2b:null 2c:["$","title",null,{"children":"Dynamic Cobb-Douglas Indifference Curves | Ralphs, Alexander | Observable"}] 31:T11b6,function plotcurves () { let alpha = cobb_douglas_params['alpha'] let beta = cobb_douglas_params['beta'] let bc1_on = params1['bc1_on'] let bc1_color = params1['bc1_color'] let wage1 = params1['wage1'] let price1 = params1['price1'] let ic1_on = params1['ic1_on'] let ic1_color = params1['ic1_color'] // let Utility_1 = params1['Utility_1'] let bc2_on = params2['bc2_on'] let bc2_color = params2['bc2_color'] let wage2 = params2['wage2'] let price2 = params2['price2'] let ic2_on = params2['ic2_on'] let ic2_color = params2['ic2_color'] // let Utility_2 = params2['Utility_2'] let hyp_bc_on = params3['hyp_bc_on'] let hyp_bc_color = params3['hyp_bc_color'] let hyp_income = params3['hyp_income'] const ic = function (t, alpha, beta, u) { return (u/(t**alpha)) ** (1/beta) } const bc = function (t, w, p) { return w*(24-t)/p } const hyp_bc = function (t, w, p, inc) { return w*(24-t)/p + inc } if (bc2_on == true) { var max_y = 24*Math.max(wage1/price1, wage2/price2)+4 } else { var max_y = 24*wage1/price1+4 } let data = [] for (let t = 0; t <= 24; t=t+0.01) { if (ic1_on == true) { data.push({'line': 'ic_1', 't': t, 'y': ic(t, alpha, beta, Utility_1), 'stroke': ic1_color}) } else { data.push({'line': 'ic_1', 't': t, 'y': NaN, 'stroke': ic1_color}) } if (bc1_on == true) { data.push({'line': 'bc_1', 't': t, 'y': bc(t, wage1, price1), 'stroke': bc1_color}) } else { data.push({'line': 'bc_1', 't': t, 'y': NaN, 'stroke': bc1_color}) } if (ic2_on == true) { data.push({'line': 'ic_2', 't': t, 'y': ic(t, alpha, beta, Utility_2), 'stroke': ic2_color}) } else { data.push({'line': 'ic_2', 't': t, 'y': NaN, 'stroke': ic2_color}) } if (bc2_on == true) { data.push({'line': 'bc_2', 't': t, 'y': bc(t, wage2, price2), 'stroke': bc2_color}) } else { data.push({'line': 'bc_2', 't': t, 'y': NaN, 'stroke': bc2_color}) } if (hyp_bc_on == true) { data.push({'line': 'hyp_bc', 't': t, 'y': hyp_bc(t, wage1, price1, hyp_income), 'stroke': hyp_bc_color}) } else { data.push({'line': 'hyp_bc', 't': t, 'y': NaN, 'stroke': hyp_bc_color}) } } let labels = [] if (ic1_on == true) { labels.push({'line': 'ic_1', 't': 24.5, 'y': ic(24, alpha, beta, Utility_1), 'stroke': ic1_color, 'label': 'IC1'}) } else { labels.push({'line': 'ic_1', 't': 24.5, 'y': ic(24, alpha, beta, Utility_1), 'stroke': ic1_color, 'label': ''}) } if (ic2_on == true) { labels.push({'line': 'ic_2', 't': 24.5, 'y': ic(24, alpha, beta, Utility_2), 'stroke': ic2_color, 'label': 'IC2'}) } else { labels.push({'line': 'ic_2', 't': 24.5, 'y': ic(24, alpha, beta, Utility_2), 'stroke': ic2_color, 'label': ''}) } if (bc1_on == true) { labels.push({'line': 'bc_1', 't': 21, 'y': bc(20, wage1, price1), 'stroke': bc1_color, 'label': 'BC1'}) } else { labels.push({'line': 'bc_1', 't': 21, 'y': bc(20, wage1, price1), 'stroke': bc1_color, 'label': ''}) } if (bc2_on == true) { labels.push({'line': 'bc_2', 't': 21, 'y': bc(20, wage2, price2), 'stroke': bc2_color, 'label': 'BC2'}) } else { labels.push({'line': 'bc_2', 't': 21, 'y': bc(20, wage2, price2), 'stroke': bc2_color, 'label': ''}) } if (hyp_bc_on == true) { labels.push({'line': 'hyp_bc', 't': 24.5, 'y': hyp_bc(24, wage1, price1, hyp_income), 'stroke': hyp_bc_color, 'label': 'HBC'}) } else { labels.push({'line': 'hyp_bc', 't': 24.5, 'y': hyp_bc(24, wage1, price1, hyp_income), 'stroke': hyp_bc_color, 'label': ''}) } const plt = Plot.plot({ style: "display: inline-block", x: { label: "Leisure, t", line: true, domain: [0, 26], ticks: 13, }, y: { label: "Consumption, y", line: true, domain: [0, max_y] }, grid: true, width: 1200, height: 700, marks: [ Plot.line(data, {x: 't', y: 'y', z: 'line', stroke: 'stroke'}), Plot.text(labels, {x: 't', y: 'y', text: 'label', fill: 'stroke'}), Plot.crosshair(data, {x: 't', y: 'y', color: 'stroke'}), ] }) return plt }32:[] 2f:{"id":"9e4707032d228994","slug":"dynamic-cobb-douglas-indifference-curves","title":"Dynamic Cobb-Douglas Indifference Curves","thumbnail":"ed194cc0aac138ebd3ec767e50be2e039a89c59befb7a896adac12e8eb916881","access_level":"public","create_time":"$D2023-10-19T15:21:09.400Z","update_time":"$D2024-01-30T15:54:20.412Z","view_time":null,"first_public_time":"$D2023-10-19T15:21:09.400Z","fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"4b29738293f35bb8","login":"alexralphs","name":"Ralphs, Alexander","avatar_url":"https://avatars-next.observableusercontent.com/6a13bac7ae8fe6b5c86d7f8d75ed2c4aaaacf00f0d35cf7d8a77834634cf5975","tier":"starter_2024"},"version":324,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"cb79e48781a92ce2","login":"alexralphs","name":"Ralphs, Alexander","avatar_url":"https://avatars-next.observableusercontent.com/6a13bac7ae8fe6b5c86d7f8d75ed2c4aaaacf00f0d35cf7d8a77834634cf5975","tier":null}],"members":[{"type":"individual","id":"cb79e48781a92ce2","login":"alexralphs","name":"Ralphs, Alexander","avatar_url":"https://avatars-next.observableusercontent.com/6a13bac7ae8fe6b5c86d7f8d75ed2c4aaaacf00f0d35cf7d8a77834634cf5975","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"Dynamic Cobb-Douglas Indifference Curves","cells":[{"id":0,"value":"# Dynamic Cobb-Douglas Indifference Curves","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":14,"value":"md`Cobb-Douglas Utility Function: ${tex`U=t^{\\alpha}y^{\\beta}`}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":39,"value":"md`Budget Constraint: ${tex`\\frac{w}{p}(24-t)`}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":258,"value":"controls = {\n return html`

