barrettruth.com/scripts/posts/models-of-production.js

696 lines
17 KiB
JavaScript

function setUpParameters(render, parameters, modelPrefix) {
parameters.forEach((param) => {
const slider = document.getElementById(`slider${modelPrefix}${param}`);
slider.oninput = function () {
slider.previousElementSibling.innerText = this.value;
render();
};
});
return parameters.map((param) => {
return parseFloat(
document.getElementById(`output${modelPrefix}${param}`).textContent,
);
});
}
function drawSolowGraph() {
const L = 150,
K_MAX = 500,
margin = { top: 20, right: 30, bottom: 20, left: 50 };
const [A, d, s, alpha] = setUpParameters(
drawSolowGraph,
["A", "d", "s", "alpha"],
"S",
);
const solowOutput = (K) => A * Math.pow(K, alpha) * Math.pow(L, 1 - alpha);
const solowDepreciation = (K) => d * K;
const solowInvestment = (Y) => s * Y;
const container = document.getElementById("solow-visualization");
const width = container.clientWidth - margin.left - margin.right;
const height = container.clientHeight - margin.top - margin.bottom;
container.innerHTML = "";
const svg = d3
.select("#solow-visualization")
.append("svg")
.attr("width", width + margin.left + margin.right)
.attr("height", height + margin.top + margin.bottom)
.append("g")
.attr("transform", `translate(${margin.left}, ${margin.top})`);
const x = d3.scaleLinear().domain([0, K_MAX]).range([0, width]);
svg
.append("g")
.attr("transform", `translate(0, ${height})`)
.call(d3.axisBottom(x))
.append("text")
.attr("fill", "#000")
.attr("x", width + 10)
.attr("y", -10)
.style("text-anchor", "end")
.style("font-size", "1.5em")
.text("K");
const Y_MAX = solowOutput(K_MAX) + K_MAX / 10;
const y = d3.scaleLinear().domain([0, Y_MAX]).range([height, 0]);
svg
.append("g")
.call(d3.axisLeft(y))
.append("text")
.attr("fill", "#000")
.attr("x", 0)
.attr("y", -10)
.style("text-anchor", "start")
.style("font-size", "1.5em")
.text("Y");
const outputData = Array.from({ length: K_MAX }, (_, k) => ({
K: k,
Y: solowOutput(k),
}));
svg
.append("path")
.datum(outputData)
.attr("fill", "none")
.attr("stroke", getTopicColor(urlToTopic()))
.attr("stroke-width", 2)
.attr(
"d",
d3
.line()
.x((d) => x(d.K))
.y((d) => y(d.Y)),
);
svg
.append("foreignObject")
.attr("width", "2em")
.attr("height", "2em")
.attr("x", x(K_MAX))
.attr("y", y(outputData[K_MAX - 1].Y))
.append("xhtml:body")
.style("font-size", "0.75em")
.html(`\\(Y\\)`);
const depreciationData = Array.from({ length: K_MAX }, (_, k) => ({
K: k,
Y: solowDepreciation(k),
}));
svg
.append("path")
.datum(depreciationData)
.attr("fill", "none")
.attr("stroke", "red")
.attr("stroke-width", 2)
.attr(
"d",
d3
.line()
.x((d) => x(d.K))
.y((d) => y(d.Y)),
);
svg
.append("foreignObject")
.attr("width", "2em")
.attr("height", "2em")
.attr("x", x(K_MAX))
.attr("y", y(depreciationData[K_MAX - 1].Y))
.append("xhtml:body")
.style("font-size", "0.75em")
.append("xhtml:div")
.html("\\(\\bar{d}K\\)");
const investmentData = outputData.map((d) => ({
K: d.K,
Y: solowInvestment(d.Y),
}));
svg
.append("path")
.datum(investmentData)
.attr("fill", "none")
.attr("stroke", "purple")
.attr("stroke-width", 2)
.attr(
"d",
d3
.line()
.x((d) => x(d.K))
.y((d) => y(d.Y)),
);
svg
.append("foreignObject")
.attr("width", "1em")
.attr("height", "2em")
.attr("x", x(K_MAX))
.attr("y", y(investmentData[K_MAX - 1].Y))
.append("xhtml:body")
.style("font-size", "0.75em")
.html("\\(I\\)");
const k_star = L * Math.pow((s * A) / d, 1 / (1 - alpha));
svg
.append("line")
.attr("x1", x(k_star))
.attr("y1", y((d * k_star) / s))
.attr("x2", x(k_star))
.attr("y2", y(0))
.attr("stroke", "black")
.attr("stroke-width", 1)
.attr("stroke-dasharray", "5,5");
const y_star = solowOutput(k_star);
svg
.append("foreignObject")
