<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/ea2b9e07-b8d7-4ddc-8f88-43a3a339476c/bg1.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls37 ws0">Gabarito da Lista de Exerc<span class="_0 blank"></span>´<span class="_1 blank"></span>\u0131cios I<span class="_2 blank"> </span>I - Micro<span class="_2 blank"> </span>economia</div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls37 ws0">Univ<span class="_3 blank"></span>ersidade de Bras<span class="_0 blank"></span>´<span class="_1 blank"></span>\u0131lia - Departamen<span class="_3 blank"></span>to de Economia</div><div class="t m0 x3 h3 y3 ff1 fs0 fc0 sc0 ls37 ws1">Exerc<span class="_0 blank"></span>´<span class="_1 blank"></span>\u0131cio 1:<span class="_4 blank"> </span><span class="ff2 ws2">Deriv<span class="_3 blank"></span>e as agrega¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>oes de Engel e Cournot para o caso de <span class="ff3 ls0">n</span><span class="ws3">b ens.<span class="_6 blank"> </span>Reescrev<span class="_7 blank"></span>a<span class="_8 blank"> </span>essas</span></span></div><div class="t m0 x3 h3 y4 ff2 fs0 fc0 sc0 ls37 ws4">agrega¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>oes em termos de elasticidades.<span class="_9 blank"> </span>In<span class="_3 blank"></span>terprete (p<span class="_2 blank"> </span>or exemplo,<span class="_a blank"> </span>´<span class="_b blank"></span>e p<span class="_2 blank"> </span>oss<span class="_0 blank"></span>´<span class="_c blank"></span>\u0131v<span class="_3 blank"></span>el que to<span class="_2 blank"> </span>dos os b<span class="_2 blank"> </span>ens que</div><div class="t m0 x3 h3 y5 ff2 fs0 fc0 sc0 ls37 ws5">um indiv<span class="_0 blank"></span>´<span class="_c blank"></span>\u0131duo consuma sejam b<span class="_2 blank"> </span>ens inferiores?<span class="_d blank"> </span>P<span class="_3 blank"></span>or qu<span class="_3 blank"></span>\u02c6<span class="_b blank"></span>e?<span class="_d blank"> </span>Se um indiv<span class="_e blank"></span>´<span class="_c blank"></span>\u0131duo consome <span class="ff3 ls1">n</span><span class="ws3">bens,<span class="_f blank"> </span>no</span></div><div class="t m0 x3 h3 y6 ff2 fs0 fc0 sc0 ls37 ws6">m´<span class="_5 blank"></span>aximo quan<span class="_3 blank"></span>tos b<span class="_2 blank"> </span>ens po<span class="_2 blank"> </span>dem ser inferiores?<span class="_f blank"> </span>Justi\ufb01que sua resposta).</div><div class="t m0 x3 h3 y7 ff2 fs0 fc0 sc0 ls37 ws6">S: Deriv<span class="_7 blank"></span>ando a rela¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>ao de \u201c<span class="ff4 ws7">adding-up </span>\u201d,</div><div class="t m0 x4 h3 y8 ff3 fs0 fc0 sc0 ls2">p<span class="ff5 fs1 ls3 v1">1</span><span class="ls4">x<span class="ff5 fs1 ls5 v1">1</span><span class="ff2 ls37 ws8">(<span class="ff1 ws9">p</span></span><span class="ls37 wsa">, m<span class="ff2 wsb">) + </span></span></span>p<span class="ff5 fs1 ls3 v1">2</span><span class="ls4">x<span class="ff5 fs1 ls3 v1">2</span><span class="ff2 ls6">(<span class="ff1 ls37 ws9">p</span></span><span class="ls37 wsa">, m<span class="ff2 wsb">) + <span class="ff6 wsc">· · ·<span class="_10 blank"> </span></span><span class="ls7">+</span></span></span></span>p<span class="ff7 fs1 ls8 v1">n</span><span class="ls4">x<span class="ff7 fs1 ls9 v1">n</span><span class="ff2 ls37 ws8">(<span class="ff1 ws9">p</span></span><span class="ls37 wsa">, m<span class="ff2 wsd">) = </span>m,</span></span></div><div class="t m0 x3 h3 y9 ff2 fs0 fc0 sc0 ls37 wse">com rela¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>ao `<span class="_5 blank"></span>a renda, obtemos a <span class="ff4 wsf">agr<span class="_7 blank"></span>e<span class="_7 blank"></span>ga¸<span class="_b blank"></span>c\u02dc<span class="_5 blank"></span>ao de Engel<span class="_11 blank"> </span><span class="ff2">:</span></span></div><div class="t m0 x5 h3 ya ff3 fs0 fc0 sc0 ls2">p<span class="ff5 fs1 ls37 v1">1</span></div><div class="t m0 x6 h3 yb ff3 fs0 fc0 sc0 ls37 ws10">\u2202 x<span class="ff5 fs1 ls5 v1">1</span><span class="ff2 ws8">(<span class="ff1 ws9">p</span></span><span class="wsa">, m<span class="ff2">)</span></span></div><div class="t m0 x7 h4 yc ff3 fs0 fc0 sc0 ls37 ws10">\u2202 m<span class="_12 blank"> </span><span class="ff2 ls7 v2">+</span><span class="ls2 v2">p</span><span class="ff5 fs1 v3">2</span></div><div class="t m0 x8 h3 yb ff3 fs0 fc0 sc0 ls37 ws10">\u2202 x<span class="ff5 fs1 ls3 v1">2</span><span class="ff2 ls6">(</span><span class="ff1 ws9">p</span><span class="wsa">, m<span class="ff2">)</span></span></div><div class="t m0 x9 h4 yc ff3 fs0 fc0 sc0 ls37 ws10">\u2202 m<span class="_12 blank"> </span><span class="ff2 ls7 v2">+</span><span class="ff6 wsc v2">· · ·<span class="_10 blank"> </span><span class="ff2 lsa">+<span class="ff3 ls2">p</span></span></span><span class="ff7 fs1 v3">n</span></div><div class="t m0 xa h3 yb ff3 fs0 fc0 sc0 ls37 ws10">\u2202 x<span class="ff7 fs1 ls9 v1">n</span><span class="ff2 ws8">(<span class="ff1 ws9">p</span></span><span class="wsa">, m<span class="ff2">)</span></span></div><div class="t m0 xb h4 yc ff3 fs0 fc0 sc0 ls37 ws10">\u2202 m<span class="_13 blank"> </span><span class="ff2 ws11 v2">= 1</span></div><div class="t m0 x3 h3 yd ff2 fs0 fc0 sc0 ls37 ws11">Multiplicando o lado esquerdo da equa¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>ao acima p<span class="_2 blank"> </span>or <span class="ff3 ls4">x<span class="ff5 fs1 ls3 v1">1</span><span class="ls37 ws12">m/x<span class="ff5 fs1 ls3 v1">1</span><span class="lsb">m</span></span></span>e rearranjando os termos obtemos:</div><div class="t m0 x0 h3 ye ff3 fs0 fc0 sc0 ls2">p<span class="ff5 fs1 ls3 v1">1</span><span class="ls4">x<span class="ff5 fs1 ls37 v1">1</span></span></div><div class="t m0 x1 h5 yf ff3 fs0 fc0 sc0 lsc">m<span class="ff8 lsd v4">\ue012</span><span class="ls37 v5">m</span></div><div class="t m0 xc h3 yf ff3 fs0 fc0 sc0 ls4">x<span class="ff5 fs1 ls37 v1">1</span></div><div class="t m0 xd h3 ye ff3 fs0 fc0 sc0 ls37 ws10">\u2202 x<span class="ff5 fs1 v1">1</span></div><div class="t m0 xd h5 yf ff3 fs0 fc0 sc0 ls37 ws10">\u2202 m<span class="_14 blank"> </span><span class="ff8 lse v4">\ue013</span><span class="ff2 lsf v2">+</span><span class="ls2 v5">p</span><span class="ff5 fs1 ls3 v6">2</span><span class="ls4 v5">x</span><span class="ff5 fs1 v6">2</span></div><div class="t m0 xe h5 yf ff3 fs0 fc0 sc0 ls10">m<span class="ff8 ls11 v4">\ue012</span><span class="ls37 v5">m</span></div><div class="t m0 x9 h3 yf ff3 fs0 fc0 sc0 ls4">x<span class="ff5 fs1 ls37 v1">2</span></div><div class="t m0 xf h3 ye ff3 fs0 fc0 sc0 ls37 ws10">\u2202 x<span class="ff5 fs1 v1">2</span></div><div class="t m0 xf h5 yf ff3 fs0 fc0 sc0 ls37 ws10">\u2202 m<span class="_14 blank"> </span><span class="ff8 lse v4">\ue013</span><span class="ff2 ls7 v2">+</span><span class="ff6 wsc v2">· · ·<span class="_10 blank"> </span><span class="ff2 lsf">+</span></span><span class="ls2 v5">p</span><span class="ff7 fs1 ls8 v6">n</span><span class="ls4 v5">x</span><span class="ff7 fs1 v6">n</span></div><div class="t m0 x10 h5 yf ff3 fs0 fc0 sc0 ls12">m<span class="ff8 ls13 v4">\ue012</span><span class="ls37 v5">m</span></div><div class="t m0 x11 h3 yf ff3 fs0 fc0 sc0 ls4">x<span class="ff7 fs1 ls37 v1">n</span></div><div class="t m0 x12 h3 ye ff3 fs0 fc0 sc0 ls37 ws10">\u2202 x<span class="ff7 fs1 v1">n</span></div><div class="t m0 x13 h5 yf ff3 fs0 fc0 sc0 ls37 ws10">\u2202 m<span class="_15 blank"> </span><span class="ff8 ls14 v4">\ue013</span><span class="ff2 ws11 v2">= 1</span></div><div class="t m0 x3 h3 y10 ff2 fs0 fc0 sc0 ls37 ws6">Logo, a agrega¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>ao de Engel escrita em termos de elasticidades<span class="_a blank"> </span>´<span class="_b blank"></span>e:</div><div class="t m0 x14 h3 y11 ff3 fs0 fc0 sc0 ls15">s<span class="ff5 fs1 ls5 v1">1</span><span class="ls37 ws12">\u03b7<span class="ff5 fs1 ls16 v1">1</span><span class="ff2 lsa">+</span></span>s<span class="ff5 fs1 ls3 v1">2</span><span class="ls37 ws12">\u03b7<span class="ff5 fs1 ls16 v1">2</span><span class="ff2 lsa">+</span><span class="ff6 wsc">· · ·<span class="_10 blank"> </span><span class="ff2 ls7">+</span></span></span>s<span class="ff7 fs1 ls8 v1">n</span><span class="ls37 ws12">\u03b7<span class="ff7 fs1 ls17 v1">n</span><span class="ff2 ws11">= 1</span>,</span></div><div class="t m0 x3 h3 y12 ff2 fs0 fc0 sc0 ls37 ws13">onde <span class="ff3 ls15">s<span class="ff7 fs1 ls18 v1">i</span></span><span class="ls19">=<span class="ff3 ls2">p<span class="ff7 fs1 ls1a v1">i</span><span class="ls4">x<span class="ff7 fs1 ls1b v1">i</span><span class="ls37 ws14">/m </span></span></span></span><span class="ws6">´<span class="_b blank"></span>e a fra¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>ao da renda gasta com o b<span class="_2 blank"> </span>em <span class="ff3 ls1c">i</span><span class="ls1d">e</span><span class="ff3 ws12">\u03b7<span class="ff7 fs1 ls1e v1">i</span></span>´<span class="_5 blank"></span>e a elasticidade-renda do b<span class="_2 blank"> </span>em <span class="ff3 ws12">i</span>.</span></div><div class="t m0 x3 h3 y13 ff2 fs0 fc0 sc0 ls37 ws3">P<span class="_3 blank"></span>o demos<span class="_16 blank"> </span>concluir<span class="_16 blank"> </span>que:</div><div class="t m0 x15 h3 y14 ff2 fs0 fc0 sc0 ls37 ws15">1.<span class="_17 blank"> </span>T<span class="_e blank"></span>o<span class="_2 blank"> </span>das as elasticidades-renda p<span class="_2 blank"> </span>o<span class="_2 blank"> </span>dem ser iguais a um.<span class="_9 blank"> </span>Nesse caso, um aumen<span class="_3 blank"></span>to da renda lev<span class="_7 blank"></span>a</div><div class="t m0 x16 h3 y15 ff2 fs0 fc0 sc0 ls37 ws16">a um aumen<span class="_3 blank"></span>to na mesma prop<span class="_2 blank"> </span>or¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>ao do consumo de todos os b<span class="_2 blank"> </span>ens (se a renda aumentou em</div><div class="t m0 x16 h3 y16 ff2 fs0 fc0 sc0 ls37 ws6">10%, o consumo de cada b<span class="_2 blank"> </span>em aumen<span class="_3 blank"></span>ta em 10%).</div><div class="t m0 x15 h3 y17 ff2 fs0 fc0 sc0 ls37 ws17">2.<span class="_17 blank"> </span>Se <span class="ff3 ws12">\u03b7<span class="ff7 fs1 ls1f v1">i</span><span class="ls20">></span></span><span class="ws18">1 para algum b<span class="_2 blank"> </span>em <span class="ff3 ls21">i</span><span class="ws19">, ent\u02dc<span class="_5 blank"></span>ao dev<span class="_7 blank"></span>e existir algum b<span class="_2 blank"> </span>em <span class="ff3 ls22">j</span><span class="ws3">diferente<span class="_8 blank"> </span>do<span class="_9 blank"> </span>b em<span class="_9 blank"> </span><span class="ff3 ls23">i</span><span class="ws18">tal que</span></span></span></span></div><div class="t m0 x16 h3 y18 ff3 fs0 fc0 sc0 ls24">\u03b7<span class="ff7 fs1 ls25 v1">j</span><span class="ls26"><<span class="ff2 ls37 ws1a">1:<span class="_18 blank"> </span>se a fra¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>ao da renda consumida do b<span class="_2 blank"> </span>em <span class="ff3 ls27">i</span>aumen<span class="_7 blank"></span>tou mais prop<span class="_2 blank"> </span>orcionalmente `<span class="_19 blank"></span>a</span></span></div><div class="t m0 x16 h3 y19 ff2 fs0 fc0 sc0 ls37 ws1b">renda,<span class="_f blank"> </span>o consumo de algum outro b<span class="_2 blank"> </span>em <span class="ff3 ls28">j</span><span class="ws1c">ter´<span class="_19 blank"></span>a que aumentar menos proporcionalmente `<span class="_19 blank"></span>a</span></div><div class="t m0 x16 h3 y1a ff2 fs0 fc0 sc0 ls37">renda.</div><div class="t m0 x15 h3 y1b ff2 fs0 fc0 sc0 ls37 ws1d">3. No<span class="_4 blank"> </span>m´<span class="_19 blank"></span>aximo<span class="_4 blank"> </span><span class="ff3 ls29">n<span class="ff6 ls2a">\u2212</span></span><span class="ws1e">1 bens p<span class="_2 blank"> </span>o<span class="_2 blank"> </span>dem ser inferiores (se to<span class="_2 blank"> </span>dos os b<span class="_2 blank"> </span>ens s\u02dc<span class="_19 blank"></span>ao inferiores,<span class="_6 blank"> </span>en<span class="_7 blank"></span>t\u02dc<span class="_5 blank"></span>ao a</span></div><div class="t m0 x16 h3 y1c ff2 fs0 fc0 sc0 ls37 ws1f">elasticidade-renda <span class="ff3 ws12">\u03b7<span class="ff7 fs1 ls2b v1">i</span></span><span class="ws20">ser´<span class="_19 blank"></span>a negativ<span class="_7 blank"></span>a para to<span class="_2 blank"> </span>do b<span class="_2 blank"> </span>em <span class="ff3 ls2c">i</span><span class="ws21">= 1<span class="ff3 ls2d">,</span><span class="ws8">2<span class="ff3 wsa">, . . . , n</span><span class="ws22">.<span class="_1a blank"> </span>Como <span class="ff3 ls15">s<span class="ff7 fs1 ls2e v1">i</span><span class="ff6 ls2f">\u2265</span></span></span></span></span>0 (<span class="ff3 ls15">s<span class="ff7 fs1 ls30 v1">i</span></span>´<span class="_b blank"></span>e a</span></div><div class="t m0 x16 h3 y1d ff2 fs0 fc0 sc0 ls37 ws23">fra¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao da renda gasta com o b<span class="_2 blank"> </span>em <span class="ff3 ls21">i</span>), ent\u02dc<span class="_19 blank"></span>ao se to<span class="_2 blank"> </span>das as elasticidades-renda forem negativ<span class="_7 blank"></span>as,</div><div class="t m0 x16 h3 y1e ff2 fs0 fc0 sc0 ls37 wse">a igualdade acima n\u02dc<span class="_19 blank"></span>ao ser´<span class="_5 blank"></span>a v<span class="_3 blank"></span>eri\ufb01cada).</div><div class="t m0 x3 h3 y1f ff2 fs0 fc0 sc0 ls37 ws24">Se deriv<span class="_7 blank"></span>armos a rela¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao de \u201c<span class="ff4 ws7">adding-up </span>\u201d com<span class="_8 blank"> </span>respeito ao b<span class="_2 blank"> </span>em <span class="ff3 ls21">i</span><span class="ws25">, obtemos a <span class="ff4 ws26">agr<span class="_7 blank"></span>e<span class="_7 blank"></span>ga¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao de Cournot</span></span></div><div class="t m0 x3 h3 y20 ff2 fs0 fc0 sc0 ls37 ws6">(com rela¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao ao b<span class="_2 blank"> </span>em <span class="ff3 ls21">i</span>):</div><div class="t m0 x17 h3 y21 ff3 fs0 fc0 sc0 ls4">x<span class="ff7 fs1 ls1a v1">i</span><span class="ff2 ls37 ws8">(<span class="ff1 ws9">p</span></span><span class="ls37 wsa">, m<span class="ff2 wsb">) +</span></span></div><div class="t m0 x18 h6 y22 ff7 fs1 fc0 sc0 ls37">n</div><div class="t m0 x19 h7 y23 ff8 fs0 fc0 sc0 ls37">X</div><div class="t m0 x1a h8 y24 ff7 fs1 fc0 sc0 ls31">j<span class="ff5 ls37">=1</span></div><div class="t m0 x1b h3 y21 ff3 fs0 fc0 sc0 ls2">p<span class="ff7 fs1 ls37 v1">j</span></div><div class="t m0 x1c h3 y25 ff3 fs0 fc0 sc0 ls37 ws10">\u2202 x<span class="ff7 fs1 ls32 v1">j</span><span class="ff2 ws8">(<span class="ff1 ws9">p</span></span><span class="wsa">, m<span class="ff2">)</span></span></div><div class="t m0 x1d h3 y26 ff3 fs0 fc0 sc0 ls37 ws10">\u2202 p<span class="ff7 fs1 v1">i</span></div><div class="t m0 xa h3 y21 ff2 fs0 fc0 sc0 ls37 ws11">= 0</div><div class="t m0 x3 h3 y27 ff2 fs0 fc0 sc0 ls37 ws27">Multiplicando a express\u02dc<span class="_19 blank"></span>ao acima p<span class="_2 blank"> </span>or <span class="ff3 ls2">p<span class="ff7 fs1 ls1a v1">i</span><span class="ls37 ws12">/m</span></span>, obtemos a agrega¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>ao de Cournot em termos de elas-</div><div class="t m0 x3 h3 y28 ff2 fs0 fc0 sc0 ls37">ticidades:</div><div class="t m0 x5 h3 y29 ff3 fs0 fc0 sc0 ls4">x<span class="ff7 fs1 ls1b v1">i</span><span class="ls2">p<span class="ff7 fs1 ls37 v1">i</span></span></div><div class="t m0 x1e h4 y2a ff3 fs0 fc0 sc0 ls33">m<span class="ff2 ls37 v2">+</span></div><div class="t m0 x1f h6 y2b ff7 fs1 fc0 sc0 ls37">n</div><div class="t m0 x20 h7 y2c ff8 fs0 fc0 sc0 ls37">X</div><div class="t m0 x21 h8 y2d ff7 fs1 fc0 sc0 ls31">j<span class="ff5 ls37">=1</span></div><div class="t m0 x17 h3 y29 ff3 fs0 fc0 sc0 ls2">p<span class="ff7 fs1 ls32 v1">j</span><span class="ls4">x<span class="ff7 fs1 ls37 v1">j</span></span></div><div class="t m0 x22 h3 y2a ff3 fs0 fc0 sc0 ls37">m</div><div class="t m0 x23 h3 y29 ff3 fs0 fc0 sc0 ls2">p<span class="ff7 fs1 ls37 v1">i</span></div><div class="t m0 x23 h3 y2a ff3 fs0 fc0 sc0 ls4">x<span class="ff7 fs1 ls37 v1">j</span></div><div class="t m0 x24 h3 y29 ff3 fs0 fc0 sc0 ls37 ws10">\u2202 x<span class="ff7 fs1 v1">j</span></div><div class="t m0 x24 h3 y2a ff3 fs0 fc0 sc0 ls37 ws10">\u2202 p<span class="ff7 fs1 v1">i</span></div><div class="t m0 x25 h3 y2e ff2 fs0 fc0 sc0 ls37 ws11">= 0<span class="_1b blank"> </span><span class="ff6 ls34">\u21d2</span><span class="ws28">0 = <span class="ff3 ls15">s<span class="ff7 fs1 ls35 v1">i</span></span>+</span></div><div class="t m0 x26 h6 y2b ff7 fs1 fc0 sc0 ls37">n</div><div class="t m0 x11 h7 y2c ff8 fs0 fc0 sc0 ls37">X</div><div class="t m0 x11 h8 y2d ff7 fs1 fc0 sc0 ls31">j<span class="ff5 ls37">=1</span></div><div class="t m0 x27 h9 y2e ff3 fs0 fc0 sc0 ls15">s<span class="ff7 fs1 ls32 v1">j</span><span class="ls36">\u03b5<span class="ff7 fs1 ls37 v7">M</span></span></div><div class="t m0 x28 h6 y2f ff7 fs1 fc0 sc0 ls37 ws29">j i</div><div class="t m0 x29 h3 y30 ff2 fs0 fc0 sc0 ls37">1</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 x2a y31 w2 ha" alt="" src="https://files.passeidireto.com/ea2b9e07-b8d7-4ddc-8f88-43a3a339476c/bg2.png"><div class="t m0 x3 h3 y1 ff2 fs0 fc0 sc0 ls37 wse">Rearranjando os termos da<span class="_1c blank"> </span>´<span class="_19 blank"></span>ultima equ¸<span class="_b blank"></span>c\u02dc<span class="_5 blank"></span>ao acima, obtemos:</div><div class="t m0 x2b h9 y32 ff3 fs0 fc0 sc0 ls15">s<span class="ff7 fs1 ls1b v1">i</span><span class="ff2 ls37 wsb">(1 + </span><span class="ls38">\u03b5<span class="ff7 fs1 ls37 v7">M</span></span></div><div class="t m0 x2c hb y33 ff7 fs1 fc0 sc0 ls37 ws2b">ii <span class="ff2 fs0 wsd v8">) = <span class="ff6">\u2212</span></span></div><div class="t m0 x1d h6 y34 ff7 fs1 fc0 sc0 ls37">n</div><div class="t m0 x2d h7 y35 ff8 fs0 fc0 sc0 ls37">X</div><div class="t m0 x2e h8 y36 ff7 fs1 fc0 sc0 ls31">j<span class="ff5 ls37 ws2c">=1</span><span class="ls37 ws2d">,<span class="_16 blank"> </span>j <span class="ff9 ws2e">6<span class="ff5 ls39">=</span></span>i</span></div><div class="t m0 x2f h9 y32 ff3 fs0 fc0 sc0 ls15">s<span class="ff7 fs1 ls32 v1">j</span><span class="ls38">\u03b5<span class="ff7 fs1 ls37 v7">M</span></span></div><div class="t m0 xa hb y33 ff7 fs1 fc0 sc0 ls37 ws29">j i<span class="_1d blank"> </span><span class="ff2 fs0 v8">(1)</span></div><div class="t m0 x3 hc y37 ff2 fs0 fc0 sc0 ls37 ws2f">Se<span class="_9 blank"> </span>o<span class="_9 blank"> </span>b em<span class="_9 blank"> </span><span class="ff3 ls3a">i</span><span class="ws30">´<span class="_b blank"></span>e el´<span class="_5 blank"></span>astico (inel´<span class="_19 blank"></span>astico),<span class="_f blank"> </span>ent\u02dc<span class="_19 blank"></span>ao <span class="ff3 ls38">\u03b5</span><span class="ff7 fs1 v9">M</span></span></div><div class="t m0 x30 hb y38 ff7 fs1 fc0 sc0 ls37 ws31">ii <span class="ff3 fs0 ls3b v8"><<span class="ff6 ls37 ws32">\u2212<span class="ff2 ws33">1,<span class="_f blank"> </span>e o lado esquerdo de (1)<span class="_1e blank"> </span>´<span class="_b blank"></span>e negativ<span class="_3 blank"></span>o (p<span class="_2 blank"> </span>osi-</span></span></span></div><div class="t m0 x3 h3 y39 ff2 fs0 fc0 sc0 ls37 ws34">tiv<span class="_3 blank"></span>o).