfgzoy ftzfykoy Wvpocfc xvf fl wfgzoy kczfykoy fwzè moybhjo poy fl wfgzoy pyk}hjo { fl wfgzoy pñilkgo Wvpocfc xvf wfgzoy pyk}hjo fwzè moybhjo poy donhyfw { fbpyfwhw Fl bojflo jfl bvcjo co zkfcf poy xvë wfy yfhlkwzh1 ihwzh goc xvf wfh ñzkl phyh goczfwzhy h lhw pyfnvczhw xvf cow kczfyfwhc •

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Fl Wfgzoy Pñilkgo Fl Wfgzoy Pñilkgo kcglv{f h zojow low oynhckwbow jf lhw hjbkckwzyhgkocfw fvyopfhw, fwzhzhlfw, yfnkochlfw, { loghlfw Fl Wfgzoy Pñilkgo wf fwzvjkh gobo wk mvfyh vch nyhc fbpyfwh jfjkghjh h lh pyojvggk÷c jf lhw bfyghcgâhw pñilkghw pñ ilkghw Yfgvywow1 Fl Wfgzoy Pñilkgo wf mkchcgkh goc yfgvywow pyopkow $Z1 kbpvfwzow, zhwhw, bvlzhw, ozyow+ { goc yfgvywow hafcow fbkzkfcjo jfvjh pñilkgh $FCJ+ •

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Vck÷c jf Fwzvjkhczfw jf Gkfcgkhw Fgoc÷bkghw •

Fbplfow1 Fl Wfgzoy Pñilkgo phnh low whlhykow jf low fbplfhjow pñilkgow { gobpyh bfyghcgâhw jf gocwvbo { jf kc}fywk÷c h low pyojvgzoyfw kczfykoyfw { ftzfykoyfw $N+5 yfhlkqh zyhcwmfyfcgkhw wkc goczyhphyzkjh hl wfgzoy pyk}hjo { hl wfgzoy ftzfykoy $Q+5 { phnh low kczfyfwfw jf lh jfvjh pñilkgh h wvw pyopkfzhykow $KCZ+

Low Pyfwvpvfwzow, fl Jëmkgkz { lh Jfvjh Pñilkgow Lh Yfwzykggk÷c Pyfwvpvfwzhykh jfl Wfgzoy Pñilkgo N % Q % KCZ 2 Z % FCJ Fl Jëmkgkz jfl Wfgzoy Pñilkgo $JFM+ JFM 2 FCJ 2 $N % Q % KCZ+ ‗ Z Lh F}olvgk÷c jf lh Jfvjh Pñilkgh $JP+ JPz % 8 2 JPz % JFMz Lhw Jfgkwkocfw jf low Donhyfw jfl Bojflo ‗ Lh Hwknchgk÷c jfl Zkfbpo1 low donhyfw jfgkjfc gvèczo zkfbpo jfjkghy h hgzk}kjhjfw yfbvcfyhjhw { co yfbvcfyhjhw Yfczh1 low donhyfw jfgkjfc jfgkjfc gvèczo gocwvbky { gvèczo ‗ Lhw Hwknchgk÷c jf lh Yfczh1 hdoyyhy ‗ Lh Hwknchgk÷c jfl Hdoyyo1 low donhyfw jfgkjfc lh gobpowkgk÷c jf wvw ghyzfyhw ‗ Fwzhw zyfw jfgkwkocfw wf zobhc jf moybh wkbvlzècfh Lh Hwknchgk÷c jfl Zkfbpo d % 2 800 ‗ Zkfbpo jkwpockilf1 8: doyhw/jâh t > jâhw 2 800 doyhw jkwpockilfw h lh wfbhch ‗ d1 hgzk}kjhjfw yfbvcfyhjhw $zyhihao+ Yfczh lhioyhl1 { d2~!d ‗ 1 hgzk}kjhjfw wkc yfbvcfyhy $zhyfhw jobëwzkghw, fwzvjko, ogko, fzg+ ‗ ]hykhilfw xvf kcmlv{fc1 whlhyko $~+, kbpvfwzow w/ zyhihao, ykxvfqh, zkpo jf kczfyëw, ftpfgzhzk}hw,…

Lh Hwknchgk÷c jf lh Yfczh G % W 2 [J G1 Gocwvbo $zojo fl nhwzo jf low donhyfw bfcow lhw }k}kfcjhw+ W1 Hdoyyo $zojh lh yfczh jkwpockilf bfcow fl gocwvbo+ [J1 Yfczh Jkwpockilf



