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Develop notation guide for unemployment course
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‎content/courses/c1.md

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---
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title: "Unemployment"
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date: 2025-01-28
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date: 2025-01-29
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url: /c1/
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aliases:
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## Notation guide
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+ $H$ – Labor force = number of workers who are able, willing, and seeking to work
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+ $U$ – Unemployment level = number of labor force participants who do not have a job
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+ $L$ – Employment level = number of labor force participants who do have a job
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+ $V$ – Vacancy level = number of job vacancies advertised by firms
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+ $u$ – Unemployment rate = share of labor force without a job = $U / H$
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+ $v$ – Vacancy rate = $V / H$
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+ $\theta$ – Labor market tightness = number of job vacancies per job seeker = $V/U$
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+ $m(U,V)$ – Matching function
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+ $\eta$ – Matching elasticity = $\partial \ln(m)/\partial \ln(U)$
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+ $f$ – Job-finding rate = $m(U,V)/U$
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+ $q$ – Vacancy-filling rate = $m(U,V)/V$
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+ $s$ – Job-separation rate
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| Symbol | Name | Verbal Definition | Mathematical Definition |
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| -------- | ---------------------------- | ----------------------------------------- | ------------------------------------------------ |
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| $H$ | Labor force level | Number of people who are able, willing, and seeking to work | - |
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| $U$ | Unemployment level | Number of labor force participants without a job | - |
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| $L$ | Employment level | Number of labor force participants with a job | - |
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| $V$ | Vacancy level | Number of job vacancies advertised by firms | - |
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| $u$ | Unemployment rate | Share of labor force without a job | $U / H$ |
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| $v$ | Vacancy rate | Number of job vacancies as share of the labor force | $V / H$ |
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| $\theta$ | Labor market tightness | Number of job vacancies per job seeker | $V / U$ |
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| $m(U,V)$ | Matching function | Number of new worker-firm matches per period | |
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| $\eta$ | Matching elasticity | Elasticity of the matching function with respect to unemployment | $\frac{\partial \ln(m)}{\partial \ln(U)}$ |
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| $f$ | Job-finding rate | Probability that an unemployed person finds a job in a period | $\frac{m(U,V)}{U}$ |
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| $q$ | Vacancy-filling rate | Probability that a job vacancy is filled in a period | $\frac{m(U,V)}{V}$ |
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| $s$ | Job-separation rate | Probability that a worker separates from their job in a period | - |
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| $R$ | Recruiter level | Number of employees allocated to recruiting | - |
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| $N$ | Producer level | Number of employees allocated to producing | - |
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| $\tau$ | Recruiter-producer ratio | Number of recruiters per producer | $R/N$ |
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| $w$ | Real wage | | |
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| $L^s$ | Labor supply | | |
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| $L^d$ | Labor demand | | |
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| $y(N)$ | Production function | | |
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| $a$ | Technology | | |
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| $\alpha$ | Diminishing returns to labor | | |
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| $u^R$ | Rationing unemployment | | |
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| $u^F$ | Frictional unemployment | | $u - u^R$ |
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‎public/c1/index.html

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‎public/courses/index.html

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<div class="entry-content">
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<p>This course presents a matching model of unemployment. It uses the model to study unemployment fluctuations; job rationing; efficient unemployment and unemployment gap; and labor market policies such as minimum wage, public employment, and unemployment insurance.</p>
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</div>
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<footer class="entry-footer"><span title='2025-01-28 00:00:00 +0000 UTC'>January 2025</span>&nbsp;&middot;&nbsp;Pascal Michaillat</footer>
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<footer class="entry-footer"><span title='2025-01-29 00:00:00 +0000 UTC'>January 2025</span>&nbsp;&middot;&nbsp;Pascal Michaillat</footer>
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<a class="entry-link" aria-label="post link to Unemployment" href="https://pascalmichaillat.org/c1/"></a>
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</article>
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‎public/courses/index.xml

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</image>
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<generator>Hugo -- 0.135.0</generator>
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<language>en</language>
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<lastBuildDate>Tue, 28 Jan 2025 00:00:00 +0000</lastBuildDate>
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<lastBuildDate>Wed, 29 Jan 2025 00:00:00 +0000</lastBuildDate>
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<atom:link href="https://pascalmichaillat.org/courses/index.xml" rel="self" type="application/rss+xml" />
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<item>
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<title>Unemployment</title>
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<link>https://pascalmichaillat.org/c1/</link>
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<pubDate>Tue, 28 Jan 2025 00:00:00 +0000</pubDate>
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<pubDate>Wed, 29 Jan 2025 00:00:00 +0000</pubDate>
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<guid>https://pascalmichaillat.org/c1/</guid>
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<description>This course presents a matching model of unemployment and uses it to study unemployment fluctuations, efficient unemployment, and labor market policies.</description>
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</item>

