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: sX, value: .02, min: 0.001, max: .15, round: 0.001}
- {name: Kinit, value: 2.1, min: 1, max: 10, round: .01}
- {name: Ainit, value: 2, min: 1, max: 5, round: .5}
- {name: Linit, value: 1, min: .5, max: 4, round: .5}
- {name: Xinit, value: 1, min: .5, max: 10, round: .5}
- {name: KYold, value: 2.5, min: 0, max: 4, round: 0.1}
- {name: alpha, value: .3, min: .001, max: .5, round: 0.001}
- {name: beta, value: .1, min: .001, max: .4, round: 0.001}
calcs:
a: (params.alpha)/(1-params.alpha)
b: (params.beta)/(1-params.alpha)
Binit: (params.Ainit)^(1-calcs.b)*((params.sX*params.Xinit/params.Linit)^(calcs.b))
gBss: (1 - calcs.b)*(params.gA) - (calcs.b)*(params.sX + params.gL)
KYss: (params.sK)/(params.gL + calcs.gBss + params.delta)
KYinit: ((params.Kinit)/(calcs.Binit*params.Linit))^(1/(1-params.alpha))
layout:
TwoVerticalGraphsPlusSidebar:
topGraph:
xAxis:
max: 15
ticks: 15
yAxis:
title: Growth rate
max: .05
min: -.02
objects:
- Line:
yIntercept: .0129
slope: 0
color: blue
lineStyle: dashed
label:
text: \text{Old BGP}
x: 15
- Line:
yIntercept: (calcs.gBss)
slope: 0
color: green
lineStyle: dashed
label:
text: \text{New BGP}
x: 15
- Curve:
univariateFunction:
fn: (calcs.gBss)+(params.alpha*params.sK)*(calcs.KYss*(1-(.9)^(x)) + calcs.KYinit*((.9)^(x)))^(-1) - (params.alpha)*(params.delta + calcs.gBss + 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: 1.5
min: 0
objects:
- Curve:
univariateFunction:
fn: (calcs.a)log(2.74) + log(1.035) + (.0129)*(x)
ind: x
color: blue
lineStyle: dashed
label:
text: \text{Old BGP}
x: 15
- Curve:
univariateFunction:
fn: (calcs.a)log(calcs.KYss) + log(calcs.Binit) + (calcs.gBss)*(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(calcs.Binit) + (calcs.gBss)*(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: sX, label: s_X}
- {param: delta, label: \delta}
- {param: alpha, label: \alpha}
- {param: beta, label: \beta}
- 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. Compare the effects of X versus K, in particular.
sliders:
- {param: Kinit, label: K_0}
- {param: Ainit, label: A_0}
- {param: Linit, label: L_0}
- {param: Xinit, label: X_0}
- title: Steady state
description: See how changing resource use or endowment changes the growth rate in steady state. It can also change the steady state K/Y ratio, and note in the graph what changes the level of the BGP (and what does not).
divs:
- html: "`$$\\\\text{S.S. } g_y = \\\\left(1-\\\\frac{\\\\beta}{1-\\\\alpha}\\\\right)g_A - \\\\frac{\\\\beta}{1-\\\\alpha}(s_X + g_L) $$`"
- html: "`$$\\\\Rightarrow ${calcs.gBss.toFixed(4)}$$`"
- html: "`$$(K/Y)_{ss} = \\\\frac{s_K}{g_B + g_L + \\\\delta} = ${calcs.KYss.toFixed(2)}$$`"