schema: EconSchema aspectRatio: 1.25 params: - name: p1 value: 1 min: 1 max: 3 round: 0.1 - name: p2 value: 1 min: 1 max: 3 round: 0.1 - name: m value: 8 min: 1 max: 15 round: 0.1 - name: a value: 0.5 min: 0.01 max: 1.5 precision: 0.001 round: 0.01 - name: b value: 0.5 min: 0.1 max: 1 precision: 0.01 round: 0.01 calcs: Dm1CES: (params.m)*(((params.b)*(params.p1))^(1/(params.a-1))/(((params.p1)^(params.a/(params.a-1)))(params.b)^((1)/(params.a-1))+(1-params.b)^(1/(params.a-1))(params.p2)^(params.a/(params.a-1)))) Dm2CES: (params.m)*(((1-params.b)*(params.p2))^(1/(params.a-1))/(((params.p1)^(params.a/(params.a-1)))(params.b)^((1)/(params.a-1))+((1-params.b)^(1/(params.a-1))(params.p2)^(params.a/(params.a-1))))) UCES: (((1-params.b)*(calcs.Dm1CES^(params.a))+(params.b)*(calcs.Dm2CES^(params.a)))^(1/params.a)) RO: (-((0)*(params.p2)/(params.p1))+(params.m)/(params.p1)) RO2: (-((0)*(params.p1)/(params.p2))+(params.m)/(params.p2)) pr: (params.p2/params.p1) px: (params.m*(1-params.b)*(6^(params.a-1))/((1-params.b)(6^(params.a))+(params.b)(calcs.Dm2CES^(params.a)))) px2: (params.m*(params.b)*(6^(params.a-1))/((1-params.b)(calcs.Dm1CES^(params.a))+(params.b)(6^(params.a)))) rmg1: (((params.m)*(params.a)*(calcs.Dm2CES)^(params.a)*(6)^(params.a-1))/((6)^(params.a)+(calcs.Dm2CES^(params.a)))^2) rmg2: (((params.m)*(params.a)*(calcs.Dm1CES)^(params.a)*(6)^(params.a-1))/((6)^(params.a)+(calcs.Dm1CES^(params.a)))^2) rc: (((11)((params.b*params.p1)/(params.p2*(1-params.b)))^(1/(params.a-1)))) layout: FourGraphsPlusSidebar: topLeftGraph: xAxis: min: 0 max: 12 ticks: 4 yAxis: min: 0 max: 12 ticks: 4 objects: #45-degree Line - Line: slope: 1 strokeWidth: 3 color: grey - AngleMarker: measure: 45 strokeWidth: 2.5 color: black r: 2 label: text: "`45\\\\degree`" fontSize: 11 #Canva - Segment: a: [0, 12] b: [0, 12] color: black label: text: "`x_{1}`" position: r - Segment: a: [12, 0.1] b: [12, 0.1] color: black label: text: "`x_{1}`" position: t - Point: coordinates: [calcs.Dm1CES, calcs.Dm1CES] color: green r: 5 - Segment: a: [calcs.Dm1CES, 0] b: [calcs.Dm1CES, calcs.Dm1CES] color: "'#36a854'" lineStyle: dashed strokeWidth: 2.5 - Segment: a: [12, calcs.Dm1CES] b: [0, calcs.Dm1CES] color: "'#36a854'" lineStyle: dashed strokeWidth: 2.5 - Segment: a: [calcs.Dm1CES, 0] b: [calcs.Dm1CES, 0] bgcolor: "'#36a854'" color: black label: text: calcs.Dm1CES.toFixed(0) position: t fontSize: 12 - Segment: a: [0, calcs.Dm1CES] b: [0, calcs.Dm1CES] bgcolor: "'#36a854'" color: black label: text: calcs.Dm1CES.toFixed(0) position: r fontSize: 12 bottomLeftGraph: xAxis: min: 0 max: 12 ticks: 4 yAxis: min: 0 max: 4 ticks: 4 objects: #Curva de Demanda X1 - Curve: fn: "(params.m*(1-params.b)*(x^(params.a-1))/((1-params.b)(x^(params.a))+(params.b)(calcs.Dm2CES^(params.a))))" ind: x color: supply min: 0 max: 100 lineStyle: solid strokeWidth: 3.5 samplePoints: 1000 #Curva de RMg X1 - Curve: fn: "(params.b(1-params.b)params.m(params.a)((x)^(params.a-1))calcs.Dm2CES^(params.a))/(((params.b)(calcs.Dm2CES^(params.a))+(1-params.b)(x^(params.a))))^2" ind: x color: supply min: 0 max: 100 lineStyle: dashed