params:
- {name: nu, value: .1, min: 0, max: 1, round: 0.01}
- {name: cbar, value: .95, min: 0, max: 2, round: 0.01}
- {name: gA, value: .02, min: 0, max: .1, round: 0.001}
- {name: beta, value: .3, min: 0, max: 1, round: 0.01}
- {name: Linit, value: 1, min: 0.01, max: 10, round: .01}
- {name: Ainit, value: 1, min: 0.01, max: 10, round: .01}
- {name: Xinit, value: 1, min: 0.01, max: 10, round: .01}
calcs:
AXLinit: (params.Ainit)*(params.Xinit)/(params.Linit)
gAss: (params.lam)*(params.gL)/(1-params.phi)
gL: (params.nu)*(calcs.AXLinit)^(params.beta)-(params.nu)*(params.cbar)
AXLss: ((params.gA)/(params.nu)+(params.cbar))^(1/(params.beta))
yss: (params.gA)/(params.nu)+(params.cbar)
gy: (params.beta)*(params.gA - calcs.gL)
yinit: (calcs.AXLinit)^(params.beta)
layout:
OneGraphPlusSidebar:
graph:
xAxis:
title: AX/L
max: 3
min: 0
intercept: 0
yAxis:
title: Growth rates
max: .04
min: -.02
intercept: 0
objects:
- Point:
coordinates: [calcs.AXLss,params.gA]
color: red
droplines:
vertical: (AX/L)_{ss}
- Point:
coordinates: [calcs.AXLinit, calcs.gL]
droplines:
vertical: \text{Initial } AX/L
horizontal: g_L
- Arrow:
begin: [calcs.AXLinit,.002]
end: [calcs.AXLss,.002]
color: blue
trim: .1
- Arrow:
begin: [.1,calcs.gL]
end: [.1,params.gA]
color: blue
trim: .1
- Curve:
univariateFunction:
fn: (params.nu)*((x))^(params.beta) - (params.nu)*(params.cbar)
ind: x
color: blue
lineStyle: dashed
strokeWidth: 4
label:
text: g_L= \nu \left(\frac{AX}{L}\right)^{\beta} - \nu \overline{c}
x: 8
- Line:
yIntercept: (params.gA)
slope: 0
lineStyle: dashed
strokeWidth: 4
color: green
label:
text: g_A
x: 9
sidebar:
controls:
- title: Parameters
description: Adjust parameter(s) to see effect on growth rate of population. You can adjust multiple parameters. Reload the page to reset.
sliders:
- {param: nu, label: \nu}
- {param: cbar, label: c(bar) }
- {param: gA, label: g_A}
- {param: beta, label: \beta}
- title: Initial conditions
description: You can adjust the initial AX/L ratio here. Note how it affects the initial living standards and how it influences (or does not) the steady state outcomes.
sliders:
- {param: Linit, label: L }
- {param: Ainit, label: A }
- {param: Xinit, label: X }
- title: Calculations
description: Given the initial conditions and parameters we can calculate these...
divs:
- html: "`$$\\\\text{Initial } g_y = \\\\beta (g_A - g_L) = ${calcs.gy.toFixed(4)}$$`"
- html: "`$$\\\\text{Steady state } g_y = 0$$`"
- html: "`$$\\\\text{Initial } g_L = \\\\nu \\\\left(\\\\frac{AX}{L}\\\\right)^{\\\\beta} - \\\\nu \\\\overline{c} = ${calcs.gL.toFixed(4)}$$`"
- html: "`$$\\\\text{Steady state } g_L = ${params.gA.toFixed(4)}$$`"
- html: "`$$\\\\text{Initial } y = \\\\left(\\\\frac{AX}{L}\\\\right)^{\\\\beta} = ${calcs.yinit.toFixed(4)}$$`"
- html: "`$$\\\\text{Steady state } y = \\\\frac{g_A}{\\\\nu} - \\\\overline{c} = ${calcs.yss.toFixed(4)}$$`"