[J 2 [ % Q % KCZ % YFC ‗ Z [1 Yfczh 2 PKI $whlhykow, hlxvklfyfw, yfczhw jfl ghpkzhl, { ifcfmkgkow iyvzow+ Q1 Zyhcwmfyfcgkhw $phnow jfl wfgzoy pñilkgo wkc goczyhphyzkjh+ KCZ1 Kczfyfwfw jf lh jfvjh pñilkgh YFC1 Yfczh ftzfykoy cfzh Z1 Kbpvfwzow { ozyow phnow hl wfgzoy pñilkgo G % W % Z 2 [ % Q % KCZ % YFC ]hykhilfw xvf kcmlv{fc fc lh jfgkwk÷c jf gocwvbo/hdoyyo1 yfczh jkwpockilf, kbpvfwzow w/gocwvbo, w/hdoyyo, ykxvfqh, zkpo jf kczfyëw, ftpfgzhzk}hw Lh Hwknchgk÷c jfl Hdoyyo jf vc Donhy Kcjk}kjvhl ‗ Ghjh donhy flknf lh gobpowkgk÷c jf wv Ghyzfyh $2 jfgkwk÷c hwknchgk÷c jfl hdoyyo+ ‗ Jfpowkzh vch phyzf jf wv hdoyyo fc fl Wkwzfbh Mkchcgkfyo { goc fl yfwzo gobpyh Hgzk}ow Yfhlfw o Hgzk}ow Mkchcgkfyow ‗Fl Wkwzfbh Mkchcgkfyo kczfybfjkh fczyf low donhyfw { lhw fbpyfwhw pyfwzhbkwzhw { low donhyfw { lhw fbpyfwhw pyfwzhzhykow ‗ Low pyëwzhbow fczyf low donhyfw { lhw fbpyfwhw jfl Wfgzoy Pyk}hjo wf ghcgflhc { jfwhphyfgfc jfl Hdoyyo Cfzo jfl Wfgzoy Pyk}hjo Lh Hwknchgk÷c jfl Hdoyyo Cfzo jfl Wfgzoy Pyk}hjo K%L2W W1 Hdoyyo K1 Kc}fywk÷c $nhwzow fc }k}kfcjhw, ghpkzhl pyojvgzk}o { ftkwzfcgkhw+ L1 ]hykhgk÷c jf low Hgzk}ow Mkchcgkfyow Cfzow jfl Wfgzoy Pyk}hjo# ‗ Wk W3K, fczocgfw L30 { fl Wfgzoy Pyk}hjo mkchcgkh hl Wfgzoy Pñilkgo o hl Wfgzoy Ftzfykoy ‗ Wk W
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Lhw Fbpyfwhw jfl Bojflo ‗ Fl bojflo ièwkgo wkbplkmkgh yhjkghlbfczf lh fcoybf gobplfakjhj jf lhw oynhckqhgkocfw fbpyfwhykhlfw ‗ Fl bojflo ièwkgo wvpocf xvf lhw fbpyfwhw woc pyopkfjhj jf low donhyfw { xvf lh yhq÷c jf wv ftkwzfcgkh fw h{vjhy h wvw pyopkfzhykow h gvbplky wvw oiafzk}ow ‗ Fl bojflo ièwkgo wolo gocwkjfyh lh hgzk}kjhj pyojvgzk}h jf lhw fbpyfwhw [ 2 H M$E, C+ [1 Pyojvggk÷c jf ikfcfw { wfy}kgkow mkchlfw H1 Zfgcolonâh E1 Ghpkzhl pyojvgzk}o C1 Zyhihao ‗ Lhw fbpyfwhw jfl bojflo gobpyhc bfyghcgâhw kczfybfjkhw, goczyhzhc low wfy}kgkow jf low mhgzoyfw pyojvgzk}ow, lfw phnhc lhw yfczhw mhgzoykhlfw goyyfwpocjkfczfw, { pyojvgfc lhw bfyghcgâhw mkchlfw jfl bojflo bo jflo Fl Wfgzoy Ftzfykoy ‗ Lhw Ftpoyzhgkocfw jfl Wfgzoy Ftzfykoy $T+ woc kcnyfwow poy lhw }fczhw jf ikfcfw { wfy}kgkow h pyojvgzoyfw yfwkjfczfw fc fl Wfgzoy Kczfykoy ‗ Lhw Kbpoyzhgkocfw jfl Wfgzoy Ftzfykoy $KB+ woc low phnow poy lhw gobpyhw jf ikfcfw { wfy}kgkow h pyojvgzoyfw yfwkjfczfw fc fl Wfgzoy Kczfykoy ‗ Fl Whljo jf lh Ihlhcqh Gobfygkhl $WIG+ fw fl }hloy xvf yfwvlzh hl yfwzhy h lhw ftpoyzhgkocfw lhw kbpoyzhgkocfw $WIG 2 T ‗ KB+ ‗ Fwzhw jfmkckgkocfw fwzèc dfgdhw jfwjf fl pvczo jf }kwzh jfl Wfgzoy Ftzfykoy1 lhw Ftpoyzhgkocfw jfl Wfgzoy Ftzfykoy woc lhw Kbpoyzhgkocfw jfl Wfgzoy Kczfykoy { }kgf}fywh ‗ Wk co dvikfyh fyyoyfw { obkwkocfw fc lh goczhiklkjhj jf lhw zyhcwhggkocfw ftzfykoyfw lh wvbh jf low whljow jf lhw Ihlhcqhw Gobfygkhlfw jf zojow low phâwfw wfyâh knvhl h gfyo ‗ Lh Yfczh Ftzfykoy Cfzh $YFC+ fw fl whljo jf low kcnyfwow { low phnow jf ozyhw yfczhw $yfphzykhgk÷c jf low ifcfmkgkow, yfbfwhw jf low fbknyhczfw, kczfyfwfw jf lh jfvjh ftzfych, phnow jf Iyvwflhw, fzg+ WIGG 2 WIG % YFC 2 T ‗ KB % YFC ‗ Fl

Whljo jf lh Ihlhcqh poy Gvfczh Goyykfczf $WIGG+ $WIGG+ fw fl }hloy xvf yfwvlzh jf wvbhy lh Yfczh Ftzfykoy Cfzh hl Whljo jf lh Ihlhcqh Gobfygkhl ‗ Fl jëmkgkz jf lh ihlhcqh poy gvfczh goyykfczf pvfjf mkchcgkhywf yfjvgkfcjo lhw yfwfy}hw jf jk}kwhw, }fcjkfcjo hgzk}ow kczfykoyfw h co yfwkjfczfw o fbkzkfcjo jfvjh# Lh jfvjh fbkzkjh poy fl wfgzoy kczfykoy { mkchcgkhjh poy co yfwkjfczfw fw lh jfvjh ftzfych#



‗ Wk co dvikfyh fyyoyfw { obkwkocfw fc lh goczhiklkjhj jf lhw zyhcwhggkocfw

ftzfykoyfw lh wvbh jf low whljow jf lhw Ihlhcqhw poy Gvfczh Goyykfczf jf zojow low phâwfw wfyâh knvhl h gfyo#



ZFBH 91 Fl Pyojvgzo Kczfykoy Iyvzo { lh Goczhiklkjhj Chgkochl ¿G÷bo wf bkjf lh Hgzk}kjhj Fgoc÷bkgh jf vc phâw? x8, x9, … ,xc """"X x8 % x9 % ### % x c 2 X ]$x8+ % ]$x9+ % ### % ]$x c+ 2 ] ]$x+ 2 p t x ] 2 8px8 % p9x9 % ### % p cxc ¿Xvë Bfyghcgâhw wf kcglv{fc? Bfyghcgâhw pyojvgkjhw $pyojvggk÷c cvf}h  }fczhw+ Bfyghcgâhw yfbvcfyhjhw $lh pyojvggk÷c jobëwzkgh, fl fwzvjko { fl ogko co wf kcglv{fc+ Bfyghcgâhw lfnhlfw $lfnâzkbhw { jfglhyhjhw+ Bfyghcgâhw kczfykoyfw $PKI1 zfyykzoyko5 PCI1 chgkochlkjhj+ Bfyghcgâhw mkchlfw $}ëhwf fl }hloy høhjkjo+ •

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Lhw Bfyghcgâhw Mkchlfw { lhw Bfyghcgâhw Kczfybfjkhw ‗ Fl pyfgko jf vch bfyghcgâh kcglv{f low pyfgkow jf zojhw lhw bfyghcgâhw xvf kczfy}kfcfc fc wv mhiykghgk÷c ‗ Vch moybh jf f}kzhy lh goczhiklkjhj bñlzkplf jf lhw bfyghcgâhw kczfybfjkhw fc fl gèlgvlo jfl PKI fw kcglvky ñckghbfczf lhw bfyghcgâhw mkchlfw# ‗ Fc lh pyègzkgh lhw bfyghcgâhw mkchlfw f kczfybfjkhw co wf pvfjfc jkwzkcnvky Fl ]hloy Høhjkjo { low Pyfgkow Fc lh pyègzkgh, phyh f}kzhy lh goczhiklkjhj bñlzkplf jf lhw bfyghcgâhw kczfybfjkhw, fl PKI PKI wf ghlgvlh wvbhcjo low }hloyfw høhjkjow høhjkjow jf jf low pyojvgzoyfw kczfykoyfw, yfbvcfyhjow { lfnhlfw#



¿Xvë pfgkow wf gcwkjfyhc? ‗ Low Pyfgkow Ghbikhc Pyfgkow goyykfczfw1 pyfgkow jfl pfykojo fc gvywo $PKI COBKCHL+ Pyfgkow gocwzhczfw1 pyfgkow jf vc pfykojo jf yfmfyfcgkh $PKI YFHL+ ‗ Low Kbpvfwzow Kcjkyfgzow { lhw Wvi}fcgkocfw Pyfgkow jf bfyghjo1 low xvf phnhc low gobpyhjoyfw Pyfgkow h gowzf jf low mhgzoyfw1 low xvf yfgkifc low }fcjfjoyfw ‗ Fl ]hloy jf low Wfy}kgkow Pñilkgow1 Pñilkgow 1 wf }hloyhc ghlgvlhcjo low whlhykow jf lhw pfywochw xvf low pyojvgfc •

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Fl Pyojvgzo Kczfykoy Iyvzo $PKI+ Fl Pyojvgzo Kczfykoy Iyvzo jf vch fgocobâh fw lh wvbh jf low }hloyfw høhjkjow jf zojhw lhw bfyghcgâhw pyojvgkjhw yfbvcfyhjh { lfnhlbfczf fc wv zfyykzoyko jvyhczf vc pfyâojo jf zkfbpo jfzfybkchjo# ¿Poy xvë fl PKI fw Iyvzo?



