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2026-02-22-ai-cost-curves.qmd

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1. Generally, agents are cheaper but less capable.
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2. Can simplify to say agents are free, without much loss.

_freeze/2026-02-22-ai-cost-curves/execute-results/html.json

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"engine": "knitr",
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"markdown": "---\ntitle: AI cost curves\ndraft: true\nengine: knitr\nexecute:\n echo: false\n warning: false\n error: false\n cache: true # caches chunk output\n---\n\n\n\nIt's super useful to draw plots showing achievement vs expenditure for humans vs computers, like this:\n\n\n\n::: {.cell}\n::: {.cell-output-display}\n![](2026-02-22-ai-cost-curves_files/figure-html/unnamed-chunk-1-1.png){width=672}\n:::\n:::\n\n\n\nYou can read the y-axis in a few ways: (1) score on a benchmark; (2) quality of the output; (3) score on some optimization problem.\n\nSome observations:\n\n1. Today, for a given levcomputers are either cheaper than humans or .\n\n\n\n\n::: {.cell}\n::: {.cell-output-display}\n![](2026-02-22-ai-cost-curves_files/figure-html/unnamed-chunk-2-1.png){width=672}\n:::\n:::\n",
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"markdown": "---\ntitle: AI cost curves\ndraft: true\nengine: knitr\nexecute:\n echo: false\n warning: false\n error: false\n cache: true # caches chunk output\n---\n\n\n\nThree spaces\n: \n - three\n \n - three\n\nFour spaces\n: \n - four\n \n - four\n\n\n\n\nObservatinons:\n\n1. Generally, agents are cheaper but less capable.\n2. Can simplify to say agents are free, without much loss.\n3. We can see three types of growth: (A) cheaper inference; (B) ; \n4. This theory maps exactly to time horizon. \n5. Can derive these curves from a theory (???).\n\n\n\nIt's super useful to draw plots showing achievement vs expenditure for humans vs computers, like this:\n\n\n\n::: {.cell}\n::: {.cell-output-display}\n![](2026-02-22-ai-cost-curves_files/figure-html/unnamed-chunk-1-1.png){width=672}\n:::\n:::\n\n\n\nYou can read the y-axis in a few ways: (1) score on a benchmark; (2) quality of the output; (3) score on some optimization problem.\n\nSome observations:\n\n1. Today, for a given levcomputers are either cheaper than humans or .\n\n\n\n\n::: {.cell}\n::: {.cell-output-display}\n![](2026-02-22-ai-cost-curves_files/figure-html/unnamed-chunk-2-1.png){width=672}\n:::\n:::\n",
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docs/2026-02-22-ai-cost-curves.html

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<dt>Three spaces</dt>
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<li>three</li>
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<li><p>four</p></li>
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<p>Observatinons:</p>
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<ol type="1">
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<li>Generally, agents are cheaper but less capable.</li>
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<li>Can simplify to say agents are free, without much loss.</li>
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<li>We can see three types of growth: (A) cheaper inference; (B) ;</li>
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<li>This theory maps exactly to time horizon.</li>
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<li>Can derive these curves from a theory (???).</li>
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</ol>
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<p>It’s super useful to draw plots showing achievement vs expenditure for humans vs computers, like this:</p>
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docs/index.html

