{"id":1467,"date":"2021-07-13T21:07:56","date_gmt":"2021-07-13T19:07:56","guid":{"rendered":"https:\/\/interactivemicroeconomics.com\/?page_id=1467"},"modified":"2021-07-16T10:04:54","modified_gmt":"2021-07-16T08:04:54","slug":"estatica-comparativa","status":"publish","type":"page","link":"https:\/\/interactivemicroeconomics.com\/index.php\/es\/ejemplos\/estatica-comparativa\/","title":{"rendered":"Est\u00e1tica comparativa"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"1467\" class=\"elementor elementor-1467\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5e242f6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5e242f6\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-a205048\" data-id=\"a205048\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-fd2ce23 elementor-widget elementor-widget-html\" data-id=\"fd2ce23\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t <style>\n \n .botondef {\n\t\tborder: none;\n\t\tbackground-color:transparent;\n\t\tpadding: 3px;\n\t\tfont-family:inherit;\n\t\tfont-size:inherit;\n\t\tfont-weight:bolder;\n\t\ttext-decoration: none;\n\t\tcolor: blue;\n\t\tcursor: pointer;\n\t\t}\n\t\t\n     .mostrar{\n\tpadding: 5px;\n\tbackground: lightblue;\n\twidth: 120px;\n\tborder-radius:6px;\n\tcursor: pointer;\n\tmargin-top: 10px;\n\tmargin-bottom: 10px;\n\tbox-shadow: 2px 2px 5px #000;\n\tdisplay: inline-block;\n\tfont-size: 12pt;\n\tcolor: black;\n\tfont-weight: 100;\n}\n@media screen and (max-width: 750px) {\n  .mostrar {\n   font-size: 10pt;\n  }\n}\n.textomath{\n\tdisplay: none; 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\n<\/script>\n<h2>Est\u00e1tica comparativa<\/h2>\n<div class=\"texto\">\n<p>Generalmente un ejercicio de est\u00e1tica comparativa consiste en observar c\u00f3mo cambia la soluci\u00f3n de un problema en respuesta a un cambio en alguno de los datos.<\/p>\n<p>La curva de demanda relaciona el precio de un bien con la cantidad que los consumidores demandan. Pero hay otras variables que tambi\u00e9n pueden influir en la decisi\u00f3n del consumidor. Por ejemplo, piensa en un bien  $x$ para el que existe otro bien, $y$, que es un sustituto cercano. La demanda de  $x$ depender\u00e1 de su precio, pero tambi\u00e9n del precio del otro bien.  As\u00ed tenemos que la demanda de $x$ es funci\u00f3n de ambos precios \\[x_d=x_d(p_x,p_y)\\] <\/p>\n      <p>\n\u00bfC\u00f3mo depender\u00e1  $x_d$ de $p_x$? <span class=\"sol\"  data-tooltip-content=\"#tip1\" >Sol.<\/span>\n<div class=\"tooltip_templates\">\n<span id=\"tip1\" style=\"maxWidth=400;\" >\nCuanto m\u00e1s alto sea el precio menor ser\u00e1 la cantidad demandada.\n<\/span><\/div>\u00bfY c\u00f3mo depender\u00e1 la demanda de $x$ de $p_y$? <span class=\"sol\"  data-tooltip-content=\"#tip2\" >Sol.<\/span>\n<div class=\"tooltip_templates\">\n<span id=\"tip2\" style=\"maxWidth=400;\" >\nComo $x$ e $y$ son sustitutivos, si $y$ se encarece podemos esperar que la demanda del bien $x$ aumente, incluso aunque su propio precio no haya variado.\n    \n<\/span><\/div>\n<p><button class=\"mostrar\"  id=\"ButSh1\" onclick=\"divMostrar('cuadro1'); divMostrarOno('ButSh1') \">Ver mates <\/button><\/p>\n\n<div class=\"textomath\" id=\"cuadro1\">\n<p>Podemos usar esto utilizando derivadas parciales.\n\\[ \\frac{\\partial x_d(p_x, p_y)}{\\partial p_x} < 0 \\]\n        significa que a mayor $p_x$, menor ser\u00e1 la demanda de bien $x$.