Lh Goczhiklkjhj Chgkochl Zyfw Moybhw Fxvk}hlfczfw jf Fczfcjfy fl PKI Lh Pyojvggk÷c ¿Xvë bfyghcgâhw wf pyojvgfc? ¿Fc xvë ghczkjhjfw? Fl Nhwzo ¿Xvë zkpow jf nhwzow woc? ¿Xvkëcfw low yfhlkqhc? Lh Yfczh ¿Xvkëcfw wf xvfjhc goc fl }hloy jf lh pyojvggk÷c? Lh Pyojvggk÷c1 Lhw Yhbhw jf lh Hgzk}kjhj Glhwkmkghgk÷c jf lhw Hgzk}kjhjfw Fgoc÷bkghw $Yhbhw+ Wfgzoy Pykbhyko1 Hnvkgvlzvyh,Pfwgh### Wfgzoy Wfgvcjhyko1 Fcfynâh, Kcjvwzykh, Gocwzyvggk÷c### Wfgzoy Zfygkhyko1 Wfy}kgkow $Wfy}kgkow jf bfyghjo { Wfygkgkow jf co bfyghjo+ Kbpvfwzow cfzow woiyf low pyojvgzow PKI h pyfgkow jf bfyghjo Fl Nhwzo ‗ NHWZO 2 GOBPYHW 2 JFBHCJH ‗ ¿Xvë zkpow jf nhwzo woc? Nhwzow goyykfczfw 2 Gocwvbo Nhwzow jf ghpkzhl 2 Kc}fywk÷c $Moybhgk÷c Iyvzh jf Ghpkzhl+ ‗ ¿Xvkëcfw nhwzhc?



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PKI 2 YHW % FIF % KCP 2 [



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Fl Pyfwvpvfwzo jf lh Vck÷c Fvyopfh Gvhczâh1 8#96& jfl PKI jf lh VF $8:& jfl PKI Fwphøol+ Gobpowkgk÷c Wvi}fcgkocfw h lh hnykgvlzvyh1 :0& ¿Poy xvë? o Pyozfggkockwbo myfczf h low phâwfw bèw poiyfw o Mocjow fwzyvgzvyhlfw { jf godfwk÷c1 70& Ozyow nhwzow1 70& $h{vjhw h low ghcjkjhzow h lh hjdfwk÷c, hggk÷c •

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Lh Polâzkgh Mkwghl ¿Gvèczo Wfgzoy Pñilkgo Xvfyfbow? Wfgzoy Pyk}hjo $lkiyf gobpfzfcgkh+ ‗ Phyh hxvfllow xvf fwzèc jkwpvfwzow h phnhy p hnhy bèw ‗ Bh{oy fmkgkfcgkh ‗ Bh{oy jk}fywkjhj Wfgzoy Pñilkgo $jfgkwkocfw gfczyhlkqhjhw+ ‗ Phyh zojow, mkchcgkhjo fczyf zojow ‗ Bfcoy fmkgkfcgkh ‗ Bfcoy jk}fywkjhj •

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• Zhbhøo bâckbo1 yfnlhw jfl avfno $jkwføo { nhyhczâh+ • Zhbhøo bètkbo1 fwzhjo jfl ikfcfwzhy fvyopfo $høow >0+ • Zhbhøo kczfybfjko1 ¿gvèczo? ¿xvë hgzk}kjhjfw?

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‗ Hczf fl hcvcgko jf gvhlxvkfy polâzkgh mkwghl jfifbow pyfnvczhycow wk fl

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ihwfw nyhcjfw ‗ Coybhlbfczf gvhcjo low zkpow jkwbkcv{fc lh yfghvjhgk÷c zhbikëc jkwbkcv{f ‗ Fc lh pyègzkgh lh moybh fthgzh jf lh Gvy}h jf Lhmmfy fw bv{ jkmâgkl jf fwzkbhy ‗ Fl gvfczo jf dhjhw jf lh polâzkgh mkwghl fw xvf wf pvfjfc jkwbkcvky low zkpow { hvbfczhy lh yfghvjhgk÷c $Y# Yfhnhc mvf fl ñlzkbo fc kczfczhylo+ ‗ Zf÷ykghbfczf fw powkilf pfyo pyoihilfbfczf cvcgh dh{h ogvyykjo fc lh pyègzkgh

Gocglvwk÷c Lh yfwzykggk÷c pyfwvpvfwzhykh jfl Wfgzoy Pñilkgo cow yfgvfyjh xvf zojhw lhw polâzkghw ftphcwk}hw zkfcfc xvf mkchcgkhywf jf hlnvch moybh { xvf low fmfgzow mvzvyow jfl fcjfvjhbkfczo pñilkgo zkfcjfc h ghcgflhy low fmfgzow kcbfjkhzow Hgzk}kwzhw Low fmfgzow kcbfjkhzow pyf}hlfgfc poy lo xvf lh polâzkgh mkwghl fw fmfgzk}h Low fmfgzow yfjkwzykivzk}ow woc kbpoyzhczfw Co hgzk}kwzhw Low fmfgzow mvzvyow pyf}hlfgfc { lkbkzhc lh fmfgzk}kjhj jf lh polâzkgh mkwghl Low fmfgzow wfgvcjhykow kbpoyzhc $ftpvlwk÷c, ftpfgzhzk}hw, •

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kcmlhgk÷c+ Low yfzyhwow jf lh polâzkgh mkwghl woc pflknyowow



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LH FPH1 PYOILFBHW Lhw fcgvfwzhw jf fbplfo wvifwzkbhc low pyoilfbhw jf phyo ‗Poilhgk÷c wvifbplfhjh ‗Poilhgk÷c jfwhckbhjh Lhw fcgvfwzhw jf fbplfo fthnfyhc fl pyoilfbh jfl phyo ‗ ]hghczfw jf fbplfow jf ihah gvhlkmkghgk÷c ‗ ]fczhahw lfnhlfw jf jfglhyhywf phyhjo ‗ Hbiknüfjhj fc lh kczfcwkjhj jf iñwxvfjh Lhw fcgvfwzhw jhc vch }kwk÷c fwzèzkgh jf lhw wkzvhgkocfw lhioyhlfw

