<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/ab3ff7a0-b2be-4c23-b3d1-b036e3d036b6/bg1.png"><div class="c x0 y1 w2 h2"><div class="t m0 x1 h3 y2 ff1 fs0 fc0 sc0 ls2 ws0">EA<span class="_0 blank"></span>E0<span class="_0 blank"></span>207<span class="_0 blank"></span>:<span class="_1 blank"> </span>M<span class="_0 blank"></span>ate<span class="_0 blank"></span>mát<span class="_0 blank"></span>ica A<span class="_0 blank"></span>pli<span class="_0 blank"></span>cad<span class="_0 blank"></span>a à Eco<span class="_0 blank"></span>nom<span class="_0 blank"></span>ia</div><div class="t m0 x2 h4 y3 ff1 fs1 fc0 sc0 ls2 ws1">Aula<span class="_2 blank"> </span>1:<span class="_3 blank"> </span>Intro dução</div><div class="t m0 x3 h4 y4 ff1 fs1 fc1 sc0 ls2 ws2">Ma<span class="_0 blank"></span>rcos Y. Nakaguma</div><div class="t m0 x4 h4 y5 ff1 fs1 fc1 sc0 ls2 ws3">03/08/2016</div><div class="t m0 x5 h5 y6 ff1 fs2 fc1 sc0 ls2">1</div></div><div class="c x0 y7 w2 h2"><div class="t m0 x6 h3 y8 ff1 fs0 fc0 sc0 ls2 ws4">P<span class="_0 blank"></span>o<span class="_0 blank"></span>r q<span class="_0 blank"></span>ue E<span class="_0 blank"></span>stud<span class="_0 blank"></span>a<span class="_0 blank"></span>r Ec<span class="_0 blank"></span>ono<span class="_0 blank"></span>mi<span class="_0 blank"></span>a Ma<span class="_0 blank"></span>tem<span class="_0 blank"></span>áti<span class="_0 blank"></span>ca?</div><div class="t m0 x7 h4 y9 ff1 fs1 fc1 sc0 ls2 ws5">A matemática é uma das <span class="fc2 ws6">linguagens p<span class="_0 blank"></span>redominantes <span class="fc1 ws7">na economia</span></span></div><div class="t m0 x7 h4 ya ff1 fs1 fc1 sc0 ls2 ws1">mo derna.</div><div class="t m0 x8 h6 yb ff2 fs3 fc0 sc0 ls0">I<span class="ff1 fs4 fc1 ls2 ws8 v1">Mesmo áreas como história e so<span class="_4 blank"> </span>ciologia econômica vêm se tornando</span></div><div class="t m0 x9 h7 yc ff1 fs4 fc1 sc0 ls2 ws9">cada vez mais for<span class="_0 blank"></span>malizadas, com o uso de te<span class="_4 blank"> </span>o<span class="_0 blank"></span>ria dos jogos e</div><div class="t m0 x9 h7 yd ff1 fs4 fc1 sc0 ls2 wsa">econometria.</div><div class="t m0 x7 h4 ye ff1 fs1 fc1 sc0 ls2 wsb">Além disso, a matemática ajuda a <span class="fc2 ws1">disciplina<span class="_0 blank"></span>r<span class="_2 blank"> </span>o<span class="_2 blank"> </span>racio cínio<span class="fc1">.</span></span></div><div class="t m0 x8 h6 yf ff2 fs3 fc0 sc0 ls0">I<span class="ff1 fs4 fc1 ls2 wsc v1">A<span class="_5 blank"> </span>linguagem<span class="_5 blank"> </span>matemática<span class="_5 blank"> </span>to<span class="_0 blank"></span>rna<span class="_5 blank"> </span>p ossível<span class="_5 blank"> </span>mo delar<span class="_5 blank"> </span>situações<span class="_5 blank"> </span>complexas,</span></div><div class="t m0 x9 h7 y10 ff1 fs4 fc1 sc0 ls2 wsd">enfatizando<span class="_5 blank"> </span>seus<span class="_5 blank"> </span>asp ectos<span class="_5 blank"> </span>centrais.</div><div class="t m0 x8 h8 y11 ff2 fs3 fc0 sc0 ls0">I<span class="ff1 fs4 fc1 ls2 wse v1">A<span class="_5 blank"> </span>linguagem<span class="_5 blank"> </span>fo<span class="_0 blank"></span>rmal<span class="_5 blank"> </span>da<span class="_5 blank"> </span>matemática<span class="_5 blank"> </span>torna<span class="_5 blank"> </span>evidente<span class="_5 blank"> </span>quais<span class="_5 blank"> </span>hipóteses</span></div><div class="t m0 x9 h7 y12 ff1 fs4 fc1 sc0 ls2 wse">estão<span class="_5 blank"> </span>p o<span class="_0 blank"></span>r<span class="_5 blank"> </span>trás<span class="_5 blank"> </span>dos<span class="_5 blank"> </span>resultados<span class="_5 blank"> </span>de<span class="_5 blank"> </span>um<span class="_5 blank"> </span>mo delo.</div><div class="t m0 x5 h5 y13 ff1 fs2 fc1 sc0 ls2">2</div></div><div class="c x0 y14 w2 h9"><div class="t m0 x6 h3 y15 ff1 fs0 fc0 sc0 ls2 wsf">M<span class="_0 blank"></span>ate<span class="_0 blank"></span>mát<span class="_0 blank"></span>ica<span class="_6 blank"> </span>e<span class="_6 blank"> </span>Eco<span class="_0 blank"></span>nom<span class="_0 blank"></span>ia<span class="_0 blank"></span>:<span class="_1 blank"> </span>M<span class="_0 blank"></span>etodol<span class="_0 blank"></span>ogi<span class="_0 blank"></span>a</div><div class="t m0 x7 h4 y16 ff1 fs1 fc1 sc0 ls1">O<span class="fc2 ls2 ws10">lab o<span class="_0 blank"></span>ratório<span class="_2 blank"> </span><span class="fc1 ws11">de<span class="_2 blank"> </span>um<span class="_2 blank"> </span>economista<span class="_2 blank"> </span>é<span class="_2 blank"> </span>o<span class="_2 blank"> </span>seu<span class="_2 blank"> </span>mo delo:</span></span></div><div class="t m0 x5 h5 y17 ff1 fs2 fc1 sc0 ls2">3</div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/ab3ff7a0-b2be-4c23-b3d1-b036e3d036b6/bg2.png"><div class="c x0 y1 w2 h2"><div class="t m0 x6 h3 y18 ff1 fs0 fc0 sc0 ls2 ws13">Ob<span class="_0 blank"></span>jet<span class="_0 blank"></span>ivo<span class="_0 blank"></span>s</div><div class="t m0 x7 h4 y19 ff1 fs1 fc1 sc0 ls2 ws14">Este curso não é uma disciplina de matemática formal nem substitu<span class="_0 blank"></span>i</div><div class="t m0 x7 h4 y1a ff1 fs1 fc1 sc0 ls2 ws15">um<span class="_2 blank"> </span>b om<span class="_2 blank"> </span>curso<span class="_2 blank"> </span>de<span class="_2 blank"> </span>Álgeb<span class="_0 blank"></span>ra<span class="_2 blank"> </span>Linear<span class="_5 blank"> </span>ou<span class="_2 blank"> </span>Cálculo<span class="_2 blank"> </span>Avançado.</div><div class="t m0 x7 h4 y1b ff1 fs1 fc1 sc0 ls2 ws16">Neste curso, vamos concentra<span class="_0 blank"></span>r-nos nos tópicos mais utilizados em</div><div class="t m0 x7 h4 y1c ff1 fs1 fc1 sc0 ls2 ws17">economia.<span class="_3 blank"> </span>A ab<span class="_4 blank"> </span>o<span class="_0 blank"></span>rdagem será rigorosa, porém a ênfase será dada à</div><div class="t m0 x7 h4 y1d ff1 fs1 fc1 sc0 ls2 ws18">aplicação dos resultados, ao invés de demonstrações fo<span class="_0 blank"></span>rmais.</div><div class="t m0 x7 h4 y1e ff1 fs1 fc1 sc0 ls2 ws19">O objetivo é p<span class="_0 blank"></span>rover o aluno com os conceitos necessários para cursa<span class="_0 blank"></span>r</div><div class="t m0 x7 h4 y1f ff1 fs1 fc1 sc0 ls2 ws1a">as<span class="_2 blank"> </span>disciplinas<span class="_2 blank"> </span>de<span class="_2 blank"> </span>Macro economia,<span class="_2 blank"> </span>Micro economia<span class="_2 blank"> </span>e<span class="_2 blank"> </span>Econometria.