29:null 2a:["$","title",null,{"children":"Phillips curve and the WS-PS model | Ralphs, Alexander | Observable"}] 2f:Ta68,function plot_ws_ps () { let data = [] data.push({'line': 'labour force', 'x': LF, 'y': '0', 'stroke': 'black'}) data.push({'line': 'labour force', 'x': LF, 'y': APL, 'stroke': 'black'}) data.push({'line': 'PS', 'x': 50, 'y': PS_curve(), 'stroke': 'black'}) data.push({'line': 'PS', 'x': LF, 'y': PS_curve(), 'stroke': 'black'}) for (let N=50; N<=LF-0.1; N=N+0.1) { data.push({'line': 'WS', 'x': N, 'y': WS_curve(LF, N), 'stroke': 'blue'}) } let y_gap = D_shock/(1-c_1) let n_gap = y_gap/APL let dotted_lines_data = [] dotted_lines_data.push({'line': 'APL', 'x': 50, 'y': APL, 'stroke': 'red'}) dotted_lines_data.push({'line': 'APL', 'x': LF, 'y': APL, 'stroke': 'red'}) dotted_lines_data.push({'line': 'eq', 'x': solve_N_eq(), 'y': PS_curve(), 'stroke': 'blue'}) dotted_lines_data.push({'line': 'eq', 'x': solve_N_eq(), 'y': 0, 'stroke': 'blue'}) dotted_lines_data.push({'line': 'n_gap', 'x': solve_N_eq()+n_gap, 'y': 0, 'stroke': 'limegreen'}) dotted_lines_data.push({'line': 'n_gap', 'x': solve_N_eq()+n_gap, 'y': Math.max(WS_curve(LF, solve_N_eq()+n_gap), PS_curve()), 'stroke': 'limegreen'}) let labels = [] labels.push({'line': 'labour_force', 'x': 1.02*LF, 'y': APL-1, 'stroke': 'black', 'label': 'Labour Force'}) labels.push({'line': 'APL', 'x': 1.02*LF, 'y': APL+0.3, 'stroke': 'red', 'label': 'Average Product'}) labels.push({'line': 'APL', 'x': 1.02*LF, 'y': APL-0.3, 'stroke': 'red', 'label': 'of Labour, λ'}) labels.push({'line': 'PS', 'x': 1.025*LF, 'y': PS_curve()+0.3, 'stroke': 'black', 'label': 'Price-Setting Curve'}) labels.push({'line': 'PS', 'x': 1.025*LF, 'y': PS_curve()-0.3, 'stroke': 'black', 'label': `= ${PS_curve().toFixed(2)}`}) labels.push({'line': 'WS', 'x': LF-LF/9.5+3, 'y': APL-0.5, 'stroke': 'blue', 'label': 'Wage-Setting Curve'}) labels.push({'line': 'eq', 'x': solve_N_eq(), 'y': -0.2, 'stroke': 'blue', 'label': 'N*'}) const plt = Plot.plot({ style: "display: inline-block", x: { label: "Employment, N", line: true, domain: [50, LF+4], ticks: 10, }, y: { label: "$", line: true, domain: [0, APL] }, grid: true, width: 1000, height: 600, marks: [ Plot.line(data, {x: 'x', y: 'y', z: 'line', stroke: 'stroke'}), Plot.line(dotted_lines_data, {x: 'x', y: 'y', z: 'line', stroke: 'stroke', strokeDasharray: '5 5'}), Plot.text(labels, {x: 'x', y: 'y', text: 'label', fill: 'stroke'}), Plot.crosshair(data, {x: 'x', y: 'y', color: 'stroke'}) ] }) return plt }30:T8a6,function plot_pc () { let data = [] let dotted_lines_data = [] let labels = [] let inflation = [] let n_eq = solve_N_eq() for (let N=50; N<=LF-0.1; N=N+0.1) { let n_gap = N-n_eq data.push({'line': 'PC', 'x': N, 'y': P_curve(pi_exp, bargaining_gap(n_gap*APL*(1-c_1))), 'stroke': 'blue'}) } let y_gap = D_shock/(1-c_1) let n_gap = y_gap/APL dotted_lines_data.push({'line': 'eq', 'x': solve_N_eq(), 'y': 10, 'stroke': 'blue'}) dotted_lines_data.push({'line': 'eq', 'x': solve_N_eq(), 'y': -5, 'stroke': 'blue'}) dotted_lines_data.push({'line': 'pi_exp', 'x': 50, 'y': pi_exp, 'stroke': 'blue'}) dotted_lines_data.push({'line': 'pi_exp', 'x': solve_N_eq(), 'y': pi_exp, 'stroke': 'blue'}) dotted_lines_data.push({'line': 'n_gap', 'x': solve_N_eq()+n_gap, 'y': -5, 'stroke': 'limegreen'}) dotted_lines_data.push({'line': 'n_gap', 'x': solve_N_eq()+n_gap, 'y': 10, 'stroke': 'limegreen'}) labels.push({'line': 'pc', 'x': LF-2, 'y': 9, 'stroke': 'blue', 'label': 'Phillips Curve'}) labels.push({'line': 'pc', 'x': LF-2, 'y': 8.6, 'stroke': 'blue', 'label': `(Expected Inflation = ${pi_exp})`}) labels.push({'line': 'eq', 'x': solve_N_eq(), 'y': -5.2, 'stroke': 'blue', 'label': 'N*'}) inflation.push({'line': 'pi', 'x': solve_N_eq()+n_gap, 'y': P_curve(2, bargaining_gap(n_gap*APL*(1-c_1))), 