<span class="_17 blank"> </span>O lado direito de (1) dev<span class="_3 blank"></span>e ser negativo (positivo) tam<span class="_7 blank"></span>b´<span class="_5 blank"></span>em, ou seja, a soma p<span class="_2 blank"> </span>onderada das</div><div class="t m0 x3 h3 y3a ff2 fs0 fc0 sc0 ls37 ws35">elasticidades-pre¸<span class="_1 blank"></span>co cruzadas dos outros b<span class="_2 blank"> </span>ens com rela¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao ao b<span class="_2 blank"> </span>em <span class="ff3 ls3c">i</span>deve ser na m<span class="_7 blank"></span>´<span class="_b blank"></span>edia p<span class="_2 blank"> </span>ositiv<span class="_7 blank"></span>a</div><div class="t m0 x3 h3 y3b ff2 fs0 fc0 sc0 ls37 ws36">(negativ<span class="_7 blank"></span>a).<span class="_17 blank"> </span>Portan<span class="_7 blank"></span>to,<span class="_8 blank"> </span>se a demanda do b<span class="_2 blank"> </span>em <span class="ff3 ls3d">i</span>´<span class="_5 blank"></span>e el´<span class="_5 blank"></span>astica (inel´<span class="_5 blank"></span>astica), ent\u02dc<span class="_19 blank"></span>ao os outros b<span class="_2 blank"> </span>ens dev<span class="_7 blank"></span>em</div><div class="t m0 x3 h3 y3c ff2 fs0 fc0 sc0 ls37 ws37">ser, na m<span class="_3 blank"></span>´<span class="_b blank"></span>edia p<span class="_2 blank"> </span>onderada p<span class="_2 blank"> </span>ela fra¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao gasta em cada b<span class="_2 blank"> </span>em, substitutos (complementares) do bem <span class="ff3 ws12">i</span>,</div><div class="t m0 x3 h3 y3d ff4 fs0 fc0 sc0 ls37 wsf">indep<span class="_7 blank"></span>endente de c<span class="_7 blank"></span>omo esses b<span class="_7 blank"></span>ens afetem a fun¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao de utilidade<span class="ff2">.</span></div><div class="t m0 x3 h3 y3e ff2 fs0 fc0 sc0 ls37 ws38">Outra implica¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao que p<span class="_2 blank"> </span>o<span class="_2 blank"> </span>de ser tirada da equa¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>ao (1)<span class="_1f blank"> </span>´<span class="_5 blank"></span>e a rea¸<span class="_20 blank"></span>c\u02dc<span class="_19 blank"></span>ao dos gastos nos outros b<span class="_2 blank"> </span>ens devido</div><div class="t m0 x3 h3 y3f ff2 fs0 fc0 sc0 ls37 ws39">a uma m<span class="_3 blank"></span>udan¸<span class="_1 blank"></span>ca no pre¸<span class="_1 blank"></span>co do b<span class="_2 blank"> </span>em <span class="ff3 ws12">i</span>:<span class="_1e blank"> </span>essa rea¸<span class="_20 blank"></span>c\u02dc<span class="_19 blank"></span>ao dep<span class="_2 blank"> </span>ende da elasticidade-pre¸<span class="_1 blank"></span>co de <span class="ff3 ls21">i</span>.<span class="_9 blank"> </span>Se a demanda</div><div class="t m0 x3 h3 y40 ff2 fs0 fc0 sc0 ls37 ws2f">do<span class="_16 blank"> </span>b em<span class="_16 blank"> </span><span class="ff3 ls3e">i</span><span class="ws3a">´<span class="_b blank"></span>e el´<span class="_5 blank"></span>astica, ent\u02dc<span class="_19 blank"></span>ao quando o pre¸<span class="_1 blank"></span>co do b<span class="_2 blank"> </span>em <span class="ff3 ls3f">i</span>dimin<span class="_3 blank"></span>ui, o gasto com os outros b<span class="_2 blank"> </span>ens dimin<span class="_3 blank"></span>ui</span></div><div class="t m0 x3 h3 y41 ff2 fs0 fc0 sc0 ls37 ws8">tam<span class="_3 blank"></span>b<span class="_3 blank"></span>´<span class="_b blank"></span>em.</div><div class="t m0 x3 h3 y42 ff1 fs0 fc0 sc0 ls37 ws0">Exerc<span class="_0 blank"></span>´<span class="_1 blank"></span>\u0131cio 2:<span class="_9 blank"> </span><span class="ff2 ws6">A utilidade de Maria ´<span class="_5 blank"></span>e dada p<span class="_2 blank"> </span>or <span class="ff3 ws12">u</span><span class="ws8">(<span class="ff3 ls40">x<span class="ff5 fs1 ls3 v1">1</span><span class="ls37 wsa">, x<span class="ff5 fs1 ls3 v1">2</span></span></span><span class="ws11">) = ln(<span class="ff3 ls4">x<span class="ff5 fs1 ls5 v1">1</span></span><span class="wsb">) + <span class="ff3 ls4">x<span class="ff5 fs1 ls3 v1">2</span></span>.</span></span></span></span></div><div class="t m0 x31 h3 y43 ff2 fs0 fc0 sc0 ls37 ws11">a)<span class="_17 blank"> </span>Encon<span class="_3 blank"></span>tre as demandas Marshallianas de Maria.<span class="_1e blank"> </span>Derive as elasticidades-pre¸<span class="_b blank"></span>co,<span class="_a blank"> </span>pre¸<span class="_1 blank"></span>co-cruzada</div><div class="t m0 x16 h3 y44 ff2 fs0 fc0 sc0 ls37 ws6">e renda para os dois b<span class="_2 blank"> </span>ens.</div><div class="t m0 x16 h3 y45 ff2 fs0 fc0 sc0 ls37 ws6">S: O problema do consumidor<span class="_a blank"> </span>´<span class="_b blank"></span>e:</div><div class="t m0 x32 h3 y46 ff2 fs0 fc0 sc0 ls37">max</div><div class="t m0 x23 h6 y47 ff7 fs1 fc0 sc0 ls41">x<span class="ffa fs2 ls37 va">1</span></div><div class="t m0 x33 h3 y46 ff2 fs0 fc0 sc0 ls37 ws3b">ln <span class="ff3 ls4">x<span class="ff5 fs1 ls16 v1">1</span></span><span class="ls7">+</span><span class="ff3 ws12">m/p<span class="ff5 fs1 ls16 v1">2</span><span class="ff6 ls42">\u2212</span></span><span class="ws8">(<span class="ff3 ls2">p<span class="ff5 fs1 ls5 v1">1</span><span class="ls37 ws12">/p<span class="ff5 fs1 ls3 v1">2</span></span></span>)<span class="ff3 ls40">x</span><span class="ff5 fs1 v1">1</span></span></div><div class="t m0 x16 h3 y48 ff2 fs0 fc0 sc0 ls37 ws3c">A<span class="_16 blank"> </span>CPO ´<span class="_5 blank"></span>e:<span class="_21 blank"> </span><span class="vb">1</span></div><div class="t m0 x2a hd y49 ff3 fs0 fc0 sc0 ls4">x<span class="ff9 fs1 ls37 v9">\u2217</span></div><div class="t m0 x34 h8 y4a ff5 fs1 fc0 sc0 ls37">1</div><div class="t m0 x35 he y4b ff2 fs0 fc0 sc0 ls43">=<span class="ff3 ls2 v2">p</span><span class="ff5 fs1 ls37 v3">1</span></div><div class="t m0 x36 h3 y49 ff3 fs0 fc0 sc0 ls2">p<span class="ff5 fs1 ls37 v1">2</span></div><div class="t m0 xf h9 y4b ff6 fs0 fc0 sc0 ls44">\u21d2<span class="ff3 ls4">x<span class="ff7 fs1 ls37 v7">M</span></span></div><div class="t m0 x2d hf y4c ff5 fs1 fc0 sc0 ls45">1<span class="ff2 fs0 ls37 ws8 v8">(<span class="ff3 ls2">p</span></span><span class="ls5 vc">1</span><span class="ff3 fs0 ls37 wsa v8">, p</span><span class="ls3 vc">2</span><span class="ff3 fs0 ls37 wsa v8">, m<span class="ff2 ws11">) =<span class="_8 blank"> </span><span class="ff3 ls2 v2">p</span></span></span><span class="ls37 vd">2</span></div><div class="t m0 x37 h3 y49 ff3 fs0 fc0 sc0 ls2">p<span class="ff5 fs1 ls37 v1">1</span></div><div class="t m0 x16 h3 y4d ff2 fs0 fc0 sc0 ls37 ws3d">A demanda do outro b<span class="_2 blank"> </span>em<span class="_15 blank"> </span>´<span class="_5 blank"></span>e encontrada substituindo a demanda do bem 1 na reta or¸<span class="_1 blank"></span>cament´<span class="_19 blank"></span>aria:</div><div class="t m0 x2 h9 y4e ff3 fs0 fc0 sc0 ls4">x<span class="ff5 fs1 ls46 v1">2</span><span class="ff2 ls47">=</span><span class="ls37 ws12">m/p<span class="ff5 fs1 ls16 v1">2</span><span class="ff6 ls42">\u2212<span class="ff2 ls6">(</span></span><span class="ls2">p<span class="ff5 fs1 ls3 v1">1</span></span>/p<span class="ff5 fs1 ls5 v1">2</span><span class="ff2 ws8">)</span></span>x<span class="ff9 fs1 ls37 v7">\u2217</span></div><div class="t m0 x38 h10 y4f ff5 fs1 fc0 sc0 ls46">1<span class="ff2 fs0 ls47 v8">=<span class="ff3 ls37 ws12">m/p</span></span><span class="ls16 vc">2</span><span class="ff6 fs0 ls42 v8">\u2212<span class="ff2 ls48">1<span class="ff6 ls44">\u21d2<span class="ff3 ls4">x</span></span></span></span><span class="ff7 ls37 ve">M</span></div><div class="t m0 x39 h11 y4f ff5 fs1 fc0 sc0 ls45">2<span class="ff2 fs0 ls37 ws8 v8">(<span class="ff3 ls2">p</span></span><span class="ls5 vc">1</span><span class="ff3 fs0 ls37 wsa v8">, p</span><span class="ls3 vc">2</span><span class="ff3 fs0 ls37 wsa v8">, m<span class="ff2 wsd">) = <span class="ff3 ws12">m/p</span></span></span><span class="ls16 vc">2</span><span class="ff6 fs0 ls42 v8">\u2212<span class="ff2 ls37">1</span></span></div><div class="t m0 x16 h3 y50 ff2 fs0 fc0 sc0 ls37 ws3e">Mais rigorosamen<span class="_3 blank"></span>te, note que se <span class="ff3 ws3f">m < p<span class="ff5 fs1 ls3 v1">2</span></span>, o consumidor n\u02dc<span class="_19 blank"></span>ao consegue comprar a quantidade</div><div class="t m0 x16 h12 y51 ff3 fs0 fc0 sc0 ls2">p<span class="ff5 fs1 ls5 v1">2</span><span class="ls37 ws12">/p<span class="ff5 fs1 ls49 v1">1</span><span class="ff2 ws39">do b<span class="_2 blank"> </span>em 1 (p<span class="_2 blank"> </span>ois </span></span>p<span class="ff5 fs1 ls5 v1">1</span><span class="ls4">x<span class="ff9 fs1 ls37 v9">\u2217</span></span></div><div class="t m0 x3a hb y52 ff5 fs1 fc0 sc0 ls46">1<span class="ff2 fs0 ls19 v8">=<span class="ff3 ls4a">p</span></span><span class="vc">2</span><span class="ff3 fs0 ls37 ws40 v8">> m<span class="ff2 ws39">).<span class="_9 blank"> </span>Logo, as demandas dos b<span class="_2 blank"> </span>ens 1 e 2 s\u02dc<span class="_19 blank"></span>ao completamente</span></span></div><div class="t m0 x16 h3 y53 ff2 fs0 fc0 sc0 ls37 ws3">de\ufb01nidas<span class="_16 blank"> </span>p or:</div><div class="t m0 x20 h9 y54 ff3 fs0 fc0 sc0 ls4">x<span class="ff7 fs1 ls37 v7">M</span></div><div class="t m0 x1f h13 y55 ff5 fs1 fc0 sc0 ls45">1<span class="ff2 fs0 ls37 ws8 v8">(<span class="ff3 ls2">p</span></span><span class="ls3 vc">1</span><span class="ff3 fs0 ls37 wsa v8">, p</span><span class="ls3 vc">2</span><span class="ff3 fs0 ls37 wsa v8">, m<span class="ff2 ws41">) = <span class="ff8 ls4b vf">\ue01a</span></span></span><span class="ff7 ls4c vf">p</span><span class="ffa fs2 ls37 v10">2</span></div><div class="t m0 x3b h14 y56 ff7 fs1 fc0 sc0 ls4c">p<span class="ffa fs2 ls4d va">1</span><span class="ff2 fs0 ls37 ws42 v9">se <span class="ff3 ls2">p</span></span><span class="ff5 ls46 v11">2</span><span class="ff6 fs0 ls4e v9">\u2264<span class="ff3 ls37">m</span></span></div><div class="t m0 x3b h6 y57 ff7 fs1 fc0 sc0 ls37">m</div><div class="t m0 x3b h14 y58 ff7 fs1 fc0 sc0 ls4c">p<span class="ffa fs2 ls4d va">1</span><span class="ff2 fs0 ls37 ws42 v9">se <span class="ff3 ls2">p</span></span><span class="ff5 ls46 v11">2</span><span class="ff3 fs0 ls37 ws40 v9">> m</span></div><div class="t m0 x20 h9 y59 ff3 fs0 fc0 sc0 ls4">x<span class="ff7 fs1 ls37 v7">M</span></div><div class="t m0 x1f h15 y5a ff5 fs1 fc0 sc0 ls45">2<span class="ff2 fs0 ls37 ws8 v8">(<span class="ff3 ls2">p</span></span><span class="ls5 vc">1</span><span class="ff3 fs0 ls37 wsa v8">, p</span><span class="ls3 vc">2</span><span class="ff3 fs0 ls37 wsa v8">, m<span class="ff2 ws41">) = <span class="ff8 ls4f vf">\ue01a</span><span class="ff7 fs1 v12">m</span></span></span></div><div class="t m0 x3b h14 y5b ff7 fs1 fc0 sc0 ls4c">p<span class="ffa fs2 ls50 va">2</span><span class="ff6 fs0 ls42 v9">\u2212<span class="ff2 ls37 ws43">1 se <span class="ff3 ls4a">p</span></span></span><span class="ff5 ls46 v11">2</span><span class="ff6 fs0 ls4e v9">\u2264<span class="ff3 ls37">m</span></span></div><div class="t m0 x2e h3 y5c ff2 fs0 fc0 sc0 ls37 ws44">0<span class="_22 blank"> </span>se <span class="ff3 ls4a">p<span class="ff5 fs1 ls46 v1">2</span><span class="ls37 ws40">> m</span></span></div><div class="t m0 x31 h3 y5d ff2 fs0 fc0 sc0 ls37 ws6">b)<span class="_17 blank"> </span>Classi\ufb01que os b<span class="_2 blank"> </span>ens em termos de cada uma dessas elasticidades, como visto em sala.</div><div class="t m0 x16 h3 y5e ff2 fs0 fc0 sc0 ls37 ws45">S: V<span class="_e blank"></span>amos calcular as elasticidades dos dois b<span class="_2 blank"> </span>ens para o caso em que a renda ´<span class="_5 blank"></span>e grande o</div><div class="t m0 x16 h3 y5f ff2 fs0 fc0 sc0 ls37 ws46">su\ufb01cien<span class="_3 blank"></span>te, de mo<span class="_2 blank"> </span>do de que as demandas sejam p<span class="_2 blank"> </span>ositiv<span class="_7 blank"></span>as.<span class="_17 blank"> </span>Nesse caso,<span class="_8 blank"> </span>para o b<span class="_2 blank"> </span>em <span class="ff3 ls40">x<span class="ff5 fs1 ls51 v1">1</span></span>temos</div><div class="t m0 x16 h3 y60 ff2 fs0 fc0 sc0 ls37">que:</div><div class="t m0 x35 h3 y61 ff3 fs0 fc0 sc0 ls38">\u03b5<span class="ff5 fs1 ls46 v1">1</span><span class="ff2 ls19">=<span class="ff6 ls52">\u2212</span><span class="ls37 ws8">1</span></span><span class="ls37 ws47">, \u03b5<span class="ff5 fs1 ws48 v1">12 </span><span class="ff2 ws11">= 1</span>, \u03b7<span class="ff5 fs1 ls46 v1">1</span><span class="ff2 ws11">= 0</span></span></div><div class="t m0 x29 h3 y30 ff2 fs0 fc0 sc0 ls37">2</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 x14 y62 w3 h16" alt="" src="https://files.passeidireto.com/ea2b9e07-b8d7-4ddc-8f88-43a3a339476c/bg3.png"><div class="t m0 x16 h3 y1 ff2 fs0 fc0 sc0 ls37 wsf">P<span class="_3 blank"></span>ortan<span class="_3 blank"></span>to o b<span class="_2 blank"> </span>em 1 tem elasticidade-pre¸<span class="_1 blank"></span>co unit´<span class="_19 blank"></span>aria, ´<span class="_b blank"></span>e um b<span class="_2 blank"> </span>em normal, cuja demanda n\u02dc<span class="_5 blank"></span>ao<span class="_16 blank"> </span>´<span class="_b blank"></span>e</div><div class="t m0 x16 h3 y2 ff2 fs0 fc0 sc0 ls37 ws6">afetada p<span class="_2 blank"> </span>ela renda (<span class="ff3 ws12">\u03b7<span class="ff5 fs1 ls53 v1">1</span></span>=<span class="_1f blank"> </span>0), e<span class="_a blank"> </span>´<span class="_b blank"></span>e substituto bruto do b<span class="_2 blank"> </span>em 2.<span class="_9 blank"> </span>Para o bem <span class="ff3 ls40">x<span class="ff5 fs1 ls54 v1">2</span></span>temos que:</div><div class="t m0 x3c he y63 ff3 fs0 fc0 sc0 ls38">\u03b5<span class="ff5 fs1 ls46 v1">2</span><span class="ff2 ls47">=<span class="ff6 ls55">\u2212</span><span class="ls37 ve">1</span></span></div><div class="t m0 x3d h17 y64 ff2 fs0 fc0 sc0 ls56">1<span class="ff6 ls42">\u2212<span class="ff3 ls2">p<span class="ff5 fs1 ls3 v1">2</span><span class="ls37 ws49">/m <span class="ws47 v2">, \u03b5</span><span class="ff5 fs1 ws48 v3">21 </span></span></span></span><span class="ls37 ws11 v2">= 0<span class="ff3 ws47">, \u03b7<span class="ff5 fs1 ls46 v1">2</span><span class="ff2 ls57">=<span class="ls37 ve">1</span></span></span></span></div><div class="t m0 x3e h3 y64 ff2 fs0 fc0 sc0 ls58">1<span class="ff6 ls42">\u2212<span class="ff3 ls4a">p<span class="ff5 fs1 ls3 v1">2</span><span class="ls37">/m</span></span></span></div><div class="t m0 x16 h3 y65 ff2 fs0 fc0 sc0 ls37 ws39">Logo o b<span class="_2 blank"> </span>em 2<span class="_1f blank"> </span>´<span class="_5 blank"></span>e um b<span class="_2 blank"> </span>em com<span class="_3 blank"></span>um (p<span class="_2 blank"> </span>ois estamos analisando o caso <span class="ff3 ls59">m<span class="ff6 ls4e">\u2265</span><span class="ls2">p<span class="ff5 fs1 ls3 v1">2</span></span></span>), ´<span class="_5 blank"></span>e um b<span class="_2 blank"> </span>em normal</div><div class="t m0 x16 h3 y66 ff2 fs0 fc0 sc0 ls37 ws6">de luxo, e n\u02dc<span class="_19 blank"></span>ao ´<span class="_5 blank"></span>e nem substituto bruto nem complementar bruto do bem 1.</div><div class="t m0 x31 h3 y67 ff2 fs0 fc0 sc0 ls37 ws4a">c)<span class="_17 blank"> </span>Encon<span class="_3 blank"></span>tre as demandas Hic<span class="_3 blank"></span>ksianas dos dois b<span class="_2 blank"> </span>ens.<span class="_1a blank"> </span>Compare a demanda Hicksiana com a</div><div class="t m0 x16 h3 y68 ff2 fs0 fc0 sc0 ls37 ws6">demanda Marshalliana do b<span class="_2 blank"> </span>em 1, quando as demandas s\u02dc<span class="_19 blank"></span>ao p<span class="_2 blank"> </span>ositiv<span class="_7 blank"></span>as.<span class="_9 blank"> </span>Interprete.</div><div class="t m0 x16 h3 y69 ff2 fs0 fc0 sc0 ls37 ws6">S: O problema dual do consumidor p<span class="_2 blank"> </span>o<span class="_2 blank"> </span>de ser escrito como:</div><div class="t m0 x3f h3 y6a ff2 fs0 fc0 sc0 ls37">min</div><div class="t m0 x8 h6 y6b ff7 fs1 fc0 sc0 ls41">x<span class="ffa fs2 ls37 va">1</span></div><div class="t m0 x30 h3 y6a ff3 fs0 fc0 sc0 ls2">p<span class="ff5 fs1 ls5 v1">1</span><span class="ls4">x<span class="ff5 fs1 ls16 v1">1</span><span class="ff2 ls7">+</span></span>p<span class="ff5 fs1 ls5 v1">2</span><span class="ff2 ls37 ws4b">( ¯<span class="_23 blank"></span><span class="ff3 ls5a">u<span class="ff6 ls42">\u2212<span class="ff2 ls37 ws8">ln(</span></span><span class="ls40">x<span class="ff5 fs1 ls3 v1">1</span><span class="ff2 ls37">))</span></span></span></span></div><div class="t m0 x16 h3 y6c ff2 fs0 fc0 sc0 ls37 ws3c">A<span class="_16 blank"> </span>CPO ´<span class="_5 blank"></span>e:</div><div class="t m0 x14 he y6d ff3 fs0 fc0 sc0 ls2">p<span class="ff5 fs1 ls46 v1">1</span><span class="ff2 ls5b">=</span><span class="ve">p</span><span class="ff5 fs1 ls37 v3">2</span></div><div class="t m0 x8 hd y6e ff3 fs0 fc0 sc0 ls4">x<span class="ff9 fs1 ls37 v9">\u2217</span></div><div class="t m0 x40 h8 y6f ff5 fs1 fc0 sc0 ls37">1</div><div class="t m0 x41 h9 y6d ff6 fs0 fc0 sc0 ls44">\u21d2<span class="ff3 ls4">x<span class="ff7 fs1 ls37 v7">h</span></span></div><div class="t m0 x42 h18 y70 ff5 fs1 fc0 sc0 ls5c">1<span class="ff2 fs0 ls37 ws8 v8">(<span class="ff3 ls2">p</span></span><span class="ls5 vc">1</span><span class="ff3 fs0 ls37 wsa v8">, p</span><span class="ls3 vc">2</span><span class="ff3 fs0 ls5d v8">,<span class="ff2 ls37 ws8">¯<span class="_23 blank"></span><span class="ff3 ws12">u<span class="ff2 ws11">) =<span class="_8 blank"> </span></span><span class="ls2 ve">p</span><span class="ff5 fs1 v3">2</span></span></span></span></div><div class="t m0 x43 h3 y6e ff3 fs0 fc0 sc0 ls2">p<span class="ff5 fs1 ls37 v1">1</span></div><div class="t m0 x16 h3 y71 ff2 fs0 fc0 sc0 ls37 ws4c">A demanda hic<span class="_3 blank"></span>ksiana do outro b<span class="_2 blank"> </span>em<span class="_1e blank"> </span>´<span class="_b blank"></span>e encontrada substituindo a demanda do bem 1<span class="_f blank"> </span>na</div><div class="t m0 x16 h3 y72 ff2 fs0 fc0 sc0 ls37 ws6">restri¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao do problema:</div><div class="t m0 x44 h9 y73 ff3 fs0 fc0 sc0 ls4">x<span class="ff7 fs1 ls37 v7">h</span></div><div class="t m0 x45 h18 y74 ff5 fs1 fc0 sc0 ls5c">2<span class="ff2 fs0 ls37 ws8 v8">(<span class="ff3 ls2">p</span></span><span class="ls5 vc">1</span><span class="ff3 fs0 ls37 wsa v8">, p</span><span class="ls3 vc">2</span><span class="ff3 fs0 ls5d v8">,<span class="ff2 ls37 ws8">¯<span class="_23 blank"></span><span class="ff3 ls5e">u<span class="ff2 ls37 ws11">) =<span class="_16 blank"> </span>¯<span class="_23 blank"></span><span class="ff3 ls5f">u<span class="ff6 ls60">\u2212</span><span class="ls2 ve">p</span><span class="ff5 fs1 ls37 v3">2</span></span></span></span></span></span></div><div class="t m0 x46 h3 y75 ff3 fs0 fc0 sc0 ls2">p<span class="ff5 fs1 ls37 v1">1</span></div><div class="t m0 x16 h3 y76 ff2 fs0 fc0 sc0 ls37 ws4d">P<span class="_3 blank"></span>ortan<span class="_3 blank"></span>to, para o primeiro b<span class="_2 blank"> </span>em,<span class="_8 blank"> </span>no caso de as demandas serem p<span class="_2 blank"> </span>ositiv<span class="_7 blank"></span>as,<span class="_1e blank"> </span>a demanda mar-</div><div class="t m0 x16 h3 y77 ff2 fs0 fc0 sc0 ls37 ws6">shalliana<span class="_a blank"> </span>´<span class="_b blank"></span>e igual `<span class="_5 blank"></span>a demanda hic<span class="_3 blank"></span>ksiana.