schema: EconSchema
aspectRatio: 1.3
params:
- name: a
value: 0.3
min: 0
max: 1
round: 0.01
- name: L
value: 50
min: 20
max: 70
round: 0.01
- name: s
value: 0.3
min: 0.1
max: 0.6
round: 0.01
calcs:
Keq: (((calcs.req)/((params.a)((params.L)^(1-params.a))))^(1/(params.a-1)))
req: (((params.a)*(calcs.S)^(params.a-1))(params.L)^(1-params.a))
Yeq: (((calcs.Keq)^(params.a))(params.L)^(1-params.a))
Yeq2: (((30)^(params.a))*(params.L)^(1-params.a))
K: (((params.a)(30)^(params.a-1))(params.L)^(1-params.a))
S: (((params.s)*(params.L)^(1-params.a))^(1/(1-params.a)))
WLreal: ((1-params.a)((calcs.Keq)^(params.a))((params.L)^(-params.a)))
pi1: -(((calcs.P)*(calcs.Yeq))-(((params.L)*(calcs.WLreal))+((calcs.Keq)*(calcs.req))))
P: (((calcs.WLreal)/((1-params.a)((calcs.Keq)^(params.a))))(((calcs.Yeq)/((calcs.Keq)^(params.a)))^((params.a)/(1-params.a))))
iso: (((calcs.pi1/calcs.P)+((calcs.WLreal)*(params.L)/(calcs.P))+((calcs.req)*(calcs.Keq+14)/(calcs.P))))
layout:
TwoVerticalGraphsPlusSidebar:
topGraph:
xAxis:
min: 0
max: 30
ticks: 4
yAxis:
min: 0
max: 60
ticks: 4
objects:
#Função de Produção de Curto-prazo
- Curve:
fn: "((x)^(params.a))*(params.L)^(1-params.a)"
ind: x
min: 0
max: 100
color: red
strokeWidth: 3.5
samplePoints: 400
#Função de Isolucro
- Curve:
fn: "((calcs.pi1/calcs.P)+((calcs.WLreal)*(params.L)/(calcs.P))+((calcs.req)*(x)/(calcs.P)))"
ind: x
min: 0
max: calcs.Keq +12
color: grey
strokeWidth: 3.5
samplePoints: 300
- Segment:
a: [0,60]
b: [0, 60]
color: Black
bgcolor: white
strokeWidth: 1
label:
text: Y
position: r
fontSize: 11
- Segment:
a: [30,0]
b: [30,0]
color: Black
bgcolor: white
strokeWidth: 1
label:
text: \ K
position: t
fontSize: 11
- Segment:
a: [calcs.Keq, 0]
b: [calcs.Keq, 0]
color: black
bgcolor: "'#36a854'"
label:
text: calcs.Keq.toFixed(1)
position: t
fontSize: 11
- Segment:
a: [0, calcs.Yeq]
b: [0, calcs.Yeq]
color: black
bgcolor: "'#36a854'"
label:
text: calcs.Yeq.toFixed(2)
position: r
fontSize: 11
- Segment:
a: [calcs.Keq, calcs.Yeq]
b: [calcs.Keq, 0]
color: green
lineStyle: dotted
strokeWidth: 2
- Segment:
a: [calcs.Keq, calcs.Yeq]
b: [0, calcs.Yeq]
color: green
lineStyle: dotted
strokeWidth: 2
- Point:
coordinates: [calcs.Keq, calcs.Yeq]
color: black
r: 5
- Segment:
a: [30, calcs.Yeq2]
b: [30, calcs.Yeq2]
color: white
bgcolor: "'#d62728'"
label:
text: F(K,L)
position: l
fontSize: 10
- Segment:
a: [30, calcs.iso]
b: [30, calcs.iso]
color: white
bgcolor: grey
show: (calcs.Keq+10)>30
label:
text: "`\\\\frac{\\\\pi}{P} + \\\\frac{W\\\\cdot L}{P} + \\\\frac{r\\\\cdot K}{P}`"
position: bl
fontSize: 10
- Segment:
a: [calcs.Keq+10, calcs.iso]
b: [calcs.Keq+10, calcs.iso]
color: white
bgcolor: grey
label:
text: "`\\\\frac{\\\\pi}{P} + \\\\frac{w_{L}\\\\cdot L}{P} + \\\\frac{w_{K}\\\\cdot K}{P}`"
position: bl
fontSize: 10
bottomGraph:
xAxis:
min: 0
max: 30
ticks: 4
yAxis:
min: 0
max: 1.99
ticks: 4
objects:
#Função de Demanda de Capital
