params:
- {name: lam, value: .9, min: 0, max: 1, round: 0.01}
- {name: gL, value: .01, min: 0, max: .05, round: 0.001}
- {name: phi, value: 0, min: -.5, max: .9, round: 0.01}
- {name: sR, value: .05, min: 0, max: .15, round: 0.01}
- {name: theta, value: .1, min: 0, max: 1, round: 0.01}
- {name: Linit, value: 100, min: 1, max: 200, round: 1}
- {name: Ainit, value: 47.7, min: 1, max: 100, round: .01}
- {name: LAinit, value: 2, min: 0, max: 4, round: .01}
calcs:
LAss: (params.lam*params.gL)/((1-params.phi)*(params.theta)*(params.sR)^(params.lam))
gAss: (params.lam)*(params.gL)/(1-params.phi)
gA: (params.theta)*(params.sR)^(params.lam)*(params.LAinit)
layout:
OneGraphPlusSidebar:
graph:
xAxis:
title: $L^{\lambda}/A^{1-\phi}$
max: 3
min: 0
intercept: 0
yAxis:
title: Growth rates
max: .03
min: 0
intercept: 0
objects:
- Point:
coordinates: [params.LAinit,0]
drag:
- horizontal: LAinit
- Point:
coordinates: [calcs.LAss,(calcs.gAss)]
color: red
droplines:
vertical: (L^{\lambda}/A^{1-\phi})_{ss}
- Point:
coordinates: [params.LAinit, calcs.gA]
droplines:
vertical: \text{Initial } L^{\lambda}/A^{1-\phi}
horizontal: g_A
- Arrow:
begin: [params.LAinit,.001]
end: [calcs.LAss,.001]
color: blue
trim: .1
- Arrow:
begin: [.1,calcs.gA]
end: [.1,calcs.gAss]
color: blue
trim: .1
- Curve:
univariateFunction:
fn: (params.theta)*(params.sR)^(params.lam)*(x)
ind: x
color: blue
lineStyle: dashed
strokeWidth: 4
label:
text: g_A= \theta s_R^{\lambda} \frac{L^{\lambda}}{A^{1-\phi}}
x: 2.5
- Line:
yIntercept: (calcs.gAss)
slope: 0
lineStyle: dashed
strokeWidth: 4
color: green
label:
text: \frac{\lambda}{1-\phi}g_L
x: 3
sidebar:
controls:
- title: Parameters
description: Adjust parameter(s) to see effect on growth rate and level of GDP per capita. You can adjust multiple parameters. Reload the page to reset.
sliders:
- {param: gL, label: g_L}
- {param: lam, label: \lambda}
- {param: phi, label: \phi}
- {param: theta, label: \theta}
- {param: sR, label: s_R}
- title: Initial conditions
description: You can adjust the initial L/A ratio using the dot on the x-axis or this control. The exponents (lambda,phi) don't display well here, but you're adjusting the right thing.
sliders:
- {param: LAinit, label: L/A }
- title: Calculations
description: Given the initial conditions and parameters we can calculate these...
divs:
- html: "`$$\\\\text{Initial } g_A = \\\\theta s_R^{\\\\lambda} L^{\\\\lambda}/A^{1-\\\\phi} = ${calcs.gA.toFixed(4)}$$`"
- html: "`$$\\\\text{Steady state } g_A = \\\\lambda g_L / (1-\\\\phi) = ${calcs.gAss.toFixed(4)}$$`"