params:
- {name: sK, value: .2, min: 0, max: .4, round: 0.01}
- {name: gA, value: .02, min: -.01, max: .05, round: 0.01}
- {name: gL, value: .01, min: -.05, max: .15, 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: KALinit, value: 2, min: 0, max: 7, round: 0.1}
calcs:
KYss: (params.sK/(params.gL + params.gA + params.delta))
KALss: (calcs.KYss)^(1/(1-params.alpha))
gK: (params.sK)*(1/params.KALinit)^(1-params.alpha) - (params.delta)
gy: (params.alpha)*(calcs.gK - params.gA - params.gL) + params.gA
layout:
OneGraphPlusSidebar:
graph:
xAxis:
title: K/AL ratio
max: 7
min: 0
intercept: 0
yAxis:
title: Growth rates
max: .10
min: -.03
intercept: 0
objects:
- Point:
coordinates: [params.KALinit,0]
drag:
- horizontal: KALinit
- Point:
coordinates: [calcs.KALss,(params.gA + params.gL)]
color: red
droplines:
vertical: (K/AL)_{ss}
- Point:
coordinates: [params.KALinit, calcs.gK]
droplines:
vertical: \text{Initial } K/AL
horizontal: g_K
- Arrow:
begin: [params.KALinit,.002]
end: [calcs.KALss,.002]
color: blue
trim: .1
label:
text: K/AL \text{ moves}
x: (params.KALinit + (calcs.KALss - params.KALinit)/2)
- Curve:
univariateFunction:
fn: (params.sK)*(1/(x))^(1-params.alpha) - (params.delta)
ind: x
color: blue
lineStyle: dashed
strokeWidth: 4
label:
text: g_K = s_K \left(\frac{AL}{K}\right)^{1-\alpha} - \delta
x: 6.5
- Line:
yIntercept: (params.gA + params.gL)
slope: 0
lineStyle: dashed
strokeWidth: 4
color: green
label:
text: g_A + g_L
x: 6.5
sidebar:
controls:
- title: Initial conditions
description: You can adjust the initial K/AL ratio using the dot on the x-axis or this control
sliders:
- {param: KALinit, label: K/AL}
- title: Parameters
description: Adjust these to see how steady state and the growth rate of capital change
sliders:
- {param: gL, label: g_L}
- {param: gA, label: g_A}
- {param: sK, label: s_K}
- {param: delta, label: \delta}
- {param: alpha, label: \alpha}
- title: Calculations
description: Given the initial conditions and parameters we can calculate these...
divs:
- html: "`$$(K/AL)_{ss} = ${calcs.KALss.toFixed(2)}$$`"
- html: "`$$(K/Y)_{ss} = ${calcs.KYss.toFixed(2)}$$`"
- html: "`$$g_K = s_K (AL/K)^{1-\\\\alpha} - \\\\delta = ${calcs.gK.toFixed(4)}$$`"
- html: "`$$g_y = \\\\alpha (g_K - g_A - g_L) + g_A = ${calcs.gy.toFixed(4)}$$`"