strokeWidth: 2 samplePoints: 1000 #Canva - Segment: a: [0, 4] b: [0, 4] color: black label: text: "`P_{1}`" position: r - Segment: a: [12, 0.1] b: [12, 0.1] color: black label: text: "`x_{1}`" position: t - Segment: a: [calcs.Dm1CES, 0] b: [calcs.Dm1CES, 20] color: "'#36a854'" lineStyle: dashed strokeWidth: 2.5 - Segment: a: [0, params.p1] b: [calcs.Dm1CES, params.p1] color: "'#36a854'" lineStyle: dashed strokeWidth: 2.5 - Point: coordinates: [calcs.Dm1CES, params.p1] color: green r: 5 - Segment: a: [0, params.p1] b: [0, params.p1] bgcolor: "'#36a854'" color: black label: text: "`(\\\\$)\\\\ ${params.p1.toFixed(2)}`" position: r fontSize: 12 - Segment: a: [calcs.Dm1CES, 0] b: [calcs.Dm1CES, 0] bgcolor: "'#36a854'" color: black label: text: calcs.Dm1CES.toFixed(0) position: t fontSize: 12 - Segment: a: [calcs.px, 4] b: [calcs.px, 4] bgcolor: "'#fc7e0f'" color: white label: text: "`P_{1}(X_{1})`" position: l fontSize: 12 - Segment: a: [12, calcs.rmg1] b: [12, calcs.rmg1] bgcolor: "'#fc7e0f'" color: white label: text: "`RMg_{1}(X_{1})`" position: p fontSize: 8 topRightGraph: xAxis: min: 0 max: 12 ticks: 4 yAxis: min: 0 max: 12 ticks: 4 objects: #Curva de Indiferença - Curve: fn: "((((calcs.UCES^(params.a))-((params.b)(x)^(params.a)))/(1-params.b)))^(1/params.a)" ind: x color: red min: 0 max: 100 lineStyle: solid strokeWidth: 4 samplePoints: 500 show: (params.a >= 0.1) - Curve: fn: "((((calcs.UCES^(params.a))-((params.b)(y)^(params.a)))/(1-params.b)))^(1/params.a)" ind: y min: 0 max: 100 color: red lineStyle: solid strokeWidth: 4 samplePoints: 500 show: (params.a <= 0.1) #Restrição Orçamentaria - Curve: fn: "(-((x)*(params.p2)/(params.p1))+(params.m)/(params.p1))" ind: x color: blue strokeWidth: 4 samplePoints: 300 #Curva de renda-consumo - Curve: fn: "((x)((params.b*params.p1)/(params.p2*(1-params.b)))^(1/(params.a-1)))" ind: x color: black lineStyle: solid strokeWidth: 2 samplePoints: 300 - Point: coordinates: [calcs.Dm2CES, calcs.Dm1CES] color: green #Canva - Segment: a: [0, 12] b: [0, 12] color: black label: text: "`x_{1}`" position: r - Segment: a: [12, 0.1] b: [12, 0.1] color: black label: text: "`x_{2}`" position: t - Segment: a: [calcs.Dm2CES, 0] b: [calcs.Dm2CES, calcs.Dm1CES] color: "'#36a854'" lineStyle: dashed strokeWidth: 2.5 - Segment: a: [0, calcs.Dm1CES] b: [calcs.Dm2CES, calcs.Dm1CES] color: "'#36a854'" lineStyle: dashed strokeWidth: 2.5 - Segment: a: [calcs.Dm2CES, 0] b: [calcs.Dm2CES, 0] bgcolor: "'#36a854'" color: black label: text: calcs.Dm2CES.toFixed(0) position: t fontSize: 12 - Segment: a: [0, calcs.Dm1CES] b: [0, calcs.Dm1CES] bgcolor: "'#36a854'" color: black label: text: calcs.Dm1CES.toFixed(0) position: r fontSize: 12 - Segment: a: [calcs.Dm2CES, calcs.Dm1CES+1] b: [calcs.Dm2CES, calcs.Dm1CES+1] color: black bgcolor: "'#FFCC90'" label: text: "`TMS=|-\\\\frac{p_{2}}{p_{1}}| =${calcs.pr.toFixed(2)}`" position: l fontSize: 11 - Segment: a: [11, calcs.rc] b: [11, calcs.rc] color: black bgcolor: grey label: text: "`renda-consumo`" position: br fontSize: 8 - 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 bottomRightGraph: xAxis: min: 0 max: 12 ticks: 4 yAxis: min: 0 max: 4 ticks: 4 objects: #Curva de Demanda X2 - Curve: fn: "(params.m*(params.b)*(x^(params.a-1))/((1-params.b)(calcs.Dm1CES^(params.a))+(params.b)(x^(params.a))))" ind: x color: blue min: 0 max: 100 lineStyle: solid strokeWidth: 3.5 samplePoints: 1000 #Curva de RMg X2 - Curve: fn: "(params.b(1-params.b)params.m(params.a)((x)^(params.a-1))calcs.Dm1CES^(params.a))/(((1-params.b)(calcs.Dm1CES^(params.a))+(params.b)(x^(params.a))))^2" ind: x color: blue min: 0 max: 100 lineStyle: dashed strokeWidth: 2 samplePoints: 1000 #Canva - Segment: a: [0, 4] b: [0, 4] color: black label: text: "`P_{2}`" position: r - Segment: a: [12, 0.1] b: [12, 0.1] color: black label: text: "`x_{2}`" position: t - Segment: a: [calcs.Dm2CES, 0] b: [calcs.Dm2CES, 20] color: "'#36a854'" lineStyle: dashed strokeWidth: 2.5 - Segment: a: [0, params.p2] b: [calcs.Dm2CES, params.p2] color: "'#36a854'" lineStyle: dashed strokeWidth: 2.5 - Segment: a: [0, params.p2] b: [0, params.p2] bgcolor: "'#36a854'" color: black label: text: "`(\\\\$)\\\\ ${params.p2.toFixed(2)}`" position: r fontSize: 12 - Segment: a: [calcs.Dm2CES, 0] b: [calcs.Dm2CES, 0] bgcolor: "'#36a854'" color: black label: text: calcs.Dm2CES.toFixed(0) position: t fontSize: 12 - Point: coordinates: [calcs.Dm2CES, params.p2] color: green r: 5 - Segment: a: [12, calcs.px2] b: [12, calcs.px2] bgcolor: "'#1f77b4'" color: white label: text: "`P_{2}(X_{2})`" position: p fontSize: 12 - Segment: a: [12, calcs.rmg2] b: [12, calcs.rmg2] bgcolor: "'#1f77b4'" color: white label: text: "`RMg_{2}(X_{2})`" position: p fontSize: 8 sidebar: controls: - title: Decisão Ótima de Consumo CES e Funções de Demanda Marshallianas sliders: - param: m label: m digits: 3 - param: p1 label: p_{1} digits: 3 - param: p2 label: p_{2} digits: 3 - param: a label: \rho digits: 3 - param: b label: \alpha digits: 3 divs: - html: 'A forma funcional da função de Utilidade CES é: $${U(X_{1},X_{2}) = [(1-\alpha)X_{1}^\rho + \alpha X_{2}^\rho]^\frac{1}{\rho}}$$' - html: 'A função de demanda inversa marshalliana para ${X_{1}}$: $${P(X_{1}) = \frac{(1-\alpha)X_{1}^{\rho-1}m}{(1-\alpha)X_{1}^{\rho}+ \alpha X_{2}^{\rho}}}$$' - html: 'A função de demanda inversa marshalliana para ${X_{2}}$: $${P(X_{2}) = \frac{\alpha X_{2}^{\rho-1}m}{(1-\alpha)X_{1}^{\rho}+\alpha X_{2}^{\rho}}}$$' - html: 'A função de Receita Marginal para ${X_{1}}$ é: $${RT(X_{1}) = P(X_{1})\cdot X_{1}}$$ $${\\\\\ \\\Longleftrightarrow}$$ $${RT(X_{1}) = \frac{(1-\alpha)X_{1}^{\rho}m}{(1-\alpha)X_{1}^{\rho}+ \alpha X_{2}^{\rho}}}$$ $${\\\\\ \\\Longleftrightarrow}$$ $${RMg(X_{1})= \frac{\alpha(1-\alpha)m\rho X_{1}^{\rho-1} X_{2}^{\rho}}{[(1-\alpha)X_{1}^{\rho}+ \alpha X_{2}^{\rho}]^2}}$$' - html: 'A função de Receita Marginal para ${X_{2}}$ é: $${RT(X_{2}) = P(X_{2})\cdot X_{2}}$$ $${\\\\\ \\\Longleftrightarrow}$$ $${RT(X_{2}) = \frac{\alpha X_{2}^{\rho}m}{(1-\alpha)X_{1}^{\rho}+ \alpha X_{2}^{\rho}}}$$ $${\\\\\ \\\Longleftrightarrow}$$ $${RMg(X_{2})= \frac{\alpha(1-\alpha)m\rho X_{2}^{\rho-1} X_{1}^{\rho}}{[(1-\alpha)X_{1}^{\rho}+\alpha X_{2}^{\rho}]^2}}$$'