.attr("width", "20em")
.attr("height", "2em")
.attr("x", x(k_star) - 40)
.attr("y", y(y_star) - 40)
.append("xhtml:body")
.style("font-size", "0.75em")
.html(`(${k_star.toFixed(0)}, ${y_star.toFixed(0)})`);
}
const formatNumber = (num) => {
return `~${num.toExponential(0)}`;
};
const normalFont = `style="font-weight: normal"`;
const updateRomerTable = (romerData) => {
const tableHeader = document.getElementById("romer-table-header");
const rowA_t = document.getElementById("row-A_t");
const rowY_t = document.getElementById("row-Y_t");
tableHeader.innerHTML = `<th ${normalFont}>t</th>`;
rowA_t.innerHTML = `<td class="romer-table-at">A_t</td>`;
rowY_t.innerHTML = `<td class="romer-table-yt">Y_t</td>`;
romerData.forEach((d) => {
if (d.year % 20 === 0 || d.year === 1) {
tableHeader.innerHTML += `<th ${normalFont}>${d.year}</th>`;
rowA_t.innerHTML += `<td>${formatNumber(d.A)}</td>`;
rowY_t.innerHTML += `<td>${formatNumber(d.Y)}</td>`;
}
});
};
function drawRomerGraph() {
const T_MAX = 100,
margin = { top: 20, right: 100, bottom: 20, left: 50 };
const [z, L, l, A0] = setUpParameters(
drawRomerGraph,
["z", "L", "l", "A0"],
"R",
);
const container = document.getElementById("romer-visualization");
const width = container.clientWidth - margin.left - margin.right;
const height = container.clientHeight - margin.top - margin.bottom;
container.innerHTML = "";
const svg = d3
.select("#romer-visualization")
.append("svg")
.attr("width", width + margin.left + margin.right)
.attr("height", height + margin.top + margin.bottom)
.append("g")
.attr("transform", `translate(${margin.left}, ${margin.top})`);
let A = A0;
const romerData = [];
for (let t = 1; t <= T_MAX; ++t) {
const A_t = A * (1 + z * l * L);
const Y_t = A_t * (1 - l) * L;
romerData.push({ year: t, A: A_t, Y: Math.log10(Y_t) });
A = A_t;
}
const x = d3.scaleLinear().domain([1, T_MAX]).range([0, width]);
svg
.append("g")
.attr("transform", `translate(0, ${height})`)
.call(d3.axisBottom(x))
.append("text")
.attr("fill", "#000")
.attr("x", width + 10)
.attr("y", -10)
.style("text-anchor", "end")
.style("font-size", "1.5em")
.text("t");
const y = d3
.scaleLinear()
.domain([0, romerData[romerData.length - 1].Y])
.range([height, 0]);
svg
.append("g")
.call(d3.axisLeft(y).ticks(10, d3.format(".1s")))
.append("text")
.attr("fill", "#000")
.attr("x", 0)
.attr("y", -10)
.style("text-anchor", "start")
.style("font-size", "1.5em")
.text("log(Y)");
svg
.append("path")
.datum(romerData)
.attr("fill", "none")
.attr("stroke", getTopicColor(urlToTopic()))
.attr("stroke-width", 2)
.attr(
"d",
d3
.line()
.x((d) => x(d.year))
.y((d) => y(d.Y)),
);
svg
.append("foreignObject")
.attr("width", "4em")
.attr("height", "2em")
.attr("x", x(T_MAX))
.attr("y", y(romerData[T_MAX - 1].Y))
.append("xhtml:body")
.style("font-size", "0.75em")
.html(`\\(log_{10}Y\\)`);
updateRomerTable(romerData);
}
function drawRomerlGraph() {
const T_MAX = 100,
z = 0.01,
L = 50,
A0 = 50,
margin = { top: 20, right: 100, bottom: 20, left: 50 };
const [l, t0] = setUpParameters(drawRomerlGraph, ["lChange", "t0"], "");
const container = document.getElementById("romer-lchange-visualization");
const width = container.clientWidth - margin.left - margin.right;
const height = container.clientHeight - margin.top - margin.bottom;
container.innerHTML = "";
const svg = d3
.select("#romer-lchange-visualization")
.append("svg")
.attr("width", width + margin.left + margin.right)
.attr("height", height + margin.top + margin.bottom)
.append("g")
.attr("transform", `translate(${margin.left}, ${margin.top})`);
let A = A0,
l_ = 0.1;
const romerData = [];
for (let t = 1; t <= t0; ++t) {
const A_t = A * (1 + z * l_ * L);
const Y_t = A_t * (1 - l_) * L;
