schema: EconSchema
params:
- name: s
value: 0.3
min: 0.1
max: 0.35
round: 0.01
- name: d
value: 0.06
min: 0.01
max: 0.1
round: 0.001
- name: n
value: 0.05
min: 0.01
max: 0.1
round: 0.001
- name: a
value: 0.6
min: 0.1
max: 0.9
precision: 0.01
round: 0.01
calcs:
k: (((params.s)/(params.n+params.d))^(1/(1-params.a)))
sy: ((calcs.k)*(params.n+params.d))
r1: ((20)*(params.n+params.d))
r2: (((params.s)*(18)^(params.a)))
layout:
OneGraphPlusSidebar:
graph:
xAxis:
min: 0
max: 20
ticks: 4
yAxis:
min: -0.1
max: 2.5
ticks: 4
objects:
#Investimento Per capita
- Curve:
fn: "(((params.s)*(x^(params.a))))"
ind: x
color: red
min: 0
max: 18
lineStyle: solid
strokeWidth: 4
samplePoints: 3000
#Taxa de crescimento da população e depreciação
- Curve:
fn: "((x)*(params.n+params.d))"
ind: x
min: 0
max: 19
color: blue
lineStyle: solid
strokeWidth: 4
samplePoints: 300
- Curve:
fn: "(((params.s)*x^(params.a))-(x)*(params.n+params.d))"
ind: x
min: -0.1
max: 20
color: "'#58975b'"
lineStyle: solid
strokeWidth: 4
samplePoints: 300
- Point:
coordinates: [calcs.k, 0]
color: black
r: 5
- Point:
coordinates: [calcs.k, calcs.sy]
color: black
r: 5
- Segment:
a: [calcs.k, calcs.sy]
b: [calcs.k, 0]
color: green
lineStyle: dotted
strokeWidth: 2
- Segment:
a: [0, calcs.sy]
b: [calcs.k, calcs.sy]
color: green
lineStyle: dotted
strokeWidth: 2
- Segment:
a: [0, 2.5]
b: [0, 2.5]
color: Black
bgcolor: white
strokeWidth: 1
label:
text: sf(k)
position: r
fontSize: 11
- Segment:
a: [20, 0]
b: [20, 0]
color: Black
bgcolor: white
strokeWidth: 1
label:
text: k
position: t
fontSize: 11
- Segment:
a: [0, calcs.sy]
b: [0, calcs.sy]
color: Black
bgcolor: "'#36a854'"
strokeWidth: 1
label:
text: calcs.sy.toFixed(2)
position: r
fontSize: 11
- Segment:
a: [calcs.k, 0]
b: [calcs.k, 0]
color: Black
bgcolor: "'#36a854'"
strokeWidth: 1
label:
text: calcs.k.toFixed(2)
position: t
fontSize: 11
- Segment:
a: [15, calcs.r1]
b: [15, calcs.r1]
color: white
bgcolor: "'#2177b5'"
strokeWidth: 1
label:
text: k(t)(n+d)
position: l
fontSize: 11
- Segment:
a: [18, calcs.r2]
b: [18, calcs.r2]
color: white
bgcolor: "'#d62728'"
strokeWidth: 1
label:
text: sf(k(t))
position: l
fontSize: 11
sidebar:
controls:
- title: Modelo de Crescimento de Solow
sliders:
- param: s
label: s
digits: 4
- param: d
label: d
digits: 4
- param: a
label: \alpha
digits: 4
- param: n
label: n
digits: 4
divs:
- html: '`A equação fundamental de Solow é: $$dk = s \\cdot y(k(t)) - k(t)(n+d)$$ $$\\Longleftrightarrow$$ $$ dk = s \\cdot k(t)^a - k(t)(n+d)$$ Ou, simplesmente $$ \\dot{k} = s \\cdot k^a - k(n+d)$$`'
- html: '`O estado estácionário é encontrado quando o $\\dot{k}$ é igual a zero: $$ \\dot{k} = s \\cdot k^a - k(n+d) = 0 $$ $$\\Longleftrightarrow$$ $$ s \\cdot k^a - k(n+d) = 0 $$ Resolvendo para $k$, temos: $$ k^* = \\left( \\frac{s}{n+d} \\right)^{\\frac{1}{1-a}}$$ `'
- html: '`Para encontrar o $y^*$, basta substituir em $y(k)$ $$y(k)=k^a$$ $$\\Longleftrightarrow$$ $$y(k^*)= (k^*)^a $$`'