<\/p>\n    <p>Y, siendo sustitutivos,\n    \\[ \\frac{\\partial x_d(p_x, p_y)}{\\partial p_x} > 0 \\]\n    cuanto mayor sea $p_y$, mayor ser\u00e1 la demanda de $x$.<\/p>\n    \n<\/div>\n\n\n    <p>Propongamos la siguiente cuesti\u00f3n de est\u00e1tica comparativa: \u00bfC\u00f3mo afectar\u00e1 al precio de equilibrio del bien $x$ un aumento de $p_y$ ?<\/p>\n    \n    \n    <p>Si tenemos unos datos concretos podr\u00edamos calcular el equilibrio inicial y el final, y compararlos. 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+3]], {strokeColor:'black',strokeWidth:1, \n\tstraightFirst:false, straightLast:false});\nvar qstarlabel = figura.create('text',[qopt,-7,'q*'], {fontSize: 11});\t\n\nvar tickpstar = figura.create('line',[[-2.5, popt], [2.5, popt]], {strokeColor:'black',strokeWidth:1, \n\tstraightFirst:false, straightLast:false});\nvar pstarlabel = figura.create('text',[-10, popt,'p*'], {fontSize: 11});\t\n\n\n\n\t\nvar demlabel = 0;\n\nvar demanda = figura.create('functiongraph', [function(x){return a1.Value()-b1.Value()*x+ 20;},0,100], {strokeColor:'blue',strokeWidth:2,  withLabel: true, name:'Demand curve', label:{color:'blue', visible:function(){ return (demlabel<0.5)? false : true ;}}});\n\ndemanda.on('down', function(){return demlabel<0.5 ? demlabel=1: demlabel=0});\n\n\n\nvar oferlabel = 0;\n\nvar oferta = figura.create('functiongraph', [function(x){return c1.Value() + d1.Value() * x;},0,100], { strokeColor:'orange', strokeWidth:2, name:'Curva de oferta', withLabel: true , label:{color:'orange', 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color:\"red\", showInfobox:false, withLabel: true, name:\"equilibrium\", label:{visible:function(){ return (equilabel<0.5)? false : true ;}} });\nequilibrio.on('down', function(){ if(equilabel<0.5) { equilabel=1; demlabel=0; oferlabel=0;} else {equilabel=0; demlabel=0; oferlabel=0;};\nreturn equilabel});\n\nvar li = figura.create('line',[equilibrio,[qopt, 0]], {strokeColor:'gray',strokeWidth:1, straightFirst:false, straightLast:false,dash:2});\nvar li2 = figura.create('line',[equilibrio,[0, popt]], {strokeColor:'gray',strokeWidth:1, straightFirst:false, straightLast:false,dash:2});\n\n\t\n\n\n\nfigura.create('polygon', [[0, 100], [0,150], [150,150], [150,100]], { layer:8, borders: { visible:false, color:'black'},vertices: {visible: false, fixed:true}, color:'white', highlight:false, opacity:1});\n\nfigura.create('polygon', [[0, 0], [110,0], [110,-20], [0,-20]], { layer:8, borders: { visible:false, color:'black'},vertices: {visible: false, fixed:true}, color:'white', highlight:false, opacity:1});\n\n\n\n<\/script>\n<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-1433d5b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1433d5b\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-9c13980\" data-id=\"9c13980\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-51fd151 elementor-widget elementor-widget-html\" data-id=\"51fd151\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"texto\">\n    \n    <p>La curva de demanda inicial corresponde a un precio $p_y^o$ del bien sustitutivo. \u00bfQu\u00e9 ocurre si este precio,  $p_y$, cambia?<\/p>\n    <p>La figura te permite proponer una  <a class=\"botondef\"  href=\"\/index.php\/ejemplos\/estatica-comparativa\/def-variacion\/\"> variaci\u00f3n<\/a> de $p_y$. Un valor positivo, $\\Delta p_y>0$, significa un aumento del precio (si $\\Delta p_y<0$ estamos ante una bajada).