</div><div class="t m0 x3 h3 y78 ff1 fs0 fc0 sc0 ls37 ws4e">Exerc<span class="_0 blank"></span>´<span class="_1 blank"></span>\u0131cio 3:<span class="_18 blank"> </span><span class="ff2 ws1c">Suponha a exist\u02c6<span class="_5 blank"></span>encia de <span class="ff3 ls61">n</span><span class="ws4f">b<span class="_2 blank"> </span>ens.<span class="_1a blank"> </span>Usando a propriedade de<span class="_1e blank"> </span>homogeneidade das</span></span></div><div class="t m0 x3 h3 y79 ff2 fs0 fc0 sc0 ls37 ws50">fun¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>oes de demanda Marshalliana,<span class="_1e blank"> </span>mostre que as elasticidades-pre¸<span class="_1 blank"></span>co e renda de um dado b<span class="_2 blank"> </span>em <span class="ff3">i</span></div><div class="t m0 x3 h3 y7a ff2 fs0 fc0 sc0 ls37 wse">satisfazem a seguin<span class="_3 blank"></span>te igualdade:</div><div class="t m0 x44 h3 y7b ff3 fs0 fc0 sc0 ls37 ws12">\u03b7<span class="ff7 fs1 ls35 v1">i</span><span class="ff2">+</span></div><div class="t m0 x47 h6 y7c ff7 fs1 fc0 sc0 ls37">n</div><div class="t m0 x18 h7 y7d ff8 fs0 fc0 sc0 ls37">X</div><div class="t m0 xf h8 y7e ff7 fs1 fc0 sc0 ls31">j<span class="ff5 ls37">=1</span></div><div class="t m0 x48 h3 y7b ff3 fs0 fc0 sc0 ls38">\u03b5<span class="ff7 fs1 ls37 ws51 v1">ij </span><span class="ff2 ls37 ws11">= 0</span><span class="ls62">,<span class="ff2 ls37">(2)</span></span></div><div class="t m0 x3 h3 y7f ff2 fs0 fc0 sc0 ls37 ws52">onde <span class="ff3 ws12">\u03b7<span class="ff7 fs1 ls63 v1">i</span></span><span class="ws53">´<span class="_b blank"></span>e a elasticidade-renda do b<span class="_2 blank"> </span>em <span class="ff3 ls64">i</span><span class="ls65">e</span><span class="ff3 ws12">\ue00f<span class="ff7 fs1 ws54 v1">ij </span></span><span class="ws55">´<span class="_5 blank"></span>e a elasticidade-pre¸<span class="_1 blank"></span>co da demanda do b<span class="_2 blank"> </span>em <span class="ff3 ls66">i</span>com</span></span></div><div class="t m0 x3 h3 y80 ff2 fs0 fc0 sc0 ls37 ws6">rela¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao ao pre¸<span class="_20 blank"></span>co do b<span class="_2 blank"> </span>em <span class="ff3 ls67">j</span>.<span class="_9 blank"> </span>In<span class="_3 blank"></span>terprete in<span class="_3 blank"></span>tuitiv<span class="_7 blank"></span>amente a rela¸<span class="_b blank"></span>c\u02dc<span class="_5 blank"></span>ao (2) acima.</div><div class="t m0 x3 h3 y81 ff2 fs0 fc0 sc0 ls37 ws56">S: A fun¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao de demanda Marshalliana ´<span class="_5 blank"></span>e homog\u02c6<span class="_5 blank"></span>enea de grau zero nos pre¸<span class="_1 blank"></span>cos e na renda.<span class="_24 blank"> </span>Logo,</div><div class="t m0 x3 h3 y82 ff2 fs0 fc0 sc0 ls37 ws3">para<span class="_16 blank"> </span>cada<span class="_16 blank"> </span>bem<span class="_16 blank"> </span><span class="ff3 ls68">i</span><span class="ws11">= 1<span class="ff3 wsa">, . . . , n</span><span class="ws6">, temos:</span></span></div><div class="t m0 x3c h3 y83 ff3 fs0 fc0 sc0 ls4">x<span class="ff7 fs1 ls1a v1">i</span><span class="ff2 ls37 ws8">(</span><span class="ls37 ws12">t<span class="ff1 ws9">p</span><span class="ws57">,<span class="_14 blank"> </span>ty <span class="ff2 ws58">) = </span></span></span>x<span class="ff7 fs1 ls1a v1">i</span><span class="ff2 ls6">(<span class="ff1 ls37 ws9">p</span></span><span class="ls37 ws59">,<span class="_15 blank"> </span>y <span class="ff2 ls6">)</span><span class="ls69">,</span><span class="ff2 ws3">para<span class="_16 blank"> </span>to do<span class="_25 blank"> </span></span><span class="ws5a">t > <span class="ff2 ws8">0</span>.</span></span></div><div class="t m0 x3 h3 y84 ff2 fs0 fc0 sc0 ls37 ws6">Deriv<span class="_7 blank"></span>ando essa express\u02dc<span class="_19 blank"></span>ao com resp<span class="_2 blank"> </span>eito a <span class="ff3 ws12">t</span>, obtemos:</div><div class="t m0 x49 h6 y85 ff7 fs1 fc0 sc0 ls37">n</div><div class="t m0 x3a h7 y86 ff8 fs0 fc0 sc0 ls37">X</div><div class="t m0 x3a h8 y87 ff7 fs1 fc0 sc0 ls31">j<span class="ff5 ls37">=1</span></div><div class="t m0 x14 h3 y88 ff3 fs0 fc0 sc0 ls37 ws10">\u2202 x<span class="ff7 fs1 ls1a v1">i</span><span class="ff2 ws8">(</span><span class="ws12">t<span class="ff1 ws9">p</span><span class="ws57">,<span class="_14 blank"> </span>ty <span class="ff2">)</span></span></span></div><div class="t m0 x23 h3 y89 ff3 fs0 fc0 sc0 ls37 ws10">\u2202 p<span class="ff7 fs1 v1">j</span></div><div class="t m0 x18 h19 y8a ff3 fs0 fc0 sc0 ls2">p<span class="ff7 fs1 ls6a v1">j</span><span class="ff2 lsf">+</span><span class="ls37 ws10 ve">\u2202 x</span><span class="ff7 fs1 ls1a v3">i</span><span class="ff2 ls37 ws8 ve">(</span><span class="ls6b ve">t<span class="ff1 ls37 ws9">p<span class="ff3 ws57">,<span class="_14 blank"> </span>ty <span class="ff2">)</span></span></span></span></div><div class="t m0 x4a h1a y89 ff3 fs0 fc0 sc0 ls37 ws10">\u2202 y<span class="_13 blank"> </span><span class="ls6c v2">y</span><span class="ff2 ws11 v2">= 0</span><span class="ls6d v2">,</span><span class="ff2 v2">(3)</span></div><div class="t m0 x3 h3 y8b ff2 fs0 fc0 sc0 ls37 ws3">para<span class="_16 blank"> </span>to do<span class="_16 blank"> </span><span class="ff3 ws5b">t > </span><span class="wse">0.<span class="_9 blank"> </span>Dividindo a igualdade acima p<span class="_2 blank"> </span>or <span class="ff3 ls4">x<span class="ff7 fs1 ls1a v1">i</span></span><span class="ls6">(</span><span class="ff3 ws12">t<span class="ff1 ws9">p</span><span class="ws57">,<span class="_14 blank"> </span>ty </span></span><span class="ws5c">), fazendo <span class="ff3 ls6e">t</span></span>=<span class="_a blank"> </span>1 e reescrev<span class="_3 blank"></span>endo (3) em</span></div><div class="t m0 x3 h3 y8c ff2 fs0 fc0 sc0 ls37 ws6">termos de elasticidades obtemos a express\u02dc<span class="_19 blank"></span>ao desejada:</div><div class="t m0 x33 h6 y2b ff7 fs1 fc0 sc0 ls37">n</div><div class="t m0 x44 h7 y2c ff8 fs0 fc0 sc0 ls37">X</div><div class="t m0 x40 h8 y2d ff7 fs1 fc0 sc0 ls31">j<span class="ff5 ls37">=1</span></div><div class="t m0 x25 h3 y2e ff3 fs0 fc0 sc0 ls38">\u03b5<span class="ff7 fs1 ls37 ws5d v1">ij </span><span class="ff2 ls7">+</span><span class="ls24">\u03b7<span class="ff7 fs1 ls6f v1">i</span><span class="ff2 ls37 ws11">= 0<span class="ff3">,</span></span></span></div><div class="t m0 x29 h3 y30 ff2 fs0 fc0 sc0 ls37">3</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 x4b y8d w4 h1b" alt="" src="https://files.passeidireto.com/ea2b9e07-b8d7-4ddc-8f88-43a3a339476c/bg4.png"><div class="t m0 x3 h3 y1 ff2 fs0 fc0 sc0 ls37 ws3">v´<span class="_19 blank"></span>alida<span class="_16 blank"> </span>para<span class="_16 blank"> </span>to do<span class="_16 blank"> </span><span class="ff3 ls70">i</span><span class="ws11">= 1<span class="ff3 wsa">, . . . , n</span>.</span></div><div class="t m0 x3 h3 y8e ff1 fs0 fc0 sc0 ls37 ws5e">Exerc<span class="_0 blank"></span>´<span class="_1 blank"></span>\u0131cio 4:<span class="_f blank"> </span><span class="ff2 ws5f">Sup<span class="_2 blank"> </span>onha que a elasticidade-renda da demanda p<span class="_2 blank"> </span>er capita de cerveja<span class="_a blank"> </span>´<span class="_b blank"></span>e constante e</span></div><div class="t m0 x3 h3 y8f ff2 fs0 fc0 sc0 ls37 ws60">igual a 3<span class="ff3 ws12">/</span>4 e a elasticidade-pre¸<span class="_1 blank"></span>co<span class="_10 blank"> </span>´<span class="_b blank"></span>e tam<span class="_3 blank"></span>b<span class="_3 blank"></span>´<span class="_b blank"></span>em constante e igual a <span class="ff6 ws32">\u2212</span><span class="ws8">1<span class="ff3 ws12">/</span></span>2.<span class="_8 blank"> </span>Os consumidores gastam,<span class="_1f blank"> </span>em</div><div class="t m0 x3 h3 y90 ff2 fs0 fc0 sc0 ls37 ws3a">m<span class="_3 blank"></span>´<span class="_b blank"></span>edia, R$ 400,00 p<span class="_2 blank"> </span>or ano com cerv<span class="_3 blank"></span>eja.<span class="_f blank"> </span>A renda m<span class="_3 blank"></span>´<span class="_b blank"></span>edia anual destes consumidores<span class="_a blank"> </span>´<span class="_5 blank"></span>e R$ 6.000,00.</div><div class="t m0 x3 h3 y91 ff2 fs0 fc0 sc0 ls37 ws6">Cada garrafa de cerv<span class="_3 blank"></span>eja custa R$ 3,00.</div><div class="t m0 x31 h3 y92 ff2 fs0 fc0 sc0 ls37 ws61">a) Se o gov<span class="_7 blank"></span>erno pretende<span class="_17 blank"> </span>desestim<span class="_3 blank"></span>ular o consumo de cerveja pela metade,<span class="_4 blank"> </span>qual dev<span class="_7 blank"></span>e ser o</div><div class="t m0 x16 h3 y93 ff2 fs0 fc0 sc0 ls37 ws6">aumen<span class="_3 blank"></span>to no pre¸<span class="_1 blank"></span>co da cerveja que alcan¸<span class="_b blank"></span>caria esta meta?</div><div class="t m0 x16 h3 y94 ff2 fs0 fc0 sc0 ls37 ws62">S: Elasticidade-pre¸<span class="_1 blank"></span>co constan<span class="_3 blank"></span>te e igual a <span class="ff6 ls52">\u2212</span><span class="ws8">1<span class="ff3 ws12">/</span></span>2 signi\ufb01ca que um aumen<span class="_3 blank"></span>to em 10% no pre¸<span class="_1 blank"></span>co</div><div class="t m0 x16 h3 y95 ff2 fs0 fc0 sc0 ls37 ws63">lev<span class="_7 blank"></span>a a uma redu¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao na quantidade demandada em 5%.<span class="_1e blank"> </span>Logo, um aumento no pre¸<span class="_b blank"></span>co em 100%</div><div class="t m0 x16 h3 y96 ff2 fs0 fc0 sc0 ls37 ws64">lev<span class="_7 blank"></span>aria `<span class="_19 blank"></span>a redu¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>ao almejada p<span class="_2 blank"> </span>elo go<span class="_3 blank"></span>verno de 50% na quan<span class="_7 blank"></span>tidade consumida de cerveja.<span class="_1e blank"> </span>Cada</div><div class="t m0 x16 h3 y97 ff2 fs0 fc0 sc0 ls37 ws6">garrafa de cerv<span class="_3 blank"></span>eja passaria en<span class="_3 blank"></span>t\u02dc<span class="_5 blank"></span>ao a custar R$ 6,00.</div><div class="t m0 x31 h3 y98 ff2 fs0 fc0 sc0 ls37 ws5f">b)<span class="_17 blank"> </span>Sup<span class="_2 blank"> </span>onha que o go<span class="_3 blank"></span>v<span class="_3 blank"></span>erno estimou um aumen<span class="_3 blank"></span>to da renda m´<span class="_5 blank"></span>edia an<span class="_3 blank"></span>ual no pr´<span class="_5 blank"></span>oximo ano de R$</div><div class="t m0 x16 h3 y99 ff2 fs0 fc0 sc0 ls37 ws39">3.000,00.<span class="_1e blank"> </span>O gov<span class="_3 blank"></span>erno deseja man<span class="_3 blank"></span>ter o n<span class="_0 blank"></span>´<span class="_c blank"></span>\u0131v<span class="_3 blank"></span>el de consumo de cerveja constan<span class="_7 blank"></span>te no pr´<span class="_5 blank"></span>oximo ano,</div><div class="t m0 x16 h3 y9a ff2 fs0 fc0 sc0 ls37 ws65">usando um imp<span class="_2 blank"> </span>osto sobre o pre¸<span class="_1 blank"></span>co da cerv<span class="_3 blank"></span>eja.<span class="_9 blank"> </span>Qual deve ser o aumen<span class="_7 blank"></span>to no pre¸<span class="_20 blank"></span>co da cerv<span class="_3 blank"></span>eja</div><div class="t m0 x16 h3 y9b ff2 fs0 fc0 sc0 ls37 ws66">no pr´<span class="_19 blank"></span>oximo ano para que o seu consumo n\u02dc<span class="_5 blank"></span>ao se mo<span class="_2 blank"> </span>di\ufb01que, dado que a previs\u02dc<span class="_5 blank"></span>ao de aumen<span class="_3 blank"></span>to</div><div class="t m0 x16 h3 y9c ff2 fs0 fc0 sc0 ls37 ws6">de renda se realize?</div><div class="t m0 x16 h3 y9d ff2 fs0 fc0 sc0 ls37 ws67">S: Como a elasticidade-renda da demanda cerv<span class="_3 blank"></span>eja<span class="_16 blank"> </span>´<span class="_b blank"></span>e constan<span class="_3 blank"></span>te e igual a 3<span class="ff3 ws12">/</span>4 e um aumento</div><div class="t m0 x16 h3 y9e ff2 fs0 fc0 sc0 ls37 ws68">na renda de R$ 3.000,00 sobre uma renda de R$ 6.000,00 corresp<span class="_2 blank"> </span>onde a um aumen<span class="_7 blank"></span>to de</div><div class="t m0 x16 h3 y9f ff2 fs0 fc0 sc0 ls37 ws69">50% na renda, o aumen<span class="_3 blank"></span>to no consumo de cerv<span class="_3 blank"></span>eja ser´<span class="_5 blank"></span>a de 3<span class="ff3 ws12">/</span><span class="ls71">4<span class="ff6 ls72">×</span></span><span class="ws6a">50% = 37<span class="ff3 ls2d">,</span></span>50%.<span class="_9 blank"> </span>P<span class="_3 blank"></span>elo mesmo</div><div class="t m0 x16 h3 ya0 ff2 fs0 fc0 sc0 ls37 ws65">motiv<span class="_3 blank"></span>o explicado no item a), o aumen<span class="_3 blank"></span>to no pre¸<span class="_1 blank"></span>co da cerveja necess´<span class="_19 blank"></span>ario para an<span class="_3 blank"></span>ular o efeito</div><div class="t m0 x16 h3 ya1 ff2 fs0 fc0 sc0 ls37 ws6b">do aumen<span class="_3 blank"></span>to de renda<span class="_8 blank"> </span>´<span class="_b blank"></span>e de 2<span class="_1f blank"> </span><span class="ff6 ls73">×</span><span class="ws8">37<span class="ff3 ls2d">,</span></span>50% =<span class="_9 blank"> </span>75%.<span class="_26 blank"> </span>Cada garrafa de cerv<span class="_3 blank"></span>eja passaria en<span class="_3 blank"></span>t\u02dc<span class="_5 blank"></span>ao a</div><div class="t m0 x16 h3 ya2 ff2 fs0 fc0 sc0 ls37 ws6">custar R$ 5,25.</div><div class="t m0 x3 h3 ya3 ff1 fs0 fc0 sc0 ls37 ws0">Exerc<span class="_0 blank"></span>´<span class="_1 blank"></span>\u0131cio 5:<span class="_9 blank"> </span><span class="ff2 ws6">Encon<span class="_3 blank"></span>tre as demandas Hicksianas e a fun¸<span class="_b blank"></span>c\u02dc<span class="_5 blank"></span>ao disp<span class="_3 blank"></span>\u02c6<span class="_b blank"></span>endio para os seguintes casos:</span></div><div class="t m0 x31 h12 ya4 ff2 fs0 fc0 sc0 ls37 wse">a)<span class="_17 blank"> </span>Utilidade Cobb-Douglas:<span class="_9 blank"> </span><span class="ff3 ws12">u</span><span class="ws8">(<span class="ff3 ls4">x<span class="ff5 fs1 ls5 v1">1</span><span class="ls37 wsa">, x<span class="ff5 fs1 ls3 v1">2</span></span></span><span class="ws58">) = <span class="ff3 ls4">x</span><span class="ff7 fs1 v9">\u03b1</span></span></span></div><div class="t m0 x1a h1c ya5 ff5 fs1 fc0 sc0 ls74">1<span class="ff3 fs0 ls4 v8">x</span><span class="ls37 ws2c ve">1<span class="ff9 ls39">\u2212<span class="ff7 ls37">\u03b1</span></span></span></div><div class="t m0 x4c h1d ya6 ff5 fs1 fc0 sc0 ls75">2<span class="ff2 fs0 ls37 ws6c v8">,<span class="_16 blank"> </span>0 <span class="ff3 ws6d">< \u03b1 < <span class="ff2">1.</span></span></span></div><div class="t m0 x16 h3 ya7 ff2 fs0 fc0 sc0 ls37 ws6">S: O Lagrangeano deste caso<span class="_a blank"> </span>´<span class="_b blank"></span>e:</div><div class="t m0 x14 h1e ya8 ff6 fs0 fc0 sc0 ls76">L<span class="ff2 ls19">=<span class="ff3 ls2">p<span class="ff5 fs1 ls3 v1">1</span><span class="ls40">x<span class="ff5 fs1 ls16 v1">1</span></span></span><span class="ls7">+<span class="ff3 ls2">p<span class="ff5 fs1 ls3 v1">2</span><span class="ls4">x<span class="ff5 fs1 ls16 v1">2</span></span></span><span class="lsa">+<span class="ff3 ls77">µ</span><span class="ls37 ws8">(<span class="ff3 ws12">u<span class="ff5 fs1 ls16 v1">0</span></span></span></span></span></span><span class="ls78">\u2212<span class="ff3 ls4">x<span class="ff7 fs1 ls37 v7">\u03b1</span></span></span></div><div class="t m0 x4d h1f ya9 ff5 fs1 fc0 sc0 ls74">1<span class="ff3 fs0 ls4 v8">x</span><span class="ls37 ws2c ve">1<span class="ff9 ls39">\u2212<span class="ff7 ls37">\u03b1</span></span></span></div><div class="t m0 x4e hb ya9 ff5 fs1 fc0 sc0 ls75">2<span class="ff2 fs0 ls37 v8">)</span></div><div class="t m0 x16 h3 yaa ff2 fs0 fc0 sc0 ls37 ws6">As CPO s\u02dc<span class="_19 blank"></span>ao:<span class="_27 blank"> </span><span class="ff8 va">\uf8f1</span></div><div class="t m0 x36 h7 yab ff8 fs0 fc0 sc0 ls37">\uf8f2</div><div class="t m0 x36 h7 yac ff8 fs0 fc0 sc0 ls37">\uf8f3</div><div class="t m0 x2c h20 yad ff3 fs0 fc0 sc0 ls2">p<span class="ff5 fs1 ls46 v1">1</span><span class="ff2 ls47">=</span><span class="ls37 ws12">µ\u03b1x<span class="ff7 fs1 ls79 v7">\u03b1<span class="ff9 ls39">\u2212<span class="ff5 ls37">1</span></span></span></span></div><div class="t m0 x4f h21 yae ff5 fs1 fc0 sc0 ls75">1<span class="ff3 fs0 ls4 v8">x</span><span class="ls37 ws2c ve">1<span class="ff9 ls39">\u2212<span class="ff7 ls37">\u03b1</span></span></span></div><div class="t m0 x50 h8 yae ff5 fs1 fc0 sc0 ls37">2</div><div class="t m0 x2c h12 yaf ff3 fs0 fc0 sc0 ls2">p<span class="ff5 fs1 ls46 v1">2</span><span class="ff2 ls47">=</span><span class="ls37 ws12">µ<span class="ff2 ws6e">(1 <span class="ff6 ls78">\u2212</span></span><span class="ls7a">\u03b1<span class="ff2 ls6">)</span><span class="ls4">x</span></span><span class="ff7 fs1 v9">\u03b1</span></span></div><div class="t m0 x2f h22 yb0 ff5 fs1 fc0 sc0 ls74">1<span class="ff3 fs0 ls4 v8">x</span><span class="ff9 ls37 ws2e ve">\u2212<span class="ff7">\u03b1</span></span></div><div class="t m0 x46 h8 yb1 ff5 fs1 fc0 sc0 ls37">2</div><div class="t m0 x2c h12 yb2 ff3 fs0 fc0 sc0 ls37 ws12">u<span class="ff5 fs1 ls46 v1">0</span><span class="ff2 ls47">=</span><span class="ls4">x</span><span class="ff7 fs1 v9">\u03b1</span></div><div class="t m0 x48 h23 yb3 ff5 fs1 fc0 sc0 ls74">1<span class="ff3 fs0 ls4 v8">x</span><span class="ls37 ws2c ve">1<span class="ff9 ls39">\u2212<span class="ff7 ls37">\u03b1</span></span></span></div><div class="t m0 x51 h8 yb4 ff5 fs1 fc0 sc0 ls37">2</div><div class="t m0 x16 h3 yb5 ff2 fs0 fc0 sc0 ls37 ws11">Dividindo as duas primeiras CPO, ac<span class="_3 blank"></span>hamos uma express\u02dc<span class="_5 blank"></span>ao para <span class="ff3 ls4">x<span class="ff5 fs1 ls7b v1">2</span></span><span class="ws6f">em fun¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao de <span class="ff3 ls4">x<span class="ff5 fs1 ls5 v1">1</span></span><span class="ws70">. Substi-</span></span></div><div class="t m0 x16 h3 yb6 ff2 fs0 fc0 sc0 ls37 ws71">tuindo essa express\u02dc<span class="_19 blank"></span>ao na terceira CPO, encontramos a demanda para o bem 1.<span class="_9 blank"> </span>Substituindo</div><div class="t m0 x16 h3 yb7 ff2 fs0 fc0 sc0 ls37 ws27">a demanda do b<span class="_2 blank"> </span>em 1 para a express\u02dc<span class="_19 blank"></span>ao de <span class="ff3 ls4">x<span class="ff5 fs1 ls7c v1">2</span></span>em fun¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>ao de <span class="ff3 ls4">x<span class="ff5 fs1 ls5 v1">1</span></span>, encontramos a demanda do</div><div class="t m0 x16 h3 yb8 ff2 fs0 fc0 sc0 ls37 ws6">b<span class="_2 blank"> </span>em 2.