</div><div class="t m0 x5 h5 y20 ff1 fs2 fc1 sc0 ls2">4</div></div><div class="c x0 y7 w2 h2"><div class="t m0 x6 h3 y8 ff1 fs0 fc0 sc0 ls2 ws13">Pr<span class="_0 blank"></span>ogr<span class="_0 blank"></span>am<span class="_0 blank"></span>a</div><div class="t m0 x7 h4 y21 ff1 fs1 fc1 sc0 ls2 ws14">O curso está dividido em três pa<span class="_0 blank"></span>rtes principais:</div><div class="t m0 xa h7 y22 ff1 fs4 fc0 sc0 ls2 wsa">1<span class="ff3 ls3">.</span><span class="fc1 ws1b">Álgeb<span class="_0 blank"></span>ra Linear:<span class="_6 blank"> </span>Sistemas de Equações Linea<span class="_0 blank"></span>res</span></div><div class="t m0 xa h7 y23 ff1 fs4 fc0 sc0 ls2 wsa">2<span class="ff3 ls3">.</span><span class="fc1 ws9">Equações Diferenciais e Equações a Diferenças</span></div><div class="t m0 xa h7 y24 ff1 fs4 fc0 sc0 ls2 wsa">3<span class="ff3 ls3">.</span><span class="fc1 ws8">Otimização e Estática Comparativa</span></div><div class="t m0 x5 h5 y25 ff1 fs2 fc1 sc0 ls2">5</div></div><div class="c x0 y14 w2 h9"><div class="t m0 x6 h3 y15 ff1 fs0 fc0 sc0 ls2 ws1c">P<span class="_0 blank"></span>a<span class="_0 blank"></span>r<span class="_0 blank"></span>te I: Á<span class="_0 blank"></span>lgeb<span class="_7 blank"></span>ra L<span class="_0 blank"></span>ine<span class="_0 blank"></span>a<span class="_0 blank"></span>r</div><div class="t m0 x7 h4 y26 ff1 fs1 fc2 sc0 ls2 ws1d">Motivação: <span class="fc1 ws19">Sistemas de equações lineares são muito comuns em</span></div><div class="t m0 x7 h4 y27 ff1 fs1 fc1 sc0 ls2 ws16">economia, p<span class="_4 blank"> </span>ois a maio<span class="_0 blank"></span>r parte dos modelos são lineares:</div><div class="t m0 x7 ha y28 ff4 fs1 fc1 sc0 ls2">8</div><div class="t m0 x7 ha y29 ff4 fs1 fc1 sc0 ls2">></div><div class="t m0 x7 ha y2a ff4 fs1 fc1 sc0 ls2">></div><div class="t m0 x7 ha y2b ff4 fs1 fc1 sc0 ls2">></div><div class="t m0 x7 ha y2c ff4 fs1 fc1 sc0 ls2"><</div><div class="t m0 x7 ha y2d ff4 fs1 fc1 sc0 ls2">></div><div class="t m0 x7 ha y2e ff4 fs1 fc1 sc0 ls2">></div><div class="t m0 x7 ha y2f ff4 fs1 fc1 sc0 ls2">></div><div class="t m0 x7 ha y30 ff4 fs1 fc1 sc0 ls2">:</div><div class="t m0 xb hb y31 ff5 fs1 fc1 sc0 ls4">a<span class="ff1 fs2 ls2 ws1e v1">11<span class="_8 blank"> </span></span><span class="ls2 ws3">x<span class="ff1 fs2 ls5 v1">1</span><span class="ff6 fs5 ls6 v0">+</span><span class="ls7 v0">a</span><span class="ff1 fs2 ws1e v1">12<span class="_8 blank"> </span></span><span class="ls8 v0">x<span class="ff1 fs2 ls9 v1">2</span><span class="ff6 fs5 lsa">+</span><span class="ff3 lsb ws1f">... <span class="ff6 fs5 ls6">+</span></span><span class="ls7">a<span class="ff1 fs2 lsc v1">1<span class="ff5 lsd">n</span></span><span class="ls2">x<span class="fs2 lse v1">n</span><span class="ff6 fs5 lsf">=</span>b<span class="ff1 fs2 v1">1</span></span></span></span></span></div><div class="t m0 xb hc y32 ff5 fs1 fc1 sc0 ls4">a<span class="ff1 fs2 ls2 ws1e v1">21<span class="_8 blank"> </span></span><span class="ls2 ws3">x<span class="ff1 fs2 ls10 v1">1</span><span class="ff6 fs5 ls6 v0">+</span><span class="ls7 v0">a</span><span class="ff1 fs2 ws1e v1">22<span class="_8 blank"> </span></span><span class="ls8 v0">x<span class="ff1 fs2 ls9 v1">2</span><span class="ff6 fs5 lsa">+</span><span class="ff3 lsb ws1f">... <span class="ff6 fs5 ls6">+</span></span><span class="ls7">a<span class="ff1 fs2 lsc v1">2<span class="ff5 lsd">n</span></span><span class="ls2">x<span class="fs2 lse v1">n</span><span class="ff6 fs5 ls11">=</span>b<span class="ff1 fs2 v1">2</span></span></span></span></span></div><div class="t m0 xc h4 y33 ff1 fs1 fc1 sc0 ls2">.</div><div class="t m0 xc h4 y34 ff1 fs1 fc1 sc0 ls2">.</div><div class="t m0 xc h4 y35 ff1 fs1 fc1 sc0 ls2">.</div><div class="t m0 xd hd y36 ff5 fs1 fc1 sc0 ls7">a<span class="fs2 ls12 v1">m<span class="ff1 ls13">1</span></span><span class="ls8">x<span class="ff1 fs2 ls9 v1">1</span><span class="ff6 fs5 ls14 v0">+</span><span class="ls15 v0">a<span class="fs2 ls16 v1">m<span class="ff1 ls17">2</span></span><span class="ls8">x<span class="ff1 fs2 ls18 v1">2</span><span class="ff6 fs5 ls14">+</span><span class="ff3 lsb ws20">... <span class="ff6 fs5 lsa">+</span></span><span class="ls4">a<span class="fs2 ls2 ws21 v1">m n<span class="_8 blank"> </span></span></span>x<span class="fs2 ls19 v1">n</span><span class="ff6 fs5 lsf">=</span><span class="ls2 ws3">b<span class="fs2 v1">m</span></span></span></span></span></div><div class="t m0 xe he y37 ff7 fs5 fc1 sc0 ls2">)</div><div class="t m0 xf ha y38 ff4 fs1 fc1 sc0 ls2">2</div><div class="t m0 xf ha y39 ff4 fs1 fc1 sc0 ls2">6</div><div class="t m0 xf ha y3a ff4 fs1 fc1 sc0 ls2">6</div><div class="t m0 xf ha y3b ff4 fs1 fc1 sc0 ls2">6</div><div class="t m0 xf ha y3c ff4 fs1 fc1 sc0 ls2">4</div><div class="t m0 x10 hf y3d ff5 fs1 fc1 sc0 ls4">a<span class="ff1 fs2 ls2 ws22 v1">11<span class="_9 blank"> </span></span><span class="ls1a">a<span class="ff1 fs2 ls2 ws22 v1">12<span class="_a blank"> </span></span><span class="ff3 ls2 ws23">... </span><span class="ls7">a<span class="ff1 fs2 lsc v1">1<span class="ff5 ls2">n</span></span></span></span></div><div class="t m0 x10 h10 y3e ff5 fs1 fc1 sc0 ls4">a<span class="ff1 fs2 ls2 ws22 v1">21<span class="_9 blank"> </span></span><span class="ls1a">a<span class="ff1 fs2 ls2 ws22 v1">22<span class="_b blank"> </span></span><span class="ls7">a<span class="ff1 fs2 lsc v1">2<span class="ff5 ls2">n</span></span></span></span></div><div class="t m0 x11 h4 y3f ff1 fs1 fc1 sc0 ls2">.</div><div class="t m0 x11 h4 y40 ff1 fs1 fc1 sc0 ls2">.</div><div class="t m0 x11 h4 y41 ff1 fs1 fc1 sc0 ls2">.</div><div class="t m0 x12 h10 y42 ff5 fs1 fc1 sc0 ls7">a<span class="fs2 ls12 v1">m<span class="ff1 ls1b">1</span></span>a<span class="fs2 ls12 v1">m<span class="ff1 ls1c">2</span></span><span class="ls1a">a<span class="fs2 ls2 ws21 v1">m n</span></span></div><div class="t m0 x13 ha y43 ff4 fs1 fc1 sc0 ls2">3</div><div class="t m0 x13 ha y44 ff4 fs1 fc1 sc0 ls2">7</div><div class="t m0 x13 ha y45 ff4 fs1 fc1 sc0 ls2">7</div><div class="t m0 x13 ha y46 ff4 fs1 fc1 sc0 ls2">7</div><div class="t m0 x13 ha y47 ff4 fs1 fc1 sc0 ls2">5</div><div class="t m0 xf ha y48 ff4 fs1 fc1 sc0 ls1d">|<span class="ls2 ws24 v0">{ z<span class="_c blank"> </span>}</span></div><div class="t m0 x14 h5 y49 ff1 fs2 fc1 sc0 ls2 ws25">m a t r iz<span class="_5 blank"> </span>de<span class="_5 blank"> </span>co<span class="_d blank"> </span>e\u2026<span class="_4 blank"> </span>c i e n t e s<span class="_5 blank"> </span><span class="ff6 fs6 ls1e v0">(</span><span class="ff5 ls1f">A</span><span class="ff6 fs6 v0">)</span></div><div class="t m0 x7 h4 y4a ff1 fs1 fc2 sc0 ls2 ws3">Tópicos:</div><div class="t m0 x15 h7 y4b ff5 fs4 fc0 sc0 ls20">i<span class="ff3 ls21">.