${viewof cobb_douglas_params}${viewof params1}${viewof Utility_1}

${viewof params2}${viewof Utility_2}

${viewof params3}

`\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":238,"value":"plotcurves()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":318,"value":"viewof cobb_douglas_params = Inputs.form({\n alpha: Inputs.number([0, 5], {step: 0.1, value: 3, label: \"Alpha\"}),\n beta: Inputs.number([0, 5], {step: 0.1, value: 2, label: \"Beta\"})\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":138,"value":"viewof params1 = Inputs.form({\n bc1_on: Inputs.toggle({label: \"Budget Constraint 1\", value: false}),\n bc1_color: Inputs.color({label: \"Budget Constraint 1 Color\", value: \"#000000\"}),\n wage1: Inputs.number([0.1, 10], {step: 0.1, value: 2, label: \"Wage 1\"}),\n price1: Inputs.number([0.1, 10], {step: 0.1, value: 2, label: \"Price 1\"}),\n ic1_on: Inputs.toggle({label: \"Indifference Curve 1\", value: false}),\n ic1_color: Inputs.color({label: \"Indifference Curve 1 Color\", value: \"#000000\"})\n})\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":316,"value":"viewof Utility_1 = Inputs.range([0, set_utility_levels(params1['wage1'], params1['price1'])], {step: 1000, value: set_utility_levels(params1['wage1'], params1['price1'])/3, label:\"Utility 1\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":264,"value":"viewof params2 = Inputs.form({\n bc2_on: Inputs.toggle({label: \"Budget Constraint 2\", value: false}),\n bc2_color: Inputs.color({label: \"Budget Constraint 2 Color\", value: \"#ff0000\"}),\n wage2: Inputs.number([0.1, 10], {step: 0.1, value: 4, label: \"Wage 2\"}),\n price2: Inputs.number([0.1, 10], {step: 0.1, value: 2, label: \"Price 2\"}),\n ic2_on: Inputs.toggle({label: \"Indifference Curve 2\", value: false}),\n ic2_color: Inputs.color({label: \"Indifference Curve 2 Color\", value: \"#ff0000\"}),\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":314,"value":"viewof Utility_2 = Inputs.range([0, set_utility_levels(params2['wage2'], params2['price2'])], {step: 1000, value: set_utility_levels(params2['wage2'], params2['price2'])/3, label:\"Utility 2\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":276,"value":"viewof params3 = Inputs.form({\n hyp_bc_on: Inputs.toggle({label: \"Hyperthetical Budget Constraint\", value: false}),\n hyp_bc_color: Inputs.color({label: \"Hyperthetical Budget Constraint Color\", value: \"#0000ff\"}),\n hyp_income: Inputs.range([0, 20], {step: 0.1, value: 0, label: \"Hypothetical Additional Income\"})\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":283,"value":"","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":114,"value":"$31","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":311,"value":"set_utility_levels = function (w, p) {\n let alpha = cobb_douglas_params['alpha']\n let beta = cobb_douglas_params['beta']\n var utility_eq = (24/(alpha+beta))**(alpha+beta)*(alpha**alpha)*((beta*w/p)**beta)\n var utility_max = 2*utility_eq\n return utility_max\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":322,"value":"","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"}],"files":"$W32","stdlib":"1","titling":"auto"}} 30:"$2f:body"