- Curve:
fn: "(((params.a)(x)^(params.a-1))(params.L)^(1-params.a))"
ind: x
min: 0
max: 30
color: blue
strokeWidth: 3.5
samplePoints: 300
#Função de Oferta de Capital
- Segment:
a: [calcs.S, 10]
b: [calcs.S, 0]
color: red
strokeWidth: 3.5
- Segment:
a: [30,0]
b: [30,0]
color: Black
bgcolor: white
strokeWidth: 1
label:
text: \ K
position: t
fontSize: 11
- Segment:
a: [0 ,1.99]
b: [0 ,1.99]
color: Black
bgcolor: white
strokeWidth: 1
label:
text: w_{k}
position: r
fontSize: 14
- Segment:
a: [calcs.Keq, 0]
b: [calcs.Keq, 0]
color: black
bgcolor: "'#36a854'"
label:
text: calcs.Keq.toFixed(1)
position: t
fontSize: 11
- Segment:
a: [0, calcs.req]
b: [0, calcs.req]
color: black
bgcolor: "'#36a854'"
label:
text: calcs.req.toFixed(2)
position: r
fontSize: 11
- Segment:
a: [calcs.Keq, calcs.req]
b: [0, calcs.req]
color: green
lineStyle: dotted
strokeWidth: 2
- Point:
coordinates: [calcs.Keq, calcs.req]
color: black
r: 5
- Segment:
a: [30, calcs.K]
b: [30, calcs.K]
color: white
bgcolor: "'#1f77b4'"
label:
text: w_{k}(I)
position: l
- Segment:
a: [calcs.S, 1.5]
b: [calcs.S, 1.5]
color: "'#d62728'"
bgcolor: white
label:
text: S(Y)
sidebar:
controls:
- title: Modelo Clássico de Equilíbrio Geral
sliders:
- param: a
label: \alpha
digits: 3
- param: L
label: L
digits: 4
- param: s
label: s
digits: 3
divs:
- html:
- html: '`Os resultados relevantes dessa economia são: $$\\pi = ${calcs.pi1.toFixed(2)}$$ $$ P=${calcs.P.toFixed(2)} $$ $$ w_{L}= ${calcs.WLreal.toFixed(3)} $$ $$ w_{k}=${calcs.req.toFixed(2)} $$`'
- html: 'O fato do Lucro ($\pi$) dessa economia ser igual a zero nos mostra que estamos numa estrutura de mercado de Competição Perfeita.'
- html: '`$$\\pi = RT - CT$$ $$\\Longleftrightarrow$$ $$\\pi = P \\cdot Y - (w_{L} \\cdot L + w_{K} \\cdot K) $$ $$\\Longleftrightarrow$$ $$\\pi = ${calcs.P.toFixed(2)} \\cdot ${calcs.Yeq.toFixed(2)} - ( ${calcs.WLreal.toFixed(3)} \\cdot ${params.L.toFixed(2)} + ${calcs.req.toFixed(2)} \\cdot ${calcs.Keq.toFixed(2)})$$ $$\\Longleftrightarrow$$ $$\\pi=${calcs.pi1.toFixed(2)}$$`'
- html:
- html: 'A Função de Produção é do tipo Cobb-Douglas : $${F(K,L) = K^a \cdot L^{1-a}}$$'
- html: 'A função de demanda por Capital (K) é dada pela derivada parcial de ${F(K,L)}$: $${\frac{\partial F(K,L)}{\partial K}=a \cdot K^{a-1} \cdot L^{1-a}=w_{K}}$$ em que ${\bf{w_K}}$ é a remuneração do Capital (K). De modo que, $${w_{k}= (1+r)}$$ Logo, $${r= w_{k} - 1}$$'
- html: 'A função de oferta de Capital (K) — ou poupança (S) — é modelada como sendo uma proporção constante da renda (Y), dado pelo parâmetro (${s}$): $${S(Y)=s \cdot Y}$$ $${\Longleftrightarrow}$$ $${S(Y) = s \cdot (K^a \cdot L^{1-a})}$$ Resolvendo implicitamente, encontramos: $${s \cdot (K^a \cdot L^{1-a})=K}$$ $${\Longleftrightarrow}$$ $${\frac{K}{K^a}=s \cdot L^{1-a}}$$ $${\Longleftrightarrow}$$ $${K=\left( s \cdot L^{1-a} \right)^{\frac{1}{1-a}}}$$'