Zkpow jf Phyo • Phyo mykggkochl, jfikjo hl ghbiko jf yfwkjfcgkh o jf fbplfow# • Phyo zfgcol÷nkgo, jfikjo h lh yfgoc}fywk÷c kcjvwzykhl o gkfyyf hlnvcow wfgzoyfw poy hphykgk÷c jf cvf}hw zëgckghw jf pyojvggk÷c# • Phyo fwzhgkochl, jfikjo hl zyhcwgvywo jf lhw fwzhgkocfw jfl høo# • Phyo gâglkgo, jfikjo h lhw mlvgzvhgkocfw gâglkghw# Zfckfcjo fc gvfczh fwzow zkpow jf phyo, vch zhwh jf plfco fbplfo jfl 800& co zkfcf wfczkjo# Fc nfcfyhl, wf pyopocf vch zhwh jf phyo gobphzkilf goc vch



zhwh jf kcmlhgk÷c fwzhilf Lhw Zfoyâhw zyhjkgkochlfw jfl Phyo • Fl zyhihao fw vch bfyghcgâh bèw, gobo lhw chyhcahw o fl zflëmoco • Wf omyfgfc { wf jfbhcjhc doyhw jf zyhihao dobonëcfhw { hc÷ckbhw • Fl bfyghjo jfzfybkch fl whlhyko { fl fbplfo jf fxvklkiyko

Lhw Zfoyâhw bojfychw jfl Fbplfo • Fwzvjkhc lh chzvyhlfqh jf lhw yflhgkocfw lhioyhlfw1 wv moybhgk÷c, wv bhczfckbkfczo { wv jkwolvgk÷c • Jfgkwkocfw jf low fbplfhjow pozfcgkhlfw

""Lh jfgkwk÷c jf iñwxvfjh jf fbplfo ‗ Lh jfgkwk÷c jf hgfpzhy o yfgdhqhy vch omfyzh ‗ Lh jfgkwk÷c jf gocwfy}hy vc fbplfo ‗ Lh jfgkwk÷c jf yfcvcgkhy h vc fbplfo • Jfgkwkocfw jf low fbplfhjoyfw pozfcgkhlfw ‗ Lh jfgkwk÷c jf gyfhy vch }hghczf ‗ Lh jfgkwk÷c jf dhgfy vch omfyzh ‗ Lh jfgkwk÷c jf bhczfcfy fc plhczkllh h vc fbplfhjo ‗ Lh jfgkwk÷c jf jfwpfjky h vc fbplfhjo

Fl phyo fw vch hgzk}kjhj • Fl phyo fw lh gocwfgvfcgkh jf lhw jkmkgvlzhjfw jf moybhgk÷c jf lhw yflhgkocfw

lhioyhlfw ‗ Flfggk÷c }olvczhykh gvfczh pyopkh/hafch ‗ Jkmkgvlzhjfw jf nhyhczkqhy vc pvfwzo jf zyhihao phyh zojow hl nvwzo jf ghjh vco ‗ Fc vc bfyghjo co wf pvfjfc nhyhczkqhy hl bkwbo zkfbpo lhw ghczkjhjfw { low pyfgkow ‗ Yfnvlhgk÷c jfl bfyghjo lhioyhl ‗ Jkmfyfcgkhw fczyf low jfyfgdow { lhw oilknhgkocfw jf fbplfhjoyfw { fbplfhjow ‗ Low fbplfhjoyfw hwvbfc lh bh{oyâh jf low ykfwnow jf lh yflhgk÷c lhioyhl Lhw polâzkghw jfl Fbplfo • Low wfnvyow jf jfwfbplfo ‗ Wolkjhykjhj ‗ Pyolocnh fl pfykojo jf iñwxvfjh ‗ Ifcfmkgkh h low jfwfbplfhjow { wf mkchcgkh goc ghyno h low fbplfhjow •

Lh yfnvlhgk÷c jfl Bfyghjo lhioyhl Whlhyko bâckbo



Lhw bojhlkjhjfw jf goczyhzhgk÷c { jf jfwpkjo ‗ Yfwzykcnfc lhw lkifyzhjfw fgoc÷bkghw ‗ Avwzkmkghgk÷c1 pyozfnfy h low zyhihahjoyfw myfczf h low hivwow jf low fbpyfwhykow ‗ Pyoilfbhw 1 hvbfczhc low gowzfw lhioyhlfw { jfwkcgfczk}hc lh gyfhgk÷c jf pvfwzow jf zyhihao • Lhw polâzkghw jf bo}klkjhj { moybhgk÷c



ZFBH 61 Fl jkcfyo { lh Polâzkgh Bocfzhykh ¿Xvë fw fl Jkcfyo? Fl jkcfyo woc low bfjkow jf phno nfcfyhlbfczf hgfpzhjow ‗ bocfjhw ‗ ikllfzfw ‗ whljow jf lhw gvfczhw goyykfczfw ‗ gvhlxvkfy ozyo bfjko jf phno nfcfyhlbfczf hgfpzhjo ¿Poy xvë vwhbow fl jkcfyo? Fl jkcfyo yfjvgf low gowzow jf zyhcwhggk÷c Fl zyvfxvf fw kcfmkgkfczf {h xvf yfxvkfyf vch joilf gokcgkjfcgkh jf jfwfow Fl jkcfyo mh}oyfgf lh fwpfgkhlkqhgk÷c Wkc jkcfyo, jhjo xvf fl kczfyghbiko fw gowzowo, wf yfjvgfc low kcgfczk}ow h lh fwpfgkhlkqhgk÷c { wf mh}oyfgf h xvf lhw vckjhjfw mhbklkhyfw wfhc hvzowvmkgkfczfw •

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Mvcgkocfw jfl Jkcfyo "Bfjko jf Ghbiko "Jfp÷wkzo jf ]hloy "Vckjhj jf Gvfczh Pyopkfjhjfw jfl Jkcfyo "Poyzhiklkjhj $Bfjko jf Ghbiko+ "Jk}kwkiklkjhj $Bfjko jf Ghbiko+ "Kcjfczkmkghiklkjhj $Bfjko jf Ghbiko+ "Jvyhiklkjhj $Jfp÷wkzo jf ]hloy+ "Dobonfcfkjhj $Vckjhj jf Gvfczh+ IYF]F DKWZOYKH JFL JKCFYO Fl Jkcfyo Bfyghcgâh Low pykbfyow jkcfyow woc bfyghcgâhw goc }hloy kczyâcwfgo# Fwhw bfyghcgâhw woc bh{oykzhykhbfczf bfzhlfw pyfgkowow Fl Jkcfyo Goc}fyzkilf " Fl jkcfyo goc}fyzkilf o jkcfyo phnhyë woc pyobfwhw jf phnhy jkcfyo bfyghcgâh# " Lhw Lfzyhw jf Ghbiko woc fl hczfgfjfczf $wknlo TKKK+ " Powzfykoybfczf, fl jkcfyo fbkzkjo poy ihcgow Low Ihcgo Gfczyhlfw



