schema: EconSchema aspectRatio: 1.3 params: - name: C value: 40 min: 35 max: 40 round: 0.01 - name: c value: 0.6 min: 0.5 max: 0.6 round: 0.01 - name: I value: 17 min: 17 max: 30 round: 0.05 - name: d value: 500 min: 145 max: 250 round: 0.05 - name: G value: 20 min: 20 max: 35 round: 0.05 - name: T value: 20 min: 20 max: 35 round: 0.05 - name: x value: 0.001 min: 0.001 max: 0.003 round: 0.001 - name: m value: 0.2 min: 0.1 max: 0.3 round: 0.01 - name: h value: 500 min: 490 max: 510 round: 0.05 - name: k value: 0.5 min: 0.4 max: 0.5 round: 0.05 - name: Ye value: 20000 min: 10000 max: 20000 round: 0.05 - name: M value: 25 min: 15 max: 35 round: 0.05 calcs: e: ((((2)(params.m))((params.C)+(params.I)+(params.G)-((params.c)(params.T))+(((params.d)(params.M))/(params.h))))/((((params.x)(params.Ye))((1)-(params.c)+(((params.d)(params.k))/(params.h))))+((params.m)((params.C)+(params.I)+(params.G)-((params.c)(params.T))+(((params.d)(params.M))/(params.h)))))) Yeq: (((params.C)-((params.c)(params.T))+(params.I)+(params.G)+(((params.d)(params.M))/(params.h))+((params.x)(calcs.e)(params.Ye)))/((1)-(params.c)+((2)(params.m))-((params.m)(calcs.e))+(((params.d)(params.k))/(params.h)))) req: ((((params.k)(calcs.Yeq))/(params.h))-((params.M)/(params.h))) Md2: ((((params.C)(params.k))+((params.I)(params.k))+((35)(params.c))+((35)(params.m)(calcs.e))+((params.G)(params.k))+((params.Ye)(params.k)(calcs.e)(params.x))-((2)(35)(params.m))-(35)-((params.T)(params.c)(params.k)))/(((params.d)(params.k))+((2)(params.h)(params.m))+(params.h)-((params.c)(params.h))-((params.h)(params.m)(calcs.e)))) IS: (((params.C)+(params.I)-((params.d)(0))+(params.G)-((params.T)(params.c))+((params.x)(params.Ye)(calcs.e)))/((1 - params.c)+((2)(params.m))-((params.m)(calcs.e)))) LM: ((((0.075)*(params.h))/(params.k))+((params.M)/(params.k))) X: (((params.x)(params.Ye))+((params.Ye)(((calcs.e)(params.x))-(params.x)))) M: (((params.m)(calcs.Yeq))+((calcs.Yeq)((params.m)-((params.m)(calcs.e))))) req100: ((calcs.req)(100)) layout: FourGraphsPlusSidebar2: topRightGraph: xAxis: min: 0 max: 200 ticks: 6 yAxis: min: 0 max: 200 ticks: 6 objects: #45-degree Line - Line: slope: 1 strokeWidth: 2 color: grey - AngleMarker: measure: 45 strokeWidth: 2.5 color: black r: 30 label: text: "`45\\\\degree`" fontSize: 11 - Segment: a: [170, 170] b: [170, 170] color: grey label: text: "`Y_{d}=Y_{renda}=Y_{prod}`" position: a fontSize: 9 #Agreggate Expenditure - Curve: fn: "(params.C + params.c*(x - params.T) + params.G + params.I - params.d(calcs.req) + (params.x)(params.Ye) + (params.Ye)(((params.x)(calcs.e))-(params.x)) - ((params.m)(x)+(x)((params.m)-((params.m)(calcs.e)))))" ind: x color: blue min: 0 max: 500 strokeWidth: 4 samplePoints: 100 - Point: coordinates: [calcs.Yeq, calcs.Yeq] color: - Segment: a: [calcs.Yeq, 0] b: [calcs.Yeq, calcs.Yeq] color: green lineStyle: dotted strokeWidth: 2 - Segment: a: [calcs.Yeq, 