29:null 2a:["$","title",null,{"children":"Herfindahl–Hirschman Index (HHI) | puri | Observable"}] 2f:T485,viewof abc = { const div = html` A
B
C `; const x = div.querySelector('#x'); const y = div.querySelector('#y'); const z = div.querySelector('#z'); x.value = 33.4; y.value = z.value = 33.3; x.oninput = () => { let diff = x.valueAsNumber + y.valueAsNumber + z.valueAsNumber - 100; y.value -= diff/2; z.value = 100 - x.valueAsNumber - y.valueAsNumber; div.value = [x.valueAsNumber, y.valueAsNumber, z.valueAsNumber]; }; y.oninput = () => { let diff = x.valueAsNumber + y.valueAsNumber + z.valueAsNumber - 100; x.value -= diff/2; z.value = 100 - x.valueAsNumber - y.valueAsNumber; div.value = [x.valueAsNumber, y.valueAsNumber, z.valueAsNumber]; }; z.oninput = () => { let diff = x.valueAsNumber + y.valueAsNumber + z.valueAsNumber - 100; x.value -= diff/2; y.value = 100 - x.valueAsNumber - z.valueAsNumber; div.value = [x.valueAsNumber, y.valueAsNumber, z.valueAsNumber]; }; div.value = [x.valueAsNumber, y.valueAsNumber, z.valueAsNumber]; return div; }30:[] 2d:{"id":"7c739561bce11ff8","slug":"herfindahl-hirschman-index-hhi","title":"Herfindahl–Hirschman Index (HHI)","thumbnail":"f734b851765247c3e16e30791a192f83f1d8f895d62bf33c88d3e3c23d9537a3","access_level":"public","create_time":"$D2018-05-15T18:42:20.635Z","update_time":"$D2018-05-19T09:29:11.357Z","view_time":null,"first_public_time":"$D2018-05-19T08:00:25.790Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"75c85bddc2cee955","login":"puripant","name":"puri","avatar_url":"https://avatars-next.observableusercontent.com/e3a2bb727c9eca90f56b9af63f8e90e9b012d1da5787f2e7bcb8d464f5f1a46c","tier":"starter_2024"},"version":423,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"6a740fb618035a0b","login":"puripant","name":"puri","avatar_url":"https://avatars-next.observableusercontent.com/e3a2bb727c9eca90f56b9af63f8e90e9b012d1da5787f2e7bcb8d464f5f1a46c","tier":null}],"members":[{"type":"individual","id":"6a740fb618035a0b","login":"puripant","name":"puri","avatar_url":"https://avatars-next.observableusercontent.com/e3a2bb727c9eca90f56b9af63f8e90e9b012d1da5787f2e7bcb8d464f5f1a46c","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":true,"trashed":false,"lapsed":null,"subscribed":null,"forks":1,"collection":null,"type":"notebook","body":{"title":"Herfindahl–Hirschman Index (HHI)","cells":[{"id":0,"value":"md`# Herfindahl–Hirschman Index (HHI)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":12,"value":"md`The index can be informally defined as ${tex`\\sum{\\left(\\frac{part}{whole}\\right)^2}`} or the sum of squares of the ratios of part to whole. The more equal the parts are, the lower the index is and vice versa. You can probably call it *domination* or *monopoly* index.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":20,"value":"md`Assume there are only two parts (out of 100). Adjust the slider below to see the resulting HHI of different ratios.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":26,"value":"viewof ab = {\n const input = html``;\n const result = md`A ${input} B`;\n input.addEventListener(\"input\", () => result.value = input.valueAsNumber );\n \n result.value = 50;\n return result;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":28,"value":"md`HHI = ${tex`\\left(\\frac{${ab}}{100}\\right)^2 + \\left(\\frac{${100-ab}}{100}\\right)^2`} = ${((ab*ab + (100-ab)*(100-ab))/10000).toFixed(2)}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":41,"value":"md`In the case of two parts, you may notice that 0.5 is the minimum HHI. The theoretically possible range of HHI is from ${tex`\\frac{1}{\\#parts}`} to 1. The minimum will approach zero when there are many, many parts.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":214,"value":"md`Try a version with three parts that sum up to 100.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":52,"value":"$2f","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":59,"value":"md`HHI = ${tex`\\left(\\frac{${abc[0]}}{100}\\right)^2 + \\left(\\frac{${abc[1]}}{100}\\right)^2 + \\left(\\frac{${abc[2]}}{100}\\right)^2`} = ${((abc[0]*abc[0] + abc[1]*abc[1] + abc[2]*abc[2])/10000).toFixed(2)}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":225,"value":"viewof parts = {\n const input = html``;\n const result = md`Now try many parts (that the UI allows): ${input} parts`\n result.value = 4;\n input.addEventListener(\"input\", () => result.value = input.value );\n return result;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":251,"value":"viewof abcd = {\n let sliderText = '';\n for (let i = 0; i < parts; i++) {\n sliderText += `${String.fromCharCode(65+i)}
`;\n }\n const div = html`${sliderText}`;\n \n let sliders = [];\n for (let i = 0; i < parts; i++) {\n sliders.push(div.querySelector(`#slider${i}`));\n sliders[i].value = 100/parts;\n sliders[i].oninput = () => {\n let diff = sliders.map((x) => x.valueAsNumber).reduce((x, y) => x+y) - 100;\n for (let j = 0; j < parts-1; j++) {\n if(j != i) {\n sliders[j].value -= diff/(parts-1);\n }\n }\n sliders[parts-1].value -= sliders.map((x) => x.valueAsNumber).reduce((x, y) => x+y) - 100;\n div.value = sliders.map((x) => x.valueAsNumber);\n };\n }\n sliders[0].value = 100 - (sliders[0].value*(parts-1)); //default value\n \n div.value = sliders.map((x) => x.valueAsNumber);\n return div;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":228,"value":"{\n const hhi = abcd.map((x) => x*x).reduce((x, y) => x+y)/10000;\n return md`HHI = = 0.15 && hhi <= 0.25)? 'green':'red'}>${hhi.toFixed(2)}`\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":211,"value":"md`The color of the index value above reflects the HHI range that [the United States Department of Justice](https://www.justice.gov/atr/herfindahl-hirschman-index) considers *moderately concentrated* aka healthily competitive i.e. any value between 0.15 and 0.25. (This implies that the number of parts should be at least four.) Adjust the ratios of the parts or market shares above to see how many configurations yield a healthy competition.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W30","stdlib":"1","titling":"auto"}} 2e:"$2d:body"