Zojow low ihcgow pyk}hjow pvfjfc xvfiyhy $Jow fxvklkiykow jf Chwd+ Low Ihcgo Gfczyhlfw wf gyfhc phyh f}kzhy low pèckgow p èckgow ihcghykow Low Ihcgo Gfczyhlfw hjxvkfyfc fl bocopolko fc lh gyfhgk÷c jf ikllfzfw { bocfjhw, { wf gobpyobfzfc h hpo{hy h low ihcgow gobfygkhlfw gvhcjo fcmyfczhc pyoilfbhw jf lkxvkjfq Lh Zyhcwkgk÷c dhgkh fl Jkcfyo Mkjvgkhyko • Hl fbpfqhy lh Pykbfyh Nvfyyh Bvcjkhl zojow low phâwfw wvwpfcjkfyoc lh

goc}fyzkiklkjhj, ¨{ fl jkcfyo jf gvywo lfnhl bhczv}o wv }hloy( • Fc fl pfykojo jf fczyfnvfyyhw low FF#VV { fl Y#V# yfwzhvyhyoc lh goc}fyzkiklkjhj pfyo }ol}kfyoc h wvwpfcjfylh gvhcjo fbpfq÷ lh Wfnvcjh Nvfyyh Bvcjkhl# • Fc 8;:: wf gyf÷ fl Wkwzfbh jf Iyfzzoc ^oojw poy fl xvf fl VWJ }ol}âh h

wfy goc}fyzkilf { lhw jfbèw bocfjhw mkahihc wvw zkpow jf ghbiko goc fl j÷lhy# Fl Jkcfyo Mkjvgkhyko •

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kcgoc}fyzkilf { poy lo zhczo wkc ckcnñc }hloy kczyâcwfgo Fl Jkcfyo jf Gvywo Lfnhl Fl jkcfyo jf gvywo lfnhl fw vc jkcfyo goc}fyzkilf xvf pvfjf vwhywf phyh ghcgflhy lhw jfvjhw pñilkghw { pyk}hjhw#

¿Xvkëc Nhyhczkqh fl ]hloy jfl Jkcfyo Mkjvgkhyko? ‗ Lhw yfwfy}hw jf oyo jfl Ihcgo Fbkwoy CO nhyhczkqhc fl }hloy jfl jkcfyo mkjvgkhyko poyxvf low ikllfzfw { lhw bocfjhw ck woc w oc goc}fyzkilfw ck woc phnhyëw ‗ Fl Fwzhjo CO nhyhczkqh fl }hloy jfl jkcfyo mkjvgkhyko poyxvf wv gvywo lfnhl wolo wf pvfjf kc}oghy phyh ghcgflhy lhw jfvjhw# Chjkf fwzè oilknhjo oilknhjo h jhycow chjh h ghbiko jf jkcfyo mkjvgkhyko ‗ W×LO LH GOCMKHCQH FC FL JKCFYO MKJVGKHYKO LF GOCMKFYF WV ]HLOY Jow Fxvklkiykow jf Chwd ‗ Vc fxvklkiyko bocfzhyko fc fl xvf gocmkhbow fc jkcfyo mkjvgkhyko { lf gocmfykbow wv }hloy ‗ [ vc fxvklkiyko co bocfzhyko fc fl xvf jfwgocmkhbow jfl jkcfyo mkjvgkhyko { jfwzyvkbow wv }hloy



LOW HNYFNHJOW BOCFZHYKOW B8, B9 , B7, fzg… Lh Ihwf Bocfzhykh $D+ Lh Ihwf Bocfzhykh $D+ fw lh ghczkjhj jf fmfgzk}o $ikllfzfw { bocfjhw+ xvf fl Ihcgo Fbkwoy dh pvfwzo fc gkygvlhgk÷c ¿J÷cjf fwzè lh Ihwf Bocfzhykh? 8+ $F+ Fmfgzk}o fc bhcow jfl pñilkgo $fc lhw zfwoyfyâhw jf lhw fbpyfwhw co ihcghykhw { fc lhw ghyzfyhw jf lhw pfywochw+ 9+ $Y+ Yfwfy}hw jf fmfgzk}o jf low ihcgow { lhw ghahw D 2 F % Y  Lh Ihwf Bocfzhykh fw vch phyzf yflhzk}hbfczf pfxvføh jf low bfjkow jf phno jf lh bh{oyâh jf low phâwfw $fl 8=#7& jf B8 fc lh Fvyoqoch+ Lh Omfyzh Bocfzhykh $B+ Lh Omfyzh Bocfzhykh $B+ fw lh ghczkjhj zozhl jf bfjkow jf phno nfcfyhlbfczf hgfpzhjow xvf gkygvlhc fc vch fgocobâh ¿J÷cjf fwzè lh Omfyzh Bocfzhykh? 8+ $J+ Jfp÷wkzow h lh }kwzh fc low ihcgow { fc lhw ghahw 9+ $F+ Fmfgzk}o fc bhcow jfl pñilkgo B2F%J Fl cobiyf zëgckgo jf lh Omfyzh Bocfzhykh fw B8 •

Low Ihcgow Gobfygkhlfw Gyfhc Jkcfyo Low Ihcgow Gobfygkhlfw wf fcjfvjhc fc fmfgzk}o goc wvw jfpowkzhczfw { lo pyfwzhc h wvw jfvjoyfw Gvhcjo vc ihcgo gocgfjf vc gyëjkzo pfybkzf xvf jow pfywochw jkwzkczhw vwfc fl bkwbo jkcfyo5 gyfh vc jfp÷wkzo cvf}o { hl dhgfylo gyfh jkcfyo Gvhcjo vc ihcgo yfjvgf lh gvhczâh jf wvw gyëjkzow, jfwzyv{fc jfp÷wkzow { hl dhgfylo jfwzyv{fc lkzfyhlbfczf jkcfyo Lh gvhczâh jf low Jfp÷wkzow $J+ fw knvhl h lh wvbh jf lhw Yfwfy}hw Ihcghykhw $Y+ { jf low Pyëwzhbow $P+1 J 2 Y % P Fl IGF IGF oilknh h low Ihcgow h vc 9& jf wvw Jfp÷wkzow fc Yfwfy}h# Fw jfgky, Y/J20,09, fwzf cñbfyo yfgkif fl cobiyf jf gofmkgkfczf jf ghah •

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Fl Bvlzkplkghjoy Ihcghyko Jfmkckbow hl gofmkgkfczf jf ghah gobo g2Y/J { hl gofmkgkfczf jf fmfgzk}o gobo f2F/J# Poy lo zhczo, lh ihwf bocfzhykh D2 F%Y2fJ%gJ2$f%g+J poy lo xvf J2$8/f%g+D Lh ftpyfwk÷c $8/f%g+ yfgkif fl cobiyf jf bvlzkplkghjoy ihcghyko#



Fl Bvlzkplkghjoy Bocfzhyko  Jfmkckbow hl gofmkgkfczf jf ghah gobo g2Y/J# Poy lo zhczo, lh omfyzh bocfzhykh B2 F%J2fJ%J2$f%8+J Jf lh jkhpowkzk}h hczfykoy whifbow J2$8/f%g+D# Poy lo xvf,

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B2$8%f+/$f%g+D Lh ftpyfwk÷c $8%f/f%g+ yfgkif fl cobiyf jf bvlzkplkghjoy bocfzhyko, { cow jkgf fc gvhczo hvbfczh lh omfyzh bocfzhykh wk hvbfczh fc 8 fvyo lh ihwf bocfzhykh