'stroke': 'limegreen'}) const plt = Plot.plot({ style: "display: inline-block", x: { label: "Employment, N", line: true, domain: [50, LF+4], ticks: 10, }, y: { label: "$", line: true, domain: [-5, 10] }, grid: true, width: 1000, height: 600, marks: [ Plot.line(data, {x: 'x', y: 'y', z: 'line', stroke: 'stroke'}), Plot.line(dotted_lines_data, {x: 'x', y: 'y', z: 'line', stroke: 'stroke', strokeDasharray: '5 5'}), Plot.dot(inflation, {x: 'x', y: 'y', z: 'line', stroke: 'stroke'}), Plot.text(labels, {x: 'x', y: 'y', text: 'label', fill: 'stroke'}), Plot.crosshair(data, {x: 'x', y: 'y', color: 'stroke'}), Plot.ruleY([0]) ] }) return plt }31:Td21,function plot_ad_y () { let curves_data = [] let dotted_lines_data = [] let labels = [] let y_max = APL*LF let y_eq = y_equilibrium(0) // = 900 let y_eq_shock = y_equilibrium(D_shock) for (let y = 0; y <=1.05*y_max; ++y) { curves_data.push({'line': 'market_clearing', 'x': y, 'y': y, 'stroke': 'black'}) curves_data.push({'line': 'ad', 'x': y, 'y': c_0 + c_1*(y-T)+I+G, 'stroke': 'red'}) if (D_shock == 0) { curves_data.push({'line': 'ad_shock', 'x': y, 'y': c_0 + c_1*(y-T) + I + G + D_shock, stroke: 'rgba(50, 205, 50, 0)'}) } else { curves_data.push({'line': 'ad_shock', 'x': y, 'y': c_0 + c_1*(y-T) + I + G + D_shock, stroke: 'rgb(50, 205, 50)'}) } } curves_data.push({'line': 'capacity', 'x': y_max, 'y': 1250, 'stroke': 'black'}) curves_data.push({'line': 'capacity', 'x': y_max, 'y': y_max, 'stroke': 'black'}) dotted_lines_data.push({'line': 'y_eq', 'x': y_eq, 'y': 1250, 'stroke': 'red'}) dotted_lines_data.push({'line': 'y_eq', 'x': y_eq, 'y': y_eq, 'stroke': 'red'}) if (D_shock == 0) { dotted_lines_data.push({'line': 'y_eq_shock', 'x': y_eq_shock, 'y': 1250, 'stroke': 'rgba(50, 205, 50, 0)'}) dotted_lines_data.push({'line': 'y_eq_shock', 'x': y_eq_shock, 'y': y_eq_shock, 'stroke': 'rgba(50, 205, 50, 0)'}) } else { dotted_lines_data.push({'line': 'y_eq_shock', 'x': y_eq_shock, 'y': 1250, 'stroke': 'limegreen'}) dotted_lines_data.push({'line': 'y_eq_shock', 'x': y_eq_shock, 'y': y_eq_shock, 'stroke': 'limegreen'}) } labels.push({'line': 'y_eq', 'x': y_eq, 'y': 1230, 'stroke': 'red', 'label': 'y1'}) labels.push({'line': 'y=ad', 'x': 1.04*y_max, 'y': 1.02*y_max, 'stroke': 'black', 'label': 'Y=AD'}) labels.push({'line': 'ad', 'x': 0.97*y_max, 'y': c_0 + c_1*(2500-T)+I+G, 'stroke': 'red', 'label': 'AD1'}) labels.push({'line': 'capacity', 'x': y_max, 'y': y_max+50, 'stroke': 'black', 'label': 'Productive'}) labels.push({'line': 'capacity', 'x': y_max, 'y': y_max+25, 'stroke': 'black', 'label': 'Capacity'}) if (D_shock == 0) { labels.push({'line': 'ad_shock', 'x': 0.97*y_max, 'y': c_0 + c_1*(2500-T)+I+G+D_shock, 'stroke': 'rgba(50, 205, 50, 0)', 'label': "AD2"}) labels.push({'line': 'y_eq_shock', 'x': y_eq_shock, 'y': 480, 'stroke': 'rgba(50, 205, 50, 0)', 'label': 'y2'}) } else { labels.push({'line': 'ad_shock', 'x': 0.97*y_max, 'y': c_0 + c_1*(2500-T)+I+G+D_shock, 'stroke': 'limegreen', 'label': "AD2"}) labels.push({'line': 'y_eq_shock', 'x': y_eq_shock, 'y': 480, 'stroke': 'limegreen', 'label': 'y2'}) } const plt = Plot.plot({ style: "display: inline-block", x: { label: "Y, output", line: true, domain: [y_max/2, 1.04*y_max], ticks: 11, }, y: { label: "AD", line: true, domain: [y_max/2, 1.04*y_max], ticks: 11, }, grid: true, width: 1000, height: 600, marks: [ Plot.line(curves_data, {x: 'x', y: 'y', z: 'line', stroke: 'stroke'}), Plot.line(dotted_lines_data, {x: 'x', y: 'y', z: 'line', stroke: 'stroke', strokeDasharray: '5 5'}), Plot.text(labels, {x: 'x', y: 'y', text: 'label', fill: 'stroke'}), Plot.crosshair(curves_data, {x: 'x', y: 'y', color: 'stroke'}) ] }) return plt }32:[] 2d:{"id":"00901eb21726abfe","slug":null,"title":"Phillips curve and the WS-PS