<\/p>\n        <ul>\n    <li>Antes de mover $\\Delta p_y$, \u00bfpuedes anticipar qu\u00e9 ocurrir\u00e1 con la curva de demanda en la figura? <span class=\"sol\"  data-tooltip-content=\"#tip3\" >Sol.<\/span>\n<div class=\"tooltip_templates\">\n<span id=\"tip3\" style=\"maxWidth=400;\" >\nRecuerda que $x$ e $y$ son sustitutos uno del otro. Una subida de  $p_y$ aumentar\u00e1 la demanda de $x$ para cualquier valor de $p_x$. Por tanto aparecer\u00e1 una nueva curva de demanda, m\u00e1s a la derecha que la inicial.\n<\/span><\/div> Usa el deslizador para comprobar.\n\n            <\/li>\n    \n    <li>\u00bfAfectar\u00e1 la subida de $p_y$ al equilibrio de mercado del bien $x$? \u00bfC\u00f3mo? <span class=\"sol\"  data-tooltip-content=\"#tip4\" >Sol.<\/span>\n<div class=\"tooltip_templates\">\n<span id=\"tip4\" style=\"maxWidth=400;\" >\nEl nuevo equilibrio, $(x',p')$, ser\u00e1 el punto de corte de la nueva curva de demanda con la  <span class=\"tooltip\"  data-tooltip-content=\"#tip5\" >curva de oferta.<\/span><span class=\"tooltip_templates\"><span id=\"tip5\" style=\"maxWidth=400;\" >\nLa curva de oferta no variar\u00e1.\n<\/span><\/span>\n\n<\/span><\/div>\n\n            <\/li>\n      <li>\u00bfC\u00f3mo afecta el incremento de $p_y$ al precio de equilibrio del bien $x$? \u00bfY c\u00f3mo afecta a la cantidad intercambiada? <span class=\"sol\"  data-tooltip-content=\"#tip6\" >Sol.<\/span>\n<div class=\"tooltip_templates\">\n<span id=\"tip6\" style=\"maxWidth=400;\" >\nEl nuevo precio de equilibrio es mayor que el inicial. Incluso as\u00ed, la expansi\u00f3n de la demanda causa un aumento de la cantidad intercambiada (aunque se aumento de la cantidad no es tan grande como hubiera sido si el precio de  $x$ hubiera permanecido constante).<\/span><\/div>\n\n            <\/li>\n      <li>La respuesta anterior est\u00e1 basada en lo que muestra la figura. \u00bfPuedes hacer una lectura econ\u00f3mica de lo que ha ocurrido? <span class=\"sol\"  data-tooltip-content=\"#tip7\" >Sol.<\/span>\n<div class=\"tooltip_templates\">\n<span id=\"tip7\" style=\"maxWidth=400;\" >\nCuando $p_y$ sube, la demanda de bien $x$ aumenta para todos los valores de $p_x$. Pero las empresas est\u00e1n ofreciendo todo lo que les interesa al precio inicial, por lo que aparecer\u00eda un exceso de demanda. Ante el exceso de demanda el precio de $x$ tiende a subir, lo que hace que las empresas ofrezcan m\u00e1s producto. Al mismo tiempo la subida de $p_x$ hace que la cantidad que demandan los consumidores se reduzca algo (movimiento a lo largo de la nueva curva de demanda). El proceso se detendr\u00e1 cuando se alcance el nuevo equilibrio, en $(x',p')$.\n<\/span><\/div>\n      <\/li>\n    <\/ul>\n    \n  <p><span class=\"ejemplo\"  data-tooltip-content=\"#tip8\"  >Ejemplo<\/span><\/p>\n<div class=\"tooltip_templates\">\n<span id=\"tip8\" style=\"maxWidth=400;\" >\nTenemos una curva de oferta de bien $x$,  \\[x_s=p_x-8\\]\nmientras la demanda de bien $x$ viene dada por \n\\[x_d=80+p_y-2 p_x\\]\nInicialmente el precio del bien $y$, sustitutivo del $x$, es $p_y^o=20$\n        \n    <ul>\n    <li>\n\u00bfCu\u00e1l es el precio de equilibrio inicial del bien $x$ ? <span class=\"sol\"  data-tooltip-content=\"#tip9\" >Sol.