0] b: [calcs.Yeq, 0] color: black bgcolor: "'#36a854'" label: text: "`(\\\\$)\\\\ ${calcs.Yeq.toFixed(1)}`" position: t - Segment: a: [0, calcs.Yeq] b: [0, calcs.Yeq] color: black bgcolor: "'#36a854'" label: text: "`(\\\\$)\\\\ ${calcs.Yeq.toFixed(1)}`" position: r - Segment: a: [calcs.Yeq, calcs.Yeq] b: [0, calcs.Yeq] color: green lineStyle: dotted strokeWidth: 2 bottomLeftGraph: xAxis: min: 0 max: 50 ticks: 4 yAxis: min: 0 max: 0.079 ticks: 4 objects: #Demand for Money - Curve - Curve: fn: "((((params.C)(params.k))+((params.I)(params.k))+((x)(params.c))+((x)(params.m)(calcs.e))-((2)(x)(params.m))-(x)-((params.T)(params.c)(params.k))+((params.G)(params.k))+((params.Ye)(params.k)(calcs.e)(params.x)))/(-((params.c)(params.h))+((params.d)(params.k))-((params.h)(params.m)(calcs.e))+((2)(params.h)(params.m))+(params.h)))" ind: x color: blue min: 0 max: 60 strokeWidth: 4 samplePoints: 100 #Money Supply - Line - Point: coordinates: [params.M, calcs.req] color: - Line: xIntercept: params.M color: supply lineStyle: solid strokeWidth: 3 - Line: yIntercept: calcs.req color: supply lineStyle: dotted strokeWidth: 2 #Canva - Segment: a: [0,0.079] b: [0,0.079] color: black bgcolor: white label: text: r position: r fontSize: 13 - Segment: a: [50,0] b: [50,0] color: black label: text: M/P position: t - Segment: a: [0, calcs.req] b: [0, calcs.req] color: black bgcolor: "'#36a854'" label: text: "`${calcs.req100.toFixed(1)} \\\\%`" position: r - Segment: a: [params.M, 0] b: [params.M, 0] color: black bgcolor: "'#36a854'" label: text: "`(\\\\$)\\\\ ${params.M.toFixed(1)}`" position: t - Segment: a: [params.M, 0.079] b: [params.M, 0.079] color: white bgcolor: "'#fc7e0f'" label: text: M_{of} position: b - Segment: a: [45, calcs.Md2] b: [45, calcs.Md2] color: white bgcolor: "'#2177b5'" label: text: M_{d} position: a topLeftGraph: xAxis: min: 0 max: 20 ticks: false show: false yAxis: min: 0 max: 10 ticks: 6 show: false bottomRightGraph: xAxis: min: 0 max: 200 ticks: 4 yAxis: min: 0 max: 0.079 ticks: 4 objects: #IS Curve - Curve: fn: "((params.C + params.I + params.G + ((params.x)(params.Ye)) + (params.Ye)(((params.x)(calcs.e))-(params.x)) - ((params.c)(params.T)))/(params.d))-((x)(1 + ((2)(params.m)) - ((params.m)*(calcs.e)) - params.c)/(params.d))" ind: x color: blue min: 0 max: 500 strokeWidth: 4 samplePoints: 100 #LM Curve - Curve: fn: "((((x)(params.k))/(params.h))-((params.M)/(params.h)))" ind: x color: supply min: 0 max: 200 strokeWidth: 4 samplePoints: 100 - Point: coordinates: [calcs.Yeq, calcs.req] color: - Segment: a: [calcs.Yeq, 0] b: [calcs.Yeq, 0.079] color: green lineStyle: dotted strokeWidth: 2 #BP - Line: xIntercept: calcs.Yeq color: green lineStyle: solid strokeWidth: 3 label: {text: "`BP`", y: 0.01} #Canva - Segment: a: [0,0.079] b: [0,0.079] color: black bgcolor: white label: text: r position: r fontSize: 13 - Segment: a: [200, 0] b: [200, 0] color: black label: text: Y_{Eq} position: t - Segment: a: [0, calcs.req] b: [0, calcs.req] color: black bgcolor: "'#36a854'" label: text: "`${calcs.req100.toFixed(1)} \\\\%`" position: r - Segment: a: [0, 0.02] b: [0, 0.02] color: black bgcolor: "'#36a854'" label: text: "`${calcs.req.toFixed(2)}`" position: r - Segment: a: [calcs.Yeq, 0] b: [calcs.Yeq, 0] color: black bgcolor: "'#36a854'" label: text: "`(\\\\$)\\\\ ${calcs.Yeq.toFixed(2)}`" position: t - Segment: a: [calcs.IS, 0.005] b: [calcs.IS, 0.005] color: white bgcolor: "'#2177b5'" label: text: IS position: b - Segment: a: [calcs.LM, 0.07] b: [calcs.LM, 0.07] color: white bgcolor: "'#fc7e0f'" label: text: LM position: l - Segment: a: [0, calcs.req] b: [calcs.Yeq, calcs.req] color: green lineStyle: dotted strokeWidth: 2 sidebar: controls: - title: MODELO IS-LM-BP SEM MOBILIDADE DE CAPITAIS E REGIME DE CÂMBIO FLEXÍVEL sliders: - param: M label: M_{of} digits: 4 - param: G label: G digits: 4 divs: - html: '`Os resultados relevantes são: $$\\color{${colors.black}}{Y_{d} = R \\$ ${calcs.Yeq.toFixed(2)}}$$ $$\\color{${colors.black}}{e = ${calcs.e.toFixed(2)}}$$ $$\\color{${colors.black}}{X = R \\$ ${calcs.X.toFixed(2)}}$$ $$\\color{${colors.black}}{M = R \\$ ${calcs.M.toFixed(2)}}$$`' - html: 'A identidade do produto ${Y_d}$ pela ótica da despesa em Economia Aberta é: $${Y_{d}=C+I+G+(X-M)}$$ As formas funcionais para cada componente são: $${C=C_0+c(Y_{renda}-T)}$$ $${I=I_0-d \cdot r}$$ $${G= \overline{G}}$$ Para uma condição inicial de orçamento equilibrado, temos: $${G=T}$$ Para Exportações ${(X)}$: $${X=x_1 \cdot Y_e + Y_e (e \cdot x_1 - x_1)}$$ em que ${\bf{x_1}}$ é a sensibilidade de ${\bf{X}}$ em relação à renda externa ${\bf{Y_e}}$, e $${\bf{Y_e(e \cdot x_1 - x_1)}}$$ representa a sensibilidade de ${\bf{X}}$ em relação à taxa de câmbio real ${\bf{(e)}}$.' - html: 'Para as Importações ${(M)}$: $${M=m \cdot Y_{renda} + Y_{renda} (m - m \cdot e)}$$ em que ${\bf{m}}$ é a propensão marginal à importar e $${\bf{Y_{renda}(m - m \cdot e)}}$$ representa a sensibilidade das Importações ${(\bf{M})}$ em relação à taxa de câmbio real ${(\bf{e})}$.' - html: 'A curva IS é: $${IS:r(Y)=\frac{C_0 + I_0 + G - cT + x_1 Y_e + Y_e (x_1 e - x_1)}{d}- \frac{Y(1 + 2m - me -c)}{d}}$$ A curva LM é: $${LM:r(Y)= \frac{k \cdot Y}{h} - \frac{M_o}{h}}$$ O equilíbrio no Balanço de Pagamentos ${(BP)}$ é: $${CC=-CF}$$ Como não há mobilidade de Capitais, então: $${CC=0}$$ $${\Longleftrightarrow}$$ $${X-M=0}$$ $${\Longleftrightarrow}$$ $${X=x_1 \cdot Y_e + Y_e (e \cdot x_1 - x_1)-(m \cdot Y_{renda} + Y_{renda} (m - m \cdot e))}$$ Resolvendo para a taxa de câmbio ${(e)}$ $${e=\frac{2 \cdot m \cdot Y_{renda}}{x \cdot Y_{e} + m \cdot Y_{renda}}}$$ Para encontrar a Taxa de Câmbio ${(e)}$ de equilíbrio, basta substituir na equação acima a renda de equilíbrio encontrada na intersecção da curva IS com a LM e resolver para taxa de câmbio ${(e)}$.'