<span class="ff1 fc1 ls2 ws9">Sistemas de Equações Lineares</span></span></div><div class="t m0 xa h7 y4c ff5 fs4 fc0 sc0 ls2 ws26">ii <span class="ff3 ls22">.</span><span class="ff1 fc1 ws1b">Álgeb<span class="_0 blank"></span>ra Matricial</span></div><div class="t m0 x16 h7 y4d ff5 fs4 fc0 sc0 ls23 ws27">iii <span class="ff3 ls24">.<span class="ff1 fc1 ls2 wsa">Determinantes</span></span></div><div class="t m0 x16 h7 y4e ff5 fs4 fc0 sc0 ls2 ws28">iv <span class="ff3 ls25">.</span><span class="ff1 fc1 wse">Indep endência<span class="_5 blank"> </span>Linea<span class="_0 blank"></span>r</span></div><div class="t m0 xa h7 y4f ff5 fs4 fc0 sc0 ls26">v<span class="ff3 ls24">.<span class="ff1 fc1 ls2 wse">Sub espaços<span class="_5 blank"> </span>Asso ciados<span class="_5 blank"> </span>a<span class="_5 blank"> </span>uma<span class="_5 blank"> </span>Matriz</span></span></div><div class="t m0 x5 h5 y50 ff1 fs2 fc1 sc0 ls2">6</div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/ab3ff7a0-b2be-4c23-b3d1-b036e3d036b6/bg3.png"><div class="c x0 y1 w2 h2"><div class="t m0 x6 h3 y18 ff1 fs0 fc0 sc0 ls2 ws29">P<span class="_7 blank"></span>a<span class="_0 blank"></span>rte<span class="_6 blank"> </span>II:<span class="_6 blank"> </span>Equ<span class="_0 blank"></span>açõ<span class="_0 blank"></span>es<span class="_6 blank"> </span>Dif<span class="_0 blank"></span>eren<span class="_0 blank"></span>cia<span class="_0 blank"></span>is<span class="_6 blank"> </span>e<span class="_3 blank"> </span>a<span class="_6 blank"> </span>Di<span class="_0 blank"></span>fere<span class="_0 blank"></span>nça<span class="_0 blank"></span>s</div><div class="t m0 x7 h4 y51 ff1 fs1 fc2 sc0 ls2 ws3">Motivação:</div><div class="t m0 x8 h11 y52 ff2 fs3 fc0 sc0 ls0">I<span class="ff1 fs4 fc1 ls2 ws9 v1">Equações Diferenciais (T<span class="_7 blank"></span>emp<span class="_4 blank"> </span>o Contínuo):</span></div><div class="t m0 x17 h12 y53 ff5 fs4 fc1 sc0 ls2 wsa">dy</div><div class="t m0 x17 h13 y54 ff5 fs4 fc1 sc0 ls2 ws2a">dt <span class="ff6 fs7 ls27 v2">+</span><span class="ws2b v2">a<span class="_0 blank"></span>y <span class="ff6 fs7 ls28">=</span>b</span></div><div class="t m0 x8 h11 y55 ff2 fs3 fc0 sc0 ls0">I<span class="ff1 fs4 fc1 ls2 wse v1">Equações<span class="_5 blank"> </span>a<span class="_5 blank"> </span>Diferença<span class="_5 blank"> </span>(T<span class="_7 blank"></span>empo<span class="_5 blank"> </span>Discreto):</span></div><div class="t m0 x18 h14 y56 ff5 fs4 fc1 sc0 ls2 wsa">y<span class="fs2 ls29 v3">t<span class="ff6 fs8 ls2a">+<span class="ff1 fs2 ls2b">1</span><span class="fs7 ls2c v4">+</span></span></span>a<span class="_0 blank"></span>y<span class="fs2 ls2d v1">t</span><span class="ff6 fs7 ls2e">=</span>c</div><div class="t m0 x7 h4 y57 ff1 fs1 fc2 sc0 ls2 ws3">Tópicos:</div><div class="t m0 x15 h7 y58 ff5 fs4 fc0 sc0 ls20">i<span class="ff3 ls21">.<span class="ff1 fc1 ls2 ws9">Equações Diferenciais</span></span></div><div class="t m0 xa h7 y59 ff5 fs4 fc0 sc0 ls2 ws26">ii <span class="ff3 ls22">.</span><span class="ff1 fc1 ws9">Equações a Diferenças</span></div><div class="t m0 x16 h7 y5a ff5 fs4 fc0 sc0 ls23 ws27">iii <span class="ff3 ls24">.<span class="ff1 fc1 ls2 ws2c">Sistemas de Equações Diferenciais e a Diferenças</span></span></div><div class="t m0 x5 h5 y20 ff1 fs2 fc1 sc0 ls2">7</div></div><div class="c x0 y7 w2 h2"><div class="t m0 x6 h3 y8 ff1 fs0 fc0 sc0 ls2 ws0">P<span class="_7 blank"></span>a<span class="_0 blank"></span>rte II<span class="_4 blank"> </span>I: Ot<span class="_0 blank"></span>im<span class="_0 blank"></span>izaç<span class="_0 blank"></span>ão Es<span class="_0 blank"></span>táti<span class="_0 blank"></span>ca e Est<span class="_0 blank"></span>átic<span class="_0 blank"></span>a Com<span class="_0 blank"></span>pa<span class="_7 blank"></span>rat<span class="_0 blank"></span>iva</div><div class="t m0 x7 h4 y5b ff1 fs1 fc2 sc0 ls2 ws1d">Motivação: <span class="fc1 ws2d">Problema de escolha ótima do consumido<span class="_0 blank"></span>r:</span></div><div class="t m0 x19 h4 y5c ff1 fs1 fc1 sc0 ls2 ws3">max</div><div class="t m0 x1a h15 y5d ff5 fs2 fc1 sc0 ls2f">x<span class="ff8 ls30">,</span><span class="ls31">y<span class="fs1 ls32 v5">u</span><span class="ff6 fs5 ls33 v5">(</span><span class="fs1 ls34 v5">x<span class="ff3 ls35">,<span class="ff5 ls36">y<span class="ff6 fs5 ls37 v0">)<span class="ls38 v0">=</span></span><span class="ls39">x</span></span></span></span><span class="ff9 ls3a v6">\u03b1</span><span class="fs1 ls3b v5">y</span><span class="ff1 ls3c v6">1<span class="ff7 fs6 ls3d">\ue000<span class="ff9 fs2 ls2">\u03b1</span></span></span></span></div><div class="t m0 x7 h4 y5e ff1 fs1 fc1 sc0 ls2 ws14">sujeito a</div><div class="t m0 x1b h16 y5f ff5 fs1 fc1 sc0 ls2 ws3">p<span class="fs2 ls3e v3">x</span><span class="ls3f">x<span class="ff6 fs5 lsa v0">+</span></span><span class="v0">p<span class="fs2 ls40 v3">y</span><span class="ls41">y<span class="ff7 fs5 lsf">\ue014</span></span>w</span></div><div class="t m0 x7 h4 y60 ff1 fs1 fc2 sc0 ls2 ws3">Tópicos:</div><div class="t m0 x15 h7 y61 ff5 fs4 fc0 sc0 ls20">i<span class="ff3 ls21">.<span class="ff1 fc1 ls2 ws8">Otimização Não-Condicionada</span></span></div><div class="t m0 xa h7 y62 ff5 fs4 fc0 sc0 ls2 ws26">ii <span class="ff3 ls22">.</span><span class="ff1 fc1 ws8">Otimização com Restrições de Igualdade (Lagrange)</span></div><div class="t m0 x16 h7 y63 ff5 fs4 fc0 sc0 ls23 ws27">iii <span class="ff3 ls24">.<span class="ff1 fc1 ls2 ws2e">Otimização com Restrições de Desigualdade (Kuhn-T<span class="_7 blank"></span>uck<span class="_0 blank"></span>er)</span></span></div><div class="t m0 x16 h7 y64 ff5 fs4 fc0 sc0 ls2 ws28">iv <span class="ff3 ls25">.</span><span class="ff1 fc1 ws2f">T<span class="_7 blank"></span>eo<span class="_0 blank"></span>rema do Envelop<span class="_4 blank"> </span>e (Signi\u2026cado do Multiplicador de Lagrange)</span></div><div class="t m0 xa h7 y65 ff5 fs4 fc0 sc0 ls26">v<span class="ff3 ls24">.