‎public/index.xml

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</image>
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<atom:link href="https://pascalmichaillat.org/index.xml" rel="self" type="application/rss+xml" />
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<item>
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<title>Unemployment</title>
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<link>https://pascalmichaillat.org/c1/</link>
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<pubDate>Tue, 28 Jan 2025 00:00:00 +0000</pubDate>
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<pubDate>Wed, 29 Jan 2025 00:00:00 +0000</pubDate>
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<guid>https://pascalmichaillat.org/c1/</guid>
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<description>This course presents a matching model of unemployment and uses it to study unemployment fluctuations, efficient unemployment, and labor market policies.</description>
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‎public/sitemap.xml

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xmlns:xhtml="http://www.w3.org/1999/xhtml">
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<url>
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<loc>https://pascalmichaillat.org/tags/beveridge-curve/</loc>
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<lastmod>2025-01-28T00:00:00+00:00</lastmod>
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<lastmod>2025-01-29T00:00:00+00:00</lastmod>
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</url><url>
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<loc>https://pascalmichaillat.org/courses/</loc>
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</url><url>
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<loc>https://pascalmichaillat.org/tags/dmp-model/</loc>
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<lastmod>2025-01-29T00:00:00+00:00</lastmod>
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</url><url>
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<loc>https://pascalmichaillat.org/tags/job-rationing/</loc>
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<lastmod>2025-01-29T00:00:00+00:00</lastmod>
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</url><url>
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<loc>https://pascalmichaillat.org/tags/labor-market-tightness/</loc>
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</url><url>
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<loc>https://pascalmichaillat.org/tags/matching-function/</loc>
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<lastmod>2025-01-28T00:00:00+00:00</lastmod>
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<lastmod>2025-01-29T00:00:00+00:00</lastmod>
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</url><url>
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<loc>https://pascalmichaillat.org/tags/matching-model/</loc>
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</url><url>
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<loc>https://pascalmichaillat.org/</loc>
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</url><url>
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<loc>https://pascalmichaillat.org/tags/public-employment/</loc>
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<lastmod>2025-01-29T00:00:00+00:00</lastmod>
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</url><url>
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<loc>https://pascalmichaillat.org/tags/shimer-puzzle/</loc>
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</url><url>
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<loc>https://pascalmichaillat.org/c1/</loc>
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<lastmod>2025-01-29T00:00:00+00:00</lastmod>
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</url><url>
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<loc>https://pascalmichaillat.org/tags/unemployment-fluctuations/</loc>
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<lastmod>2025-01-29T00:00:00+00:00</lastmod>
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</url><url>
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<loc>https://pascalmichaillat.org/tags/unemployment-gap/</loc>
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<lastmod>2025-01-29T00:00:00+00:00</lastmod>
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</url><url>
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<loc>https://pascalmichaillat.org/tags/unemployment-insurance/</loc>
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<lastmod>2025-01-29T00:00:00+00:00</lastmod>
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</url><url>
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<loc>https://pascalmichaillat.org/tags/wage-rigidity/</loc>
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<lastmod>2025-01-29T00:00:00+00:00</lastmod>
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</url><url>
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<loc>https://pascalmichaillat.org/officehours/</loc>
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<lastmod>2024-12-13T00:00:00+00:00</lastmod>

‎public/tags/beveridge-curve/index.html

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<p>This course presents a matching model of unemployment. It uses the model to study unemployment fluctuations; job rationing; efficient unemployment and unemployment gap; and labor market policies such as minimum wage, public employment, and unemployment insurance.</p>
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</div>
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<footer class="entry-footer"><span title='2025-01-28 00:00:00 +0000 UTC'>January 2025</span>&nbsp;&middot;&nbsp;Pascal Michaillat</footer>
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<footer class="entry-footer"><span title='2025-01-29 00:00:00 +0000 UTC'>January 2025</span>&nbsp;&middot;&nbsp;Pascal Michaillat</footer>
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<a class="entry-link" aria-label="post link to Unemployment" href="https://pascalmichaillat.org/c1/"></a>
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</article>
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‎public/tags/beveridge-curve/index.xml

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</image>
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<atom:link href="https://pascalmichaillat.org/tags/beveridge-curve/index.xml" rel="self" type="application/rss+xml" />
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<title>Unemployment</title>
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<link>https://pascalmichaillat.org/c1/</link>
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<pubDate>Tue, 28 Jan 2025 00:00:00 +0000</pubDate>
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<pubDate>Wed, 29 Jan 2025 00:00:00 +0000</pubDate>
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<guid>https://pascalmichaillat.org/c1/</guid>
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<description>This course presents a matching model of unemployment and uses it to study unemployment fluctuations, efficient unemployment, and labor market policies.</description>
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‎public/tags/dmp-model/index.html