<\/span>\n<div class=\"tooltip_templates\">\n<span id=\"tip9\" style=\"maxWidth=400;\" >\nIgualando oferta y demanda (y usando $p_y=20$)\\[80+20-2 p_x=p_x-8 \\Longrightarrow p_x^*=36 \\;\\mathrm{ ,}\\;\\;x^*=28\\]\n<\/span><\/div>\n            <\/li>\n      <li>\u00bfCu\u00e1l ser\u00eda el equilibrio si  $p_y$ sube hasta $p_y'=32$? <span class=\"sol\"  data-tooltip-content=\"#tip10\" >Sol.<\/span>\n<div class=\"tooltip_templates\">\n<span id=\"tip10\" style=\"maxWidth=400;\" >\nRepetimos el c\u00e1lculo, ahora para el nuevo $p_y$ \\[80+32-2 p_x=p_x-8 \\Longrightarrow p_x'=\\frac{120}{3}=40 \\;\\mathrm{ ,}\\;\\;x'=28\\]\n<\/span><\/div>\n\n            <\/li>\n\n      <li>\u00bfCu\u00e1l ha sido el impacto de la subida de $p_y$ ? <span class=\"sol\"  data-tooltip-content=\"#tip11\" >Sol.<\/span>\n<div class=\"tooltip_templates\">\n<span id=\"tip11\" style=\"maxWidth=400;\" >\nComparando el equilibrio final con el inicial tenemos que un incremento  $\\Delta p_y=12$ ha causado las siguientes variaciones en el equilibrio:\n    \\[\\Delta p_x=40-36=4 \\quad \\textrm{and}\\quad \\Delta x=32-28=4\\]\n<\/span><\/div>\n\n            <\/li>\n          \n    <\/ul>\n<\/span>\n<\/div>\n  \n <button class=\"mostrar\"  id=\"ButSh2\" onclick=\"divMostrar('cuadro2'); divMostrarOno('ButSh2') \">Ver mates <\/button>\n\n<div class=\"textomath\" id=\"cuadro2\">\n<p>Un poco de c\u00e1lculo nos permite obtener una expresi\u00f3n general para el impacto de un cambio en  $p_y$ sobre el precio de equilibrio del bien $x$. Tenemos una oferta de $x$ que depende de $p_x$, y una demanda que depende de $p_x$ pero tambi\u00e9n de $p_y$. La ecuaci\u00f3n de equilibrio ser\u00e1 <\/p>\n\\[x_d(p_x,p_y)=x_s(p_x)\\]\nDespejando $p_x$ obtenemos una expresi\u00f3n en la que el precio de equilibrio,  $p_x^*$, depende de $p_y$ \\[x_d(p_x(p_y),p_y)=x_s(p_x(p_y))\\]\n<p>Si derivamos la expresi\u00f3n respecto de $p_y$ tenemos<\/p>\n\\[\\frac{\\partial x_d(\\cdot)}{\\partial p_x}\\frac{\\mathrm{d}p_x(\\cdot)}{\\mathrm{d}p_y}+\\frac{\\partial x_d(\\cdot)}{\\partial p_y}=\\frac{\\mathrm{d}x_s(\\cdot)}{\\mathrm{d}p_x}\\frac{\\mathrm{d} p_x(\\cdot)}{\\mathrm{d}p_y}\\] \n\ny reordenando,\n\\[\\frac{\\mathrm{d}p_x(\\cdot)}{\\mathrm{d}p_y}\\left(\\frac{\\mathrm{d} x_s(\\cdot)}{\\mathrm{d} p_x}-\\frac{\\partial x_d(\\cdot)}{\\partial  p_x}\\right)=\\frac{\\partial x_d(\\cdot)}{\\partial p_y}\\] \n\nFinalmente, \n\\[\\frac{\\mathrm{d}p_x(\\cdot)}{\\mathrm{d}p_y}=\\frac{\\frac{\\partial x_d(\\cdot)}{\\partial p_y}}{\\left(\\frac{\\mathrm{d} x_s(\\cdot)}{\\mathrm{d} p_x}-\\frac{\\partial x_d(\\cdot)}{\\partial  p_x}\\right)}\\] \nEl efecto de un cambio en $p_y$ sobre el precio de equilibrio del bien $x$ est\u00e1 determinado por la derivada de $x_d$ respecto de $p_y$ (que ser\u00eda el desplazamiento horizontal de la curva de demanda de $x$ por unidad de aumento de $p_y$) y la diferencia entre las derivadas de la oferta y la demanda respecto de  $p_x$  (que son las inversas de las pendientes).