romerData.push({ year: t, A: A_t, Y: Math.log10(Y_t) });
A = A_t;
}
for (let t = t0 + 1; t <= T_MAX; ++t) {
const A_t = A * (1 + z * l * L);
const Y_t = A_t * (1 - l) * L;
romerData.push({ year: t, A: A_t, Y: Math.log10(Y_t) });
A = A_t;
}
const x = d3.scaleLinear().domain([1, T_MAX]).range([0, width]);
svg
.append("g")
.attr("transform", `translate(0, ${height})`)
.call(d3.axisBottom(x))
.append("text")
.attr("fill", "#000")
.attr("x", width + 10)
.attr("y", -10)
.style("text-anchor", "end")
.style("font-size", "1.5em")
.text("t");
const y = d3
.scaleLinear()
.domain([0, romerData[romerData.length - 1].Y])
.range([height, 0]);
svg
.append("g")
.call(d3.axisLeft(y).ticks(10, d3.format(".1s")))
.append("text")
.attr("fill", "#000")
.attr("x", 0)
.attr("y", -10)
.style("text-anchor", "start")
.style("font-size", "1.5em")
.text("log(Y)");
svg
.append("path")
.datum(romerData)
.attr("fill", "none")
.attr("stroke", getTopicColor(urlToTopic()))
.attr("stroke-width", 2)
.attr(
"d",
d3
.line()
.x((d) => x(d.year))
.y((d) => y(d.Y)),
);
svg
.append("line")
.attr("x1", x(t0))
.attr("y1", y(romerData[T_MAX - 1].Y))
.attr("x2", x(t0))
.attr("y2", height)
.attr("stroke", "black")
.attr("stroke-width", 1)
.attr("stroke-dasharray", "4");
svg
.append("foreignObject")
.attr("width", "5em")
.attr("height", "2em")
.attr("x", x(0) + 15)
.attr("y", y(romerData[0].Y))
.append("xhtml:body")
.style("font-size", "0.6em")
.html(`\\(\\bar{l}_0=${l_}\\)`);
svg
.append("foreignObject")
.attr("width", "5em")
.attr("height", "2em")
.attr("x", x(t0) + 15)
.attr("y", y(romerData[t0].Y))
.append("xhtml:body")
.style("font-size", "0.6em")
.html(`\\(\\bar{l}_1=${l}\\)`);
svg
.append("foreignObject")
.attr("width", "4em")
.attr("height", "2em")
.attr("x", x(T_MAX))
.attr("y", y(romerData[T_MAX - 1].Y))
.append("xhtml:body")
.style("font-size", "0.75em")
.html(`\\(log_{10}Y\\)`);
}
function calculateRomerSolowData(
T_MAX,
L,
l,
A0,
alpha,
s,
d,
z,
t0 = Infinity,
L0,
l0,
alpha0,
z0,
) {
let A = A0,
K_t = 1,
romerSolowData = [];
for (let t = 1; t <= T_MAX; ++t) {
if (t > t0) {
alpha = alpha0;
z = z0;
l = l0;
L = L0;
}
const Y_t = A * Math.pow(K_t, alpha) * Math.pow((1 - l) * L, 1 - alpha);
const A_t = A * (1 + z * l * L);
K_t = K_t + s * Y_t - d * K_t;
romerSolowData.push({ year: t, A: A_t, K: K_t, Y: Math.log10(Y_t) });
A = A_t;
}
return romerSolowData;
}
function drawRomerSolowGraph() {
const T_MAX = 100,
margin = { top: 20, right: 100, bottom: 20, left: 50 };
const [z, l, L, A0, s, d, alpha] = setUpParameters(
drawRomerSolowGraph,
["z", "l", "L", "A0", "s", "d", "alpha"],
"RS",
);
const container = document.getElementById("romer-solow-visualization");
const width = container.clientWidth - margin.left - margin.right;
const height = container.clientHeight - margin.top - margin.bottom;
container.innerHTML = "";
const svg = d3
.select("#romer-solow-visualization")
.append("svg")
.attr("width", width + margin.left + margin.right)
.attr("height", height + margin.top + margin.bottom)
.append("g")
.attr("transform", `translate(${margin.left}, ${margin.top})`);
const romerSolowData = calculateRomerSolowData(
T_MAX,
L,
l,
A0,
alpha,
s,
d,
z,
);
const x = d3.scaleLinear().domain([1, T_MAX]).range([0, width]);
svg
.append("g")
.attr("transform", `translate(0, ${height})`)
.call(d3.axisBottom(x))
.append("text")
.attr("fill", "#000")
.attr("x", width + 10)
.attr("y", -10)
.style("text-anchor", "end")
.style("font-size", "1.5em")
.text("t");
const y = d3
.scaleLinear()
.domain([0, romerSolowData[romerSolowData.length - 1].Y])
.range([height, 0]);
svg
.append("g")
.call(d3.axisLeft(y).ticks(10, d3.format(".1s")))
.append("text")
.attr("fill", "#000")
.attr("x", 0)
.attr("y", -10)
.style("text-anchor", "start")