<span class="_9 blank"> </span>Essas demandas s\u02dc<span class="_19 blank"></span>ao:</div><div class="t m0 x52 h7 yb9 ff8 fs0 fc0 sc0 ls7d">(<span class="ff3 ls4 v13">x</span><span class="ff7 fs1 ls37 v14">h</span></div><div class="t m0 x53 h24 yba ff5 fs1 fc0 sc0 ls5c">1<span class="ff2 fs0 ls6 v8">(<span class="ff3 ls2">p</span></span><span class="ls3 vc">1</span><span class="ff3 fs0 ls37 wsa v8">, p</span><span class="ls5 vc">2</span><span class="ff3 fs0 ls37 wsa v8">, u</span><span class="ls5 vc">0</span><span class="ff2 fs0 ls37 wsd v8">) = <span class="ff8 ls7e v15">\ue000</span></span><span class="ff7 ls37 ve">\u03b1</span></div><div class="t m0 x4b h25 ybb ff5 fs1 fc0 sc0 ls7f">1<span class="ff9 ls37 ws2e">\u2212<span class="ff7 ls80">\u03b1<span class="ff8 fs0 ls81 v16">\ue001</span></span></span><span class="ls37 ws2c v17">1<span class="ff9 ls39">\u2212<span class="ff7 ls82">\u03b1<span class="ff3 fs0 ls2 v18">p</span><span class="ls79 v19">\u03b1</span></span><span class="v19">\u2212</span></span><span class="v19">1</span></span></div><div class="t m0 xa h21 ybc ff5 fs1 fc0 sc0 ls75">1<span class="ff3 fs0 ls2 v8">p</span><span class="ls37 ws2c ve">1<span class="ff9 ls39">\u2212<span class="ff7 ls37">\u03b1</span></span></span></div><div class="t m0 x54 h1d ybc ff5 fs1 fc0 sc0 ls75">2<span class="ff3 fs0 ls37 ws12 v8">u</span><span class="ls37 vc">0</span></div><div class="t m0 x22 hc ybd ff3 fs0 fc0 sc0 ls4">x<span class="ff7 fs1 ls37 v9">h</span></div><div class="t m0 x53 h24 ybe ff5 fs1 fc0 sc0 ls5c">2<span class="ff2 fs0 ls6 v8">(<span class="ff3 ls2">p</span></span><span class="ls3 vc">1</span><span class="ff3 fs0 ls37 wsa v8">, p</span><span class="ls5 vc">2</span><span class="ff3 fs0 ls37 wsa v8">, u</span><span class="ls5 vc">0</span><span class="ff2 fs0 ls37 wsd v8">) = <span class="ff8 ls7e v15">\ue000</span></span><span class="ff7 ls37 ve">\u03b1</span></div><div class="t m0 x4b h26 ybf ff5 fs1 fc0 sc0 ls7f">1<span class="ff9 ls37 ws2e">\u2212<span class="ff7 ls80">\u03b1<span class="ff8 fs0 ls81 v16">\ue001</span></span><span class="v17">\u2212<span class="ff7 ls83">\u03b1<span class="ff3 fs0 ls2 v18">p</span><span class="ls37 v1a">\u03b1</span></span></span></span></div><div class="t m0 x55 h27 ybe ff5 fs1 fc0 sc0 ls74">1<span class="ff3 fs0 ls2 v8">p</span><span class="ff9 ls39 ve">\u2212<span class="ff7 ls37">\u03b1</span></span></div><div class="t m0 x4d h1d yc0 ff5 fs1 fc0 sc0 ls84">2<span class="ff3 fs0 ls37 ws12 v8">u</span><span class="ls37 vc">0</span></div><div class="t m0 x16 h3 yc1 ff2 fs0 fc0 sc0 ls37 ws6">A fun¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao de disp\u02c6<span class="_5 blank"></span>endio ´<span class="_5 blank"></span>e:</div><div class="t m0 x56 h9 yc2 ff3 fs0 fc0 sc0 ls85">e<span class="ff2 ls37 ws8">(</span><span class="ls2">p<span class="ff5 fs1 ls5 v1">1</span><span class="ls37 wsa">, p<span class="ff5 fs1 ls3 v1">2</span>, u<span class="ff5 fs1 ls3 v1">0</span><span class="ff2 ws58">) = </span></span>p<span class="ff5 fs1 ls3 v1">1</span><span class="ls4">x<span class="ff7 fs1 ls37 v7">h</span></span></span></div><div class="t m0 x9 h10 yc3 ff5 fs1 fc0 sc0 ls86">1<span class="ff2 fs0 ls7 v8">+<span class="ff3 ls4a">p</span></span><span class="ls3 vc">2</span><span class="ff3 fs0 ls4 v8">x</span><span class="ff7 ls37 ve">h</span></div><div class="t m0 x1c h1f yc3 ff5 fs1 fc0 sc0 ls87">2<span class="ff2 fs0 ls19 v8">=<span class="ff3 ls88">\u03b1</span></span><span class="ff9 ls39 ve">\u2212<span class="ff7 ls89">\u03b1<span class="ff2 fs0 ls37 ws6e v1b">(1 <span class="ff6 ls42">\u2212<span class="ff3 ls7a">\u03b1<span class="ff2 ls6">)</span></span></span></span><span class="ls79">\u03b1<span class="ff9 ls37 ws2e">\u2212<span class="ff5 ls5">1<span class="ff3 fs0 ls2 v1b">p</span></span><span class="ff7">\u03b1</span></span></span></span></span></div><div class="t m0 x12 h1f yc3 ff5 fs1 fc0 sc0 ls74">1<span class="ff3 fs0 ls2 v8">p</span><span class="ls37 ws2c ve">1<span class="ff9 ls39">\u2212<span class="ff7 ls37">\u03b1</span></span></span></div><div class="t m0 x57 h11 yc3 ff5 fs1 fc0 sc0 ls75">2<span class="ff3 fs0 ls37 ws12 v8">u</span><span class="ls37 vc">0</span></div><div class="t m0 x29 h3 y30 ff2 fs0 fc0 sc0 ls37">4</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 x19 yc4 w5 h28" alt="" src="https://files.passeidireto.com/ea2b9e07-b8d7-4ddc-8f88-43a3a339476c/bg5.png"><div class="t m0 x31 h3 y1 ff2 fs0 fc0 sc0 ls37 wse">b)<span class="_17 blank"> </span>Utilidade linear:<span class="_9 blank"> </span><span class="ff3 ws12">u</span><span class="ls6">(<span class="ff3 ls4">x<span class="ff5 fs1 ls3 v1">1</span><span class="ls37 wsa">, x<span class="ff5 fs1 ls5 v1">2</span></span></span></span><span class="wsd">) = <span class="ff3 ws12">ax<span class="ff5 fs1 ls16 v1">1</span></span><span class="lsa">+</span><span class="ff3 ws12">bx<span class="ff5 fs1 ls3 v1">2</span></span><span class="ls8a">,</span><span class="ff3 wsa">a, b<span class="_1f blank"> </span>><span class="_a blank"> </span></span>0.</span></div><div class="t m0 x16 h3 yc5 ff2 fs0 fc0 sc0 ls37 ws16">S: Neste caso, n\u02dc<span class="_19 blank"></span>ao p<span class="_2 blank"> </span>o<span class="_2 blank"> </span>demos montar o Lagrangeano para resolv<span class="_7 blank"></span>er o problema, p<span class="_2 blank"> </span>ois a solu¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>ao</div><div class="t m0 x16 h3 yc6 ff2 fs0 fc0 sc0 ls37 ws36">ser´<span class="_19 blank"></span>a de canto (a n\u02dc<span class="_19 blank"></span>ao ser que usemos o m<span class="_3 blank"></span>´<span class="_b blank"></span>eto<span class="_2 blank"> </span>do de Kuhn-T<span class="_28 blank"></span>uc<span class="_3 blank"></span>k<span class="_3 blank"></span>er, que p<span class="_2 blank"> </span>ermite lidarmos com</div><div class="t m0 x16 h3 yc7 ff2 fs0 fc0 sc0 ls37 ws72">solu¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>oes de canto - no caso, solu¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>oes onde ap<span class="_2 blank"> </span>enas um dos b<span class="_2 blank"> </span>ens ser´<span class="_19 blank"></span>a consumido).<span class="_26 blank"> </span>Por<span class="_7 blank"></span>´<span class="_b blank"></span>em,</div><div class="t m0 x16 h3 yc8 ff2 fs0 fc0 sc0 ls37 ws73">p<span class="_2 blank"> </span>o<span class="_2 blank"> </span>demos resolv<span class="_7 blank"></span>er o problema usando intui¸<span class="_b blank"></span>c\u02dc<span class="_5 blank"></span>ao econ\u02c6<span class="_5 blank"></span>omica.<span class="_1e blank"> </span>O problema que queremos resolver</div><div class="t m0 x16 h3 yc9 ff2 fs0 fc0 sc0 ls37 ws8">´<span class="_b blank"></span>e:</div><div class="t m0 x49 h3 yca ff2 fs0 fc0 sc0 ls37">min</div><div class="t m0 x49 h6 ycb ff7 fs1 fc0 sc0 ls41">x<span class="ffa fs2 ls8b va">1</span><span class="ls37 ws74">,x<span class="ffa fs2 va">2</span></span></div><div class="t m0 x32 h3 yca ff3 fs0 fc0 sc0 ls2">p<span class="ff5 fs1 ls3 v1">1</span><span class="ls4">x<span class="ff5 fs1 ls16 v1">1</span><span class="ff2 lsa">+</span></span>p<span class="ff5 fs1 ls3 v1">2</span><span class="ls4">x<span class="ff5 fs1 ls8c v1">2</span><span class="ff2 ls37 ws75">s.a </span><span class="ls37 ws12">ax<span class="ff5 fs1 ls16 v1">1</span><span class="ff2 lsa">+</span>bx<span class="ff5 fs1 ls46 v1">2</span><span class="ff2 ls47">=</span>u<span class="ff5 fs1 v1">0</span></span></span></div><div class="t m0 x16 h3 ycc ff2 fs0 fc0 sc0 ls37 ws76">In<span class="_3 blank"></span>tuitiv<span class="_7 blank"></span>amen<span class="_3 blank"></span>te, o consumidor ir´<span class="_5 blank"></span>a adquirir ap<span class="_2 blank"> </span>enas o b<span class="_2 blank"> </span>em relativ<span class="_7 blank"></span>amen<span class="_3 blank"></span>te mais barato, na quan-</div><div class="t m0 x16 h3 ycd ff2 fs0 fc0 sc0 ls37 ws6">tidade que lhe assegure o n<span class="_0 blank"></span>´<span class="_c blank"></span>\u0131v<span class="_3 blank"></span>el de utilidade <span class="ff3 ws12">u<span class="ff5 fs1 ls5 v1">0</span></span>.<span class="_9 blank"> </span>Por isso, as demandas Hic<span class="_7 blank"></span>ksianas s\u02dc<span class="_5 blank"></span>ao:</div><div class="t m0 x5 h9 yce ff3 fs0 fc0 sc0 ls4">x<span class="ff7 fs1 ls37 v7">h</span></div><div class="t m0 x58 h29 ycf ff5 fs1 fc0 sc0 ls5c">1<span class="ff2 fs0 ls37 ws8 v8">(<span class="ff3 ls4a">p</span></span><span class="ls3 vc">1</span><span class="ff3 fs0 ls37 wsa v8">, p</span><span class="ls5 vc">2</span><span class="ff3 fs0 ls37 wsa v8">, u</span><span class="ls3 vc">0</span><span class="ff2 fs0 ls37 ws58 v8">) = <span class="ff8 v1c">\uf8f1</span></span></div><div class="t m0 x23 h7 yd0 ff8 fs0 fc0 sc0 ls37">\uf8f2</div><div class="t m0 x23 h7 yd1 ff8 fs0 fc0 sc0 ls37">\uf8f3</div><div class="t m0 x44 h3 yd2 ff3 fs0 fc0 sc0 ls5e">u<span class="ff5 fs1 ls3 v1">0</span><span class="ls8d">,<span class="ff2 ls37 ws77">se </span><span class="ls2">p<span class="ff5 fs1 ls3 v1">1</span><span class="ls37 ws3f">/a < p<span class="ff5 fs1 ls3 v1">2</span>/b</span></span></span></div><div class="t m0 x44 h3 yd3 ff2 fs0 fc0 sc0 ls37 ws6">qq coisa en<span class="_3 blank"></span>tre 0 e <span class="ff3 ws12">u<span class="ff5 fs1 ls5 v1">0</span><span class="ls8e">,</span></span><span class="ws77">se <span class="ff3 ls2">p<span class="ff5 fs1 ls3 v1">1</span><span class="ls37 ws78">/a </span></span><span class="ls19">=<span class="ff3 ls4a">p<span class="ff5 fs1 ls3 v1">2</span><span class="ls37">/b</span></span></span></span></div><div class="t m0 x44 h3 yd4 ff2 fs0 fc0 sc0 ls37 ws8">0<span class="ff3 ls8f">,</span><span class="ws77">se <span class="ff3 ls2">p<span class="ff5 fs1 ls3 v1">1</span><span class="ls37 ws3f">/a > p<span class="ff5 fs1 ls3 v1">2</span>/b</span></span></span></div><div class="t m0 x16 h3 yd5 ff2 fs0 fc0 sc0 ls37 ws8">Similarmen<span class="_3 blank"></span>te,</div><div class="t m0 x5 h9 yd6 ff3 fs0 fc0 sc0 ls4">x<span class="ff7 fs1 ls37 v7">h</span></div><div class="t m0 x58 h2a yd7 ff5 fs1 fc0 sc0 ls5c">2<span class="ff2 fs0 ls37 ws8 v8">(<span class="ff3 ls4a">p</span></span><span class="ls3 vc">1</span><span class="ff3 fs0 ls37 wsa v8">, p</span><span class="ls5 vc">2</span><span class="ff3 fs0 ls37 wsa v8">, u</span><span class="ls3 vc">0</span><span class="ff2 fs0 ls37 ws58 v8">) = <span class="ff8 v1c">\uf8f1</span></span></div><div class="t m0 x23 h7 yd8 ff8 fs0 fc0 sc0 ls37">\uf8f2</div><div class="t m0 x23 h7 yd9 ff8 fs0 fc0 sc0 ls37">\uf8f3</div><div class="t m0 x44 h3 yda ff2 fs0 fc0 sc0 ls37 ws8">0<span class="ff3 ls8f">,</span><span class="ws77">se <span class="ff3 ls2">p<span class="ff5 fs1 ls3 v1">1</span><span class="ls37 ws3f">/a < p<span class="ff5 fs1 ls5 v1">2</span>/b</span></span></span></div><div class="t m0 x44 h3 ydb ff2 fs0 fc0 sc0 ls37 ws6">qq coisa en<span class="_3 blank"></span>tre 0 e <span class="ff3 ws12">u<span class="ff5 fs1 ls5 v1">0</span><span class="ls8e">,</span></span><span class="ws77">se <span class="ff3 ls2">p<span class="ff5 fs1 ls3 v1">1</span><span class="ls37 ws78">/a </span></span><span class="ls19">=<span class="ff3 ls2">p<span class="ff5 fs1 ls5 v1">2</span><span class="ls37">/b</span></span></span></span></div><div class="t m0 x44 h3 ydc ff3 fs0 fc0 sc0 ls5e">u<span class="ff5 fs1 ls3 v1">0</span><span class="ls8d">,<span class="ff2 ls37 ws77">se </span><span class="ls2">p<span class="ff5 fs1 ls3 v1">1</span><span class="ls37 ws3f">/a > p<span class="ff5 fs1 ls3 v1">2</span>/b</span></span></span></div><div class="t m0 x16 h3 ydd ff2 fs0 fc0 sc0 ls37 ws79">A<span class="_16 blank"> </span>fun¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao<span class="_16 blank"> </span>disp\u02c6<span class="_5 blank"></span>endio ´<span class="_b blank"></span>e:</div><div class="t m0 x59 h9 yde ff3 fs0 fc0 sc0 ls85">e<span class="ff2 ls37 ws8">(</span><span class="ls2">p<span class="ff5 fs1 ls3 v1">1</span><span class="ls37 wsa">, p<span class="ff5 fs1 ls3 v1">2</span>, u<span class="ff5 fs1 ls3 v1">0</span><span class="ff2 ws58">) = </span></span>p<span class="ff5 fs1 ls3 v1">1</span><span class="ls4">x<span class="ff7 fs1 ls37 v7">h</span></span></span></div><div class="t m0 x5a h2b ydf ff5 fs1 fc0 sc0 ls86">1<span class="ff2 fs0 ls7 v8">+<span class="ff3 ls2">p</span></span><span class="ls5 vc">2</span><span class="ff3 fs0 ls4 v8">x</span><span class="ff7 ls37 ve">h</span></div><div class="t m0 x9 h18 ydf ff5 fs1 fc0 sc0 ls87">2<span class="ff2 fs0 ls37 ws7a v8">=<span class="_1f blank"> </span>min <span class="ff8 ls90 v1d">n<span class="ff3 ls2 v1b">p</span></span></span><span class="ls37 vd">1</span></div><div class="t m0 x5b h2c ye0 ff3 fs0 fc0 sc0 ls91">a<span class="ls5e v2">u</span><span class="ff5 fs1 ls3 v3">0</span><span class="ls92 v2">,</span><span class="ls2 v5">p</span><span class="ff5 fs1 ls37 v6">2</span></div><div class="t m0 x55 h2c ye0 ff3 fs0 fc0 sc0 ls93">b<span class="ls37 ws12 v2">u</span><span class="ff5 fs1 ls3 v3">0</span><span class="ff8 ls94 v1e">o</span><span class="ff2 ls37 ws7a v2">=<span class="_1f blank"> </span>min </span><span class="ff8 ls95 v1e">n</span><span class="ls2 v5">p</span><span class="ff5 fs1 ls37 v6">1</span></div><div class="t m0 x5c h2c ye0 ff3 fs0 fc0 sc0 ls96">a<span class="ls92 v2">,</span><span class="ls2 v5">p</span><span class="ff5 fs1 ls37 v6">2</span></div><div class="t m0 x5d h2d ye0 ff3 fs0 fc0 sc0 ls93">b<span class="ff8 ls97 v1e">o</span><span class="ls5e v2">u</span><span class="ff5 fs1 ls3 v3">0</span><span class="ls37 v2">.</span></div><div class="t m0 x31 h3 ye1 ff2 fs0 fc0 sc0 ls37 wse">c)<span class="_17 blank"> </span>Utilidade Leon<span class="_3 blank"></span>tief:<span class="_9 blank"> </span><span class="ff3 ws12">u</span><span class="ls6">(<span class="ff3 ls4">x<span class="ff5 fs1 ls3 v1">1</span><span class="ls37 wsa">, x<span class="ff5 fs1 ls5 v1">2</span></span></span></span><span class="ws6a">) = min<span class="ff6 ls98">{</span><span class="ff3 ws12">ax<span class="ff5 fs1 ls3 v1">1</span><span class="wsa">, bx<span class="ff5 fs1 ls5 v1">2</span><span class="ff6 ws32">}</span></span></span><span class="ls8a">,</span><span class="ff3 wsa">a, b<span class="_1f blank"> </span>><span class="_a blank"> </span></span>0.</span></div><div class="t m0 x16 h3 ye2 ff2 fs0 fc0 sc0 ls37 ws60">S: Este<span class="_10 blank"> </span>´<span class="_5 blank"></span>e outro caso onde n\u02dc<span class="_5 blank"></span>ao p<span class="_2 blank"> </span>o<span class="_2 blank"> </span>demos usar o m<span class="_3 blank"></span>´<span class="_b blank"></span>eto<span class="_2 blank"> </span>do de Lagrange, p<span class="_2 blank"> </span>ois a fun¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>ao de utilidade</div><div class="t m0 x16 h3 ye3 ff2 fs0 fc0 sc0 ls37 ws7b">n\u02dc<span class="_19 blank"></span>ao ´<span class="_5 blank"></span>e diferenci´<span class="_5 blank"></span>av<span class="_3 blank"></span>el.<span class="_1e blank"> </span>Devemos, mais uma v<span class="_3 blank"></span>ez, resolver o problema usando in<span class="_7 blank"></span>tui¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>ao econ\u02c6<span class="_5 blank"></span>omica.</div><div class="t m0 x16 h3 ye4 ff2 fs0 fc0 sc0 ls37 ws6">O problema que queremos resolv<span class="_3 blank"></span>er<span class="_a blank"> </span>´<span class="_b blank"></span>e:</div><div class="t m0 x21 h3 ye5 ff2 fs0 fc0 sc0 ls37">min</div><div class="t m0 x21 h6 ye6 ff7 fs1 fc0 sc0 ls41">x<span class="ffa fs2 ls8b va">1</span><span class="ls37 ws74">,x<span class="ffa fs2 va">2</span></span></div><div class="t m0 x22 h3 ye5 ff3 fs0 fc0 sc0 ls2">p<span class="ff5 fs1 ls3 v1">1</span><span class="ls4">x<span class="ff5 fs1 ls16 v1">1</span><span class="ff2 lsa">+</span></span>p<span class="ff5 fs1 ls3 v1">2</span><span class="ls4">x<span class="ff5 fs1 ls99 v1">2</span><span class="ff2 ls37 ws7c">s.a min<span class="ff6 ls98">{</span></span><span class="ls37 ws12">ax<span class="ff5 fs1 ls3 v1">1</span><span class="wsa">, bx<span class="ff5 fs1 ls5 v1">2</span><span class="ff6 ls9a">}<span class="ff2 ls47">=</span></span></span>u<span class="ff5 fs1 v1">0</span></span></span></div><div class="t m0 x16 h3 ye7 ff2 fs0 fc0 sc0 ls37 ws7d">In<span class="_3 blank"></span>tuitiv<span class="_7 blank"></span>amen<span class="_3 blank"></span>te,<span class="_f blank"> </span>o consumidor tem que consumir ambos os b<span class="_2 blank"> </span>ens em quan<span class="_3 blank"></span>tidades tais que</div><div class="t m0 x16 h3 ye8 ff3 fs0 fc0 sc0 ls37 ws12">ax<span class="ff5 fs1 ls46 v1">1</span><span class="ff2 ls47">=</span>bx<span class="ff5 fs1 ls3 v1">2</span><span class="ff2 ws39">, j´<span class="_5 blank"></span>a que os b<span class="_2 blank"> </span>ens s\u02dc<span class="_19 blank"></span>ao complementares perfeitos,<span class="_a blank"> </span>de mo<span class="_2 blank"> </span>do que alcance a utilidade <span class="ff3 ls5e">u<span class="ff5 fs1 ls3 v1">0</span></span>.</span></div><div class="t m0 x16 h3 ye9 ff2 fs0 fc0 sc0 ls37 ws6">P<span class="_3 blank"></span>or isso, as demandas Hic<span class="_3 blank"></span>ksianas s\u02dc<span class="_5 blank"></span>ao:</div><div class="t m0 x3c h9 yea ff3 fs0 fc0 sc0 ls4">x<span class="ff7 fs1 ls37 v7">h</span></div><div class="t m0 x21 h18 yeb ff5 fs1 fc0 sc0 ls5c">1<span class="ff2 fs0 ls6 v8">(<span class="ff3 ls2">p</span></span><span class="ls3 vc">1</span><span class="ff3 fs0 ls37 wsa v8">, p</span><span class="ls5 vc">2</span><span class="ff3 fs0 ls37 wsa v8">, u</span><span class="ls5 vc">0</span><span class="ff2 fs0 ls37 ws11 v8">) =<span class="_8 blank"> </span><span class="ff3 ws12 ve">u</span></span><span class="ls37 vd">0</span></div><div class="t m0 x1a h2e yec ff3 fs0 fc0 sc0 ls9b">a<span class="ff2 ls9c v2">e</span><span class="ls4 v2">x</span><span class="ff7 fs1 ls37 v1d">h</span></div><div class="t m0 x5e hf yed ff5 fs1 fc0 sc0 ls5c">2<span class="ff2 fs0 ls37 ws8 v8">(<span class="ff3 ls2">p</span></span><span class="ls5 vc">1</span><span class="ff3 fs0 ls37 wsa v8">, p</span><span class="ls3 vc">2</span><span class="ff3 fs0 ls37 wsa v8">, u</span><span class="ls3 vc">0</span><span class="ff2 fs0 ls37 ws11 v8">) =<span class="_8 blank"> </span><span class="ff3 ls5e ve">u</span></span><span class="ls37 vd">0</span></div><div class="t m0 x5f h3 yec ff3 fs0 fc0 sc0 ls37">b</div><div class="t m0 x16 h3 yee ff2 fs0 fc0 sc0 ls37 ws6">A fun¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao disp\u02c6<span class="_5 blank"></span>endio ´<span class="_5 blank"></span>e:</div><div class="t m0 x5 h9 yef ff3 fs0 fc0 sc0 ls85">e<span class="ff2 ls37 ws8">(</span><span class="ls2">p<span class="ff5 fs1 ls5 v1">1</span><span class="ls37 wsa">, p<span class="ff5 fs1 ls3 v1">2</span>, u<span class="ff5 fs1 ls3 v1">0</span><span class="ff2 ws58">) = </span></span>p<span class="ff5 fs1 ls3 v1">1</span><span class="ls4">x<span class="ff7 fs1 ls37 v7">h</span></span></span></div><div class="t m0 x60 h10 yf0 ff5 fs1 fc0 sc0 ls86">1<span class="ff2 fs0 ls7 v8">+<span class="ff3 ls2">p</span></span><span class="ls5 vc">2</span><span class="ff3 fs0 ls4 v8">x</span><span class="ff7 ls37 ve">h</span></div><div class="t m0 x61 h11 yf0 ff5 fs1 fc0 sc0 ls87">2<span class="ff2 fs0 ls19 v8">=<span class="ff3 ls2">p</span></span><span class="ls37 vc">1</span></div><div class="t m0 x5b h3 yf1 ff3 fs0 fc0 sc0 ls5e">u<span class="ff5 fs1 ls37 v1">0</span></div><div class="t m0 x4a h1a yf2 ff3 fs0 fc0 sc0 ls9d">a<span class="ff2 ls7 v2">+</span><span class="ls4a v2">p</span><span class="ff5 fs1 ls37 v3">2</span></div><div class="t m0 x62 h3 yf1 ff3 fs0 fc0 sc0 ls5e">u<span class="ff5 fs1 ls37 v1">0</span></div><div class="t m0 x4d h17 yf2 ff3 fs0 fc0 sc0 ls9e">b<span class="ff2 ls47 v2">=</span><span class="ff8 ls9f v1e">\ue010</span><span class="ls2 v5">p</span><span class="ff5 fs1 ls37 v6">1</span></div><div class="t m0 x63 h17 yf2 ff3 fs0 fc0 sc0 lsa0">a<span class="ff2 lsf v2">+</span><span class="ls2 v5">p</span><span class="ff5 fs1 ls37 v6">2</span></div><div class="t m0 x64 h2d yf2 ff3 fs0 fc0 sc0 ls93">b<span class="ff8 lsa1 v1e">\ue011</span><span class="ls5e v2">u</span><span class="ff5 fs1 ls3 v3">0</span><span class="ls37 v2">.