Low Ihcgow Gobfygkhlfw Gyfhc Jkcfyo 8+ Fczyf bèw yfwfy}hw zfcnhc xvf zfcfy low ihcgow phyh yfwphljhy jfp÷wkzow, bfcow pvfjfc pyfwzhy, poy lo xvf gyfhc bfcow jkcfyo 9+ Fczyf bèw jkcfyo xvkfyhc bhczfcfy fc fmfgzk}o lhw mhbklkhw, bfcow jkcfyo jfpowkzhc, poy lo zhczo low ihcgow bfcow pvfjfc pyfwzhy { poy lo bkwbo gyfhc bfcow jkcfyo 7+ Poy lo zhczo wk yfwfy}hw/jfp÷wkzow o fmfgzk}o/jfp÷wkzow wvif, lh ghczkjhj jf jkcfyo fc lh fgocobâh jfif jkwbkcvky Ozyow Hnyfnhjow Bocfzhykow B9 2 B8 % Ozyow jfp÷wkzow h goyzo plhqo $fczyf zyfw bfwfw { jow høow+ B7 2 B9 % Ozyow phwk}ow jf lhw kcwzkzvgkocfw mkchcgkfyhw B7 fw lh }hykhilf jf goczyol jfl Ihcgo Gfczyhl Fvyopfo •

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LH POLÂZKGH BOCFZHYKH Low Oiafzk}ow jf lh Polâzkgh Bocfzhykh ‗ Fl Ihcgo Ihcgo Gfczyhl Gfczyhl Fvyopfo $IGF+1 Fl oiafzk}o pykcgkphl jf jf lh Polâzkgh Bocfzhykh jfl IGF fw bhczfcfy lh fwzhiklkjhj jf low pyfgkow# Fl IGF IGF bhczfcjyè vch zhwh jf kcmlhgk÷c kcmfykoy pfyo gfyghch hl 9& fc fl bfjko plhqo# Fl Fvyowkwzfbh goczykivkyè h bhczfcfy vch zhwh jf gyfgkbkfczo )wowzfckilf { co"kcmlhgkochykh)# ‗Lh Yfwfy}h Mfjfyhl Mfjfyhl jf Fwzhjow Vckjow $MFJ+1 Wf mkahyè mkahyè lh zhwh jf gyfgkbkfczo h lhyno plhqo jf low hnyfnhjow bocfzhykow { gyfjkzkgkow phyh gocwfnvky low oiafzk}ow jf bètkbo fbplfo, pyfgkow fwzhilfw { zkpow jf kczfyëw h lhyno plhqo bojfyhjow# ¿G÷bo wf Gocwknvfc fwow Oiafzk}ow? "" Lh mhlzh jf lkxvkjfq pvfjf pyo}oghy vch yfgfwk÷c { lh hivcjhcgkh jf lkxvkjfq pvfjf mh}oyfgfy vch ftphcwk÷c



"" Poy lo xvf goczyolhcjo lh lkxvkjfq jfl wkwzfbh low ihcgow gfczyhlfw pvfjfc kcmlvfcgkhy fc low gkglow fgoc÷bkgow Lh Hyzkgvlhgk÷c jf lh Polâzkgh Bocfzhykh

Opfyhgkocfw jf Bfyghjo Hikfyzo Lh zhwh jf kczfyëw kbplâgkzh jf vc ioco jfl zfwoyo z fwoyo fw1

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Lh Zyhcwbkwk÷c jf lh Polâzkgh Bocfzhykh Opfyhgkocfw jf bfyghjo hikfyzo xvf bojkmkghc lh ihwf bocfzhykh $kcwzyvbfczo+ Ghbikow fc fl zkpo jf kczfyëw jfl bfyghjo $}hykhilf kczfybfjkh+ Ghbikow fc lhw jfgkwkocfw jf gocwvbo, hdoyyo f kc}fywk÷c •

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Ghbikow fc lh jfbhcjh hnyfnhjh { fc lh zhwh jf kcmlhgk÷c $oiafzk}o+

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PKI Yfhl

Jfmlhgzoy jfl PKI



Lh Kcmlhgk÷c { low Whlhykow  Fl pojfy hjxvkwkzk}o jf low whlhykow fw fl }hloy yfhl jf low whlhykow o, lo xvf fw lo bkwbo, lh ghczkjhj jf bfyghcgâhw xvf wf pvfjfc gobpyhy goc fllow  Phyh xvf fl whlhyko yfhl jkwbkcv{h co fw wvmkgkfczf goc xvf wvihc low pyfgkow Low Gowzfw jf lh Kcmlhgk÷c 8# Lh zhwh jf kcmlhgk÷c xvf bèw cow kbpoyzh fw lh zhwh jf }hykhgk÷c jfl âcjkgf jf pyfgkow kcjk}kjvhl jf ghjh vco poyxvf fw lh xvf jfzfybkch fl gowzf jf cvfwzyhw }kjhw# 9# Co fw gkfyzo xvf lh kcmlhgk÷c fyowkocf wkwzfbèzkghbfczf fl pojfy hjxvkwkzk}o jf low whlhykow# 7# Lh kcmlhgk÷c yflhzk}h cow dhgf bfcow gobpfzkzk}ow fc low bfyghjow kczfychgkochlfw# Lh Zfoyâh Gvhczkzhzk}h jfl Jkcfyo B t } 2 P t [ B" Jkcfyo }" ]flogkjhj jf gkygvlhgk÷c jfl jkcfyo P " Kcjkgf jf Pyfgkow [" PKI yfhl Fc zhwhw jf gyfgkbkfczo $N+1 Nb % N} 2 Np % N{ Wk lh }flogkjhj fw gocwzhczf $}+, { gobo Np fw kcmlhgk÷c, Nb

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LOW ZKPOW JF KCZFYËW ¿Xvë woc low zkpow jf kczfyëw? ‗Low zkpow jf kczfyëw woc low pyfgkow jf fwpfyhy dhwzh vc bobfczo



jfzfybkchjo jfl mvzvyo ‗Fl zkpo jf kczfyëw cobkchl $k+1 fw fl pyfgko jf fwpfyhy bfjkjo fc vckjhjfw bocfzhykhw ‗Fl zkpo jf kczfyëw yfhl $y+1 fw fl pyfgko jf fwpfyhy bfjkjo fc vckjhjfw jf gocwvbo Low Zkpow jf Kczfyëw Yfhlfw pyfwzhjo h vc zkpo jf kczfyëw kczfyëw cobkchl mkao, ‗ Pyoilfbh1 Gvhcjo pyfwzo o pkjo pyfwzhjo k, co wf gvèl }h h wfy bk zkpo jf kczfyëw yfhl, y, poyxvf co wë gvèl }h h wfy lh zhwh jf kcmlhgk÷c, π ‗ Ft"hczf1 fl zkpo jf kczfyëw kczfyëw yfhl fwpfyhjo fw hpyotkbhjhbfczf hpyotkbhjhbfczf knvhl knvhl hl zkpo jf kczfyëw cobkchl bfcow lh zhwh jf kcmlhgk÷c fwpfyhjh, yf 2 k ‗ πf kczfyëw yfhl oizfckjo fw hpyotkbhjhbfczf hpyotkbhjhbfczf knvhl hl zkpo ‗ Ft"powz1 fl zkpo jf kczfyëw jf kczfyëw cobkchl bfcow lh zhwh jf kcmlhgk÷c oiwfy}hjh, y 2 k ‗ π ‗ Wk lh zhwh jf kcmlhgk÷c oiwfy}hjh fw bh{oy xvf lh fwpfyhjh wf pyojvgf vch nhchcgkh phyh low pyfwzhbkwzhw { vch pfyjkjh phyh low pyfwzhzhykow knvhl h y ‗ yf 2 π ‗ πf

Lh Fgvhgk÷c jf Mkwdfy

¿Poy xvë cow kbpoyzhc low Zkpow jf Kczfyëw?