<span class="ff1 fc1 ls2 ws30">Estática Compa<span class="_0 blank"></span>rativa</span></span></div><div class="t m0 x5 h5 y66 ff1 fs2 fc1 sc0 ls2">8</div></div><div class="c x0 y14 w2 h9"><div class="t m0 x6 h3 y15 ff1 fs0 fc0 sc0 ls2 ws13">Li<span class="_0 blank"></span>vro<span class="_0 blank"></span>s-T<span class="_e blank"></span>ex<span class="_0 blank"></span>tos</div><div class="t m0 x7 h4 y67 ff1 fs1 fc1 sc0 ls2 ws31">As aulas serão baseadas nos seguintes livros-textos:</div><div class="t m0 x8 h17 y68 ff2 fs3 fc0 sc0 ls0">I<span class="ff1 fs4 fc1 ls2 ws32 v1">Simon, C. e L. Blume.<span class="_6 blank"> </span>"Matemática para Economistas".<span class="_6 blank"> </span>P<span class="_0 blank"></span>orto Alegre:</span></div><div class="t m0 x9 h7 y69 ff1 fs4 fc1 sc0 ls2 ws33">Bo okman,<span class="_5 blank"> </span>2004.<span class="_6 blank"> </span>(510<span class="_5 blank"> </span>S594m)</div><div class="t m0 x8 h17 y6a ff2 fs3 fc0 sc0 ls0">I<span class="ff1 fs4 fc1 ls2 ws34 v1">Chiang, A. e K. W<span class="_0 blank"></span>ainwright.<span class="_6 blank"> </span>"Matemática para Economistas".<span class="_6 blank"> </span>São</span></div><div class="t m0 x9 h7 y6b ff1 fs4 fc1 sc0 ls2 ws35">P<span class="_0 blank"></span>aulo: Campus-Elsevier,<span class="_5 blank"> </span>2005. (330.0151<span class="_5 blank"> </span>C532mt)</div><div class="t m0 x7 h4 y6c ff1 fs1 fc1 sc0 ls2 ws36">O<span class="_2 blank"> </span>seguinte<span class="_2 blank"> </span>livro<span class="_2 blank"> </span>tamb ém<span class="_2 blank"> </span>é<span class="_2 blank"> </span>recomendado:</div><div class="t m0 x8 h18 y6d ff2 fs3 fc0 sc0 ls0">I<span class="ff1 fs4 fc1 ls2 ws37 v1">Sydsaeter, K e P<span class="_7 blank"></span>. Hammond.<span class="_6 blank"> </span>"Mathematics fo<span class="_0 blank"></span>r Economic Analysis".</span></div><div class="t m0 x9 h7 y6e ff1 fs4 fc1 sc0 ls2 ws34">Englew<span class="_0 blank"></span>o<span class="_4 blank"> </span>o<span class="_4 blank"> </span>d Cli¤s, NJ: Prentice Hall, 1995.<span class="_6 blank"> </span>(330.0182 S982m)</div><div class="t m0 x5 h5 y17 ff1 fs2 fc1 sc0 ls2">9</div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/ab3ff7a0-b2be-4c23-b3d1-b036e3d036b6/bg4.png"><div class="c x0 y1 w2 h2"><div class="t m0 x6 h3 y18 ff1 fs0 fc0 sc0 ls2 ws38">M<span class="_0 blank"></span>ate<span class="_0 blank"></span>rial<span class="_6 blank"> </span>e<span class="_6 blank"> </span>Apoi<span class="_0 blank"></span>o</div><div class="t m0 x7 h4 y6f ff1 fs1 fc1 sc0 ls2 ws1a">Notas<span class="_2 blank"> </span>de<span class="_2 blank"> </span>Aula<span class="_2 blank"> </span>(a<span class="_2 blank"> </span>serem<span class="_2 blank"> </span>p ostados<span class="_2 blank"> </span>no<span class="_2 blank"> </span>Mo o dle)</div><div class="t m0 x7 h4 y70 ff1 fs1 fc1 sc0 ls2 ws14">Listas de Exercício (<span class="ff7 fs5 ls42">\ue018</span><span class="ws2d">a cada duas semanas)</span></div><div class="t m0 x7 h4 y71 ff1 fs1 fc1 sc0 ls2 ws39">Monito<span class="_0 blank"></span>rias e Plantão de Dúvidas</div><div class="t m0 x7 h4 y72 ff1 fs1 fc1 sc0 ls2 ws18">A<span class="_0 blank"></span>tendimento (sextas-feiras ap<span class="_4 blank"> </span>ós a aula)</div><div class="t m0 x1c h5 y6 ff1 fs2 fc1 sc0 ls2 ws1e">10</div></div><div class="c x0 y7 w2 h2"><div class="t m0 x6 h3 y8 ff1 fs0 fc0 sc0 ls2 ws1c">Si<span class="_0 blank"></span>stem<span class="_0 blank"></span>a de A<span class="_0 blank"></span>va<span class="_0 blank"></span>liaç<span class="_0 blank"></span>ão</div><div class="t m0 x7 h4 y73 ff1 fs1 fc1 sc0 ls2 ws3a">A<span class="_2 blank"> </span>avaliação<span class="_2 blank"> </span>será<span class="_2 blank"> </span>comp osta<span class="_2 blank"> </span>de<span class="_2 blank"> </span><span class="fc2 ws3b">duas p<span class="_0 blank"></span>rovas <span class="fc1 ls43">e</span><span class="wsb">exercícios em sala de</span></span></div><div class="t m0 x7 h19 y74 ff1 fs1 fc2 sc0 ls2 ws3">aula<span class="fc1 wsb v0">.<span class="_3 blank"> </span>A nota \u2026nal será calculada de aco<span class="_0 blank"></span>rdo com os seguintes p<span class="_4 blank"> </span>esos:</span></div><div class="t m0 x1d h4 y75 ff1 fs1 fc1 sc0 ls2 ws2d">Prova 1<span class="_f blank"> </span>40<span class="ff3">%</span></div><div class="t m0 x1d h4 y76 ff1 fs1 fc1 sc0 ls2 wsb">Prova 2<span class="_f blank"> </span>50<span class="ff3">%</span></div><div class="t m0 x1e h4 y77 ff1 fs1 fc1 sc0 ls2 ws3c">Exercícios 10<span class="ff3">%</span></div><div class="t m0 x7 h4 y78 ff1 fs1 fc1 sc0 ls2 ws14">As p<span class="_0 blank"></span>rovas serão realizadas no horário das aulas nas seguintes <span class="fc2 ws3">datas</span>:</div><div class="t m0 x3 h4 y79 ff1 fs1 fc1 sc0 ls2 ws3d">P1:<span class="_10 blank"> </span>23<span class="ffa ls44">/</span><span class="ws14">09 (sexta-feira)</span></div><div class="t m0 x3 h4 y7a ff1 fs1 fc1 sc0 ls2 ws3d">P2:<span class="_10 blank"> </span>25<span class="ffa ls44">/</span><span class="ws14">11 (sexta-feira)</span></div><div class="t m0 x7 h4 y7b ff1 fs1 fc1 sc0 ls2 ws14">A realização de <span class="fc2 ws3e">p<span class="_0 blank"></span>rova substitutiva <span class="fc1 wsb">somente será autorizada com</span></span></div><div class="t m0 x7 h4 y7c ff1 fs1 fc1 sc0 ls2 ws7">ap<span class="_0 blank"></span>resentação de atestado médico.<span class="_3 blank"> </span>A substitutiva<span class="_11 blank"> </span>será realizada no</div><div class="t m0 x7 h1a y7d ff1 fs1 fc1 sc0 ls2 ws1a">\u2026nal<span class="_2 blank"> </span>do<span class="_2 blank"> </span>semestre<span class="_2 blank"> </span>e<span class="_2 blank"> </span>cob<span class="_0 blank"></span>rirá<span class="_2 blank"> </span>to da<span class="_2 blank"> </span><span class="ws2d v0">a matéria do curso.</span></div><div class="t m0 x1c h5 y25 ff1 fs2 fc1 sc0 ls2 ws1e">11</div></div><div class="c x0 y14 w2 h9"><div class="t m0 x6 h3 y15 ff1 fs0 fc0 sc0 ls2 ws1c">Si<span class="_0 blank"></span>stem<span class="_0 blank"></span>a de A<span class="_0 blank"></span>va<span class="_0 blank"></span>liaç<span class="_0 blank"></span>ão</div><div class="t m0 x7 h4 y7e ff1 fs1 fc1 sc0 ls2 wsb">P<span class="_0 blank"></span>ara a composição da nota de exercícios, será descartada a nota mais</div><div class="t m0 x7 h4 y7f ff1 fs1 fc1 sc0 ls2 ws3">baixa.</div><div class="t m0 x7 h4 y80 ff1 fs1 fc1 sc0 ls2 ws3f">As p<span class="_0 blank"></span>rovas serão baseadas no material discutido em aula e<span class="_2 blank"> </span>nas listas de</div><div class="t m0 x7 h4 y81 ff1 fs1 fc1 sc0 ls2 ws2d">exercícios.