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<p>This course presents a matching model of unemployment. It uses the model to study unemployment fluctuations; job rationing; efficient unemployment and unemployment gap; and labor market policies such as minimum wage, public employment, and unemployment insurance.</p>
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</div>
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<footer class="entry-footer"><span title='2025-01-28 00:00:00 +0000 UTC'>January 2025</span>&nbsp;&middot;&nbsp;Pascal Michaillat</footer>
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<footer class="entry-footer"><span title='2025-01-29 00:00:00 +0000 UTC'>January 2025</span>&nbsp;&middot;&nbsp;Pascal Michaillat</footer>
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<a class="entry-link" aria-label="post link to Unemployment" href="https://pascalmichaillat.org/c1/"></a>
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</article>
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‎public/tags/dmp-model/index.xml

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<title>Unemployment</title>
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<link>https://pascalmichaillat.org/c1/</link>
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‎public/tags/index.xml

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<atom:link href="https://pascalmichaillat.org/tags/index.xml" rel="self" type="application/rss+xml" />
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<title>Beveridge curve</title>
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<link>https://pascalmichaillat.org/tags/beveridge-curve/</link>
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<pubDate>Wed, 29 Jan 2025 00:00:00 +0000</pubDate>
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<guid>https://pascalmichaillat.org/tags/beveridge-curve/</guid>
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<description></description>
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</item>
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<item>
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<title>DMP model</title>
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<link>https://pascalmichaillat.org/tags/dmp-model/</link>
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<pubDate>Wed, 29 Jan 2025 00:00:00 +0000</pubDate>
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<guid>https://pascalmichaillat.org/tags/dmp-model/</guid>
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<description></description>
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</item>
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<title>job rationing</title>
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<link>https://pascalmichaillat.org/tags/job-rationing/</link>
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<pubDate>Wed, 29 Jan 2025 00:00:00 +0000</pubDate>
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<guid>https://pascalmichaillat.org/tags/job-rationing/</guid>
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<description></description>
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</item>
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<title>labor market tightness</title>
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<link>https://pascalmichaillat.org/tags/labor-market-tightness/</link>
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<pubDate>Wed, 29 Jan 2025 00:00:00 +0000</pubDate>
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<guid>https://pascalmichaillat.org/tags/labor-market-tightness/</guid>
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<description></description>
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</item>
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<title>matching function</title>
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<link>https://pascalmichaillat.org/tags/matching-function/</link>
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<guid>https://pascalmichaillat.org/tags/matching-function/</guid>
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<description></description>
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</item>
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<title>matching model</title>
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<link>https://pascalmichaillat.org/tags/matching-model/</link>
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<guid>https://pascalmichaillat.org/tags/matching-model/</guid>
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<description></description>
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</item>
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<title>public employment</title>
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<link>https://pascalmichaillat.org/tags/public-employment/</link>
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<guid>https://pascalmichaillat.org/tags/public-employment/</guid>
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<description></description>
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<title>Shimer puzzle</title>
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<link>https://pascalmichaillat.org/tags/shimer-puzzle/</link>
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<guid>https://pascalmichaillat.org/tags/shimer-puzzle/</guid>
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<description></description>
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</item>
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<title>unemployment fluctuations</title>
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<link>https://pascalmichaillat.org/tags/unemployment-fluctuations/</link>
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<pubDate>Wed, 29 Jan 2025 00:00:00 +0000</pubDate>
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<guid>https://pascalmichaillat.org/tags/unemployment-fluctuations/</guid>
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<description></description>
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</item>
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<title>unemployment gap</title>
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<link>https://pascalmichaillat.org/tags/unemployment-gap/</link>
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<pubDate>Wed, 29 Jan 2025 00:00:00 +0000</pubDate>
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<guid>https://pascalmichaillat.org/tags/unemployment-gap/</guid>
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<description></description>
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<title>unemployment insurance</title>
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<link>https://pascalmichaillat.org/tags/unemployment-insurance/</link>
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<guid>https://pascalmichaillat.org/tags/unemployment-insurance/</guid>
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<description></description>
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<title>wage rigidity</title>
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<link>https://pascalmichaillat.org/tags/wage-rigidity/</link>
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‎public/tags/job-rationing/index.html

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<p>This course presents a matching model of unemployment. It uses the model to study unemployment fluctuations; job rationing; efficient unemployment and unemployment gap; and labor market policies such as minimum wage, public employment, and unemployment insurance.</p>
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</div>
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<footer class="entry-footer"><span title='2025-01-28 00:00:00 +0000 UTC'>January 2025</span>&nbsp;&middot;&nbsp;Pascal Michaillat</footer>
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<footer class="entry-footer"><span title='2025-01-29 00:00:00 +0000 UTC'>January 2025</span>&nbsp;&middot;&nbsp;Pascal Michaillat</footer>
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<a class="entry-link" aria-label="post link to Unemployment" href="https://pascalmichaillat.org/c1/"></a>
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</article>
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‎public/tags/job-rationing/index.xml

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<title>Unemployment</title>
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<description>This course presents a matching model of unemployment and uses it to study unemployment fluctuations, efficient unemployment, and labor market policies.</description>
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