\n<\/div>\n\n<script>\n       \n\t\t\n\t$('.tooltip').tooltipster({\n    \t\ttheme: ['tooltipster-light', 'tooltipster-light-customized'],\n\t\t\ttrigger: 'click',\n\t\t\tmaxWidth: '250',\n\t\t\tinteractive: true\n\n\t\t});\n     \n\t$('.tooltipfig').tooltipster({\n    \t\ttheme: ['tooltipster-light', 'tooltipster-light-customized'],\n\t\t\ttrigger: 'click',\n\t\t\tmaxWidth: '150'\n\t\t});\n\n\t$('.botondef').tooltipster({\n    \t\ttheme: ['tooltipster-light', 'tooltipster-light-customized'],\n\t\t\tmaxWidth: '250'\n\t\t});\n\t$('.btnmark').tooltipster({\n    \t\ttheme: ['tooltipster-light', 'tooltipster-light-customized'],\n\t\t\tmaxWidth: '250'\n\t\t});\n\t$('.ejemplo').tooltipster({\n    \t\ttheme: ['tooltipster-light', 'tooltipster-light-customized'],\n\t\t\tplugins: ['sideTip', 'scrollableTip'],\n\t\t\ttrigger: 'click',\n\t\t\tmaxWidth: '450',\n\t\t\tinteractive: true\n\t\t});\n\t$('.sol').tooltipster({\n    \t\ttheme: ['tooltipster-light', 'tooltipster-light-customized'],\n\t\t\tplugins: ['sideTip', 'scrollableTip'],\n\t\t\ttrigger: 'click',\n\t\t\tmaxWidth: '220',\n\t\t\tinteractive: true\n\t\t});\n\t\n\t$('.resputest').tooltipster({\n\t   \t\ttheme: ['tooltipster-shadow', 'tooltipster-shadow-customized'],\n\t\t\ttrigger: 'custom',\n\t\t\tinteractive: true,\n   \t\t\ttriggerOpen: {\n        \t\t\/\/click: true,\n        \t\t\/\/tap: true\n   \t\t\t },\n    \t\ttriggerClose: {\n        \t\tclick: true,\n        \t\ttap: true\n   \t\t\t },\n\t\t\tmaxWidth: '250'\n\t\t});\n\t\t\n\t\t$('.interactivesol').tooltipster({\n    \t\ttheme: ['tooltipster-light', 'tooltipster-light-customized'],\n\t\t\tplugins: ['sideTip', 'scrollableTip'],\n\t\t\ttrigger: 'click',\n\t\t\tmaxWidth: '220',\n\t\t\tinteractive: true\n\t\t});\n\t\n    <\/script>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Est\u00e1tica comparativa Generalmente un ejercicio de est\u00e1tica comparativa consiste en observar c\u00f3mo cambia la soluci\u00f3n de un problema en respuesta a un cambio en alguno de los datos. La curva de demanda relaciona el precio de un bien con la cantidad que los consumidores demandan. Pero hay otras variables que tambi\u00e9n pueden influir en la &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/interactivemicroeconomics.com\/index.php\/es\/ejemplos\/estatica-comparativa\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Est\u00e1tica comparativa&#8221;<\/span><\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"parent":1445,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"elementor_header_footer","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-1467","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/interactivemicroeconomics.com\/index.php\/wp-json\/wp\/v2\/pages\/1467","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/interactivemicroeconomics.com\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/interactivemicroeconomics.com\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/interactivemicroeconomics.com\/index.php\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/interactivemicroeconomics.com\/index.php\/wp-json\/wp\/v2\/comments?post=1467"}],"version-history":[{"count":40,"href":"https:\/\/interactivemicroeconomics.com\/index.php\/wp-json\/wp\/v2\/pages\/1467\/revisions"}],"predecessor-version":[{"id":1650,"href":"https:\/\/interactivemicroeconomics.com\/index.php\/wp-json\/wp\/v2\/pages\/1467\/revisions\/1650"}],"up":[{"embeddable":true,"href":"https:\/\/interactivemicroeconomics.com\/index.php\/wp-json\/wp\/v2\/pages\/1445"}],"wp:attachment":[{"href":"https:\/\/interactivemicroeconomics.com\/index.php\/wp-json\/wp\/v2\/media?parent=1467"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}