</span></div><div class="t m0 x31 h2f yf3 ff2 fs0 fc0 sc0 ls37 ws7e">d)<span class="_17 blank"> </span>Utilidade CES: <span class="ff3 ws12">u</span><span class="ls6">(<span class="ff3 ls4">x<span class="ff5 fs1 ls3 v1">1</span><span class="ls37 wsa">, x<span class="ff5 fs1 ls5 v1">2</span></span></span></span><span class="ws6a">) = [<span class="ff3 ws12">ax<span class="ff7 fs1 v1f">\u03c1</span></span></span></div><div class="t m0 x32 h30 yf4 ff5 fs1 fc0 sc0 lsa2">1<span class="ff2 fs0 lsa v8">+<span class="ff3 ls37 ws12">bx<span class="ff7 fs1 v1f">\u03c1</span></span></span></div><div class="t m0 x2c h1d yf4 ff5 fs1 fc0 sc0 lsa3">2<span class="ff2 fs0 ls37 v8">]</span></div><div class="t m0 x1a h31 yf5 ffa fs2 fc0 sc0 ls37">1</div><div class="t m0 x1a h32 yf6 ffb fs2 fc0 sc0 lsa4">\u03c1<span class="ff2 fs0 ls8a v1a">,<span class="ff3 ls37 wsa">a, b<span class="_1f blank"> </span>><span class="_1f blank"> </span><span class="ff2 ws7f">0, </span><span class="ws80">\u03c1 < <span class="ff2 ws7f">1, </span><span class="lsa5">\u03c1</span><span class="ff6 ws32">6<span class="ff2 ws11">= 0.</span></span></span></span></span></div><div class="t m0 x16 h3 yf7 ff2 fs0 fc0 sc0 ls37 ws6">S: O Lagrangeano deste caso<span class="_a blank"> </span>´<span class="_b blank"></span>e:</div><div class="t m0 x65 h2f yf8 ff6 fs0 fc0 sc0 lsa6">L<span class="ff2 ls47">=<span class="ff3 ls2">p<span class="ff5 fs1 ls3 v1">1</span><span class="ls4">x<span class="ff5 fs1 ls16 v1">1</span></span></span><span class="lsa">+<span class="ff3 ls2">p<span class="ff5 fs1 ls3 v1">2</span><span class="ls4">x<span class="ff5 fs1 ls16 v1">2</span></span></span><span class="ls7">+<span class="ff3 ls77">µ</span><span class="ls6">(<span class="ff3 ls37 ws12">u<span class="ff5 fs1 ls16 v1">0</span></span></span></span></span></span><span class="ls42">\u2212<span class="ff2 lsa7">[<span class="ff3 ls37 ws12">ax<span class="ff7 fs1 v1f">\u03c1</span></span></span></span></div><div class="t m0 x62 h30 yf9 ff5 fs1 fc0 sc0 lsa2">1<span class="ff2 fs0 lsa v8">+<span class="ff3 ls37 ws12">bx<span class="ff7 fs1 v1f">\u03c1</span></span></span></div><div class="t m0 x37 h1d yf9 ff5 fs1 fc0 sc0 lsa8">2<span class="ff2 fs0 ls37 v8">]</span></div><div class="t m0 x66 h31 yfa ffa fs2 fc0 sc0 ls37">1</div><div class="t m0 x66 h32 yfb ffb fs2 fc0 sc0 lsa4">\u03c1<span class="ff2 fs0 ls37 v1a">)</span></div><div class="t m0 x29 h3 y30 ff2 fs0 fc0 sc0 ls37">5</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 x67 yfc w6 h33" alt="" src="https://files.passeidireto.com/ea2b9e07-b8d7-4ddc-8f88-43a3a339476c/bg6.png"><div class="t m0 x16 h3 y1 ff2 fs0 fc0 sc0 ls37 ws6">As CPO s\u02dc<span class="_19 blank"></span>ao:<span class="_29 blank"> </span><span class="ff8 v19">\uf8f1</span></div><div class="t m0 x5a h7 yfd ff8 fs0 fc0 sc0 ls37">\uf8f4</div><div class="t m0 x5a h7 yfe ff8 fs0 fc0 sc0 ls37">\uf8f2</div><div class="t m0 x5a h7 yff ff8 fs0 fc0 sc0 ls37">\uf8f4</div><div class="t m0 x5a h7 y100 ff8 fs0 fc0 sc0 ls37">\uf8f3</div><div class="t m0 x38 h2f y101 ff3 fs0 fc0 sc0 ls2">p<span class="ff5 fs1 ls46 v1">1</span><span class="ff2 ls47">=</span><span class="lsa9">µ<span class="ff2 lsa7">[</span><span class="ls37 ws12">ax<span class="ff7 fs1 v1f">\u03c1</span></span></span></div><div class="t m0 x68 h30 y102 ff5 fs1 fc0 sc0 lsa2">1<span class="ff2 fs0 ls7 v8">+<span class="ff3 ls37 ws12">bx<span class="ff7 fs1 v1f">\u03c1</span></span></span></div><div class="t m0 x69 h1d y102 ff5 fs1 fc0 sc0 lsa8">2<span class="ff2 fs0 ls37 v8">]</span></div><div class="t m0 x6a h31 y103 ffa fs2 fc0 sc0 ls37">1</div><div class="t m0 x6a h34 y104 ffb fs2 fc0 sc0 lsaa">\u03c1<span class="ff9 fs1 ls37 ws2e v8">\u2212<span class="ff5 lsab">1</span></span><span class="ff3 fs0 ls37 ws12 v1a">ax</span><span class="ff7 fs1 lsac v8">\u03c1<span class="ff9 ls37 ws2e">\u2212<span class="ff5">1</span></span></span></div><div class="t m0 x6b h8 y102 ff5 fs1 fc0 sc0 ls37">1</div><div class="t m0 x38 h2f y105 ff3 fs0 fc0 sc0 ls2">p<span class="ff5 fs1 ls46 v1">2</span><span class="ff2 ls47">=</span><span class="lsa9">µ<span class="ff2 lsa7">[</span><span class="ls37 ws12">ax<span class="ff7 fs1 v1f">\u03c1</span></span></span></div><div class="t m0 x68 h30 y106 ff5 fs1 fc0 sc0 lsa2">1<span class="ff2 fs0 ls7 v8">+<span class="ff3 ls37 ws12">bx<span class="ff7 fs1 v1f">\u03c1</span></span></span></div><div class="t m0 x69 h1d y106 ff5 fs1 fc0 sc0 lsa8">2<span class="ff2 fs0 ls37 v8">]</span></div><div class="t m0 x6a h31 y107 ffa fs2 fc0 sc0 ls37">1</div><div class="t m0 x6a h35 y108 ffb fs2 fc0 sc0 lsaa">\u03c1<span class="ff9 fs1 ls37 ws2e v8">\u2212<span class="ff5 lsab">1</span></span><span class="ff3 fs0 ls37 ws12 v1a">bx</span><span class="ff7 fs1 lsac v8">\u03c1<span class="ff9 ls37 ws2e">\u2212<span class="ff5">1</span></span></span></div><div class="t m0 x6c h8 y106 ff5 fs1 fc0 sc0 ls37">2</div><div class="t m0 x38 h36 y109 ff3 fs0 fc0 sc0 ls37 ws12">u<span class="ff5 fs1 ls46 v1">0</span><span class="ff2 ws11">= [</span>ax<span class="ff7 fs1 v1f">\u03c1</span></div><div class="t m0 x61 h30 y10a ff5 fs1 fc0 sc0 lsa2">1<span class="ff2 fs0 ls7 v8">+<span class="ff3 ls37 ws12">bx<span class="ff7 fs1 v1f">\u03c1</span></span></span></div><div class="t m0 x1d h37 y10a ff5 fs1 fc0 sc0 lsa3">2<span class="ff2 fs0 ls37 v8">]</span></div><div class="t m0 x6d h31 y10b ffa fs2 fc0 sc0 ls37">1</div><div class="t m0 x6d h38 y10c ffb fs2 fc0 sc0 ls37">\u03c1</div><div class="t m0 x16 h3 y10d ff2 fs0 fc0 sc0 ls37 ws6">Dividindo as duas primeiras CPO, ac<span class="_3 blank"></span>hamos uma express\u02dc<span class="_5 blank"></span>ao para <span class="ff3 ls4">x<span class="ff5 fs1 ls54 v1">2</span></span>em fun¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao de <span class="ff3 ls4">x<span class="ff5 fs1 ls3 v1">1</span></span>,</div><div class="t m0 x9 h39 y10e ff3 fs0 fc0 sc0 ls4">x<span class="ff5 fs1 ls46 v1">2</span><span class="ff2 ls47">=<span class="ff8 lsad vf">\ue014</span></span><span class="ls37 ws12 ve">ap<span class="ff5 fs1 v1">2</span></span></div><div class="t m0 x6e h3a y10f ff3 fs0 fc0 sc0 ls37 ws12">bp<span class="ff5 fs1 lsae v1">1</span><span class="ff8 lsaf v4">\ue015</span><span class="ffa fs2 v20">1</span></div><div class="t m0 x6f h31 y110 ffb fs2 fc0 sc0 lsb0">\u03c1<span class="ffc ls37 ws81">\u2212<span class="ffa">1</span></span></div><div class="t m0 x5e h3 y10e ff3 fs0 fc0 sc0 ls4">x<span class="ff5 fs1 ls37 v1">1</span></div><div class="t m0 x16 h3 y111 ff2 fs0 fc0 sc0 ls37 ws82">Substituindo essa express\u02dc<span class="_19 blank"></span>ao na terceira CPO, encontramos a demanda Hic<span class="_7 blank"></span>ksiana para o b<span class="_2 blank"> </span>em</div><div class="t m0 x16 h3 y112 ff2 fs0 fc0 sc0 ls37 ws83">1.<span class="_4 blank"> </span>Substituindo a demanda do b<span class="_2 blank"> </span>em 1 na express\u02dc<span class="_5 blank"></span>ao de <span class="ff3 ls4">x<span class="ff5 fs1 lsb1 v1">2</span></span><span class="ws84">em fun¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>ao de <span class="ff3 ls4">x<span class="ff5 fs1 ls3 v1">1</span></span><span class="ws83">, encontramos a</span></span></div><div class="t m0 x16 h3 y113 ff2 fs0 fc0 sc0 ls37 ws6">demanda Hic<span class="_3 blank"></span>ksiana do b<span class="_2 blank"> </span>em 2.<span class="_9 blank"> </span>Essas demandas s\u02dc<span class="_5 blank"></span>ao:</div><div class="t m0 x70 h9 y114 ff3 fs0 fc0 sc0 ls4">x<span class="ff7 fs1 ls37 v7">h</span></div><div class="t m0 x71 h3b y115 ff5 fs1 fc0 sc0 ls5c">1<span class="ff2 fs0 ls37 ws8 v8">(<span class="ff3 ls4a">p</span></span><span class="ls3 vc">1</span><span class="ff3 fs0 ls37 wsa v8">, p</span><span class="ls3 vc">2</span><span class="ff3 fs0 ls37 wsa v8">, u</span><span class="ls3 vc">0</span><span class="ff2 fs0 ls37 ws41 v8">) = <span class="ff8 ws85 v21">"</span><span class="ff3 lsb2">a<span class="ff2 ls7">+</span><span class="lsb3">b<span class="ff8 lsb4 vf">\ue012</span><span class="ls37 ws12 ve">ap</span></span></span></span><span class="ls37 vd">2</span></div><div class="t m0 x42 h3c y116 ff3 fs0 fc0 sc0 ls37 ws12">bp<span class="ff5 fs1 lsae v1">1</span><span class="ff8 lsb5 v4">\ue013</span><span class="ffb fs2 v22">\u03c1</span></div><div class="t m0 x5e h3d y117 ffb fs2 fc0 sc0 ls37 ws81">\u03c1<span class="ffc lsb6">\u2212<span class="ffa lsb7">1<span class="ff8 fs0 lsb8 vd">#</span><span class="ff9 fs1 lsb9 v23">\u2212</span><span class="ls37 v24">1</span></span></span></div><div class="t m0 xb h38 y118 ffb fs2 fc0 sc0 ls37">\u03c1</div><div class="t m0 x3e h3 y114 ff3 fs0 fc0 sc0 ls37 ws12">u<span class="ff5 fs1 v1">0</span></div><div class="t m0 x70 h9 y119 ff3 fs0 fc0 sc0 ls4">x<span class="ff7 fs1 ls37 v7">h</span></div><div class="t m0 x71 h3e y11a ff5 fs1 fc0 sc0 ls5c">2<span class="ff2 fs0 ls37 ws8 v8">(<span class="ff3 ls4a">p</span></span><span class="ls3 vc">1</span><span class="ff3 fs0 ls37 wsa v8">, p</span><span class="ls3 vc">2</span><span class="ff3 fs0 ls37 wsa v8">, u</span><span class="ls3 vc">0</span><span class="ff2 fs0 ls37 ws41 v8">) = <span class="ff8 lsad vf">\ue014</span><span class="ff3 ws12 ve">ap</span></span><span class="ls37 vd">2</span></div><div class="t m0 xf h3f y11b ff3 fs0 fc0 sc0 ls37 ws12">bp<span class="ff5 fs1 lsae v1">1</span><span class="ff8 lsaf v4">\ue015</span><span class="ffa fs2 v20">1</span></div><div class="t m0 x2e h40 y11c ffb fs2 fc0 sc0 lsb0">\u03c1<span class="ffc ls37 ws81">\u2212<span class="ffa lsba">1<span class="ff8 fs0 lsb8 vd">"<span class="ff3 lsbb v25">a<span class="ff2 lsa">+<span class="ff3 lsbc">b<span class="ff8 lsb4 vf">\ue012</span><span class="ls37 ws12 ve">ap</span></span></span></span></span></span><span class="ff5 fs1 v1b">2</span></span></div><div class="t m0 x6c h3c y11b ff3 fs0 fc0 sc0 ls37 ws12">bp<span class="ff5 fs1 lsae v1">1</span><span class="ff8 lsbd v4">\ue013</span><span class="ffb fs2 v22">\u03c1</span></div><div class="t m0 x26 h3d y11c ffb fs2 fc0 sc0 lsb0">\u03c1<span class="ffc ls37 ws81">\u2212<span class="ffa lsb7">1<span class="ff8 fs0 lsb8 vd">#</span><span class="ff9 fs1 lsbe v23">\u2212</span><span class="ls37 v24">1</span></span></span></div><div class="t m0 x28 h38 y11d ffb fs2 fc0 sc0 ls37">\u03c1</div><div class="t m0 x72 h3 y119 ff3 fs0 fc0 sc0 ls5e">u<span class="ff5 fs1 ls37 v1">0</span></div><div class="t m0 x16 h3 y11e ff2 fs0 fc0 sc0 ls37 ws6">A fun¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao de disp\u02c6<span class="_5 blank"></span>endio ´<span class="_5 blank"></span>e</div><div class="t m0 x73 h9 y11f ff3 fs0 fc0 sc0 ls37 ws12">e<span class="ff2 ls6">(</span><span class="ls2">p<span class="ff5 fs1 ls3 v1">1</span></span><span class="wsa">, p<span class="ff5 fs1 ls5 v1">2</span>, u<span class="ff5 fs1 ls5 v1">0</span><span class="ff2 wsd">) = </span><span class="ls2">p<span class="ff5 fs1 ls5 v1">1</span><span class="ls4">x</span></span><span class="ff7 fs1 v7">h</span></span></div><div class="t m0 x74 h2b y120 ff5 fs1 fc0 sc0 ls86">1<span class="ff2 fs0 ls7 v8">+<span class="ff3 ls2">p</span></span><span class="ls3 vc">2</span><span class="ff3 fs0 ls4 v8">x</span><span class="ff7 ls37 ve">h</span></div><div class="t m0 x75 hb y120 ff5 fs1 fc0 sc0 ls5c">2<span class="ff3 fs0 ls37 v8">,</span></div><div class="t m0 x16 h3 y121 ff2 fs0 fc0 sc0 ls37 ws3d">onde dev<span class="_3 blank"></span>emos substituir as demandas p<span class="_2 blank"> </span>elos dois b<span class="_2 blank"> </span>ens para obter a express\u02dc<span class="_19 blank"></span>ao \ufb01nal do disp<span class="_3 blank"></span>\u02c6<span class="_b blank"></span>endio,</div><div class="t m0 x16 h3 y122 ff2 fs0 fc0 sc0 ls37 ws6">como fun¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao dos pre¸<span class="_20 blank"></span>cos e do n<span class="_0 blank"></span>´<span class="_c blank"></span>\u0131v<span class="_3 blank"></span>el de utilidade.</div><div class="t m0 x3 h3 y123 ff1 fs0 fc0 sc0 ls37 ws86">Exerc<span class="_0 blank"></span>´<span class="_1 blank"></span>\u0131cio 6:<span class="_24 blank"> </span><span class="ff2 ws70">Resolv<span class="_28 blank"></span>a os seguintes itens para cada uma das fun¸<span class="_b blank"></span>c\u02dc<span class="_5 blank"></span>oes de utilidade elencadas no</span></div><div class="t m0 x3 h3 y124 ff2 fs0 fc0 sc0 ls37 ws6">exerc<span class="_0 blank"></span>´<span class="_c blank"></span>\u0131cio 5 acima.</div><div class="t m0 x31 h3 y125 ff2 fs0 fc0 sc0 ls37 ws6">a)<span class="_17 blank"> </span>V<span class="_e blank"></span>eri\ufb01que se as demandas Hicksianas s\u02dc<span class="_19 blank"></span>ao homog\u02c6<span class="_5 blank"></span>eneas de grau 0 nos pre¸<span class="_1 blank"></span>cos.</div><div class="t m0 x16 h3 y126 ff2 fs0 fc0 sc0 ls37 ws6">S: V<span class="_e blank"></span>amos mostrar para<span class="_16 blank"> </span>o b<span class="_2 blank"> </span>em 1, para o outro b<span class="_2 blank"> </span>em ´<span class="_5 blank"></span>e similar:</div><div class="t m0 x16 h12 y127 ff2 fs0 fc0 sc0 ls37 ws87">a.1)<span class="_17 blank"> </span>(Cobb-Douglas) <span class="ff3 ls4">x</span><span class="ff7 fs1 v9">h</span></div><div class="t m0 x76 h24 y128 ff5 fs1 fc0 sc0 ls5c">1<span class="ff2 fs0 ls6 v8">(<span class="ff3 ls37 ws12">tp</span></span><span class="ls3 vc">1</span><span class="ff3 fs0 ls37 wsa v8">, tp</span><span class="ls3 vc">2</span><span class="ff3 fs0 ls37 wsa v8">, u</span><span class="ls3 vc">0</span><span class="ff2 fs0 ls37 ws58 v8">) = <span class="ff8 lsbf v15">\ue000</span></span><span class="ff7 ls37 ve">\u03b1</span></div><div class="t m0 x41 h25 y129 ff5 fs1 fc0 sc0 ls37 ws2c">1<span class="ff9 ws2e">\u2212<span class="ff7 lsc0">\u03b1</span><span class="ff8 fs0 ws85 v16">\ue001</span></span><span class="v17">1<span class="ff9 ls39">\u2212<span class="ff7 ls82">\u03b1<span class="ff2 fs0 ls6 v18">(<span class="ff3 ls37 ws12">tp</span></span></span></span></span><span class="ls3 v11">1</span><span class="ff2 fs0 ls6 v9">)</span><span class="ff7 ls79 v26">\u03b1</span><span class="ff9 ws2e v26">\u2212</span><span class="ls3 v26">1</span><span class="ff2 fs0 ls6 v9">(<span class="ff3 ls37 ws12">tp</span></span><span class="ls3 v11">2</span><span class="ff2 fs0 ls6 v9">)</span><span class="v26">1<span class="ff9 ws2e">\u2212<span class="ff7 lsc1">\u03b1</span><span class="ff3 fs0 ws12 v27">u</span></span></span><span class="ls46 v11">0</span><span class="ff2 fs0 ls47 v9">=<span class="ff3 ls4">x</span></span><span class="ff7 v26">h</span></div><div class="t m0 x77 h11 y128 ff5 fs1 fc0 sc0 ls5c">1<span class="ff2 fs0 ls37 ws8 v8">(<span class="ff3 ls2">p</span></span><span class="ls3 vc">1</span><span class="ff3 fs0 ls37 wsa v8">, p</span><span class="ls3 vc">2</span><span class="ff3 fs0 ls37 wsa v8">, u</span><span class="ls3 vc">0</span><span class="ff2 fs0 ls37 v8">);</span></div><div class="t m0 x16 h3 y12a ff2 fs0 fc0 sc0 ls37 ws1d">a.2) (Linear)</div><div class="t m0 x78 h9 y12b ff3 fs0 fc0 sc0 ls40">x<span class="ff7 fs1 ls37 v7">h</span></div><div class="t m0 x79 h29 y12c ff5 fs1 fc0 sc0 ls5c">1<span class="ff2 fs0 ls37 ws8 v8">(<span class="ff3 ws12">tp</span></span><span class="ls5 vc">1</span><span class="ff3 fs0 ls37 wsa v8">, tp</span><span class="ls3 vc">2</span><span class="ff3 fs0 ls37 wsa v8">, u</span><span class="ls3 vc">0</span><span class="ff2 fs0 ls37 ws58 v8">) = <span class="ff8 v1c">\uf8f1</span></span></div><div class="t m0 x7a h7 y12d ff8 fs0 fc0 sc0 ls37">\uf8f2</div><div class="t m0 x7a h7 y12e ff8 fs0 fc0 sc0 ls37">\uf8f3</div><div class="t m0 x17 h3 y12f ff3 fs0 fc0 sc0 ls37 ws12">u<span class="ff5 fs1 ls5 v1">0</span><span class="ls8d">,</span><span class="ff2 ws41">se (</span>tp<span class="ff5 fs1 ls3 v1">1</span><span class="ff2 ls6">)</span><span class="ws88">/a < <span class="ff2 ws8">(</span></span>tp<span class="ff5 fs1 ls3 v1">2</span><span class="ff2 ws8">)</span>/b</div><div class="t m0 x17 h3 y130 ff2 fs0 fc0 sc0 ls37 ws6">qq coisa en<span class="_3 blank"></span>tre 0 e <span class="ff3 ws12">u<span class="ff5 fs1 ls3 v1">0</span><span class="lsc2">,</span></span><span class="ws41">se (<span class="ff3 ws12">tp<span class="ff5 fs1 ls3 v1">1</span></span><span class="ls6">)</span><span class="ff3 ws89">/a </span><span class="ws11">= (<span class="ff3 ws12">tp<span class="ff5 fs1 ls3 v1">2</span></span><span class="ws8">)<span class="ff3">/b</span></span></span></span></div><div class="t m0 x17 h41 y131 ff2 fs0 fc0 sc0 ls37 ws8">0<span class="ff3 ls8f">,</span><span class="ws41">se (<span class="ff3 ws12">tp<span class="ff5 fs1 ls3 v1">1</span></span><span class="ls6">)</span><span class="ff3 ws88">/a > </span></span>(<span class="ff3 ws12">tp<span class="ff5 fs1 ls3 v1">2</span></span>)<span class="ff3 ws8a">/b <span class="ff8 v28">\uf8fc</span></span></div><div class="t m0 x7b h7 y12d ff8 fs0 fc0 sc0 ls37">\uf8fd</div><div class="t m0 x7b h7 y12e ff8 fs0 fc0 sc0 ls37">\uf8fe</div><div class="t m0 x7c h9 y12b ff2 fs0 fc0 sc0 ls47">=<span class="ff3 ls4">x<span class="ff7 fs1 ls37 v7">h</span></span></div><div class="t m0 x7d hb y12c ff5 fs1 fc0 sc0 ls5c">1<span class="ff2 fs0 ls37 ws8 v8">(<span class="ff3 ls2">p</span></span><span class="ls5 vc">1</span><span class="ff3 fs0 ls37 wsa v8">, p</span><span class="ls3 vc">2</span><span class="ff3 fs0 ls37 wsa v8">, u</span><span class="ls3 vc">0</span><span class="ff2 fs0 ls37 v8">)</span></div><div class="t m0 x16 hc y132 ff2 fs0 fc0 sc0 ls37 ws8b">a.3)<span class="_17 blank"> </span>(Leon<span class="_3 blank"></span>tief )<span class="_16 blank"> </span><span class="ff3 ls4">x</span><span class="ff7 fs1 v9">h</span></div><div class="t m0 x1e h42 y133 ff5 fs1 fc0 sc0 ls5c">1<span class="ff2 fs0 ls37 ws8 v8">(<span class="ff3 ws12">tp</span></span><span class="ls3 vc">1</span><span class="ff3 fs0 ls37 wsa v8">, tp</span><span class="ls5 vc">2</span><span class="ff3 fs0 ls37 wsa v8">, u</span><span class="ls5 vc">0</span><span class="ff2 fs0 ls37 ws11 v8">) =<span class="_8 blank"> </span></span><span class="ff7 ls37 ws74 ve">u<span class="ffa fs2 va">0</span></span></div><div class="t m0 x36 h43 y134 ff7 fs1 fc0 sc0 lsc3">a<span class="ff2 fs0 ls47 v9">=<span class="ff3 ls4">x</span></span><span class="ls37 v26">h</span></div><div class="t m0 xf h11 y133 ff5 fs1 fc0 sc0 ls5c">1<span class="ff2 fs0 ls37 ws8 v8">(<span class="ff3 ls2">p</span></span><span class="ls5 vc">1</span><span class="ff3 fs0 ls37 wsa v8">, p</span><span class="ls3 vc">2</span><span class="ff3 fs0 ls37 wsa v8">, u</span><span class="ls3 vc">0</span><span class="ff2 fs0 ls37 v8">).