Vck÷c jf Fwzvjkhczfw jf Gkfcgkhw Fgoc÷bkghw    

Poyxvf woc vc gobpocfczf jf low nhwzow { jf low kcnyfwow jf low donhyfw { jfzfybkchc wvw jfgkwkocfw jf gocwvbo, gocw vbo, hdoyyo f kc}fywk÷c Poyxvf woc vc gobpocfczf jf low nhwzow jfl wfgzoy pñilkgo { gocjkgkochc lh polâzkgh mkwghl# Poyxvf hmfgzhc h low zkpow jf ghbiko Poyxvf pvfjfc hmfgzhy h lh zhwh jf gyfgkbkfczo gyfg kbkfczo jf lh fgocobâh



ZFBH >1 Low zkpow jf ghbiko { lh Polâzkgh Ghbikhykh Yfgoyjfbow jf Gvfczhw Chgkochlfw xvf…

K2$["G+%$Z"N+%$KB"T+ Jfwjf lvfno, phyfgf wfy xvf vc hlzo jëmkgkz fc lh ihlhcqh gobfygkhl fw hlno ivfco Wk fwzo fw gkfyzo, ¿poy xvë zhczow z hczow phâwfw wf pyfogvphc jf vc hlzo hlz o jëmkgkz? VCH BKYHJH BÈW GFYGHCH H LH IHLHCQH JF PHNOW COW JHYÈ VCH YFWPVFWZH Lh Fwzyvgzvyh jf lh Ihlhcqh jf Phnow IHLHCQH POY GVFCZH GOYYKFCZF Bfyghcgâhw Wfy}kgkow $Zvykwbo $Zvykwbo { ]khafw, Ozyow Wfy}kgkow+ Yfczh jfl Zyhihao { jfl Ghpkzhl Zyhcwmfyfcgkhw Goyykfczfw#

IHLHCQH MKCHCGKFYH Kc}fywkocfw Kc}fywkocfw jf Fwphøh fc fl ftzfykoy $Jkyfgzhw, Jf ghyzfyh+ Kc}fywkocfw jfl ftzfykoy fc Fwphøh $Jkyfgzhw o Ghyzfyh+ ]hykhgk÷c jf Yfwfy}hw

IHLHCQH POY GVFCZH JF GHPKZHL Zyhcwmfyfcghw jf ghpkzhl cfzhw

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FYYOFW [ OBKWKOCFW

Whljo jf lh Ihlhcqh Gobfygkhl $WIG+1 Jkmfyfcgkh fczyf fl }hloy jf lhw Ftpoyzhgkocfw { fl jf lhw Kbpoyzhgkocfw Whljo jf lh Ihlhcqh poy Gvfczh Goyykfczf $WIGG+1 Whljo jf zojhw lhw opfyhgkocfw goyykfczfw goc fl ftzfykoy $WIGG2WIG%YFC+

Lh Wowzfckiklkjhj jfl Jëmkgkz Ftzfykoy Mhgzoyfw h zfcfy fc gvfczh ‗Gvhczâh ‗Jvyhgk÷c ‗Ghvwhw $gocwvbo, kc}fywk÷c+ ‗Mkchcgkhgk÷c $kc}fywk÷c jkyfgzh, ghpkzhlfw h goyzo plhqo, ghpkzhlfw h lhyno plhqo+

¿Xvë woc low Zkpow jf Ghbiko?



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Fl zkpo jf ghbiko cobkchl $f+ fw fl pyfgko jf vch bocfjh fc zëybkcow jf ozyh $bocfjh ftzyhcafyh poy bocfjh chgkochl, f#n# */ €+ Fl zkpo jf ghbiko yfhl $f Y + fw fl pyfgko jf vch bfyghcgâh ftzfykoy fc zëybkcow jf vch bfyghcgâh kczfykoy $vckjhjfw jf lh bfyghcgâh ftzfykoy poy vckjhjfw jf lh bfyghcgâh kczfykoy+ $f Y 2fP/P!+ 2fP/P!+ Ozyow zkpow jf ghbiko ‗Low zkpow jf ghbiko fmfgzk}ow woc bfjkhw pocjfyhjhw jf zkpow jf ghbiko cobkchlfw o yfhlfw $wpoz/moy~hyj+1 fczyfnh hl ‗Low zkpow jf ghbiko goczhjo/mvzvyo $wpoz/moy~hyj+1 goczhjo/fczyfnh mvzvyh jf jk}kwhw

Gvhcjo cvfwzyh bocfjh wf hpyfgkh… ‗Lh pyojvggk÷c kczfykoy wf fcghyfgf phyh low ftzyhcafyow, lh pyojvggk÷c

ftzfykoy wf hihyhzh phyh low yfwkjfczfw, { pfyjfbow gobpfzkzk}kjhj $fa# low zvykwzhw ftzyhcafyow ivwghc ozyow jfwzkcow { cowozyow }khahbow bèw hl ftzyhcafyo+# ‗Lhw ftpoyzhgkocfw jkwbkcv{fc, lhw kbpoyzhgkocfw hvbfczhc { lh ihlhcqh gobfygkhl zkfcjf h }ol}fywf jfmkgkzhykh ‗Fl gowzf jf lhw bfyghcgâhw kbpoyzhjhw jkwbkcv{f { fl Kcjkgf jf Pyfgkow jf Gocwvbo zkfcjf h jkwbkcvky ‗Low hgzk}ow kczfykoyfw wf fcghyfgfc { lhw kc}fywkocfw ftzyhcafyhw fc fl kczfykoy zkfcjfc h jkwbkcvky $goc cvfwzyhw kc}fywkocfw fc fl ftzfykoy ogvyyf lo goczyhyko+ ‗Lh yfczhiklkjhj fc jk}kwhw jf lhw kc}fywkocfw kczfykoyfw jf low ftzyhcafyow hvbfczh { lh yfczhiklkjhj fc bocfjh chgkochl jf cvfwzyhw kc}fywkocfw ftzfykoyfw jkwbkcv{f ‗Zfcfbow xvf zyhihahy bfcow phyh oizfcfy vch vckjhj jf bocfjh ftzyhcafyh { cow fcykxvfgfbow fc zëybkcow jf bfyghcgâhw ftzfykoyfw ‗Low kbpoyzfw fc bocfjh kczfykoy jf lhw jfvjhw jfcobkchjhw fc jk}kwhw jkwbkcv{fc { fl ykfwno jf zfcfy vch gykwkw mkchcgkfyh jkwbkcv{f

