function drawSolowGraph() { const L = 150, K_MAX = 500, margin = { top: 20, right: 30, bottom: 20, left: 50 }; ["A", "D", "S", "Alpha"].forEach((param) => { const slider = document.getElementById(`slider${param}`); slider.oninput = function () { slider.previousElementSibling.innerText = this.value; drawSolowGraph(); }; }); const A = parseFloat(document.getElementById("outputA").textContent), D = parseFloat(document.getElementById("outputD").textContent), S = parseFloat(document.getElementById("outputS").textContent), alpha = parseFloat(document.getElementById("outputAlpha").textContent); const solowOutput = (K) => A * Math.pow(K, alpha) * Math.pow(L, 1 - alpha); const solowDepreciation = (K) => D * K; const solowInvestment = (Y) => S * Y; const container = document.getElementById("solow-visualization"); const width = container.clientWidth - margin.left - margin.right; const height = container.clientHeight - margin.top - margin.bottom; container.innerHTML = ""; const svg = d3 .select("#solow-visualization") .append("svg") .attr("width", width + margin.left + margin.right) .attr("height", height + margin.top + margin.bottom) .append("g") .attr("transform", `translate(${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(`
`); katex.render("Y", document.querySelector(".solow-visualization-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") .html(`
`); katex.render("\\bar{d}K", document.querySelector(".solow-visualization-d")); 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(`
`); katex.render("I", document.querySelector(".solow-visualization-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) - 150) .attr("y", y(y_star) - 50) .append("xhtml:body") .style("font-size", "0.75em") .html(`
`); katex.render( `(K^*,Y^*)=(${k_star.toFixed(0)},${y_star.toFixed(0)})`, document.querySelector(".solow-visualization-eq"), ); } const formatNumber = (num) => { return `~${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 = `
`; katex.render(`t`, document.querySelector(".romer-table-time")); rowA_t.innerHTML = ``; rowY_t.innerHTML = ``; katex.render("A_t", document.querySelector(".romer-table-at")); katex.render("Y_t", document.querySelector(".romer-table-yt")); romerData.forEach((d) => { if (d.year % 20 === 0 || d.year === 1) { tableHeader.innerHTML += `${d.year}`; rowA_t.innerHTML += `${formatNumber(d.A)}`; rowY_t.innerHTML += `${formatNumber(d.Y)}`; } }); }; function drawRomerGraph() { const T_MAX = 100; margin = { top: 20, right: 100, bottom: 20, left: 50 }; ["Z", "L", "l", "A0"].forEach((param) => { const slider = document.getElementById(`slider${param}`); slider.oninput = function () { slider.previousElementSibling.innerText = this.value; drawRomerGraph(); }; }); const z = parseFloat(document.getElementById("outputZ").textContent), L = parseFloat(document.getElementById("outputL").textContent), l = parseFloat(document.getElementById("outputl").textContent), A0 = parseFloat(document.getElementById("outputA0").textContent); 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, ${height})`) .call(d3.axisBottom(x)) .append("text") .attr("fill", "#000") .attr("x", width + 10) .attr("y", -10) .style("text-anchor", "end") .style("font-size", "1.5em") .text("t"); const y = d3 .scaleLinear() .domain([0, romerData[romerData.length - 1].Y]) .range([height, 0]); svg .append("g") .call(d3.axisLeft(y).ticks(10, d3.format(".1s"))) .append("text") .attr("fill", "#000") .attr("x", 0) .attr("y", -10) .style("text-anchor", "start") .style("font-size", "1.5em") .text("log(Y)"); svg .append("path") .datum(romerData) .attr("fill", "none") .attr("stroke", getTopicColor(urlToTopic())) .attr("stroke-width", 2) .attr( "d", d3 .line() .x((d) => x(d.year)) .y((d) => y(d.Y)), ); svg .append("foreignObject") .attr("width", "4em") .attr("height", "2em") .attr("x", x(T_MAX)) .attr("y", y(romerData[T_MAX - 1].Y)) .append("xhtml:body") .style("font-size", "0.75em") .html(`
`); katex.render("log_{10}Y", document.querySelector(".romer-visualization-y")); updateRomerTable(romerData); } function drawRomerlGraph() { const T_MAX = 100, z = 0.01, L = 50, A0 = 50; margin = { top: 20, right: 100, bottom: 20, left: 50 }; const slider = document.getElementById(`sliderlChange`); slider.oninput = function () { slider.previousElementSibling.innerText = this.value; drawRomerlGraph(); }; const l = parseFloat(document.getElementById("outputlChange").textContent); const container = document.getElementById("romer-lchange-visualization"); const width = container.clientWidth - margin.left - margin.right; const height = container.clientHeight - margin.top - margin.bottom; container.innerHTML = ""; const svg = d3 .select("#romer-lchange-visualization") .append("svg") .attr("width", width + margin.left + margin.right) .attr("height", height + margin.top + margin.bottom) .append("g") .attr("transform", `translate(${margin.left}, ${margin.top})`); let A = A0, l_ = 0.1; const romerData = []; for (let t = 1; t <= Math.floor(T_MAX / 2) - 1; ++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 = Math.floor(T_MAX / 2); 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, ${height})`) .call(d3.axisBottom(x)) .append("text") .attr("fill", "#000") .attr("x", width + 10) .attr("y", -10) .style("text-anchor", "end") .style("font-size", "1.5em") .text("t"); const y = d3 .scaleLinear() .domain([0, romerData[romerData.length - 1].Y]) .range([height, 0]); svg .append("g") .call(d3.axisLeft(y).ticks(10, d3.format(".1s"))) .append("text") .attr("fill", "#000") .attr("x", 0) .attr("y", -10) .style("text-anchor", "start") .style("font-size", "1.5em") .text("log(Y)"); svg .append("path") .datum(romerData) .attr("fill", "none") .attr("stroke", getTopicColor(urlToTopic())) .attr("stroke-width", 2) .attr( "d", d3 .line() .x((d) => x(d.year)) .y((d) => y(d.Y)), ); svg .append("line") .attr("x1", x(T_MAX / 2)) .attr("y1", y(romerData[T_MAX - 1].Y)) .attr("x2", x(T_MAX / 2)) .attr("y2", height) .attr("stroke", "black") .attr("stroke-width", 1) .attr("stroke-dasharray", "4"); svg .append("foreignObject") .attr("width", "5em") .attr("height", "2em") .attr("x", x(0) + 15) .attr("y", y(romerData[0].Y)) .append("xhtml:body") .style("font-size", "0.6em") .html(`
`); katex.render( `\\bar{l}_0=${l_}`, document.querySelector(".romer-changel-before"), ); svg .append("foreignObject") .attr("width", "5em") .attr("height", "2em") .attr("x", x(T_MAX / 2) + 15) .attr("y", y(romerData[T_MAX / 2].Y)) .append("xhtml:body") .style("font-size", "0.6em") .html(`
`); katex.render( `\\bar{l}_1=${l}`, document.querySelector(".romer-changel-after"), ); 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(`
`); katex.render("log_{10}Y", document.querySelector(".romer-changel-y")); } document.addEventListener("DOMContentLoaded", function () { drawSolowGraph(); window.onresize = drawSolowGraph; drawRomerGraph(); window.onresize = drawRomerGraph; drawRomerlGraph(); window.onresize = drawRomerlGraph; });