<span class="_3 blank"> </span>O aluno deve esp<span class="_4 blank"> </span>era<span class="_0 blank"></span>r uma alta correlação entre a sua</div><div class="t m0 x7 h4 y82 ff1 fs1 fc1 sc0 ls2 ws40">dedicação ao curso e a sua nota \u2026nal.</div><div class="t m0 x7 h4 y83 ff1 fs1 fc1 sc0 ls2 ws41">Os alunos que obtiverem média \u2026nal entre 3<span class="ff3 ls45">,</span><span class="ws14">0 e 5<span class="ff3 ls45">,</span>0 somente serão</span></div><div class="t m0 x7 h4 y84 ff1 fs1 fc1 sc0 ls2 ws7">auto<span class="_0 blank"></span>rizados a realizar a reaval se tiverem p<span class="_0 blank"></span>resença sup<span class="_4 blank"> </span>erior a 70<span class="ff3 ls46">%</span>,</div><div class="t m0 x7 h4 y85 ff1 fs1 fc1 sc0 ls2 ws19">confo<span class="_0 blank"></span>rme o Regimento da USP<span class="_7 blank"></span>.</div><div class="t m0 x7 h4 y86 ff1 fs1 fc1 sc0 ls2 ws19">A "cola" em p<span class="_0 blank"></span>rovas e exercícios não se<span class="_4 blank"> </span>rá tolerada.</div><div class="t m0 x1c h5 y17 ff1 fs2 fc1 sc0 ls2 ws1e">12</div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/ab3ff7a0-b2be-4c23-b3d1-b036e3d036b6/bg5.png"><div class="c x0 y1 w2 h2"><div class="t m0 x1f h1b y87 ff1 fs9 fc1 sc0 ls2 ws42">P<span class="_e blank"></span>a<span class="_7 blank"></span>r<span class="_0 blank"></span>te I<span class="_0 blank"></span>:<span class="_12 blank"> </span>Á<span class="_7 blank"></span>lg<span class="_7 blank"></span>e<span class="_0 blank"></span>b<span class="_7 blank"></span>r<span class="_0 blank"></span>a L<span class="_0 blank"></span>i<span class="_0 blank"></span>n<span class="_0 blank"></span>e<span class="_0 blank"></span>a<span class="_7 blank"></span>r</div><div class="t m0 x1c h5 y6 ff1 fs2 fc1 sc0 ls2 ws1e">13</div></div><div class="c x0 y7 w2 h2"><div class="t m0 x6 h3 y8 ff1 fs0 fc0 sc0 ls2 ws13">M<span class="_0 blank"></span>otiv<span class="_0 blank"></span>açã<span class="_0 blank"></span>o</div><div class="t m0 x7 h4 y88 ff1 fs1 fc1 sc0 ls2 ws43">Considere uma economia com <span class="ff5 ls47">n</span><span class="ws3a">mercados.<span class="_3 blank"> </span>Sup onha<span class="_2 blank"> </span>que<span class="_2 blank"> </span>as<span class="_2 blank"> </span><span class="fc2 ws44">curvas de</span></span></div><div class="t m0 x7 h4 y89 ff1 fs1 fc2 sc0 ls2 ws45">demanda <span class="fc1 ws46 v0">sejam<span class="_2 blank"> </span>dadas<span class="_2 blank"> </span>p o<span class="_0 blank"></span>r:</span></div><div class="t m0 x20 h1c y8a ff5 fs1 fc1 sc0 ls48">Q<span class="fs2 ls2 v7">D</span></div><div class="t m0 x1f h1d y8b ff1 fs2 fc1 sc0 ls49">1<span class="ff6 fs5 ls4a v8">=<span class="ff9 fs1 ls4b">\u03b1</span></span><span class="ls2 ws1e v9">10<span class="_5 blank"> </span></span><span class="ff6 fs5 ls4c v8">+<span class="ff9 fs1 ls4d">\u03b1</span></span><span class="ls2 ws22 v9">11<span class="_8 blank"> </span></span><span class="ff5 fs1 ls2 ws3 v8">P</span><span class="ls4e v9">1</span><span class="ff6 fs5 ls4f v8">+<span class="ff9 fs1 ls50">\u03b1</span></span><span class="ls2 ws22 v9">12<span class="_8 blank"> </span></span><span class="ff5 fs1 ls2 ws3 v8">P</span><span class="ls51 v9">2</span><span class="ff6 fs5 ls14 v8">+<span class="ff3 fs1 ls2 ws47">... </span><span class="ls4c">+<span class="ff9 fs1 ls52">\u03b1</span></span></span><span class="lsc v9">1<span class="ff5 ls53">n<span class="fs1 ls2 ws3 v4">P</span><span class="ls2">n</span></span></span></div><div class="t m0 x21 h4 y8c ff1 fs1 fc1 sc0 ls2">.</div><div class="t m0 x21 h4 y8d ff1 fs1 fc1 sc0 ls2">.</div><div class="t m0 x21 h4 y8e ff1 fs1 fc1 sc0 ls2">.</div><div class="t m0 x22 h1e y8f ff5 fs1 fc1 sc0 ls54">Q<span class="fs2 ls2 v7">D</span></div><div class="t m0 x23 h1f y90 ff5 fs2 fc1 sc0 ls55">n<span class="ff6 fs5 ls4a v8">=<span class="ff9 fs1 ls56">\u03b1</span></span><span class="ls57 v9">n<span class="ff1 ls58">0<span class="ff6 fs5 ls4f v4">+<span class="ff9 fs1 ls4d">\u03b1</span></span><span class="ff5 ls59">n</span><span class="ls5a">1</span></span></span><span class="fs1 ls2 ws3 v8">P</span><span class="ff1 ls5b v9">1</span><span class="ff6 fs5 ls4f v8">+<span class="ff9 fs1 ls4b">\u03b1</span></span><span class="ls59 v9">n<span class="ff1 ls13">2</span></span><span class="fs1 ls2 ws3 v8">P</span><span class="ff1 ls5c v9">2</span><span class="ff6 fs5 lsa v8">+<span class="ff3 fs1 ls2 ws48">... </span><span class="ls4c">+<span class="ff9 fs1 ls50">\u03b1</span></span></span><span class="ls2 ws49 v9">nn<span class="_8 blank"> </span></span><span class="fs1 ls2 ws3 v8">P</span><span class="ls53 v9">n</span><span class="ff3 fs1 ls2 v8">,</span></div><div class="t m0 x7 h20 y91 ff1 fs1 fc1 sc0 ls2 ws4a">e que as <span class="fc2 ws4b v0">curvas de oferta <span class="fc1 ws3a">sejam<span class="_2 blank"> </span>dadas<span class="_2 blank"> </span>p or:</span></span></div><div class="t m0 x22 h1e y92 ff5 fs1 fc1 sc0 ls5d">Q<span class="fs2 ls2 v7">S</span></div><div class="t m0 x23 h21 y93 ff1 fs2 fc1 sc0 ls5e">1<span class="ff6 fs5 ls4a v8">=<span class="ff9 fs1 ls5f">\u03b3</span></span><span class="ls2 ws22 v0">10<span class="_5 blank"> </span><span class="ff6 fs5 ls4c v8">+<span class="ff9 fs1 ls60">\u03b3</span></span>11<span class="_8 blank"> </span><span class="ff5 fs1 ws3 v8">P</span><span class="ls61 v9">1</span><span class="ff6 fs5 ls4f v8">+<span class="ff9 fs1 ls60">\u03b3</span></span>12<span class="_8 blank"> </span><span class="ff5 fs1 ws3 v8">P</span><span class="ls62 v9">2</span><span class="ff6 fs5 lsa v8">+</span><span class="ff3 fs1 ws47 v8">... <span class="ff6 fs5 ls4c">+<span class="ff9 fs1 ls63">\u03b3</span></span></span><span class="lsc">1<span class="ff5 ls64">n<span class="fs1 ls2 ws3 v8">P</span><span class="ls2 v9">n</span></span></span></span></div><div class="t m0 x21 h4 y94 ff1 fs1 fc1 sc0 ls2">.</div><div class="t m0 x21 h4 y95 ff1 fs1 fc1 sc0 ls2">.</div><div class="t m0 x21 h4 y96 ff1 fs1 fc1 sc0 ls2">.