model","thumbnail":"0c1d33c394deb7f9f09a39e2cb4e9de612f12dc9f8778f76bcdb3b46147f7e91","access_level":"public","create_time":"$D2024-02-27T13:09:25.683Z","update_time":"$D2024-02-29T17:59:56.325Z","view_time":null,"first_public_time":"$D2024-02-29T18:05:55.679Z","fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"4b29738293f35bb8","login":"alexralphs","name":"Ralphs, 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model","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":5,"value":"plot_ws_ps()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":7,"value":"$2f","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":208,"value":"plot_pc()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":45,"value":"$30","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":361,"value":"viewof pi_exp = Inputs.range([-5, 10], {step: 1, value: 2, label: 'Expected Inflation'})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":50,"value":"plot_ad_y()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":68,"value":"viewof D_shock = Inputs.range([-500, 125], {step: 5, value: 0, label: 'Demand Shock'})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":48,"value":"$31","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":82,"value":"function WS_curve (LF, N) {\n let u = (LF-N)/LF\n //return WS_const+WS_scalar/(u**0.5)\n return WS_const + WS_scalar_1*Math.exp((N-LF)/WS_scalar_2)\n }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":102,"value":"function PS_curve() {\n return APL*(1-mu)\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":108,"value":"function solve_N_eq() {\n // 1: PS = WS_const + WS_scalar/u = WS_const + WS_scalar*LF/(LF-N)\n // LF-N = LF/(PS-WS_const)\n //return LF-WS_scalar_1*LF/(PS_curve()-WS_const)\n \n // 2: PS = WS_const + WS_scalar_1*exp((N-LF)/WS_scalar_2)\n // N=LF + WS_scalar_2*ln((PS-WS_const)/WS_scalar_1)\n return LF + WS_scalar_2*Math.log((PS_curve()-WS_const)/WS_scalar_1)\n }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":131,"value":"function y_equilibrium (d_shock) {\n return (1/(1-c_1))*(c_0 - c_1*T + I + G + d_shock)\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":75,"value":"function bargaining_gap(d_shock) {\n let y_gap = d_shock/(1-c_1)\n let n_gap = y_gap/APL // y_gap/apl\n let n_eq = solve_N_eq()\n let price = nom_wage / PS_curve()\n return (WS_curve(LF, n_eq+n_gap) - PS_curve())/price\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":112,"value":"function P_curve(pi_exp, bg) {\n return pi_exp + bg\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":289,"value":"viewof nom_wage = html``","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":272,"value":"viewof WS_const = html``","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":263,"value":"viewof WS_scalar_1 = html``","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":323,"value":"viewof WS_scalar_2 = html``","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":94,"value":"viewof APL = html``","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":98,"value":"viewof mu = html``","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":100,"value":"viewof LF = html``","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":119,"value":"viewof c_0 = html``","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":121,"value":"viewof c_1 = html``","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":123,"value":"viewof T = html``","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":125,"value":"viewof G = html``","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":127,"value":"viewof I = html``","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":9,"value":"","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"}],"files":"$W32","stdlib":"1","titling":"auto"}} 2e:"$2d:body"