params:
- {name: sK, value: .2, min: 0.01, max: 1, 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: KALinit, value: 1, min: 0, max: 4, round: 0.1}
- {name: Kinit, value: 5, min: 1, max: 10, round: .5}
- {name: Ainit, value: 2, min: 1, max: 5, round: .5}
- {name: Linit, value: 1, min: .5, max: 4, round: .5}
- {name: KYold, value: 2.5, min: 0, max: 4, round: 0.1}
- {name: alpha, value: .3, min: .05, max: .95, round: 0.05}
calcs:
KYss: (params.sK/(params.gL + params.gA + params.delta))
KALss: (calcs.KYss)^(1/(1-params.alpha))
KYinit: (params.Kinit/(params.Ainit*params.Linit))
a: (params.alpha)/(1-params.alpha)
conv: 1 - (1-params.alpha)*(params.gL + params.gA + params.delta)
layout:
TwoVerticalGraphsPlusSidebar:
topGraph:
xAxis:
max: 15
ticks: 15
yAxis:
title: Growth rate
max: .05
min: -.02
objects:
- Line:
yIntercept: .02
slope: 0
color: blue
lineStyle: dashed
label:
text: \text{Old BGP}
x: 15
- Line:
yIntercept: (params.gA)
slope: 0
color: green
lineStyle: dashed
label:
text: \text{New BGP}
x: 15
- Curve:
univariateFunction:
fn: (params.gA)+(params.alpha*params.sK)*(calcs.KYss*(1-(.9)^(x)) + calcs.KYinit*((.9)^(x)))^(-1) - (params.alpha)*(params.delta + params.gA + params.gL)
ind: x
color: black
label:
text: \text{Actual}
x: 10
bottomGraph:
xAxis:
title: Time
max: 15
ticks: 15
yAxis:
title: Log GDP per capita
max: 2.5
min: 0
objects:
- Curve:
univariateFunction:
fn: (calcs.a)log(params.KYold) + log(2) + (.02)*(x)
ind: x
color: blue
lineStyle: dashed
label:
text: \text{Old BGP}
x: 15
- Curve:
univariateFunction:
fn: (calcs.a)log(calcs.KYss) + log(params.Ainit) + (params.gA)*(x)
ind: x
color: green
lineStyle: dashed
label:
text: \text{New BGP}
x: 15
- Curve:
univariateFunction:
fn: (calcs.a)*log(calcs.KYss*(1-(.9)^(x)) + calcs.KYinit*(.9)^(x)) + log(params.Ainit) + (params.gA)*(x)
ind: x
color: black
label:
text: \text{Actual}
x: 10
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: gA, label: g_A}
- {param: gL, label: g_L}
- {param: sK, label: s_K}
- {param: delta, label: \delta}
- {param: alpha, label: \alpha}
- title: Initial conditions
description: Adjust initial conditions to see effect on growth rate and level of GDP per capita. Note how these differ from adjusting parameters. Reload the page to reset.
sliders:
- {param: Kinit, label: K_0}
- {param: Ainit, label: A_0}
- {param: Linit, label: L_0}
- title: Steady state
divs:
- html: "`$$(K/Y)_{ss} = ${calcs.KYss.toFixed(2)}$$`"
- html: "`$$(K/AL)_{ss} = ${calcs.KALss.toFixed(2)}$$`"
- title: Warnings
divs:
- html: "`The steady state calculations are accurate. But the graphs are set up for visual appeal, not numeric accuracy. There will be extreme situations where the growth rate implied in the log GDP per capita graph is inconsistent with the top figure. If you want to see exact solutions, use the spreadsheet.`"