</span></div><div class="t m0 x16 hc y135 ff2 fs0 fc0 sc0 ls37 ws8c">a.4)<span class="_17 blank"> </span>(CES) <span class="ff3 ls4">x</span><span class="ff7 fs1 v9">h</span></div><div class="t m0 x7e h44 y136 ff5 fs1 fc0 sc0 ls5c">1<span class="ff2 fs0 ls37 ws8 v8">(<span class="ff3 ws12">tp</span></span><span class="ls3 vc">1</span><span class="ff3 fs0 ls37 wsa v8">, tp</span><span class="ls3 vc">2</span><span class="ff3 fs0 ls37 wsa v8">, u</span><span class="ls5 vc">0</span><span class="ff2 fs0 ls37 wsd v8">) = <span class="ff8 lsc4 vf">\ue014</span><span class="ff3 lsb2">a<span class="ff2 ls7">+</span><span class="lsb3">b<span class="ff8 ls9f v1d">\ue010</span></span></span></span><span class="ff7 ls37 ws74 v26">a</span><span class="ls37 ws2c v26">(<span class="ff7 ws74">tp<span class="ffa fs2 ls8b va">2</span><span class="ff5">)</span></span></span></div><div class="t m0 x30 h45 y137 ff7 fs1 fc0 sc0 ls37 ws74">b<span class="ff5 lsc5">(</span>tp<span class="ffa fs2 ls8b va">1</span><span class="ff5 lsc6">)<span class="ff8 fs0 lsc7 v29">\ue011</span></span><span class="ffb fs2 v2a">\u03c1</span></div><div class="t m0 x6e h3d y138 ffb fs2 fc0 sc0 lsb0">\u03c1<span class="ffc ls37 ws81">\u2212<span class="ffa lsc8">1</span><span class="ff8 fs0 ws85 vd">\ue015</span><span class="ff9 fs1 lsbe v23">\u2212</span><span class="ffa v24">1</span></span></div><div class="t m0 x6d h38 y139 ffb fs2 fc0 sc0 ls37">\u03c1</div><div class="t m0 x6a hc y135 ff3 fs0 fc0 sc0 ls5e">u<span class="ff5 fs1 ls46 v1">0</span><span class="ff2 ls19">=</span><span class="ls40">x<span class="ff7 fs1 ls37 v9">h</span></span></div><div class="t m0 x7f h11 y136 ff5 fs1 fc0 sc0 ls5c">1<span class="ff2 fs0 ls37 ws8 v8">(<span class="ff3 ls2">p</span></span><span class="ls3 vc">1</span><span class="ff3 fs0 ls37 wsa v8">, p</span><span class="ls3 vc">2</span><span class="ff3 fs0 ls37 wsa v8">, u</span><span class="ls3 vc">0</span><span class="ff2 fs0 ls37 v8">)</span></div><div class="t m0 x31 h3 y13a ff2 fs0 fc0 sc0 ls37 ws6">b)<span class="_17 blank"> </span>Cheque a v<span class="_7 blank"></span>alidade do lema de Shephard para o b<span class="_2 blank"> </span>em 1.</div><div class="t m0 x16 h3 y13b ff2 fs0 fc0 sc0 ls37 ws6">S: T<span class="_e blank"></span>emos que:</div><div class="t m0 x16 h46 y13c ff2 fs0 fc0 sc0 ls37 ws8d">b.1) (cobb-Douglas) <span class="ff7 fs1 ws8e v7">\u2202 e</span></div><div class="t m0 x67 h47 y13d ff7 fs1 fc0 sc0 ls37 ws8e">\u2202 p<span class="ffa fs2 lsc9 va">1</span><span class="ff2 fs0 ls47 v9">=<span class="ff3 ls7a">\u03b1</span></span><span class="ff9 ls39 v26">\u2212</span><span class="ls89 v26">\u03b1</span><span class="ff2 fs0 ws8 v9">(1<span class="ff6 ls52">\u2212<span class="ff3 ls7a">\u03b1<span class="ff2 ls6">)</span></span></span></span><span class="ls79 v26">\u03b1</span><span class="ff9 ws2e v26">\u2212<span class="ff5 ls3">1</span></span><span class="ff3 fs0 ws12 v9">\u03b1p</span><span class="ls79 vd">\u03b1<span class="ff9 ls39">\u2212<span class="ff5 ls37">1</span></span></span></div><div class="t m0 x68 h21 y13e ff5 fs1 fc0 sc0 ls75">1<span class="ff3 fs0 ls2 v8">p</span><span class="ls37 ws2c ve">1<span class="ff9 ls39">\u2212<span class="ff7 ls37">\u03b1</span></span></span></div><div class="t m0 x1d h48 y13e ff5 fs1 fc0 sc0 ls75">2<span class="ff3 fs0 ls37 ws12 v8">u</span><span class="ls53 vc">0</span><span class="ff2 fs0 ls19 v8">=<span class="ff8 lsbf v15">\ue000</span></span><span class="ff7 ls37 v2b">\u03b1</span></div><div class="t m0 x6b h25 y13d ff5 fs1 fc0 sc0 ls37 ws2c">1<span class="ff9 ls39">\u2212<span class="ff7 ls80">\u03b1<span class="ff8 fs0 ls81 v16">\ue001</span></span></span><span class="v17">1<span class="ff9 ws2e">\u2212<span class="ff7 ls83">\u03b1<span class="ff3 fs0 ls2 v18">p</span><span class="ls79 v19">\u03b1</span></span><span class="ls39 v19">\u2212</span></span></span><span class="vd">1</span></div><div class="t m0 x57 h21 y13e ff5 fs1 fc0 sc0 ls75">1<span class="ff3 fs0 ls2 v8">p</span><span class="ls37 ws2c v2b">1<span class="ff9 ls39">\u2212<span class="ff7 ls37">\u03b1</span></span></span></div><div class="t m0 x77 h49 y13e ff5 fs1 fc0 sc0 ls75">2<span class="ff3 fs0 ls37 ws12 v8">u</span><span class="ls46 vc">0</span><span class="ff2 fs0 ls47 v8">=<span class="ff3 ls4">x</span></span><span class="ff7 ls37 v2c">h</span></div><div class="t m0 x80 hb y13f ff5 fs1 fc0 sc0 ls5c">1<span class="ff2 fs0 ls37 ws8 v8">(<span class="ff3 ls2">p</span></span><span class="ls5 vc">1</span><span class="ff3 fs0 ls37 wsa v8">, p</span><span class="ls3 vc">2</span><span class="ff3 fs0 ls37 wsa v8">, u</span><span class="ls3 vc">0</span><span class="ff2 fs0 ls37 v8">);</span></div><div class="t m0 x16 h3 y140 ff2 fs0 fc0 sc0 ls37 ws6">b.2)<span class="_17 blank"> </span>(Linear) Neste caso, a fun¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao disp\u02c6<span class="_5 blank"></span>endio n\u02dc<span class="_5 blank"></span>ao ´<span class="_5 blank"></span>e diferenci´<span class="_19 blank"></span>avel;</div><div class="t m0 x29 h3 y30 ff2 fs0 fc0 sc0 ls37">6</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 x81 y141 w7 h4a" alt="" src="https://files.passeidireto.com/ea2b9e07-b8d7-4ddc-8f88-43a3a339476c/bg7.png"><div class="t m0 x16 h4b y1 ff2 fs0 fc0 sc0 ls37 ws8b">b.3)<span class="_17 blank"> </span>(Lenotief )<span class="_2a blank"> </span><span class="ff7 fs1 ws8e v7">\u2202 e</span></div><div class="t m0 x82 h4c y142 ff7 fs1 fc0 sc0 ls37 ws8e">\u2202 p<span class="ffa fs2 lsc9 va">1</span><span class="ff2 fs0 ls43 v9">=</span><span class="ws74 v2d">u</span><span class="ffa fs2 v2b">0</span></div><div class="t m0 x83 h43 y142 ff7 fs1 fc0 sc0 lsca">a<span class="ff2 fs0 ls19 v9">=<span class="ff3 ls4">x</span></span><span class="ls37 v26">h</span></div><div class="t m0 x14 hb y143 ff5 fs1 fc0 sc0 ls5c">1<span class="ff2 fs0 ls6 v8">(<span class="ff3 ls2">p</span></span><span class="ls3 vc">1</span><span class="ff3 fs0 ls37 wsa v8">, p</span><span class="ls5 vc">2</span><span class="ff3 fs0 ls37 wsa v8">, u</span><span class="ls5 vc">0</span><span class="ff2 fs0 ls37 v8">);</span></div><div class="t m0 x16 h4b y144 ff2 fs0 fc0 sc0 ls37 ws8d">b.4) (CES)<span class="_2a blank"> </span><span class="ff7 fs1 ws8e v7">\u2202 e</span></div><div class="t m0 x59 h43 y145 ff7 fs1 fc0 sc0 ls37 ws8e">\u2202 p<span class="ffa fs2 lsc9 va">1</span><span class="ff2 fs0 ls47 v9">=<span class="ff3 ls4">x</span></span><span class="v26">h</span></div><div class="t m0 x56 h11 y146 ff5 fs1 fc0 sc0 ls5c">1<span class="ff2 fs0 ls37 ws8 v8">(<span class="ff3 ls2">p</span></span><span class="ls5 vc">1</span><span class="ff3 fs0 ls37 wsa v8">, p</span><span class="ls3 vc">2</span><span class="ff3 fs0 ls37 wsa v8">, u</span><span class="ls3 vc">0</span><span class="ff2 fs0 ls37 ws6 v8">).<span class="_9 blank"> </span>Neste caso, a con<span class="_3 blank"></span>ta ´<span class="_5 blank"></span>e mais complicada.</span></div><div class="t m0 x31 h3 y147 ff2 fs0 fc0 sc0 ls37 ws19">c)<span class="_17 blank"> </span>Ilustre gra\ufb01camen<span class="_3 blank"></span>te a fun¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>ao disp<span class="_3 blank"></span>\u02c6<span class="_b blank"></span>endio como fun¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao do pre¸<span class="_20 blank"></span>co do b<span class="_2 blank"> </span>em 1, to<span class="_2 blank"> </span>das as outras</div><div class="t m0 x16 h3 y148 ff2 fs0 fc0 sc0 ls37 ws8f">v<span class="_7 blank"></span>ari´<span class="_19 blank"></span>aveis constan<span class="_7 blank"></span>tes.<span class="_18 blank"> </span>In<span class="_3 blank"></span>terprete economicamen<span class="_3 blank"></span>te o formato de cada gr´<span class="_19 blank"></span>a\ufb01co em termos da</div><div class="t m0 x16 h3 y149 ff2 fs0 fc0 sc0 ls37 ws6">p<span class="_2 blank"> </span>ossibilidade de substitui¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao do consumo dos dois b<span class="_2 blank"> </span>ens.</div><div class="t m0 x16 h3 y14a ff2 fs0 fc0 sc0 ls37 ws90">S: V<span class="_e blank"></span>amos denotar as fun¸<span class="_20 blank"></span>c\u02dc<span class="_19 blank"></span>oes disp\u02c6<span class="_5 blank"></span>endios ap<span class="_2 blank"> </span>enas como fun¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao do pre¸<span class="_1 blank"></span>co do b<span class="_2 blank"> </span>em 1,<span class="_1e blank"> </span>a \ufb01m de</div><div class="t m0 x16 h3 y14b ff2 fs0 fc0 sc0 ls37 ws6">ilustrar gra\ufb01camen<span class="_3 blank"></span>te o disp<span class="_3 blank"></span>\u02c6<span class="_b blank"></span>endio como fun¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>ao do pre¸<span class="_1 blank"></span>co deste b<span class="_2 blank"> </span>em.</div><div class="t m0 x84 hc y14c ff2 fs0 fc0 sc0 ls37 ws91">c.1)<span class="_17 blank"> </span>(Cobb-Douglas) <span class="ff3 ws12">e</span><span class="ws8">(<span class="ff3 ls2">p<span class="ff5 fs1 ls5 v1">1</span></span><span class="wsd">) = <span class="ff3 ws92">K p<span class="ff7 fs1 v9">\u03b1</span></span></span></span></div><div class="t m0 x3f h23 y14d ff5 fs1 fc0 sc0 ls74">1<span class="ff2 fs0 ls37 ws93 v8">, onde <span class="ff3 lscb">K<span class="ff2 ls19">=</span><span class="ls88">\u03b1</span></span></span><span class="ff9 ls37 ws2e v2c">\u2212<span class="ff7 ls89">\u03b1</span></span><span class="ff2 fs0 ls37 ws94 v8">(1 <span class="ff6 lscc">\u2212<span class="ff3 ls88">\u03b1<span class="ff2 ls6">)</span></span></span></span><span class="ff7 ls37 ws74 v2c">\u03b1<span class="ff9 ls39">\u2212<span class="ff5 ls3">1<span class="ff3 fs0 ls2 v27">p</span><span class="ls7f v2e">1</span></span><span class="ls37 ws2e v2e">\u2212<span class="ff7">\u03b1</span></span></span></span></div><div class="t m0 x11 h1d y14e ff5 fs1 fc0 sc0 ls75">2<span class="ff3 fs0 ls5e v8">u</span><span class="ls3 vc">0</span><span class="ff2 fs0 ls37 ws11 v8">.<span class="_1e blank"> </span>O formato estritamente</span></div><div class="t m0 x85 h3 y14f ff2 fs0 fc0 sc0 ls37 ws95">c\u02c6<span class="_19 blank"></span>oncav<span class="_7 blank"></span>o da fun¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>ao disp\u02c6<span class="_5 blank"></span>endio indica que o efeito substitui¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>ao en<span class="_3 blank"></span>tre os dois b<span class="_2 blank"> </span>ens n\u02dc<span class="_19 blank"></span>ao</div><div class="t m0 x85 h3 y150 ff2 fs0 fc0 sc0 ls37 ws96">´<span class="_b blank"></span>e n<span class="_3 blank"></span>ulo.<span class="_6 blank"> </span>Se o pre¸<span class="_1 blank"></span>co do b<span class="_2 blank"> </span>em 1 aumentar, p<span class="_2 blank"> </span>or exemplo, o consumidor substituir´<span class="_19 blank"></span>a parte</div><div class="t m0 x85 h3 y151 ff2 fs0 fc0 sc0 ls37 ws7d">do consumo deste b<span class="_2 blank"> </span>em p<span class="_2 blank"> </span>or consumo do outro b<span class="_2 blank"> </span>em, aumentando seu gasto em uma</div><div class="t m0 x85 h3 y152 ff2 fs0 fc0 sc0 ls37 ws97">prop<span class="_2 blank"> </span>or¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao menor do que se n\u02dc<span class="_5 blank"></span>ao alterasse sua escolha de consumo com a m<span class="_3 blank"></span>udan¸<span class="_1 blank"></span>ca do</div><div class="t m0 x85 h3 y153 ff2 fs0 fc0 sc0 ls37 ws8">pre¸<span class="_1 blank"></span>co.</div><div class="t m0 x84 h4d y154 ff2 fs0 fc0 sc0 ls37 ws98">c.2)<span class="_17 blank"> </span>(Linear) <span class="ff3 ws12">e</span><span class="ls6">(<span class="ff3 ls2">p<span class="ff5 fs1 ls3 v1">1</span></span></span><span class="ws99">)<span class="_1f blank"> </span>=<span class="_1f blank"> </span>min <span class="ff8 lscd v15">\ue008</span><span class="ff7 fs1 ls4c v2f">p</span><span class="ffa fs2 v9">1</span></span></div><div class="t m0 x2a h4e y155 ff7 fs1 fc0 sc0 lsce">a<span class="ff3 fs0 ls92 v9">,</span><span class="ls37 ws74 vd">p<span class="ffa fs2 va">2</span></span></div><div class="t m0 x35 h4f y155 ff7 fs1 fc0 sc0 lscf">b<span class="ff8 fs0 lsd0 v16">\ue009<span class="ff3 ls5e v30">u</span></span><span class="ff5 ls3 v11">0</span><span class="ff2 fs0 ls37 ws9a v9">.<span class="_1e blank"> </span>O formato da fun¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>ao disp<span class="_3 blank"></span>\u02c6<span class="_b blank"></span>endio indica uma quebra.<span class="_1e blank"> </span>Se</span></div><div class="t m0 x85 h3 y156 ff2 fs0 fc0 sc0 ls37 ws9b">o pre¸<span class="_1 blank"></span>co do b<span class="_2 blank"> </span>em 1 se altera den<span class="_3 blank"></span>tro da regi\u02dc<span class="_19 blank"></span>ao de pre¸<span class="_1 blank"></span>cos onde o b<span class="_2 blank"> </span>em contin<span class="_7 blank"></span>ua relativ<span class="_7 blank"></span>amente</div><div class="t m0 x85 h3 y157 ff2 fs0 fc0 sc0 ls37 ws9c">mais barato do que o b<span class="_2 blank"> </span>em 2 (<span class="ff3 ls2">p<span class="ff5 fs1 ls3 v1">1</span><span class="ls37 ws9d">/a < p<span class="ff5 fs1 ls5 v1">2</span><span class="ws12">/b</span></span></span>), ent\u02dc<span class="_19 blank"></span>ao o aumen<span class="_3 blank"></span>to do disp<span class="_3 blank"></span>\u02c6<span class="_b blank"></span>endio ´<span class="_5 blank"></span>e linear e</div><div class="t m0 x85 h3 y158 ff2 fs0 fc0 sc0 ls37 ws9e">n\u02dc<span class="_19 blank"></span>ao h´<span class="_5 blank"></span>a nenhuma substitui¸<span class="_b blank"></span>c\u02dc<span class="_5 blank"></span>ao de consumo - o indiv<span class="_0 blank"></span>´<span class="_c blank"></span>\u0131duo contin<span class="_7 blank"></span>ua consumindo ap<span class="_2 blank"> </span>enas o</div><div class="t m0 x85 h3 y159 ff2 fs0 fc0 sc0 ls37 ws3">b em<span class="_16 blank"> </span>1.<span class="_f blank"> </span>Por<span class="_7 blank"></span>´<span class="_b blank"></span>em,<span class="_1c blank"> </span>se<span class="_16 blank"> </span><span class="ff3 ls4a">p<span class="ff5 fs1 ls3 v1">1</span><span class="ls37 ws9f">/a </span></span><span class="ws24">for maior do que <span class="ff3 ls2">p<span class="ff5 fs1 ls3 v1">2</span><span class="ls37 ws12">/b</span></span>, ent\u02dc<span class="_19 blank"></span>ao aumentos subsequen<span class="_7 blank"></span>tes de pre¸<span class="_1 blank"></span>cos</span></div><div class="t m0 x85 h3 y15a ff2 fs0 fc0 sc0 ls37 ws5f">deste b<span class="_2 blank"> </span>em n\u02dc<span class="_19 blank"></span>ao afetar\u02dc<span class="_5 blank"></span>ao a fun¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>ao disp<span class="_3 blank"></span>\u02c6<span class="_b blank"></span>endio, j´<span class="_5 blank"></span>a que se <span class="ff3 ls2">p<span class="ff5 fs1 ls3 v1">1</span><span class="ls37 wsa0">/a > p<span class="ff5 fs1 ls3 v1">2</span><span class="wsa1">/b </span></span></span>en<span class="_3 blank"></span>t\u02dc<span class="_19 blank"></span>ao o consumidor</div><div class="t m0 x85 h3 y15b ff2 fs0 fc0 sc0 ls37 ws6">est´<span class="_19 blank"></span>a consumindo ap<span class="_2 blank"> </span>enas o b<span class="_2 blank"> </span>em 2.</div><div class="t m0 x81 h50 y15c ffd fs3 fc0 sc0 ls37">6</div><div class="t m0 x86 h50 y15d ffd fs3 fc0 sc0 ls37">-</div><div class="t m0 x87 h51 y15e ffe fs4 fc0 sc0 ls37">Gasto</div><div class="t m0 x30 h52 y15f fff fs4 fc0 sc0 lsd1">p<span class="ff5 fs1 ls37 v1">1</span></div><div class="t m0 x32 h53 y160 fff fs4 fc0 sc0 lsd2">e<span class="ffe ls37 wsa2">(</span><span class="lsd1">p<span class="ff5 fs1 ls3 v1">1</span><span class="ffe ls37 wsa3">) = </span><span class="ls37 wsa4">K p<span class="ff7 fs1 v31">\u03b1</span></span></span></div><div class="t m0 x4c h8 y161 ff5 fs1 fc0 sc0 ls37">1</div><div class="t m0 x88 h51 y162 ffe fs4 fc0 sc0 ls37 wsa5">item a</div><div class="t m0 x2f h50 y15c ffd fs3 fc0 sc0 ls37">6</div><div class="t m0 x89 h50 y15d ffd fs3 fc0 sc0 ls37">-</div><div class="t m0 x51 h51 y15e ffe fs4 fc0 sc0 ls37">Gasto</div><div class="t m0 x8a h52 y15f fff fs4 fc0 sc0 lsd1">p<span class="ff5 fs1 ls37 v1">1</span></div><div class="t m0 x2f h54 y15d ffd fs3 fc0 sc0 ls37 wsa6">\ue00a<span class="v24">\ue00a<span class="v24">\ue00a<span class="v24">\ue00a<span class="v24">\ue00a<span class="v24">\ue00a<span class="v24">\ue00a</span></span></span></span></span></span><span class="v32">\ue00a</span></div><div class="t m0 x8b h50 y163 ffd fs3 fc0 sc0 ls37">\ue00a</div><div class="t m0 x5f h55 y164 fff fs4 fc0 sc0 ls37 wsa7">e<span class="ffe lsd3">(</span><span class="lsd1">p<span class="ff5 fs1 ls3 v1">1</span></span><span class="ffe wsa8">) = min<span class="_14 blank"> </span><span class="ff8 lsd4 v2d">\ue008</span><span class="ff7 fs1 ls4c v7">p</span><span class="ffa fs2 v31">1</span></span></div><div class="t m0 x8c h56 y165 ff7 fs1 fc0 sc0 lsd5">a<span class="fff fs4 lsd6 v31">,</span><span class="ls4c v26">p</span><span class="ffa fs2 ls37 v2b">2</span></div><div class="t m0 x8d h57 y165 ff7 fs1 fc0 sc0 lsd7">b<span class="ff8 fs4 lsd8 v12">\ue009<span class="fff ls37 wsa7 vb">u</span></span><span class="ff5 ls37 v11">0</span></div><div class="t m0 x8e h50 y166 ffd fs3 fc0 sc0 ls37">\ue000</div><div class="t m0 x5f h50 y167 ffd fs3 fc0 sc0 ls37 wsa6">\ue000<span class="_2b blank"></span>\ue012</div><div class="t m0 x8f h51 y162 ffe fs4 fc0 sc0 ls37 wsa5">item b</div><div class="t m0 x63 h58 y168 ff10 fs3 fc0 sc0 ls37">r</div><div class="t m0 x90 h6 y169 ff7 fs1 fc0 sc0 ls37 ws74">p<span class="ffa fs2 va">2</span></div><div class="t m0 x63 h6 y16a ff7 fs1 fc0 sc0 ls37">b</div><div class="t m0 x84 h59 y16b ff2 fs0 fc0 sc0 ls37 ws8b">c.3)<span class="_17 blank"> </span>(Leon<span class="_3 blank"></span>tief )<span class="_1e blank"> </span><span class="ff3 ls85">e</span><span class="ws8">(<span class="ff3 ls2">p<span class="ff5 fs1 ls3 v1">1</span></span><span class="ws68">) = <span class="ff3 ws12">Ap<span class="ff5 fs1 ls7b v1">1</span></span><span class="lsd9">+<span class="ff3 lsda">B</span></span><span class="wsa9">,<span class="_9 blank"> </span>onde <span class="ff3 lsdb">A</span><span class="lsdc">=</span><span class="ff7 fs1 ws74 v7">u</span><span class="ffa fs2 v33">0</span></span></span></span></div><div class="t m0 x42 h4e y16c ff7 fs1 fc0 sc0 lsdd">a<span class="ff2 fs0 lsde v31">e<span class="ff3 lsdf">B<span class="ff2 lsdc">=</span></span></span><span class="ls4c vd">p</span><span class="ffa fs2 ls37 v2">2</span></div><div class="t m0 x7f h5a y16c ff7 fs1 fc0 sc0 lsd7">b<span class="ff3 fs0 ls5e v31">u</span><span class="ff5 ls3 v11">0</span><span class="ff2 fs0 ls37 wsaa v31">.<span class="_26 blank"> </span>O formato linear da fun¸<span class="_20 blank"></span>c\u02dc<span class="_19 blank"></span>ao</span></div><div class="t m0 x85 h3 y16d ff2 fs0 fc0 sc0 ls37 wsab">disp<span class="_3 blank"></span>\u02c6<span class="_b blank"></span>endio indica que n\u02dc<span class="_19 blank"></span>ao existe p<span class="_2 blank"> </span>ossibilidade de substitui¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>ao entre os dois bens (efeito</div><div class="t m0 x85 h3 y16e ff2 fs0 fc0 sc0 ls37 ws83">substitui¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao nulo).<span class="_4 blank"> </span>Se o pre¸<span class="_1 blank"></span>co do b<span class="_2 blank"> </span>em 1 aumentar, por exemplo,<span class="_8 blank"> </span>o disp\u02c6<span class="_5 blank"></span>endio m<span class="_e blank"></span>´<span class="_c blank"></span>\u0131nimo</div><div class="t m0 x85 h3 y16f ff2 fs0 fc0 sc0 ls37 ws4d">necess´<span class="_19 blank"></span>ario para se alcan¸<span class="_1 blank"></span>car determinado n<span class="_e blank"></span>´<span class="_c blank"></span>\u0131v<span class="_3 blank"></span>el de utilidade aumen<span class="_3 blank"></span>tar´<span class="_19 blank"></span>a na mesma pro-</div><div class="t m0 x85 h3 y170 ff2 fs0 fc0 sc0 ls37 ws3">p or¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao.</div><div class="t m0 x84 hc y171 ff2 fs0 fc0 sc0 ls37 wsac">c.4)<span class="_17 blank"> </span>(CES) P<span class="_3 blank"></span>o<span class="_2 blank"> </span>demos escrev<span class="_3 blank"></span>er <span class="ff3 ws12">e</span><span class="ls6">(<span class="ff3 ls2">p<span class="ff5 fs1 ls3 v1">1</span></span></span><span class="wsad">) = <span class="ff3 lse0">f</span><span class="ls6">(<span class="ff3 ls2">p<span class="ff5 fs1 ls3 v1">1</span></span></span></span>) e mostrar que <span class="ff3 lse0">f<span class="ff9 fs1 lse1 v9">0</span></span><span class="ws8">(<span class="ff3 ls2">p<span class="ff5 fs1 ls3 v1">1</span></span><span class="lse2">)<span class="ff3 lse3">></span></span><span class="wsae">0 e <span class="ff3 lse0">f</span><span class="ff9 fs1 wsaf v9">00 </span><span class="ls6">(<span class="ff3 ls2">p<span class="ff5 fs1 ls3 v1">1</span></span><span class="lse2">)<span class="ff3 lse3"><</span></span></span><span class="wsb0">0. Logo,</span></span></span></div><div class="t m0 x85 h3 y172 ff2 fs0 fc0 sc0 ls37 ws16">a fun¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao disp\u02c6<span class="_5 blank"></span>endio ´<span class="_5 blank"></span>e estritamente c\u02c6<span class="_19 blank"></span>onca<span class="_3 blank"></span>v<span class="_7 blank"></span>a, indicando que o efeito substitui¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>ao en<span class="_3 blank"></span>tre os</div><div class="t m0 x85 h3 y173 ff2 fs0 fc0 sc0 ls37 ws6">dois b<span class="_2 blank"> </span>ens n\u02dc<span class="_19 blank"></span>ao ´<span class="_5 blank"></span>e n<span class="_3 blank"></span>ulo (similar ao item a) acima).</div><div class="t m0 x29 h3 y30 ff2 fs0 fc0 sc0 ls37">7</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf8" class="pf w0 h0" data-page-no="8"><div class="pc pc8 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x81 y174 w8 h5b" alt="" src="https://files.passeidireto.com/ea2b9e07-b8d7-4ddc-8f88-43a3a339476c/bg8.png"><div class="t m0 x81 h50 y175 ffd fs3 fc0 sc0 ls37">6</div><div class="t m0 x86 h50 y176 ffd fs3 fc0 sc0 ls37">-</div><div class="t m0 x87 h51 y177 ffe fs4 fc0 sc0 ls37">Gasto</div><div class="t m0 x30 h52 y178 fff fs4 fc0 sc0 lsd1">p<span class="ff5 fs1 ls37 v1">1</span></div><div class="t m0 x81 h5c y176 ffd fs3 fc0 sc0 ls98">\ue000<span class="ls37 wsa6 v24">\ue000</span><span class="v34">\ue000<span class="v24">\ue000</span></span><span class="ls37 wsa6 v35">\ue000</span><span class="v36">\ue000<span class="v24">\ue000</span></span><span class="ls37 wsa6 v32">\ue000</span><span class="v37">\ue000</span><span class="ls37 v38">\ue000</span></div><div class="t m0 xd h50 y179 ffd fs3 fc0 sc0 ls37">\ue000</div><div class="t m0 x91 h51 y17a fff fs4 fc0 sc0 lsd2">e<span class="ffe ls37 wsa2">(</span><span class="lsd1">p<span class="ff5 fs1 ls3 v1">1</span><span class="ffe ls37 wsa3">) = </span><span class="ls37 wsa7">Ap<span class="ff5 fs1 lse4 v1">1</span><span class="ffe lse5">+</span>B</span></span></div><div class="t m0 x88 h51 y17b ffe fs4 fc0 sc0 ls37 wsa5">item c</div><div class="t m0 x2f h50 y175 ffd fs3 fc0 sc0 ls37">6</div><div class="t m0 x89 h50 y176 ffd fs3 fc0 sc0 ls37">-</div><div class="t m0 x51 h51 y177 ffe fs4 fc0 sc0 ls37">Gasto</div><div class="t m0 x8a h52 y178 fff fs4 fc0 sc0 lsd1">p<span class="ff5 fs1 ls37 v1">1</span></div><div class="t m0 x92 h51 y17c fff fs4 fc0 sc0 lsd2">e<span class="ffe ls37 wsa2">(</span><span class="lsd1">p<span class="ff5 fs1 ls3 v1">1</span><span class="ffe ls37 wsa3">) = </span><span class="lse6">f<span class="ffe ls37 wsa2">(</span></span>p<span class="ff5 fs1 ls3 v1">1</span><span class="ffe ls37">)</span></span></div><div class="t m0 x8f h51 y17b ffe fs4 fc0 sc0 ls37 wsa5">item d</div><div class="t m0 x3 h3 y17d ff1 fs0 fc0 sc0 ls37 wsb1">Exerc<span class="_0 blank"></span>´<span class="_1 blank"></span>\u0131cio 7:<span class="_d blank"> </span><span class="ff2 wsb2">Suponha que os<span class="_2c blank"> </span>´<span class="_19 blank"></span>unicos bens que Renata consome s\u02dc<span class="_5 blank"></span>ao guaran´<span class="_5 blank"></span>a e p\u02dc<span class="_19 blank"></span>ao e que as</span></div><div class="t m0 x3 h3 y17e ff2 fs0 fc0 sc0 ls37 ws6">prefer<span class="_3 blank"></span>\u02c6<span class="_b blank"></span>encias de Renata s\u02dc<span class="_19 blank"></span>ao estritamente con<span class="_3 blank"></span>v<span class="_3 blank"></span>exas.</div><div class="t m0 x31 h3 y17f ff2 fs0 fc0 sc0 ls37 wsb3">a)<span class="_17 blank"> </span>En<span class="_3 blank"></span>tre janeiro e fev<span class="_3 blank"></span>ereiro,<span class="_17 blank"> </span>o pre¸<span class="_1 blank"></span>co do guaran´<span class="_19 blank"></span>a sob<span class="_2 blank"> </span>e (e nada mais muda).<span class="_1a blank"> </span>Ilustre em um</div><div class="t m0 x16 h3 y180 ff2 fs0 fc0 sc0 ls37 wsb4">mesmo gr´<span class="_19 blank"></span>a\ufb01co as escolhas ´<span class="_5 blank"></span>otimas de Renata nos dois meses (denote p<span class="_2 blank"> </span>or <span class="ff3 lse7">J</span><span class="ws27">a escolha ´<span class="_19 blank"></span>otima</span></div><div class="t m0 x16 h3 y181 ff2 fs0 fc0 sc0 ls37 wsb5">em Janeiro e p<span class="_2 blank"> </span>or <span class="ff3 lse8">F</span>a escolha ´<span class="_19 blank"></span>otima em fevereiro), represen<span class="_7 blank"></span>tando o consumo de p\u02dc<span class="_5 blank"></span>ao no eixo</div><div class="t m0 x16 h3 y182 ff2 fs0 fc0 sc0 ls37 wsb6">v<span class="_3 blank"></span>ertical e o consumo do guaran´<span class="_19 blank"></span>a no eixo horizontal (man<span class="_7 blank"></span>tenha essa conv<span class="_7 blank"></span>en¸<span class="_20 blank"></span>c\u02dc<span class="_19 blank"></span>ao para o resto</div><div class="t m0 x16 h3 y183 ff2 fs0 fc0 sc0 ls37 ws6">do exerc<span class="_0 blank"></span>´<span class="_c blank"></span>\u0131cio).</div><div class="t m0 x16 h3 y184 ff2 fs0 fc0 sc0 ls37 wsb7">S: Como ap<span class="_2 blank"> </span>enas o pre¸<span class="_1 blank"></span>co do guaran´<span class="_19 blank"></span>a mudou, a reta or¸<span class="_1 blank"></span>camen<span class="_3 blank"></span>t´<span class="_19 blank"></span>aria se altera,<span class="_1e blank"> </span>e a escolha do</div><div class="t m0 x16 h3 y185 ff2 fs0 fc0 sc0 ls37 ws6">consumidor se altera, conforme mostra a \ufb01gura abaixo.</div><div class="t m0 x3a h50 y186 ffd fs3 fc0 sc0 ls37">6</div><div class="t m0 x27 h50 y187 ffd fs3 fc0 sc0 ls37">-</div><div class="t m0 x67 h51 y188 ffe fs4 fc0 sc0 ls37 wsa2">P\u02dc<span class="_b blank"></span>ao</div><div class="t m0 x28 h51 y189 ffe fs4 fc0 sc0 ls37 wsa2">Guaran´<span class="_b blank"></span>a</div><div class="t m0 xd h6 y18a ff7 fs1 fc0 sc0 ls37">m</div><div class="t m0 xd h6 y18b ff7 fs1 fc0 sc0 ls4c">p<span class="ffa fs2 ls37 va">2</span></div><div class="t m0 x26 h6 y18c ff7 fs1 fc0 sc0 ls37">m</div><div class="t m0 x26 h6 y18d ff7 fs1 fc0 sc0 ls37 ws74">p<span class="ffa fs2 va">1</span></div><div class="t m0 x3a h50 y18e ffd fs3 fc0 sc0 ls98">Q<span class="v39">Q</span><span class="ls37 wsa6 v3a">Q</span><span class="v3b">Q<span class="v39">Q</span></span><span class="ls37 wsa6 v3c">Q</span><span class="v3d">Q<span class="v39">Q</span></span><span class="ls37 wsa6 v3e">Q</span><span class="v3f">Q<span class="v39">Q</span></span><span class="ls37 wsa6 v40">Q</span><span class="v41">Q</span><span class="ls37 wsa6 v42">Q</span><span class="v43">Q<span class="v39">Q</span></span><span class="ls37 wsa6 v44">Q</span><span class="v45">Q</span><span class="ls37 v46">Q</span></div><div class="t m0 x93 h50 y18f ffd fs3 fc0 sc0 ls37">Q</div><div class="t m0 x68 h6 y18c ff7 fs1 fc0 sc0 ls37">m</div><div class="t m0 x68 h6 y18d ff7 fs1 fc0 sc0 ls37 ws74">p<span class="ffa fs2 va">1</span></div><div class="t m0 x3a h50 y190 ffd fs3 fc0 sc0 lse9">S<span class="v47">S<span class="v47">S<span class="v47">S<span class="v47">S<span class="v47">S<span class="v47">S<span class="v47">S<span class="v47">S<span class="v47">S<span class="v47">S<span class="v47">S</span></span></span></span></span></span></span></span></span></span></span><span class="ls37 v46">S</span></div><div class="t m0 x1b h50 y191 ffd fs3 fc0 sc0 ls37">S</div><div class="t m0 x36 h58 y192 ff10 fs3 fc0 sc0 ls37">q</div><div class="t m0 x36 h52 y193 fff fs4 fc0 sc0 lsea">F<span class="ff10 fs3 ls37 v9">q</span></div><div class="t m0 x4c h52 y194 fff fs4 fc0 sc0 ls37">J</div><div class="t m0 x94 h50 y195 ffd fs3 fc0 sc0 ls37">\ue000</div><div class="t m0 x30 h50 y196 ffd fs3 fc0 sc0 ls37 wsa6">\ue000<span class="_2b blank"></span>\ue009</div><div class="t m0 x4b h50 y197 ffd fs3 fc0 sc0 ls37">\ue011</div><div class="t m0 x48 h50 y198 ffd fs3 fc0 sc0 ls37">\ue011</div><div class="t m0 x29 h50 y199 ffd fs3 fc0 sc0 ls37 wsa6">\ue011<span class="_2b blank"></span>+</div><div class="t m0 x31 h3 y19a ff2 fs0 fc0 sc0 ls37 wsb4">b)<span class="_17 blank"> </span>Em mar¸<span class="_1 blank"></span>co, o pre¸<span class="_1 blank"></span>co do guaran´<span class="_5 blank"></span>a v<span class="_3 blank"></span>olta ao mesmo n<span class="_e blank"></span>´<span class="_c blank"></span>\u0131v<span class="_7 blank"></span>el de janeiro,<span class="_8 blank"> </span>p<span class="_2 blank"> </span>or<span class="_3 blank"></span>´<span class="_5 blank"></span>em a renda de Renata</div><div class="t m0 x16 h3 y19b ff2 fs0 fc0 sc0 ls37 wsb8">dimin<span class="_3 blank"></span>ui em um mon<span class="_3 blank"></span>tan<span class="_3 blank"></span>te tal que agora ela alcan¸<span class="_1 blank"></span>ca o mesmo b<span class="_2 blank"> </span>em-estar de fev<span class="_3 blank"></span>ereiro.<span class="_9 blank"> </span>Ilustre</div><div class="t m0 x16 h3 y19c ff2 fs0 fc0 sc0 ls37 ws3c">a escolha ´<span class="_19 blank"></span>otima de Renata em mar¸<span class="_1 blank"></span>co (denote<span class="_16 blank"> </span>essa escolha ´<span class="_19 blank"></span>otima p<span class="_2 blank"> </span>or <span class="ff3 lseb">M</span>) jun<span class="_3 blank"></span>tamente com as</div><div class="t m0 x16 h3 y19d ff2 fs0 fc0 sc0 ls37 ws6">outras duas escolhas ´<span class="_19 blank"></span>otimas de Renata.</div><div class="t m0 x16 h3 y19e ff2 fs0 fc0 sc0 ls37 wsb9">S: O p<span class="_2 blank"> </span>on<span class="_3 blank"></span>to c<span class="_3 blank"></span>ha<span class="_3 blank"></span>v<span class="_3 blank"></span>e ´<span class="_5 blank"></span>e que a dimin<span class="_3 blank"></span>ui¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>ao da renda de Renata em mar¸<span class="_1 blank"></span>co<span class="_16 blank"> </span>´<span class="_b blank"></span>e tal que ela mant<span class="_7 blank"></span>´<span class="_b blank"></span>em</div><div class="t m0 x16 h3 y19f ff2 fs0 fc0 sc0 ls37 wsba">a mesma utilidade que obtev<span class="_3 blank"></span>e em fev<span class="_3 blank"></span>ereiro.<span class="_2d blank"> </span>P<span class="_3 blank"></span>ortan<span class="_3 blank"></span>to,<span class="_17 blank"> </span>as escolhas ´<span class="_5 blank"></span>otimas representadas</div><div class="t m0 x16 h3 y1a0 ff2 fs0 fc0 sc0 ls37 ws3">p elos<span class="_16 blank"> </span>p on<span class="_3 blank"></span>tos<span class="_16 blank"> </span><span class="ff3 lsec">F</span><span class="lsed">e<span class="ff3 lsee">M</span></span><span class="wsbb">est\u02dc<span class="_19 blank"></span>ao sobre a mesma curv<span class="_7 blank"></span>a de indiferen¸<span class="_20 blank"></span>ca.<span class="_9 blank"> </span>A \ufb01gura abaixo ilustra essa</span></div><div class="t m0 x16 h3 y1a1 ff2 fs0 fc0 sc0 ls37 ws8">situa¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao.</div><div class="t m0 x29 h3 y30 ff2 fs0 fc0 sc0 ls37">8</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf9" class="pf w0 h0" data-page-no="9"><div class="pc pc9 w0 h0"><img fetchpriority="low" loading="lazy" class="bi xd y1a2 w9 h5d" alt="" src="https://files.passeidireto.com/ea2b9e07-b8d7-4ddc-8f88-43a3a339476c/bg9.png"><div class="t m0 x3a h50 y1a3 ffd fs3 fc0 sc0 ls37">6</div><div class="t m0 x27 h50 y1a4 ffd fs3 fc0 sc0 ls37">-</div><div class="t m0 x67 h51 y1a5 ffe fs4 fc0 sc0 ls37 wsa2">P\u02dc<span class="_b blank"></span>ao</div><div class="t m0 x28 h51 y1a6 ffe fs4 fc0 sc0 ls37 wsa2">Guaran´<span class="_b blank"></span>a</div><div class="t m0 xd h6 y1a7 ff7 fs1 fc0 sc0 ls37">m</div><div class="t m0 xd h6 y1a8 ff7 fs1 fc0 sc0 ls4c">p<span class="ffa fs2 ls37 va">2</span></div><div class="t m0 x26 h6 y1a9 ff7 fs1 fc0 sc0 ls37">m</div><div class="t m0 x26 h6 y1aa ff7 fs1 fc0 sc0 ls37 ws74">p<span class="ffa fs2 va">1</span></div><div class="t m0 x3a h50 y1ab ffd fs3 fc0 sc0 ls98">Q<span class="v39">Q</span><span class="ls37 wsa6 v3a">Q</span><span class="v3b">Q<span class="v39">Q</span></span><span class="ls37 wsa6 v3c">Q</span><span class="v3d">Q<span class="v39">Q</span></span><span class="ls37 wsa6 v3e">Q</span><span class="v3f">Q<span class="v39">Q</span></span><span class="ls37 wsa6 v40">Q</span><span class="v41">Q</span><span class="ls37 wsa6 v42">Q</span><span class="v43">Q<span class="v39">Q</span></span><span class="ls37 wsa6 v44">Q</span><span class="v45">Q</span><span class="ls37 v46">Q</span></div><div class="t m0 x93 h50 y1ac ffd fs3 fc0 sc0 ls37">Q</div><div class="t m0 x68 h6 y1a9 ff7 fs1 fc0 sc0 ls37">m</div><div class="t m0 x68 h6 y1aa ff7 fs1 fc0 sc0 ls37 ws74">p<span class="ffa fs2 va">1</span></div><div class="t m0 x3a h50 y1ad ffd fs3 fc0 sc0 lse9">S<span class="v47">S<span class="v47">S<span class="v47">S<span class="v47">S<span class="v47">S<span class="v47">S<span class="v47">S<span class="v47">S<span class="v47">S<span class="v47">S<span class="v47">S</span></span></span></span></span></span></span></span></span></span></span><span class="ls37 v46">S</span></div><div class="t m0 x1b h50 y1ae ffd fs3 fc0 sc0 ls37">S</div><div class="t m0 x36 h58 y1af ff10 fs3 fc0 sc0 ls37">q</div><div class="t m0 x36 h52 y1b0 fff fs4 fc0 sc0 lsea">F<span class="ff10 fs3 ls37 v9">q</span></div><div class="t m0 x4c h52 y1b1 fff fs4 fc0 sc0 ls37">J</div><div class="t m0 x17 h50 y1b2 ffd fs3 fc0 sc0 ls37 wsa6">Q<span class="ls98 v39">Q<span class="v39">Q</span></span><span class="v3b">Q</span><span class="ls98 v48">Q<span class="v39">Q</span></span><span class="v3d">Q</span><span class="ls98 v49">Q</span><span class="v3e">Q</span><span class="ls98 v3f">Q</span><span class="v4a">Q</span></div><div class="t m0 x95 h50 y1b3 ffd fs3 fc0 sc0 ls37">Q</div><div class="t m0 x25 h58 y1b4 ff10 fs3 fc0 sc0 ls37">q</div><div class="t m0 x94 h52 y1b5 fff fs4 fc0 sc0 ls37">M</div><div class="t m0 x31 h3 y1b6 ff2 fs0 fc0 sc0 ls37 ws6">c)<span class="_17 blank"> </span>Analise os seguin<span class="_3 blank"></span>tes itens, dizendo sob quais condi¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>oes ser\u02dc<span class="_19 blank"></span>ao verdadeiros.</div><div class="t m0 x84 h3 y1b7 ff2 fs0 fc0 sc0 ls37 wsbc">c.1) <span class="ff3 lsef">J</span><span class="wse">est´<span class="_19 blank"></span>a `<span class="_5 blank"></span>a esquerda de <span class="ff3 lsf0">F</span>.</span></div><div class="t m0 x85 h3 y1b8 ff2 fs0 fc0 sc0 ls37 ws6">S: Ocorre se guaran´<span class="_19 blank"></span>a ´<span class="_5 blank"></span>e um b<span class="_2 blank"> </span>em de Gi\ufb00en.</div><div class="t m0 x84 h3 y1b9 ff2 fs0 fc0 sc0 ls37 wsbc">c.2) <span class="ff3 lsf1">F</span><span class="wse">est´<span class="_19 blank"></span>a `<span class="_5 blank"></span>a esquerda de <span class="ff3 lseb">M</span>.</span></div><div class="t m0 x85 h3 y1ba ff2 fs0 fc0 sc0 ls37 wse">S: Sempre v<span class="_3 blank"></span>erdadeiro.<span class="_9 blank"> </span>Essa mud<span class="_3 blank"></span>an¸<span class="_1 blank"></span>ca ´<span class="_5 blank"></span>e um efeito substitui¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>ao, que sempre<span class="_a blank"> </span>´<span class="_b blank"></span>e negativ<span class="_3 blank"></span>o.</div><div class="t m0 x84 h3 y1bb ff2 fs0 fc0 sc0 ls37 wsbc">c.3) <span class="ff3 lsef">J</span><span class="wse">est´<span class="_19 blank"></span>a `<span class="_5 blank"></span>a esquerda de <span class="ff3 lseb">M</span>.</span></div><div class="t m0 x85 h3 y1bc ff2 fs0 fc0 sc0 ls37 ws6">S: Ocorre se guaran´<span class="_19 blank"></span>a ´<span class="_5 blank"></span>e um b<span class="_2 blank"> </span>em inferior.</div><div class="t m0 x31 h3 y1bd ff2 fs0 fc0 sc0 ls37 wsbd">d)<span class="_17 blank"> </span>Justi\ufb01que a a\ufb01rma¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao <span class="ff4 ws5">\u201cT<span class="_7 blank"></span>o<span class="_7 blank"></span>do o b<span class="_7 blank"></span>em de Gi\ufb00en ´<span class="_19 blank"></span>e um b<span class="_7 blank"></span>em inferior\u201d<span class="_f blank"> </span><span class="ff2 wsbd">em termos do que v<span class="_3 blank"></span>o<span class="_2 blank"> </span>c<span class="_3 blank"></span>\u02c6<span class="_b blank"></span>e</span></span></div><div class="t m0 x16 h3 y1be ff2 fs0 fc0 sc0 ls37 ws6">fez nesse exerc<span class="_0 blank"></span>´<span class="_c blank"></span>\u0131cio, n\u02dc<span class="_5 blank"></span>ao recorra `<span class="_19 blank"></span>a teoria vista em sala.</div><div class="t m0 x16 h3 y1bf ff2 fs0 fc0 sc0 ls37 wsbe">S: P<span class="_3 blank"></span>elas \ufb01guras e itens acima,<span class="_17 blank"> </span>se guaran´<span class="_19 blank"></span>a ´<span class="_5 blank"></span>e um b<span class="_2 blank"> </span>em de Gi\ufb00en,<span class="_17 blank"> </span>en<span class="_3 blank"></span>t\u02dc<span class="_19 blank"></span>ao o p<span class="_2 blank"> </span>onto <span class="ff3 lsf2">J</span>est´<span class="_19 blank"></span>a `<span class="_19 blank"></span>a</div><div class="t m0 x16 h3 y1c0 ff2 fs0 fc0 sc0 ls37 wsbf">esquerda de <span class="ff3 lsf3">F</span>.<span class="_2c blank"> </span>Como o p<span class="_2 blank"> </span>onto <span class="ff3 lsf4">F</span><span class="wsc0">est´<span class="_19 blank"></span>a sempre `<span class="_19 blank"></span>a esquerda de <span class="ff3 lsf5">M</span><span class="wsbf">, ent\u02dc<span class="_19 blank"></span>ao quando guaran´<span class="_5 blank"></span>a for</span></span></div><div class="t m0 x16 h3 y1c1 ff2 fs0 fc0 sc0 ls37 ws90">um b<span class="_2 blank"> </span>em de Gi\ufb00en o p<span class="_2 blank"> </span>on<span class="_7 blank"></span>to <span class="ff3 lsf6">J</span>necessariamente estar´<span class="_19 blank"></span>a `<span class="_5 blank"></span>a esquerda de <span class="ff3 lseb">M</span><span class="ws36">,<span class="_8 blank"> </span>ou<span class="_8 blank"> </span>seja,<span class="_1e blank"> </span>guaran´<span class="_5 blank"></span>a ´<span class="_b blank"></span>e</span></div><div class="t m0 x16 h3 y1c2 ff2 fs0 fc0 sc0 ls37 ws2f">um<span class="_16 blank"> </span>b em<span class="_16 blank"> </span>inferior.