¿Poy xvë cow kbpoyzhc low Zkpow jf Ghbiko? ‗Gobpfzkzk}kjhj1 low zkpow jf ghbiko ghbiko jfzfybkchc fl pyfgko yflhzk}o jf lh pyojvggk÷c kczfykoy { lh pyojvggk÷c ftzfykoy ‗Yfczhiklkjhj jf lhw kc}fywkocfw1 low zkpow jf ghbiko jfzfybkchc low gowzfw jf low hgzk}ow { lhw yfczhiklkjhjfw yflhzk}hw jf lhw kc}fywkocfw kczfykoyfw { ftzfykoyfw



Low Jfzfybkchczfw jf low Zkpow jf Ghbiko • Lh f}olvgk÷c jf lh yfczhiklkjhj bfjkjh poy fl jkmfyfcgkhl jf low zkpow jf

kczfyëw • Lh f}olvgk÷c jf low whljow poy gvfczh goyykfczf { low ghbikow fc fl

fcjfvjhbkfczo { fc fl ykfwno jf ghjh phâw Lh Jfzfybkchgk÷c jf low Zkpow jf Ghbiko Whljo jf lh ihlhcqh goyykfczf { jf ghpkzhl % Kc}fywkocfw ftzyhcafyhw jkyfgzhw $cfzhw+ % Ghpkzhlfw h lhyno plhqo $cfzow+ Wvpfyè}kz jf lh I# jf Phnow

Jëmkgkz jf lh I# Jf Phnow

$ftgfwo $ftgfwo jf jfbhcjh jf lh

$ftgfwo $ftgfwo jf omfyzh jf lh

bocfjh chgkochl+

bocfjh chgkochl+

Hpyfgkhgk÷c jf lh bocfjh

Jfpyfgkhgk÷c jf lh bocfjh

Chgkochl

Chgkochl

$Ivfc bobfczo phyh }kwkzhy lh

$Zhl }fq ghcgflfbow fl }khaf

Nyhc Bhcqhch+

h C[G+

Lh Phykjhj jf low Zkpow jf Kczfyëw 8%k2$8%k!+fz/fz%8 •

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HL ZKPO JF GHBIKO FWPFYHJO $fz%8 z%8+ WF HAVWZH JF ZHL BHCFYH XVF FWZHW KCJKMFYFCZF H KC]FYZKY FCZYF HBIOW PHÂWFW# POY LO BKWBO, FC BFYGHJOW JF MVZVYOW, FL MOY^HYJ WF HAVWZH DHWZH WHZKWMHGFY LH KNVHLJHJ HCZFYKOY, JF LO GOCZYHYKO HIYÂH HYIKZYHAF $¿poy xvë?+ Fc zhwhw jf }hykhgk÷c, fwzh ftpyfwk÷c fxvk}hlf h f

2 k! ‗ k

Fl Lhyno Plhqo1 Lh Phykjhj jfl Pojfy Hjxvkwkzk}o Yfgoyjfbow hl zkpo jf Ghbiko Yfhl jocjf 1 $f 2 P!/P  fY 28+ 28+ Wk wf gvbplf lh Zfoyâh jf lh Phykjhj jfl Pojfy Hjxvkwkzk}o lh }hykhgk÷c jfl zkpo jf ghbiko ghbiko fczyf lhw bocfjhw jf jow phâwfw wf •

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jfzfybkch poy lh jkmfyfcgkh fczyf wvw zhwhw jf kcmlhgk÷c $ f 2 p! " p+ Low phâwfw goc vc jkmfyfcgkhl jf kcmlhgk÷c pfywkwzfczf zkfcjfc h pfyjfy gobpfzkzk}kjhj { wvw bocfjhw zkfcjfc h jfpyfgkhywf Lkbkzhgkocfw ‗Lhw bfyghcgâhw co gobfygkhilfw ‗Lhw bfyghcgâhw kczfykoyfw { ftzfykoyfw co wkfbpyf woc wvwzkzvzhw pfymfgzhw

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LH POLKZKGH GHBIKHYKH Low Yfnâbfcfw Ghbikhykow Zkpow jf ghbiko mlftkilfw Hpyfgkhgk÷c / jfpyfgkhgk÷c Zkpow jf ghbiko mkaow Yfmfyfcgkh1 oyo, ozyh bocfjh, vch gfwzh jf bocfjhw b ocfjhw Yf}hlvhgk÷c / jf}hlvhgk÷c Zkpo ñckgo / ihcjh Phzy÷c oyo, ghahw jf goc}fywk÷c, jolhykqhgk÷c Zkpow jf ghbiko mkaow havwzhilfw Mlozhgk÷c wvgkh / Kczfy}fcgk÷c jfl Ihcgo Gfczyhl Phpfl jf lhw yfwfy}hw Goczyolfw jf ghbiko Low Zkpow jf Ghbiko Mlftkilfw Zf÷ykghbfczf woc kcbvcfw h lhw gykwkw •

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Jfpfcjfc w÷lo jf mhgzoyfw “mvcjhbfczhlfw‒

Lh fwpfgvlhgk÷c fw bv{ jkmâgkl Fc lh pyègzkgh woc kcfwzhilfw Owgklhgkocfw myfgvfczfw h goyzo plhqo Hbplkhw jfwhlkcfhgkocfw h lhyno plhqo Fl phâw gocwfy}h fl goczyol jf wv polâzkgh bocfzhykh Fafbplow1 j÷lhy, fvyo, {fc, lkiyh, myhcgo wvkqo, fzg Zkpow jf Ghbiko Mkaow Wf vzklkqhc gobo hcglhaf jf lh polâzkgh bocfzhykh Pfybkzfc goczyolhy lh kcmlhgk÷c f kcgfczk}hc lhw fczyhjhw jf ghpkzhlfw Lh polâzkgh bocfzhykh jfif wvioyjkchywf hl bhczfckbkfczo jfl zkpo jf ghbiko Lhw ftphcwkocfw bocfzhykhw woc kc}khilfw Fafbplow1 Vck÷c Fgoc÷bkgh { Bocfzhykh Fvyopfh, Ghahw jf goc}fywk÷c, Phzy÷c Oyo Zkpow jf Ghbiko Havwzhilfw Fc zfoyâh woc fwzhilfw jfczyo jf vch ihcjh i hcjh jf mlvgzvhgk÷c Lhw ihcjhw wf pvfjfc havwzhy gvhcjo lhw gkygvcwzhcgkhw lo yfxvkfyfc ‗

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Fc lh pyègzkgh woc bv{ kcfwzhilfw f kcgfczk}hc low bo}kbkfczow fwpfgvlhzk}ow Lh polâzkgh bocfzhykh zkfcf vc gkfyzo bhynfc jf lkifyzhj jfczyo jf lh ihcjh pfyo wf }f lkbkzhjh poy fl bhczfckbkfczo b hczfckbkfczo jfl zkpo jf ghbiko Fafbplow1 Iyfzzoc ^oojw,Wkwzfbh Bocfzhyko Fvyopfo $WBF+ VCKOCFW BOCFZHYKHW ]FCZHAHW1 Vch bocfjh fwzhilf pyobvf}f fl gobfygko fczyf low phâwfw bkfbiyow jf lh vck÷c# JFW]FCZHAHW1 Low bkfbiyow zkfcfc xvf gfjfy fl goczyol jf lh polâzkgh bocfzhykh# •

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Principios de Economía: Introducción a la Macroeconomía

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