params:
- {name: sKset, value: 4, min: 3, max: 6, round: 0.01}
- {name: gAset, value: 4, min: 3, max: 6, round: 0.01}
- {name: gLset, value: 4, min: 3, max: 6, round: 0.01}
- {name: delta, value: .05, min: 0, max: .15, round: 0.01}
- {name: alpha, value: .3, min: .05, max: .95, round: 0.05}
- {name: Ainit, value: 4, min: 3, max: 6, round: 0.1}
- {name: Kinit, value: 4, min: 3, max: 6, round: 0.1}
- {name: Linit, value: 4, min: 3, max: 6, round: 0.1}
calcs:
Kscale: (params.Kinit)*10
sK: (params.sKset - 3)*.2
gA: (params.gAset - 3)*.01
gL: (params.gLset - 3)*.01
KALinit: (calcs.Kscale)/(params.Ainit*params.Linit)
KYinit: ((calcs.Kscale)/(params.Ainit*params.Linit))^(1-params.alpha)
KYss: (calcs.sK/(calcs.gL + calcs.gA + params.delta))
KALss: (calcs.sK/(calcs.gL + calcs.gA + params.delta))^(1/(1-params.alpha))
gK: (calcs.sK)*(1/calcs.KYinit) - (params.delta)
gy: (params.alpha)*(calcs.gK - calcs.gA - calcs.gL) + calcs.gA
a: (params.alpha)/(1-params.alpha)
layout:
SquarePlusTwoVerticalGraphs:
bigGraph:
xAxis:
title: K/AL ratio
max: 7
min: 0
intercept: 0
yAxis:
title: Growth rates
max: .10
min: -.03
intercept: 0
objects:
- Segment:
a: [3,.095]
b: [6,.095]
Linestyle: dotted
color: purple
- Segment:
a: [3,.09]
b: [6,.09]
Linestyle: dotted
color: purple
- Segment:
a: [3,.085]
b: [6,.085]
Linestyle: dotted
color: purple
- Segment:
a: [3,.08]
b: [6,.08]
Linestyle: dotted
color: purple
- Segment:
a: [3,.075]
b: [6,.075]
Linestyle: dotted
color: purple
- Segment:
a: [3,.07]
b: [6,.07]
Linestyle: dotted
color: purple
- Point:
coordinates: [params.Kinit,.095]
color: purple
label:
text: K_0
drag:
- horizontal: Kinit
- Point:
coordinates: [params.Ainit,.09]
color: purple
label:
text: A_0
drag:
- horizontal: Ainit
- Point:
coordinates: [params.Linit,.085]
color: purple
label:
text: L_0
drag:
- horizontal: Linit
- Point:
coordinates: [params.sKset,.08]
color: purple
label:
text: s_K
drag:
- horizontal: sKset
- Point:
coordinates: [params.gLset,.075]
color: purple
label:
text: g_L
drag:
- horizontal: gLset
- Point:
coordinates: [params.gAset,.07]
color: purple
label:
text: g_A
drag:
- horizontal: gAset
- Point:
coordinates: [calcs.KALss,(calcs.gA + calcs.gL)]
color: green
droplines:
vertical: (K/AL)_{ss}
label:
text: \text{Steady State}
- Point:
coordinates: [calcs.KALinit, calcs.gK]
droplines:
vertical: \text{Initial } K/AL
horizontal: g_K
- Arrow:
begin: [calcs.KALinit,.002]
end: [calcs.KALss,.002]
color: blue
trim: .1
- Curve:
univariateFunction:
fn: (calcs.sK)*(1/(x))^(1-params.alpha) - (params.delta)
ind: x
color: blue
strokeWidth: 4
label:
text: g_K = s_K \left(\frac{AL}{K}\right)^{1-\alpha} - \delta
x: 6.5
- Line:
yIntercept: (calcs.gA + calcs.gL)
slope: 0
strokeWidth: 4
color: orange
label:
text: g_A + g_L
x: 6.5
topGraph:
xAxis:
max: 15
ticks: 15
yAxis:
title: Growth rate
max: .05
min: -.02
objects:
- Line:
yIntercept: (calcs.gA)
slope: 0
color: green
lineStyle: dashed
label:
text: g_A
x: 15
- Curve:
univariateFunction:
fn: (calcs.gA)+(params.alpha*calcs.sK)*(calcs.KYss*(1-(.9)^(x)) + calcs.KYinit*((.9)^(x)))^(-1) - (params.alpha)*(params.delta + calcs.gA + calcs.gL)
ind: x
color: black
label:
text: \alpha(g_K - g_A - g_L) + g_A
x: 5
bottomGraph:
xAxis:
title: Time
max: 15
ticks: 15
intercept: .5
yAxis:
title: Log GDP per capita
max: 1.5
min: .5
objects:
- Curve:
univariateFunction:
fn: (calcs.a)log(calcs.KYss) + log(params.Ainit/2) + (calcs.gA)*(x)
ind: x
color: green
lineStyle: dashed
label:
text: \ln y_t^{BGP}
x: 15
- Curve:
univariateFunction:
fn: (calcs.a)*log(calcs.KYss*(1-(.9)^(x)) + calcs.KYinit*(.9)^(x)) + log(params.Ainit/2) + (calcs.gA)*(x)
ind: x
color: black
label:
text: \ln y_t
x: 10