<p>This paper proposes a novel pandemic response paradigm, and shows that it would have been the right middle ground between lockdown and ignore-the-virus for Covid-19: maximize social welfare subject to <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10058_2025_379_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(R\,{\le }\,1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <mspace width="0.166667em" /> <mo>≤</mo> <mspace width="0.166667em" /> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> as a <i>constraint</i>. A simple graphical argument shows that this formulation is an approximately optimal way to balance socioeconomic and health objectives, because of a sharp kink in the benefits-of-risk-reduction curve at <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10058_2025_379_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">\(R\,{=}\,1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <mspace width="0.166667em" /> <mo>=</mo> <mspace width="0.166667em" /> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> (both the curve and its kink are novel to this paper). Two critical insights emerge from this approach to the pandemic. First, the <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10058_2025_379_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(R\,{\le }\,1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <mspace width="0.166667em" /> <mo>≤</mo> <mspace width="0.166667em" /> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> constraint imposes a “risk budget” on society. Society should optimally spend this budget on the social and economic activities with the highest ratio of socioeconomic value to disease-transmission risk, with targeted activity bans for activities with too low a ratio of value-to-risk. For example, schools have a much higher ratio of value-to-risk than bars, so society should optimally spend its risk budget on schools over bars. Second, what I call “low-cost risk reducers” (LCRRs) can significantly improve activities’ value-to-risk ratios and hence significantly reduce the cost of satisfying the <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10058_2025_379_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(R\,{\le }\,1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <mspace width="0.166667em" /> <mo>≤</mo> <mspace width="0.166667em" /> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> constraint. Examples of LCRRs for Covid-19 include rapid testing, high-quality facemasks, stay-home-if-sick rules and improved air circulation. A simple numerical example, based on estimates from the medical literature for <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10058_2025_379_Article_IEq6.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(R_{0}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> and the efficacy of LCRRs for Covid-19, suggests the potential gains from this paper’s approach to the pandemic would have been enormous—plausibly trillions of dollars and hundreds of thousands of lives in the United States alone.</p>

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R < 1 as an economic constraint

  • Eric Budish

摘要

This paper proposes a novel pandemic response paradigm, and shows that it would have been the right middle ground between lockdown and ignore-the-virus for Covid-19: maximize social welfare subject to \(R\,{\le }\,1\) R 1 as a constraint. A simple graphical argument shows that this formulation is an approximately optimal way to balance socioeconomic and health objectives, because of a sharp kink in the benefits-of-risk-reduction curve at \(R\,{=}\,1\) R = 1 (both the curve and its kink are novel to this paper). Two critical insights emerge from this approach to the pandemic. First, the \(R\,{\le }\,1\) R 1 constraint imposes a “risk budget” on society. Society should optimally spend this budget on the social and economic activities with the highest ratio of socioeconomic value to disease-transmission risk, with targeted activity bans for activities with too low a ratio of value-to-risk. For example, schools have a much higher ratio of value-to-risk than bars, so society should optimally spend its risk budget on schools over bars. Second, what I call “low-cost risk reducers” (LCRRs) can significantly improve activities’ value-to-risk ratios and hence significantly reduce the cost of satisfying the \(R\,{\le }\,1\) R 1 constraint. Examples of LCRRs for Covid-19 include rapid testing, high-quality facemasks, stay-home-if-sick rules and improved air circulation. A simple numerical example, based on estimates from the medical literature for \(R_{0}\) R 0 and the efficacy of LCRRs for Covid-19, suggests the potential gains from this paper’s approach to the pandemic would have been enormous—plausibly trillions of dollars and hundreds of thousands of lives in the United States alone.