</div><div class="t m0 x3 h3 y1c3 ff1 fs0 fc0 sc0 ls37 wsc1">Exerc<span class="_0 blank"></span>´<span class="_1 blank"></span>\u0131cio 8:<span class="_6 blank"> </span><span class="ff2 wsc2">A utilidade de Carlos ´<span class="_5 blank"></span>e dada p<span class="_2 blank"> </span>or <span class="ff3 ls5e">u</span><span class="ws8">(<span class="ff3 ls4">x<span class="ff5 fs1 ls5 v1">1</span><span class="ls37 wsa">, x<span class="ff5 fs1 ls3 v1">2</span></span></span><span class="wsc3">) = min<span class="ff6 ws32">{<span class="ff3 ls40">x<span class="ff5 fs1 ls3 v1">1</span><span class="ls37 wsa">, x<span class="ff5 fs1 ls3 v1">2</span></span></span><span class="ls98">}</span></span></span></span>.<span class="_18 blank"> </span>A renda de Carlos ´<span class="_5 blank"></span>e</span></div><div class="t m0 x3 h3 y1c4 ff2 fs0 fc0 sc0 ls37 ws5f">R$20, e os pre¸<span class="_1 blank"></span>cos dos b<span class="_2 blank"> </span>ens 1 e 2 s\u02dc<span class="_19 blank"></span>ao R$1 e R$1.<span class="_17 blank"> </span>Sup<span class="_2 blank"> </span>onha que o pre¸<span class="_1 blank"></span>co do b<span class="_2 blank"> </span>em 1 aumen<span class="_3 blank"></span>tou para</div><div class="t m0 x3 h3 y1c5 ff2 fs0 fc0 sc0 ls37">R$2.</div><div class="t m0 x31 h3 y1c6 ff2 fs0 fc0 sc0 ls37 ws6">a)<span class="_17 blank"> </span>Encon<span class="_3 blank"></span>tre o efeito total desse aumen<span class="_3 blank"></span>to na demanda de Carlos p<span class="_2 blank"> </span>elo b<span class="_2 blank"> </span>em 1.</div><div class="t m0 x16 hc y1c7 ff2 fs0 fc0 sc0 ls37 wsc4">S: Aos pre¸<span class="_1 blank"></span>cos an<span class="_3 blank"></span>tigos,<span class="_17 blank"> </span>a demanda de Carlos era <span class="ff3 ls4">x</span><span class="ff7 fs1 v9">M</span></div><div class="t m0 x96 h5e y1c8 ff5 fs1 fc0 sc0 lsf7">1<span class="ff2 fs0 lsf8 v8">=<span class="ff3 ls4">x</span></span><span class="ff7 ls37 v2c">M</span></div><div class="t m0 x97 h11 y1c8 ff5 fs1 fc0 sc0 lsf9">2<span class="ff2 fs0 ls37 wsc4 v8">=<span class="_17 blank"> </span>10.<span class="_2d blank"> </span>Aos no<span class="_3 blank"></span>v<span class="_3 blank"></span>os pre¸<span class="_1 blank"></span>cos,<span class="_17 blank"> </span>a</span></div><div class="t m0 x16 hc y1c9 ff2 fs0 fc0 sc0 ls37 ws66">demanda de Carlos se mo<span class="_2 blank"> </span>di\ufb01ca para<span class="_8 blank"> </span>\u02c6<span class="_23 blank"></span><span class="ff3 ls4">x<span class="ff7 fs1 ls37 v9">M</span></span></div><div class="t m0 x19 h5f y1ca ff5 fs1 fc0 sc0 lsfa">1<span class="ff2 fs0 ls37 wsc5 v8">= \u02c6<span class="_23 blank"></span><span class="ff3 ls4">x<span class="ff7 fs1 ls37 v9">M</span></span></span></div><div class="t m0 x98 h60 y1cb ff5 fs1 fc0 sc0 lsfa">2<span class="ff2 fs0 ls43 v8">=</span><span class="ls37 v2b">20</span></div><div class="t m0 x74 h14 y1cc ff5 fs1 fc0 sc0 lsfb">3<span class="ff2 fs0 ls37 ws66 v31">.<span class="_9 blank"> </span>O efeito total do aumen<span class="_3 blank"></span>to do pre¸<span class="_1 blank"></span>co do</span></div><div class="t m0 x16 h61 y1cd ff2 fs0 fc0 sc0 ls37 wse">b<span class="_2 blank"> </span>em na demanda por esse b<span class="_2 blank"> </span>em ´<span class="_5 blank"></span>e uma redu¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>ao de consumo igual 10<span class="_10 blank"> </span><span class="ff6 lsfc">\u2212</span><span class="ff5 fs1 v7">20</span></div><div class="t m0 x77 h5a y1ce ff5 fs1 fc0 sc0 lsfd">3<span class="ff6 fs0 ls4e v31">\u2248<span class="ff2 ls37 ws8">3<span class="ff3 ls2d">,</span>33</span></span></div><div class="t m0 x31 h3 y1cf ff2 fs0 fc0 sc0 ls37 ws23">b)<span class="_17 blank"> </span>Decomp<span class="_2 blank"> </span>onha o efeito total em efeito substitui¸<span class="_b blank"></span>c\u02dc<span class="_5 blank"></span>ao Hicksiano e efeito renda.<span class="_f blank"> </span>In<span class="_3 blank"></span>terprete in<span class="_3 blank"></span>tu-</div><div class="t m0 x16 h3 y1d0 ff2 fs0 fc0 sc0 ls37 ws6">itiv<span class="_7 blank"></span>amen<span class="_3 blank"></span>te o seu resultado.</div><div class="t m0 x16 h3 y1d1 ff2 fs0 fc0 sc0 ls37 wsb5">S: Na utilidade de Leon<span class="_3 blank"></span>tief, os b<span class="_2 blank"> </span>ens s\u02dc<span class="_19 blank"></span>ao complementares perfeitos - n\u02dc<span class="_5 blank"></span>ao existe p<span class="_2 blank"> </span>ossibilidade</div><div class="t m0 x16 h3 y1d2 ff2 fs0 fc0 sc0 ls37 wsb6">de substitui¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao entre os dois bens<span class="_1c blank"> </span>(note que o efeito total na demanda do b<span class="_2 blank"> </span>em 2 devido ao</div><div class="t m0 x16 h3 y1d3 ff2 fs0 fc0 sc0 ls37 wsc6">aumen<span class="_3 blank"></span>to do pre¸<span class="_1 blank"></span>co do b<span class="_2 blank"> </span>em 1<span class="_1f blank"> </span>´<span class="_b blank"></span>e tamb<span class="_7 blank"></span>´<span class="_b blank"></span>em igual a 3,33).<span class="_9 blank"> </span>Portan<span class="_7 blank"></span>to, o efeito substitui¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>ao ´<span class="_5 blank"></span>e zero e</div><div class="t m0 x16 h3 y1d4 ff2 fs0 fc0 sc0 ls37 ws6">to<span class="_2 blank"> </span>do o efeito<span class="_a blank"> </span>´<span class="_b blank"></span>e efeito renda.<span class="_9 blank"> </span>O gr´<span class="_5 blank"></span>a\ufb01co abaixo ilustra essa situa¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao.</div><div class="t m0 x29 h3 y30 ff2 fs0 fc0 sc0 ls37">9</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pfa" class="pf w0 h0" data-page-no="a"><div class="pc pca w0 h0"><img fetchpriority="low" loading="lazy" class="bi x4 y1d5 wa h62" alt="" src="https://files.passeidireto.com/ea2b9e07-b8d7-4ddc-8f88-43a3a339476c/bga.png"><div class="t m0 x67 h50 y1d6 ffd fs3 fc0 sc0 ls37">6</div><div class="t m0 x99 h50 y1d7 ffd fs3 fc0 sc0 ls37">-</div><div class="t m0 x6 h52 y1d8 fff fs4 fc0 sc0 lsfe">x<span class="ff5 fs1 ls37 v1">2</span></div><div class="t m0 x9a h52 y1d9 fff fs4 fc0 sc0 lsfe">x<span class="ff5 fs1 ls37 v1">1</span></div><div class="t m0 x4 h6 y1da ff7 fs1 fc0 sc0 ls37">m</div><div class="t m0 x4 h6 y1db ff7 fs1 fc0 sc0 ls4c">p<span class="ffa fs2 ls37 va">2</span></div><div class="t m0 x67 h50 y1dc ffd fs3 fc0 sc0 ls98">@<span class="ls37 wsa6 v47">@</span><span class="v3b">@<span class="v47">@</span></span><span class="ls37 wsa6 v3d">@</span><span class="v4b">@<span class="v47">@</span></span><span class="ls37 wsa6 v4c">@</span><span class="v41">@</span><span class="ls37 wsa6 v4d">@</span><span class="v4e">@<span class="v47">@</span></span><span class="ls37 wsa6 v46">@</span><span class="v4f">@<span class="v47">@</span></span><span class="ls37 wsa6 v50">@<span class="v47">@</span></span></div><div class="t m0 x9b h50 y1dd ffd fs3 fc0 sc0 ls37">@</div><div class="t m0 x19 h58 y1de ff10 fs3 fc0 sc0 ls37">s</div><div class="t m0 x18 h52 y1df fff fs4 fc0 sc0 ls37">E</div><div class="t m0 x67 h50 y1dc ffd fs3 fc0 sc0 ls37 wsa6">A<span class="lsff v47">A</span><span class="v3b">A<span class="v47">A</span></span><span class="lsff v3d">A</span><span class="v4b">A<span class="v47">A</span></span><span class="lsff v4c">A</span><span class="v41">A<span class="v47">A</span></span><span class="lsff v4e">A</span><span class="v51">A<span class="v47">A</span></span><span class="lsff v4f">A</span><span class="v52">A<span class="v47">A</span></span><span class="v53">A</span></div><div class="t m0 x9 h50 y1dd ffd fs3 fc0 sc0 ls37">A</div><div class="t m0 x9c h58 y1e0 ff10 fs3 fc0 sc0 ls37">s</div><div class="t m0 x5a h51 y1e1 ffe fs4 fc0 sc0 ls37">\u02c6</div><div class="t m0 x3d h52 y1e2 fff fs4 fc0 sc0 ls37">E</div><div class="t m0 x53 h50 y1dc ffd fs3 fc0 sc0 ls37 wsa6">A<span class="lsff v47">A</span><span class="v3b">A<span class="v47">A</span></span><span class="lsff v3d">A</span><span class="v4b">A<span class="v47">A</span></span><span class="lsff v4c">A</span><span class="v41">A<span class="v47">A</span></span><span class="lsff v4e">A</span><span class="v51">A<span class="v47">A</span></span><span class="lsff v4f">A</span><span class="v52">A</span><span class="v50">A</span></div><div class="t m0 x98 h50 y1e3 ffd fs3 fc0 sc0 ls37">A</div><div class="t m0 x40 h50 y1e4 ffd fs3 fc0 sc0 ls37">\ue000</div><div class="t m0 x9d h50 y1e5 ffd fs3 fc0 sc0 ls37">\ue000</div><div class="t m0 x9d h50 y1e6 ffd fs3 fc0 sc0 ls37 wsa6">\ue000<span class="_2b blank"></span>\ue009</div><div class="t m0 x9e h51 y1e7 ffe fs4 fc0 sc0 ls37 wsa5">Pre¸<span class="_20 blank"></span>co do b<span class="_2 blank"> </span>em 1 aumen<span class="_3 blank"></span>tou</div><div class="t m0 x9e h51 y1e8 ffe fs4 fc0 sc0 ls37 wsa5">Efeito Substitui¸<span class="_20 blank"></span>c\u02dc<span class="_b blank"></span>ao ´<span class="_1 blank"></span>e n<span class="_3 blank"></span>ulo</div><div class="t m0 x9e h51 y1e9 ffe fs4 fc0 sc0 ls37 wsa5">Efeito T<span class="_28 blank"></span>otal = Efeito Renda</div><div class="t m0 x31 h3 y1ea ff2 fs0 fc0 sc0 ls37 wsc7">c) Decomp<span class="_2 blank"> </span>onha o efeito total em efeito substitui¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao de Slutsky e efeito renda.<span class="_2e blank"> </span>In<span class="_3 blank"></span>terprete</div><div class="t m0 x16 h3 y1eb ff2 fs0 fc0 sc0 ls37 ws6">in<span class="_3 blank"></span>tuitiv<span class="_7 blank"></span>amen<span class="_3 blank"></span>te o seu resultado.</div><div class="t m0 x16 h3 y1ec ff2 fs0 fc0 sc0 ls37 ws3e">S: P<span class="_3 blank"></span>ara o caso de Slutsky<span class="_28 blank"></span>, a comp<span class="_2 blank"> </span>ensa¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao ´<span class="_5 blank"></span>e feita de mo<span class="_2 blank"> </span>do que o consumidor p<span class="_2 blank"> </span>ossa comprar</div><div class="t m0 x16 h3 y1ed ff2 fs0 fc0 sc0 ls37 wsae">a mesma cesta que compra<span class="_3 blank"></span>v<span class="_7 blank"></span>a aos pre¸<span class="_1 blank"></span>cos antigos, mas agora aos pre¸<span class="_b blank"></span>cos nov<span class="_7 blank"></span>os.<span class="_6 blank"> </span>P<span class="_3 blank"></span>ortan<span class="_3 blank"></span>to, o</div><div class="t m0 x16 h3 y1ee ff2 fs0 fc0 sc0 ls37 ws6">efeito substitui¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao de Slutsky v<span class="_7 blank"></span>ai tamb<span class="_3 blank"></span>´<span class="_5 blank"></span>em ser zero e o efeito total ´<span class="_5 blank"></span>e to<span class="_2 blank"> </span>do efeito renda.</div><div class="t m0 x3 h3 y1ef ff1 fs0 fc0 sc0 ls37 wsc8">Exerc<span class="_0 blank"></span>´<span class="_1 blank"></span>\u0131cio 9:<span class="_17 blank"> </span><span class="ff2 wsc9">No exerc<span class="_0 blank"></span>´<span class="_c blank"></span>\u0131cio 1 vimos que a utilidade de Maria<span class="_16 blank"> </span>´<span class="_5 blank"></span>e dada p<span class="_2 blank"> </span>or <span class="ff3 ws12">u</span><span class="ws8">(<span class="ff3 ls4">x<span class="ff5 fs1 ls5 v1">1</span><span class="ls37 wsa">, x<span class="ff5 fs1 ls3 v1">2</span></span></span><span class="wsca">) = ln(<span class="ff3 ls4">x<span class="ff5 fs1 ls3 v1">1</span></span><span class="wscb">) + <span class="ff3 ls4">x<span class="ff5 fs1 ls3 v1">2</span></span>.</span></span></span></span></div><div class="t m0 x3 h3 y1f0 ff2 fs0 fc0 sc0 ls37 ws6">Sup<span class="_2 blank"> </span>onha que a renda de Maria<span class="_a blank"> </span>´<span class="_5 blank"></span>e R$40, e os pre¸<span class="_1 blank"></span>cos dos b<span class="_2 blank"> </span>ens 1 e 2 s\u02dc<span class="_5 blank"></span>ao R$ 1 e R$ 1.<span class="_9 blank"> </span>Sup<span class="_2 blank"> </span>onha que</div><div class="t m0 x3 h3 y1f1 ff2 fs0 fc0 sc0 ls37 wscc">o pre¸<span class="_1 blank"></span>co do b<span class="_2 blank"> </span>em 1 aumen<span class="_3 blank"></span>tou para R$ 2.<span class="_24 blank"> </span>Encon<span class="_3 blank"></span>tre o efeito total desse aumento na demanda de</div><div class="t m0 x3 h3 y1f2 ff2 fs0 fc0 sc0 ls37 ws62">Maria p<span class="_2 blank"> </span>elo b<span class="_2 blank"> </span>em 1 e pelo b<span class="_2 blank"> </span>em 2.<span class="_2c blank"> </span>Decomp<span class="_2 blank"> </span>onha esses dois efeitos em efeito substitui¸<span class="_1 blank"></span>c\u02dc<span class="_19 blank"></span>ao Hicksiano</div><div class="t m0 x3 h3 y1f3 ff2 fs0 fc0 sc0 ls37 ws6">e efeito renda.<span class="_9 blank"> </span>In<span class="_3 blank"></span>terprete intuitiv<span class="_28 blank"></span>amente o seu resultado.</div><div class="t m0 x3 h3 y1f4 ff2 fs0 fc0 sc0 ls37 ws6">S: Vimos em aula que as demandas geradas p<span class="_2 blank"> </span>or uma utilidade quase-linear ln<span class="_14 blank"> </span><span class="ff3 ls4">x<span class="ff5 fs1 ls16 v1">1</span></span><span class="ls7">+<span class="ff3 ls4">x<span class="ff5 fs1 ls100 v1">2</span></span></span><span class="ws8">s\u02dc<span class="_5 blank"></span>ao:</span></div><div class="t m0 x9f h9 y1f5 ff3 fs0 fc0 sc0 ls4">x<span class="ff7 fs1 ls37 v7">M</span></div><div class="t m0 xd h3e y1f6 ff5 fs1 fc0 sc0 ls45">1<span class="ff2 fs0 ls37 ws8 v8">(<span class="ff3 ls2">p</span></span><span class="ls5 vc">1</span><span class="ff3 fs0 ls37 wsa v8">, p</span><span class="ls3 vc">2</span><span class="ff3 fs0 ls37 wsa v8">, m<span class="ff2 ws41">) = <span class="ff8 ls101 vf">\ue01a</span><span class="ff3 ls2 v2c">p</span></span></span><span class="ls3 v26">2</span><span class="ff3 fs0 ls37 ws12 v54">/p</span><span class="ls102 v26">1</span><span class="ff2 fs0 ls37 ws77 v54">se <span class="ff3 ls2">p</span></span><span class="ls46 v26">2</span><span class="ff6 fs0 ls4e v54">\u2264<span class="ff3 ls37">m</span></span></div><div class="t m0 x1b h3 y1f7 ff3 fs0 fc0 sc0 ls37 ws12">m/p<span class="ff5 fs1 ls103 v1">1</span><span class="ff2 ws77">se </span><span class="ls2">p<span class="ff5 fs1 ls46 v1">2</span></span><span class="ws40">> m</span></div><div class="t m0 x9f h9 y1f8 ff3 fs0 fc0 sc0 ls4">x<span class="ff7 fs1 ls37 v7">M</span></div><div class="t m0 xd h3e y1f9 ff5 fs1 fc0 sc0 ls45">2<span class="ff2 fs0 ls37 ws8 v8">(<span class="ff3 ls2">p</span></span><span class="ls5 vc">1</span><span class="ff3 fs0 ls37 wsa v8">, p</span><span class="ls3 vc">2</span><span class="ff3 fs0 ls37 wsa v8">, m<span class="ff2 ws41">) = <span class="ff8 ls101 vf">\ue01a</span><span class="ff3 ws12 v2c">m/p</span></span></span><span class="ls16 v26">2</span><span class="ff6 fs0 ls42 v54">\u2212<span class="ff2 ls37 ws41">1 se <span class="ff3 ls4a">p</span></span></span><span class="ls46 v26">2</span><span class="ff6 fs0 ls4e v54">\u2264<span class="ff3 ls37">m</span></span></div><div class="t m0 x1b h3 y1fa ff2 fs0 fc0 sc0 ls37 wscd">0<span class="_2f blank"> </span>se <span class="ff3 ls4a">p<span class="ff5 fs1 ls46 v1">2</span><span class="ls37 ws40">> m</span></span></div><div class="t m0 x3 h12 y1fb ff2 fs0 fc0 sc0 ls37 wsce">Substituindo os v<span class="_7 blank"></span>alores de <span class="ff3 ls4a">p<span class="ff5 fs1 ls3 v1">1</span><span class="ls37 wsa">, p<span class="ff5 fs1 ls104 v1">2</span></span></span><span class="ls105">e</span><span class="ff3 ws12">m</span><span class="wscf">, obtemos que <span class="ff3 ls4">x</span><span class="ff7 fs1 v9">M</span></span></div><div class="t m0 x4f h5e y1fc ff5 fs1 fc0 sc0 ls45">1<span class="ff2 fs0 ls37 ws8 v8">(1<span class="ff3 ls2d">,</span>1<span class="ff3 ls2d">,</span><span class="ws6a">40) = 1 e <span class="ff3 ls4">x</span><span class="ff7 fs1 v9">M</span></span></span></div><div class="t m0 x13 hb y1fc ff5 fs1 fc0 sc0 ls45">2<span class="ff2 fs0 ls37 ws8 v8">(1<span class="ff3 ls2d">,</span>1<span class="ff3 ls2d">,</span><span class="ws6a">40) = 39.<span class="_9 blank"> </span>Aos no<span class="_3 blank"></span>v<span class="_3 blank"></span>os</span></span></div><div class="t m0 x3 hc y1fd ff2 fs0 fc0 sc0 ls37 wsd0">pre¸<span class="_1 blank"></span>cos, as demandas dos dois b<span class="_2 blank"> </span>ens s\u02dc<span class="_5 blank"></span>ao<span class="_f blank"> </span>\u02c6<span class="_23 blank"></span><span class="ff3 ls4">x<span class="ff7 fs1 ls37 v9">M</span></span></div><div class="t m0 x86 h5e y1fe ff5 fs1 fc0 sc0 ls45">1<span class="ff2 fs0 ls37 ws8 v8">(2<span class="ff3 ls2d">,</span>1<span class="ff3 ls2d">,</span><span class="wsd1">40) = 0<span class="ff3 ls2d">,</span><span class="wsd0">5 e<span class="_f blank"> </span>\u02c6<span class="_23 blank"></span><span class="ff3 ls4">x<span class="ff7 fs1 ls37 v9">M</span></span></span></span></span></div><div class="t m0 x6b h11 y1fe ff5 fs1 fc0 sc0 ls45">2<span class="ff2 fs0 ls37 ws8 v8">(1<span class="ff3 ls106">,</span>1<span class="ff3 ls2d">,</span><span class="wsd1">40) = 39<span class="ff3 ls2d">,</span><span class="wsd0">5.<span class="_24 blank"> </span>O efeito total</span></span></span></div><div class="t m0 x3 h3 y1ff ff2 fs0 fc0 sc0 ls37 ws6">desta m<span class="_3 blank"></span>udan¸<span class="_1 blank"></span>ca de pre¸<span class="_1 blank"></span>cos ´<span class="_5 blank"></span>e:</div><div class="t m0 x5a h3 y200 ff2 fs0 fc0 sc0 ls37 ws8">\u2206<span class="ff3 ls4">x<span class="ff5 fs1 ls102 v1">1</span></span><span class="wsd2">= \u02c6<span class="_23 blank"></span><span class="ff3 ls4">x<span class="ff5 fs1 ls16 v1">1</span><span class="ff6 ls42">\u2212</span>x<span class="ff5 fs1 ls46 v1">1</span><span class="ff2 ls47">=<span class="ff6 ls37 ws32">\u2212<span class="ff2 ws8">0</span></span></span><span class="ls2d">,<span class="ff2 ls37">5</span></span></span></span></div><div class="t m0 x5a h3 y201 ff2 fs0 fc0 sc0 ls37 ws8">\u2206<span class="ff3 ls4">x<span class="ff5 fs1 ls102 v1">2</span></span><span class="wsd2">= \u02c6<span class="_23 blank"></span><span class="ff3 ls4">x<span class="ff5 fs1 ls16 v1">2</span><span class="ff6 ls42">\u2212</span>x<span class="ff5 fs1 ls46 v1">2</span><span class="ff2 ls37 ws11">= 0</span><span class="ls2d">,<span class="ff2 ls37">5</span></span></span></span></div><div class="t m0 x3 h3 y202 ff2 fs0 fc0 sc0 ls37 wsd3">Neste caso, o efeito renda ´<span class="_5 blank"></span>e n<span class="_3 blank"></span>ulo, to<span class="_2 blank"> </span>do o efeito da mudan¸<span class="_b blank"></span>ca de pre¸<span class="_1 blank"></span>cos ´<span class="_5 blank"></span>e efeito substitui¸<span class="_1 blank"></span>c\u02dc<span class="_5 blank"></span>ao.<span class="_4 blank"> </span>Isso</div><div class="t m0 x3 h3 y203 ff2 fs0 fc0 sc0 ls37 wsd4">´<span class="_b blank"></span>e in<span class="_3 blank"></span>tuitiv<span class="_7 blank"></span>amen<span class="_3 blank"></span>te esp<span class="_2 blank"> </span>erado:<span class="_f blank"> </span>a demanda do b<span class="_2 blank"> </span>em 1 n\u02dc<span class="_19 blank"></span>ao dep<span class="_2 blank"> </span>ende da renda, uma mudan¸<span class="_b blank"></span>ca de pre¸<span class="_1 blank"></span>cos</div><div class="t m0 x3 h3 y204 ff2 fs0 fc0 sc0 ls37 ws6">altera sua demanda ap<span class="_2 blank"> </span>enas p<span class="_2 blank"> </span>elo efeito substitui¸<span class="_b blank"></span>c\u02dc<span class="_5 blank"></span>ao, j´<span class="_5 blank"></span>a que n\u02dc<span class="_5 blank"></span>ao existe efeito renda.</div><div class="t m0 xa0 h3 y30 ff2 fs0 fc0 sc0 ls37">10</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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