</div><div class="t m0 x22 h1e y97 ff5 fs1 fc1 sc0 ls54">Q<span class="fs2 ls2 v7">S</span></div><div class="t m0 x23 h22 y98 ff5 fs2 fc1 sc0 ls65">n<span class="ff6 fs5 ls4a v8">=<span class="ff9 fs1 ls66">\u03b3</span></span><span class="ls57 v0">n<span class="ff1 ls67">0<span class="ff6 fs5 ls4f v8">+<span class="ff9 fs1 ls5f">\u03b3</span></span></span><span class="ls68">n<span class="ff1 ls5a">1</span><span class="fs1 ls2 ws3 v8">P</span><span class="ff1 ls69 v9">1</span><span class="ff6 fs5 ls4c v8">+<span class="ff9 fs1 ls66">\u03b3</span></span></span>n<span class="ff1 ls13">2</span><span class="fs1 ls2 ws3 v8">P</span><span class="ff1 ls6a v9">2</span><span class="ff6 fs5 lsa v8">+<span class="ff3 fs1 ls2 ws48">... </span><span class="ls4c">+<span class="ff9 fs1 ls5f">\u03b3</span></span></span><span class="ls2 ws49">nn<span class="_8 blank"> </span><span class="fs1 ws3 v8">P</span><span class="v9">n</span></span></span></div><div class="t m0 x7 h4 y99 ff1 fs1 fc1 sc0 ls2 ws4c">Intuitivamente, os pa<span class="_0 blank"></span>râmetros<span class="_11 blank"> </span><span class="ff9 ls52">\u03b1</span><span class="ff5 fs2 ws4d v3">ij<span class="_12 blank"> </span></span><span class="ws4e">capturam p<span class="_0 blank"></span>ropriedades das <span class="fc2 ws3">funções</span></span></div><div class="t m0 x7 h4 y9a ff1 fs1 fc2 sc0 ls2 ws4f">utilidade <span class="fc1 ws16 v0">dos consumido<span class="_0 blank"></span>res e<span class="_11 blank"> </span><span class="ff9 ls63">\u03b3</span><span class="ff5 fs2 ws4d va">ij<span class="_12 blank"> </span></span><span class="ws50">capturam p<span class="_0 blank"></span>ropriedades das <span class="fc2 ws3">funções</span></span></span></div><div class="t m0 x7 h4 y9b ff1 fs1 fc2 sc0 ls2 ws1a">de<span class="_2 blank"> </span>p<span class="_0 blank"></span>ro dução/custo<span class="_2 blank"> </span><span class="fc1 ws16 v0">das \u2026rmas.</span></div><div class="t m0 x1c h5 y66 ff1 fs2 fc1 sc0 ls2 ws1e">14</div></div><div class="c x0 y14 w2 h9"><div class="t m0 x6 h3 y15 ff1 fs0 fc0 sc0 ls2 ws13">M<span class="_0 blank"></span>otiv<span class="_0 blank"></span>açã<span class="_0 blank"></span>o</div><div class="t m0 x7 h4 y9c ff1 fs1 fc1 sc0 ls2 ws51">Note que a economia encontra-se em <span class="fc2 ws52">equilíb<span class="_0 blank"></span>rio <span class="fc1 ws53">se, e somente se:</span></span></div><div class="t m0 x24 h1c y9d ff5 fs1 fc1 sc0 ls54">Q<span class="fs2 ls2 v7">D</span></div><div class="t m0 x25 h23 y9e ff5 fs2 fc1 sc0 ls6b">i<span class="ff6 fs5 lsf v8">=</span><span class="fs1 ls54 v8">Q</span><span class="ls2 vb">S</span></div><div class="t m0 x26 h24 y9f ff5 fs2 fc1 sc0 ls6c">i<span class="ff3 fs1 ls6d v8">,<span class="ff1 ls2 ws1">pa<span class="_0 blank"></span>ra<span class="_2 blank"> </span>to do<span class="_2 blank"> </span><span class="ff5 ls6e">i<span class="ff6 fs5 lsf">=</span></span><span class="ws3">1<span class="ff3 ws54">, ..., <span class="ff5">n</span></span></span></span></span></div><div class="t m0 x7 h4 ya0 ff1 fs1 fc1 sc0 ls2 ws55">Assim, os <span class="fc2 ws56">p<span class="_0 blank"></span>reços de<span class="_2 blank"> </span>equilíbrio <span class="fc1 ws14">são determinados pelo seguinte s<span class="_4 blank"> </span>istema</span></span></div><div class="t m0 x7 h4 ya1 ff1 fs1 fc1 sc0 ls2 ws53">de equações:</div><div class="t m0 x7 h25 ya2 ff9 fs1 fc1 sc0 ls4d">\u03b1<span class="ff1 fs2 ls2 ws1e v3">10<span class="_13 blank"> </span></span><span class="ff6 fs5 ls6f v0">+</span><span class="v0">\u03b1<span class="ff1 fs2 ls2 ws1e v3">11<span class="_8 blank"> </span></span><span class="ff5 ls2 ws3">P<span class="ff1 fs2 ls70 v3">1</span><span class="ff6 fs5 ls6f">+</span></span><span class="ls4b">\u03b1<span class="ff1 fs2 ls2 ws1e v3">12<span class="_8 blank"> </span></span><span class="ff5 ls2 ws3">P<span class="ff1 fs2 ls71 v3">2</span><span class="ff6 fs5 ls72">+</span><span class="ff3 ws57">... <span class="ff6 fs5 ls6f">+</span></span></span></span>\u03b1<span class="ff1 fs2 ls73 v3">1<span class="ff5 ls74">n</span></span><span class="ff5 ls2 ws3">P<span class="fs2 ls75 v3">n</span><span class="ff6 fs5 ls4a">=</span></span><span class="ls63">\u03b3<span class="ff1 fs2 ls2 ws22 va">10<span class="_13 blank"> </span></span><span class="ff6 fs5 ls6f">+</span><span class="ls66">\u03b3<span class="ff1 fs2 ls2 ws22 va">11<span class="_8 blank"> </span></span><span class="ff5 ls2 ws3">P<span class="ff1 fs2 ls76 v3">1</span><span class="ff6 fs5 ls6f">+</span></span><span class="ls60">\u03b3<span class="ff1 fs2 ls2 ws22 va">12<span class="_8 blank"> </span></span><span class="ff5 ls2 ws3">P<span class="ff1 fs2 ls77 v3">2</span><span class="ff6 fs5 ls72">+</span><span class="ff3 ws57">... <span class="ff6 fs5 ls6f">+</span></span></span><span class="ls5f">\u03b3<span class="ff1 fs2 lsc va">1<span class="ff5 ls64">n</span></span><span class="ff5 ls2 ws3">P<span class="fs2 v3">n</span></span></span></span></span></span></span></div><div class="t m0 x21 h4 ya3 ff1 fs1 fc1 sc0 ls2">.</div><div class="t m0 x21 h4 ya4 ff1 fs1 fc1 sc0 ls2">.</div><div class="t m0 x21 h4 ya5 ff1 fs1 fc1 sc0 ls2">.</div><div class="t m0 x7 h26 ya6 ff9 fs1 fc1 sc0 ls4d">\u03b1<span class="ff5 fs2 ls59 v3">n<span class="ff1 ls78">0<span class="ff6 fs5 ls6f v4">+</span></span></span><span class="v0">\u03b1<span class="ff5 fs2 ls79 v3">n<span class="ff1 ls13">1</span></span><span class="ff5 ls2 ws3">P<span class="ff1 fs2 ls7a v3">1</span><span class="ff6 fs5 ls6f">+</span></span><span class="ls4b">\u03b1<span class="ff5 fs2 ls68 v3">n<span class="ff1 ls5a">2</span></span><span class="ff5 ls2 ws3">P<span class="ff1 fs2 ls7b v3">2</span><span class="ff6 fs5 ls72">+</span><span class="ff3 ws57">... <span class="ff6 fs5 ls7c">+</span></span></span></span>\u03b1<span class="ff5 fs2 ls2 ws58 v3">nn<span class="_8 blank"> </span></span><span class="ff5 ls2 ws3">P<span class="fs2 ls7d v3">n</span><span class="ff6 fs5 ls4a">=</span></span><span class="ls66">\u03b3<span class="ff5 fs2 ls57 va">n<span class="ff1 ls7e">0</span></span><span class="ff6 fs5 ls7c">+</span><span class="ls5f">\u03b3<span class="ff5 fs2 ls68 va">n<span class="ff1 ls7f">1</span></span><span class="ff5 ls2 ws3">P<span class="ff1 fs2 ls80 v3">1</span><span class="ff6 fs5 ls7c">+</span></span></span>\u03b3<span class="ff5 fs2 ls57 va">n<span class="ff1 ls5a">2</span></span><span class="ff5 ls2 ws3">P<span class="ff1 fs2 ls81 v3">2</span><span class="ff6 fs5 ls82">+</span><span class="ff3 ws59">... <span class="ff6 fs5 ls7c">+</span></span></span>\u03b3<span class="ff5 fs2 ls2 ws49 va">n n<span class="_8 blank"> </span></span><span class="ff5 ls2 ws3">P<span class="fs2 v3">n</span></span></span></span></div><div class="t m0 x1c h5 ya7 ff1 fs2 fc1 sc0 ls2 ws1e">15</div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf6" class="pf w0 h0" data-page-no="6"><div