.style("font-size", "1.5em")
.text("log(Y)");
svg
.append("path")
.datum(romerSolowData)
.attr("fill", "none")
.attr("stroke", getTopicColor(urlToTopic()))
.attr("stroke-width", 2)
.attr(
"d",
d3
.line()
.x((d) => x(d.year))
.y((d) => y(d.Y)),
);
svg
.append("foreignObject")
.attr("width", "4em")
.attr("height", "2em")
.attr("x", x(T_MAX))
.attr("y", y(romerSolowData[T_MAX - 1].Y))
.append("xhtml:body")
.style("font-size", "0.75em")
.html(`\\(log_{10}Y\\)`);
}
function drawRomerSolowChangeGraph() {
const T_MAX = 100,
margin = { top: 20, right: 100, bottom: 20, left: 50 },
s = 0.2,
d = 0.2,
A0 = 50,
alpha = 0.33,
l = 0.5,
L = 100,
z = 0.5;
const [z0, l0, L0, alpha0, t0] = setUpParameters(
drawRomerSolowChangeGraph,
["z0", "l0", "L0", "alpha0", "t0"],
"RSC",
);
const container = document.getElementById("romer-solow-change-visualization");
const width = container.clientWidth - margin.left - margin.right;
const height = container.clientHeight - margin.top - margin.bottom;
container.innerHTML = "";
const svg = d3
.select("#romer-solow-change-visualization")
.append("svg")
.attr("width", width + margin.left + margin.right)
.attr("height", height + margin.top + margin.bottom)
.append("g")
.attr("transform", `translate(${margin.left}, ${margin.top})`);
const romerSolowData = calculateRomerSolowData(
T_MAX,
L,
l,
A0,
alpha,
s,
d,
z,
t0,
L0,
l0,
alpha0,
z0,
);
const x = d3.scaleLinear().domain([1, T_MAX]).range([0, width]);
svg
.append("g")
.attr("transform", `translate(0, ${height})`)
.call(d3.axisBottom(x))
.append("text")
.attr("fill", "#000")
.attr("x", width + 10)
.attr("y", -10)
.style("text-anchor", "end")
.style("font-size", "1.5em")
.text("t");
const y = d3
.scaleLinear()
.domain([0, romerSolowData[romerSolowData.length - 1].Y])
.range([height, 0]);
svg
.append("g")
.call(d3.axisLeft(y).ticks(10, d3.format(".1s")))
.append("text")
.attr("fill", "#000")
.attr("x", 0)
.attr("y", -10)
.style("text-anchor", "start")
.style("font-size", "1.5em")
.text("log(Y)");
svg
.append("path")
.datum(romerSolowData)
.attr("fill", "none")
.attr("stroke", getTopicColor(urlToTopic()))
.attr("stroke-width", 2)
.attr(
"d",
d3
.line()
.x((d) => x(d.year))
.y((d) => y(d.Y)),
);
svg
.append("line")
.attr("x1", x(t0))
.attr("y1", y(romerSolowData[T_MAX - 1].Y))
.attr("x2", x(t0))
.attr("y2", height)
.attr("stroke", "black")
.attr("stroke-width", 1)
.attr("stroke-dasharray", "4");
svg
.append("foreignObject")
.attr("width", "4em")
.attr("height", "2em")
.attr("x", x(T_MAX))
.attr("y", y(romerSolowData[T_MAX - 1].Y))
.append("xhtml:body")
.style("font-size", "0.75em")
.html(`\\(log_{10}Y\\)`);
}
document.addEventListener("DOMContentLoaded", function () {
drawSolowGraph();
window.onresize = drawSolowGraph;
drawRomerGraph();
window.onresize = drawRomerGraph;
drawRomerlGraph();
window.onresize = drawRomerlGraph;
drawRomerSolowGraph();
window.onresize = drawRomerSolowGraph;
drawRomerSolowChangeGraph();
window.onresize = drawRomerSolowChangeGraph();
});
document.addEventListener("DOMContentLoaded", function () {
// wait for mathjax
if (typeof MathJax !== "undefined") {
MathJax.typeset();
initSliderEvents();
} else {
window.MathJax = {
startup: {
pageReady: function () {
return MathJax.startup.defaultPageReady().then(function () {
initSliderEvents();
});
},
},
};
}
function initSliderEvents() {
document.querySelectorAll(".sliders").forEach((slidersDiv) => {
slidersDiv.addEventListener("input", function (event) {
const graphDiv = slidersDiv.previousElementSibling;
if (graphDiv && graphDiv.querySelector("svg")) {
const svg = graphDiv.querySelector("svg");
svg.querySelectorAll("foreignObject body").forEach((body) => {
MathJax.typesetPromise([body]);
});
}
});
});
}
});