--- aspectRatio: 2.3 params: - name: p1 value: 1 min: 1 max: 3 round: 0.01 - name: a value: 0.5 min: -1 max: 10 precision: 0.001 round: 0.01 - name: p2 value: 1 min: 1 max: 3 round: 0.01 - name: m value: 8 min: 1 max: 15 round: 0.1 calcs: RO: (params.m)/(params.p1) RO2: (params.m)/(params.p2) pr: (params.p2/params.p1) Dm1CES: (((params.m)*(params.p1^(1/(params.a-1)))/(params.p1^(params.a/(params.a-1))+params.p2^(params.a/(params.a-1))))) Dm2CES: (((params.m)*(params.p2^(1/(params.a-1)))/(params.p1^(params.a/(params.a-1))+params.p2^(params.a/(params.a-1))))) UCES: (((calcs.Dm1CES^(params.a)+calcs.Dm2CES^(params.a)))^(1/params.a)) s: (1/(1-params.a)) layout: MathboxPlusGraphPlusSidebar: graph: xAxis: max: 15 ticks: 3 yAxis: max: 15 ticks: 3 objects: #Curva de Indiferença - Curve: fn: "(((calcs.UCES^params.a)-((x)^params.a))^(1/params.a))" ind: x color: red min: 0 max: 100 lineStyle: solid strokeWidth: 4 samplePoints: 300 show: (params.a >= 0.1) - Curve: fn: "(((calcs.UCES^params.a)-((y)^params.a))^(1/params.a))" ind: y color: red min: 0 max: 100 lineStyle: solid strokeWidth: 4 samplePoints: 300 show: (params.a < 0.1) #Restrição Orçamentaria - Curve: fn: "(-((x)*(params.p2)/(params.p1))+(params.m)/(params.p1))" ind: x color: blue strokeWidth: 4 #Canva - Point: coordinates: [calcs.Dm2CES, calcs.Dm1CES] color: green r: 6 - Segment: a: [calcs.Dm2CES, calcs.Dm1CES+1.5] b: [calcs.Dm2CES, calcs.Dm1CES+1.5] color: black bgcolor: "'#FFCC90'" label: text: "`TMS=|-\\\\frac{p_{2}}{p_{1}}| =${calcs.pr.toFixed(2)}`" position: l fontSize: 10 - Segment: a: [0, calcs.RO] b: [0, calcs.RO] color: black bgcolor: "'#FFCC90'" label: text: \frac{m}{p_{1}} position: r fontSize: 15 - Segment: a: [calcs.RO2, 0] b: [calcs.RO2, 0] color: black bgcolor: "'#FFCC90'" label: text: \frac{m}{p_{2}} position: t fontSize: 15 - Segment: a: [calcs.Dm2CES, 0] b: [calcs.Dm2CES, calcs.Dm1CES] color: green lineStyle: dashed - Segment: a: [calcs.Dm2CES, calcs.Dm1CES] b: [0, calcs.Dm1CES] color: green lineStyle: dashed - Segment: a: [0, calcs.Dm1CES] b: [0, calcs.Dm1CES] color: black bgcolor: "'#36a854'" label: text: calcs.Dm1CES.toFixed(0) position: r fontSize: 15 - Segment: a: [calcs.Dm2CES, 0] b: [calcs.Dm2CES, 0] color: black bgcolor: "'#36a854'" label: text: calcs.Dm2CES.toFixed(0) position: t fontSize: 15 - Segment: a: [0, 15] b: [0, 15] color: black bgcolor: white label: text: x_{1} position: r - Segment: a: [15, 0] b: [15, 0] color: black bgcolor: white label: text: x_{2} position: t - Label: coordinates: [15,13] text: "`Elasticidade \\\\ Substituição \\\\ (s): \\\\\\\\ s= \\\\frac{1}{1- \\\\rho} =\\\\frac{1}{1- ${params.a.toFixed(1)}} \\\\\\\\ s=${calcs.s.toFixed(2)}`" bgcolor: "'#1f77b4'" color: white fontSize: 8 position: tr mathbox: xAxis: min: 0 max: 15 step: 2 yAxis: min: 0 max: 15 step: 2 zAxis: min: 0 max: calcs.UCES+10 ticks: 0 objects: - MathboxFunctionSurface: fn: fn: ((((x)^(params.a)+(y)^(params.a)))^(1/params.a)) samplePoints: 20 shaded: false fill: red opacity: 0.1 - MathboxCurve: fn: fn: (calcs.RO - calcs.pr*(x)) fnZ: calcs.UCES fnX: 5 samplePoints: 500 strokeWidth: 10 stroke: blue - MathboxCurve: fn: fn: (((calcs.UCES^params.a)-((x)^params.a))^(1/params.a)) fnZ: calcs.UCES samplePoints: 500 strokeWidth: 10 stroke: colors.red # Optimal Point - MathboxPoint: x: calcs.Dm2CES y: calcs.Dm1CES z: calcs.UCES stroke: "'#36a854'" - MathboxLabel: x: 0 y: 16 z: 1 stroke: black text: "x1" - MathboxLabel: x: 0 y: calcs.Dm1CES z: 1 stroke: black text: calcs.Dm1CES.toFixed(2) - MathboxLabel: x: calcs.Dm2CES y: 0 z: 1 stroke: black text: calcs.Dm2CES.toFixed(2) - MathboxLabel: x: -1.5 y: -1.5 z: calcs.UCES+3 stroke: black text: calcs.UCES.toFixed(2) - MathboxLabel: x: 16 y: 0 z: 1 stroke: black text: "x2" - MathboxLabel: x: 0 y: 0 z: calcs.UCES+10 stroke: black text: "Utilidade" # Vertical dropline - MathboxLine: x1: calcs.Dm2CES y1: calcs.Dm1CES x2: calcs.Dm2CES y2: calcs.Dm1CES z2: calcs.UCES stroke: "'#36a854'" strokeWidth: 10 lineStyle: dashed # Vertical dropline - MathboxLine: z1: calcs.UCES x1: calcs.Dm2CES y1: calcs.Dm1CES z2: calcs.UCES stroke: "'#36a854'" strokeWidth: 10 lineStyle: dashed # Dropline to x axis - MathboxLine: x1: calcs.Dm2CES y1: calcs.Dm1CES x2: calcs.Dm2CES stroke: "'#36a854'" strokeWidth: 10 lineStyle: dashed # Dropline to y axis - MathboxLine: x1: calcs.Dm2CES y1: calcs.Dm1CES y2: calcs.Dm1CES stroke: "'#36a854'" strokeWidth: 10 lineStyle: dashed sidebar: controls: - title: Decisão Ótima de Consumo Função CES sliders: - param: a label: \rho digits: 4 - param: p1 label: p_1 digits: 4 - param: p2 label: p_2 digits: 4 - param: m label: m digits: 4 divs: - html: 'A forma funcional da função de Utilidade CES é: $${U(X_{1},X_{2}) = (X_{1}^\rho + X_{2}^\rho)^\frac{1}{\rho}}$$' - html: 'A função de demanda inversa marshalliana para ${X_{1}}$: $${P(X_{1}) = \frac{X_{1}^{\rho-1}m}{X_{1}^{\rho}+X_{2}^{\rho}}}$$' - html: 'A função de demanda inversa marshalliana para ${X_{2}}$: $${P(X_{2}) = \frac{X_{2}^{\rho-1}m}{X_{1}^{\rho}+X_{2}^{\rho}}}$$'