class="pc pc6 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/ab3ff7a0-b2be-4c23-b3d1-b036e3d036b6/bg6.png"><div class="c x0 y1 w2 h2"><div class="t m0 x6 h3 y18 ff1 fs0 fc0 sc0 ls2 ws13">M<span class="_0 blank"></span>otiv<span class="_0 blank"></span>açã<span class="_0 blank"></span>o</div><div class="t m0 x7 h4 ya8 ff1 fs1 fc1 sc0 ls2 ws2">Note que, re-a<span class="_0 blank"></span>rranjando, p<span class="_4 blank"> </span>o<span class="_4 blank"> </span>demos expressa<span class="_0 blank"></span>r o sistema acima como:</div><div class="t m0 x7 h27 ya9 ff6 fs5 fc1 sc0 ls83">(<span class="ff9 fs1 ls4d v0">\u03b1<span class="ff1 fs2 ls2 ws5a v3">11<span class="_5 blank"> </span></span><span class="ff7 fs5 ls4f">\ue000</span><span class="ls5f">\u03b3<span class="ff1 fs2 ls2 ws1e va">11<span class="_8 blank"> </span></span></span></span><span class="ls84">)<span class="ff5 fs1 ls2 ws3 v0">P<span class="ff1 fs2 ls85 v3">1</span></span><span class="ls86 v0">+<span class="ls87 v0">(</span><span class="ff9 fs1 ls4d">\u03b1<span class="ff1 fs2 ls2 ws1e v3">1 2<span class="_14 blank"> </span></span></span><span class="ff7 ls4f">\ue000<span class="ff9 fs1 ls5f">\u03b3<span class="ff1 fs2 ls2 ws22 va">12<span class="_8 blank"> </span></span></span></span></span><span class="ls88">)<span class="ff5 fs1 ls2 ws3 v0">P<span class="ff1 fs2 ls89 v3">2</span></span><span class="ls8a v0">+<span class="ff3 fs1 ls2 ws5b">... </span><span class="ls8b">+<span class="ls8c v0">(</span><span class="ff9 fs1 ls50">\u03b1<span class="ff1 fs2 lsc v3">1<span class="ff5 ls8d">n</span></span></span><span class="ff7 ls4c">\ue000<span class="ff9 fs1 ls63">\u03b3<span class="ff1 fs2 ls73 va">1<span class="ff5 ls8e">n</span></span></span></span></span></span></span>)<span class="ff5 fs1 ls2 ws3 v0">P<span class="fs2 ls8f v3">n</span></span><span class="ls90 v0">=<span class="ls91 v0">(</span><span class="ff9 fs1 ls5f">\u03b3<span class="ff1 fs2 ls2 ws1e va">1 0<span class="_14 blank"> </span></span></span><span class="ff7 ls4c">\ue000<span class="ff9 fs1 ls4d">\u03b1<span class="ff1 fs2 ls2 ws1e v3">1 0<span class="_8 blank"> </span></span></span></span></span><span class="ls2">)</span></span></div><div class="t m0 x21 h4 yaa ff1 fs1 fc1 sc0 ls2">.</div><div class="t m0 x21 h4 yab ff1 fs1 fc1 sc0 ls2">.</div><div class="t m0 x21 h4 yac ff1 fs1 fc1 sc0 ls2">.</div><div class="t m0 x7 h28 yad ff6 fs5 fc1 sc0 ls83">(<span class="ff9 fs1 ls4d v0">\u03b1<span class="ff5 fs2 ls68 v3">n<span class="ff1 ls92">1</span></span><span class="ff7 fs5 ls4c">\ue000</span><span class="ls5f">\u03b3<span class="ff5 fs2 ls68 va">n<span class="ff1 ls93">1</span></span></span></span><span class="ls94">)<span class="ff5 fs1 ls2 ws3 v0">P<span class="ff1 fs2 ls95 v3">1</span></span><span class="ls96 v0">+<span class="ls97 v0">(</span><span class="ff9 fs1 ls4b">\u03b1<span class="ff5 fs2 ls68 v3">n<span class="ff1 ls98">2</span></span></span><span class="ff7 ls4c">\ue000<span class="ff9 fs1 ls60">\u03b3<span class="ff5 fs2 ls59 va">n<span class="ff1 ls99">2</span></span></span></span></span><span class="ls84">)<span class="ff5 fs1 ls2 ws3 v0">P<span class="ff1 fs2 ls9a v3">2</span></span><span class="ls9b v0">+<span class="ff3 fs1 ls2 ws5c">... </span><span class="ls9c">+<span class="ls9d v0">(</span><span class="ff9 fs1 ls9e">\u03b1<span class="ff5 fs2 ls2 ws49 v3">nn<span class="_5 blank"> </span></span></span><span class="ff7 ls4f">\ue000<span class="ff9 fs1 ls5f">\u03b3<span class="ff5 fs2 ls2 ws49 va">n n<span class="_8 blank"> </span></span></span></span></span></span>)<span class="ff5 fs1 ls2 ws3 v0">P<span class="fs2 ls8f v3">n</span></span><span class="ls90 v0">=<span class="ls91 v0">(</span><span class="ff9 fs1 ls5f">\u03b3<span class="ff5 fs2 ls68 va">n<span class="ff1 ls9f">0</span></span></span><span class="ff7 ls4c">\ue000<span class="ff9 fs1 ls4b">\u03b1<span class="ff5 fs2 ls68 v3">n<span class="ff1 lsa0">0</span></span></span></span></span><span class="ls2">)</span></span></span></div><div class="t m0 x7 h4 yae ff1 fs1 fc1 sc0 ls2 ws14">Simpli\u2026cando a notação, p<span class="_4 blank"> </span>o<span class="_4 blank"> </span>demos re-escrever o sistema como:</div><div class="t m0 x27 h29 yaf ff5 fs1 fc1 sc0 ls4">a<span class="ff1 fs2 ls2 ws1e v3">11<span class="_8 blank"> </span></span><span class="ls2 ws3">P<span class="ff1 fs2 lsa1 v3">1</span><span class="ff6 fs5 ls14">+</span></span>a<span class="ff1 fs2 ls2 ws22 v3">12<span class="_8 blank"> </span></span><span class="ls2 ws3">P<span class="ff1 fs2 lsa2 v3">2</span><span class="ff6 fs5 ls14">+</span><span class="ff3 ws47">... <span class="ff6 fs5 ls6">+</span></span><span class="ls1a">a<span class="ff1 fs2 lsc v3">1<span class="ff5 lsa3">n</span></span></span>P<span class="fs2 lsa4 v3">n</span><span class="ff6 fs5 lsf">=</span>b<span class="ff1 fs2 v3">1</span></span></div><div class="t m0 x21 h4 yb0 ff1 fs1 fc1 sc0 ls2">.</div><div class="t m0 x21 h4 yb1 ff1 fs1 fc1 sc0 ls2">.</div><div class="t m0 x21 h4 yb2 ff1 fs1 fc1 sc0 ls2">.</div><div class="t m0 x27 h2a yb3 ff5 fs1 fc1 sc0 ls7">a<span class="fs2 ls79 v3">n<span class="ff1 ls13">1</span></span><span class="ls2 ws3">P<span class="ff1 fs2 lsa5 v3">1</span><span class="ff6 fs5 lsa v0">+</span></span><span class="v0">a<span class="fs2 ls79 v3">n<span class="ff1 ls13">2</span></span><span class="ls2 ws3">P<span class="ff1 fs2 lsa6 v3">2</span><span class="ff6 fs5 lsa">+</span><span class="ff3 ws48">... <span class="ff6 fs5 lsa">+</span></span><span class="ls4">a</span><span class="fs2 ws5d v3">nn<span class="_8 blank"> </span></span>P<span class="fs2 lsa7 v3">n</span><span class="ff6 fs5 lsf">=</span>b<span class="fs2 v3">n</span></span></span></div><div class="t m0 x7 h4 yb4 ff1 fs1 fc1 sc0 ls2 ws5e">Uma questão fundamental em teo<span class="_0 blank"></span>ria econômica é sab<span class="_4 blank"> </span>er se existe um</div><div class="t m0 x7 h4 yb5 ff1 fs1 fc2 sc0 ls2 ws40">conjunto de p<span class="_0 blank"></span>reços<span class="_11 blank"> </span><span class="ff6 fs5 fc1 lsa8">(</span><span class="ff5 lsa9">P</span><span class="fs2 lsaa v3">1</span><span class="ff3 fc1 lsab">,</span><span class="ff5 lsac">P</span><span class="fs2 lsad v3">2</span><span class="ff3 fc1 ws5f">, ..., </span><span class="ff5 lsae">P<span class="fs2 lsaf v3">n</span><span class="ff6 fs5 fc1 lsb0">)</span></span><span class="fc1 ws1a">que<span class="_2 blank"> </span>equilib<span class="_0 blank"></span>ra<span class="_2 blank"> </span>to dos<span class="_2 blank"> </span>os<span class="_2 blank"> </span>merca dos</span></div><div class="t m0 x7 h4 yb6 ff1 fs1 fc1 sc0 ls2 ws60">simultaneamente. <span class="fs2 ws1e vc">1 6</span></div></div><div class="c x0 y7 w2 h2"><div class="t m0 x6 h3 y8 ff1 fs0 fc0 sc0 ls2 ws13">M<span class="_0 blank"></span>otiv<span class="_0 blank"></span>açã<span class="_0 blank"></span>o</div><div class="t m0 x7 h4 yb7 ff1 fs1 fc1 sc0 ls2 ws61">O economista francês <span class="fc2 ws62">Leon Walras </span><span class="ws19">foi o p<span class="_0 blank"></span>rimeiro a estuda<span class="_0 blank"></span>r</span></div><div class="t m0 x7 h4 yb8 ff1 fs1 fc1 sc0 ls2 ws63">fo<span class="_0 blank"></span>rmalmente a questão da <span class="fc2 ws19 v0">existência do equilíbrio geral<span class="fc1">.</span></span></div><div class="t m0 x7 h4 yb9 ff1 fs1 fc1 sc0 ls2 ws3a">W<span class="_0 blank"></span>alras<span class="_2 blank"> </span>cometeu<span class="_2 blank"> </span>um<span class="_2 blank"> </span>erro<span class="_2 blank"> </span>imp ortante<span class="_5 blank"> </span>em<span class="_2 blank"> </span>sua<span class="_2 blank"> </span>anális e:<span class="_3 blank"> </span>ele<span class="_2 blank"> </span>assumiu<span class="_2 blank"> </span>que</div><div class="t m0 x7 h4 yba ff1 fs1 fc1 sc0 ls2 ws64">um sistema com <span class="ff5 fc2 ls47 v0">n<span class="ff1 ls2 ws65">equações <span class="fc1 ls43">e</span></span>n<span class="ff1 ls2 ws66">incógnitas <span class="fc1 ws46">sempre<span class="_5 blank"> </span>p ossui<span class="_2 blank"> </span>solução!</span></span></span></div><div class="t m0 x7 h4 ybb ff1 fs1 fc1 sc0 ls2 ws40">Seguindo o trabalho de W<span class="_0 blank"></span>alras, <span class="fc2 ws67">Kenneth Arrow</span><span class="lsb1">,</span><span class="fc2 ws68">Géra<span class="_0 blank"></span>rd Debreu <span class="fc1">e</span></span></div><div class="t m0 x7 h4 ybc ff1 fs1 fc2 sc0 ls2 ws69">Lionel McKenzie <span class="fc1 ws17">demonstra<span class="_0 blank"></span>ram a existência do equilíbrio geral nos</span></div><div class="t m0 x7 h4 ybd ff1 fs1 fc1 sc0 ls2 ws31">anos 50.</div><div class="t m0 x1c h5 y25 ff1 fs2 fc1 sc0 ls2 ws1e">17</div></div><div class="c x0 y14 w2 h9"><div class="t m0 x6 h3 y15 ff1 fs0 fc0 sc0 ls2 ws13">M<span class="_0 blank"></span>otiv<span class="_0 blank"></span>açã<span class="_0 blank"></span>o</div><div class="t m0 x7 h4 ybe ff1 fs1 fc1 sc0 ls2 ws31">Arro<span class="_0 blank"></span>w e Debreu receberam o prêmio nobel p<span class="_4 blank"> </span>elas suas contribuições à</div><div class="t m0 x7 h4 ybf ff1 fs1 fc1 sc0 ls2 ws14">teo<span class="_0 blank"></span>ria do equilíbrio geral:</div><div class="t m0 x1c h5 y17 ff1 fs2 fc1 sc0 ls2 ws1e">18</div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf7" class="pf w0 h0" data-page-no="7"><div class="pc pc7 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 yc0 w1 h2b" alt="" src="https://files.passeidireto.com/ab3ff7a0-b2be-4c23-b3d1-b036e3d036b6/bg7.png"><div class="c x0 y1 w2 h2"><div class="t m0 x6 h3 y18 ff1 fs0 fc0 sc0 ls2 ws13">M<span class="_0 blank"></span>otiv<span class="_0 blank"></span>açã<span class="_0 blank"></span>o</div><div class="t m0 x7 h4 yc1 ff1 fs1 fc1 sc0 ls2 ws6a">Arro<span class="_0 blank"></span>w e Debreu receberam o prêmio nobel p<span class="_4 blank"> </span>elas suas contribuições à</div><div class="t m0 x7 h4 yc2 ff1 fs1 fc1 sc0 ls2 ws14">teo<span class="_0 blank"></span>ria do equilíbrio geral:</div><div class="t m0 x1c h5 y6 ff1 fs2 fc1 sc0 ls2 ws1e">19</div></div><div class="c x0 y7 w2 h2"><div class="t m0 x6 h3 y8 ff1 fs0 fc0 sc0 ls2 ws13">Qu<span class="_0 blank"></span>est<span class="_0 blank"></span>ões</div><div class="t m0 x7 h4 yc3 ff1 fs1 fc1 sc0 ls2 ws14">Dado o sistema:</div><div class="t m0 x27 h2c yc4 ff5 fs1 fc1 sc0 ls4">a<span class="ff1 fs2 ls2 ws1e v3">11<span class="_8 blank"> </span></span><span class="ls2 ws3">P<span class="ff1 fs2 lsa1 v3">1</span><span class="ff6 fs5 ls14 v0">+</span></span><span class="v0">a<span class="ff1 fs2 ls2 ws22 v3">12<span class="_8 blank"> </span></span><span class="ls2 ws3">P<span class="ff1 fs2 lsa2 v3">2</span><span class="ff6 fs5 ls14">+</span><span class="ff3 ws47">... <span class="ff6 fs5 ls6">+</span></span><span class="ls1a">a<span class="ff1 fs2 lsc v3">1<span class="ff5 lsa3">n</span></span></span>P<span class="fs2 lsa4 v3">n</span><span class="ff6 fs5 ls11">=</span>b<span class="ff1 fs2 v3">1</span></span></span></div><div class="t m0 x21 h4 yc5 ff1 fs1 fc1 sc0 ls2">.</div><div class="t m0 x21 h4 yc6 ff1 fs1 fc1 sc0 ls2">.</div><div class="t m0 x21 h4 yc7 ff1 fs1 fc1 sc0 ls2">.</div><div class="t m0 x27 h2a yc8 ff5 fs1 fc1 sc0 ls7">a<span class="fs2 ls79 v3">n<span class="ff1 ls13">1</span></span><span class="ls2 ws3">P<span class="ff1 fs2 lsb2 v3">1</span><span class="ff6 fs5 lsa v0">+</span></span><span class="v0">a<span class="fs2 ls79 v3">n<span class="ff1 ls13">2</span></span><span class="ls2 ws3">P<span class="ff1 fs2 lsa6 v3">2</span><span class="ff6 fs5 lsa">+</span><span class="ff3 ws48">... <span class="ff6 fs5 lsa">+</span></span><span class="ls4">a</span><span class="fs2 ws5d v3">nn<span class="_8 blank"> </span></span>P<span class="fs2 lsa7 v3">n</span><span class="ff6 fs5 lsf">=</span>b<span class="fs2 v3">n</span></span></span></div><div class="t m0 x7 h4 yc9 ff1 fs1 fc1 sc0 ls2 ws18">Gosta<span class="_0 blank"></span>ríamos de resp<span class="_4 blank"> </span>onder as seguintes p<span class="_4 blank"> </span>erguntas:</div><div class="t m0 x15 h7 yca ff5 fs4 fc0 sc0 ls20">i<span class="ff3 ls21">.<span class="ff1 fc1 ls2 ws8">O equilíb<span class="_0 blank"></span>rio geral existe?</span></span></div><div class="t m0 xa h7 ycb ff5 fs4 fc0 sc0 ls2 ws26">ii <span class="ff3 ls22">.</span><span class="ff1 fc1 ws8">O equilíb<span class="_0 blank"></span>rio geral é único?</span></div><div class="t m0 x16 h7 ycc ff5 fs4 fc0 sc0 ls23 ws27">iii <span class="ff3 ls24">.<span class="ff1 fc1 ls2 ws6b">Existe algum méto<span class="_4 blank"> </span>do sistemático pa<span class="_0 blank"></span>ra encontrarmos os p<span class="_0 blank"></span>reços de</span></span></div><div class="t m0 x9 h7 ycd ff1 fs4 fc1 sc0 ls2 ws8">equilíb<span class="_0 blank"></span>rio como função dos parâmetros?</div><div class="t m0 x1c h5 yce ff1 fs2 fc1 sc0 ls2 ws1e">20</div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div>
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