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docs/index.xml

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<p>Some potential applications for knowledge-generating inference: (1) optimize every part of the AI R&amp;D and serving stack; (2) do drug discovery; (3) discover new algorithms which can be used in new software (e.g.&nbsp;new codecs, new scheduling algorithms); (4) build better trading algorithms; (5) if you have a sufficiently high-quality verifier to human preferences, then build very high-quality cultural products, e.g.&nbsp;movies.</p>
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<p>Knowledge-creating LLMs will differ from knowledge-sharing LLMs in a number of ways:</p>
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<ul>
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<li><p>Knowledge-creating LLMs will have qualitatively different benchmarks: instead of seeing if they can answer questions which we already know the answer to (most existing benchmarks), we want them to answer <em>new</em> questions, e.g.&nbsp;solve an unsolved mathematical problem (<a href="https://epoch.ai/frontiermath/open-problems">FrontierMath Open Problems</a>) or set a new record on an optimization problem (e.g.&nbsp;GSO-bench, <span class="citation" data-cites="shetty2025gso">Shetty et al. (2025)</span>). We can use these new frontier benchmarks are indices for capability, but they are more challenging to interpret because the frontier is always moving.</p></li>
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<li><p>Knowledge-creating LLMs will have qualitatively different benchmarks: instead of seeing if they can answer questions which we already know the answer to (most existing benchmarks), we want them to answer <em>new</em> questions, e.g.&nbsp;solve an unsolved mathematical problem (<a href="https://epoch.ai/frontiermath/open-problems">FrontierMath Open Problems</a>) or set a new record on an optimization problem (e.g.&nbsp;GSO-bench, <span class="citation" data-cites="shetty2025gso">Shetty et al. (2025)</span>). We can use these new frontier benchmarks as indices for capability, but they are more challenging to interpret because the frontier is always moving.</p></li>
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<li><p>Knowledge-creating LLMs have high returns to compute on individual problems, unlike knowledge-sharing LLMs for which returns asymptote quickly. It can be worth spending billions of tokens to solve a single problem if the solution is generally applicable.</p></li>
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<details class="validation-checklist">
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<summary>
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Validation Checks
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<p><strong>Overall:</strong> ⚠️ Warning</p>
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<li>✅ [36/36] Cited sources exist in <code>posts/ai.bib</code> (programmatic)</li>
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<li>✅ [26/26] QMD quotes match <code>posts/ai.bib</code> (programmatic)</li>
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<li>✅ [26/26] QMD growth values match <code>posts/ai.bib</code> (programmatic)</li>
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<li>⚠️ [34/36] Abstracts present for all cited sources (programmatic)</li>
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<td>July 2024</td>
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<td><span class="citation" data-cites="tytell2024aixfactor">Tytell (2024)</span></td>
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<td style="text-align: center;">0.2-0.9%</td>
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<td style="text-align: center;">+0.2-0.9%</td>
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<td>Exhibit 1 shows a range of estimates for increases to productivity growth rates, between 0.2% and 0.9%.</td>
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<td>Jan 2025</td>
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<td><span class="citation" data-cites="wiseman2025growth">Wiseman and McClements (2025)</span></td>
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<td style="text-align: center;">3-9%</td>
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<td style="text-align: center;">+3-9%</td>
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<td><em>“We expect AI will provide a 3%-9% increase to economic growth per year in the near future”</em></td>
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<td style="text-align: center;">+0.2-0.5% (implied)</td>
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<td><em>“By 2040, output is only 4% higher than it would have been without the growth acceleration, and by 2060 the gain is still only 19%. A key reason for the slow acceleration is the prominence of”weak links” (an elasticity of substitution among tasks less than one).”</em></td>
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<td>Feb 2026</td>
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<td><span class="citation" data-cites="amodei2026nytimes">Amodei (2026)</span> (Dario Amodei)</td>
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<td style="text-align: center;">+5-15%</td>
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<td><em>“I can see a world where A.I. brings the developed world G.D.P. growth to something like 10, 15 percent. Five, 10, 15 — I mean there’s no science of calculating these numbers. It’s a totally unprecedented thing. But it could bring it to numbers that are outside the distribution of what we saw before.”</em></td>
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<div id="ref-bis2024impact" class="csl-entry">
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Aldasoro, Iñaki, Sebastian Doerr, Leonardo Gambacorta, and Divya Sharma. 2024. <span>“The Impact of AI on Output and Inflation.”</span> BIS Bulletin 85. Bank for International Settlements. <a href="https://www.bis.org/publ/work1179.pdf">https://www.bis.org/publ/work1179.pdf</a>.
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</div>
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<div id="ref-amodei2026nytimes" class="csl-entry">
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Amodei, Dario. 2026. <span>“How to Build an a.i. Economy.”</span> February 12, 2026. <a href="https://www.nytimes.com/2026/02/12/opinion/artificial-intelligence-anthropic-amodei.html">https://www.nytimes.com/2026/02/12/opinion/artificial-intelligence-anthropic-amodei.html</a>.
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</div>
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<div id="ref-arnon2025projected" class="csl-entry">
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Arnon, Alex. 2025. <span>“The Projected Impact of Generative AI on Future Productivity Growth.”</span> Brief. Penn Wharton Budget Model. <a href="https://budgetmodel.wharton.upenn.edu/issues/2025/9/8/projected-impact-of-generative-ai-on-future-productivity-growth">https://budgetmodel.wharton.upenn.edu/issues/2025/9/8/projected-impact-of-generative-ai-on-future-productivity-growth</a>.
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docs/posts/2025-10-19-forecasts-of-AI-growth.html

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<p><strong>Overall:</strong> ⚠️ Warning</p>
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<ul>
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<li>✅ [35/35] Cited sources exist in <code>posts/ai.bib</code> (programmatic)</li>
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<li>✅ [36/36] Cited sources exist in <code>posts/ai.bib</code> (programmatic)</li>
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<li>✅ [26/26] QMD quotes match <code>posts/ai.bib</code> (programmatic)</li>
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<li>✅ [26/26] QMD growth values match <code>posts/ai.bib</code> (programmatic)</li>
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<li>⚠️ [34/36] Abstracts present for all cited sources (programmatic)</li>
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<td>July 2024</td>
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<td><span class="citation" data-cites="tytell2024aixfactor">Tytell (<a href="#ref-tytell2024aixfactor" role="doc-biblioref">2024</a>)</span></td>
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<td style="text-align: center;">+0.2-0.9%</td>
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<td>Exhibit 1 shows a range of estimates for increases to productivity growth rates, between 0.2% and 0.9%.</td>
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<td><em>“We expect AI will provide a 3%-9% increase to economic growth per year in the near future”</em></td>
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<td><em>“By 2040, output is only 4% higher than it would have been without the growth acceleration, and by 2060 the gain is still only 19%. A key reason for the slow acceleration is the prominence of”weak links” (an elasticity of substitution among tasks less than one).”</em></td>
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<td>Feb 2026</td>
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<td><span class="citation" data-cites="amodei2026nytimes">Amodei (<a href="#ref-amodei2026nytimes" role="doc-biblioref">2026</a>)</span> (Dario Amodei)</td>
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<td style="text-align: center;">+5-15%</td>
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<td><em>“I can see a world where A.I. brings the developed world G.D.P. growth to something like 10, 15 percent. Five, 10, 15 — I mean there’s no science of calculating these numbers. It’s a totally unprecedented thing. But it could bring it to numbers that are outside the distribution of what we saw before.”</em></td>
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<div id="ref-bis2024impact" class="csl-entry" role="listitem">
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Aldasoro, Iñaki, Sebastian Doerr, Leonardo Gambacorta, and Divya Sharma. 2024. <span>“The Impact of AI on Output and Inflation.”</span> BIS Bulletin 85. Bank for International Settlements. <a href="https://www.bis.org/publ/work1179.pdf">https://www.bis.org/publ/work1179.pdf</a>.
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<div id="ref-amodei2026nytimes" class="csl-entry" role="listitem">
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Amodei, Dario. 2026. <span>“How to Build an a.i. Economy.”</span> February 12, 2026. <a href="https://www.nytimes.com/2026/02/12/opinion/artificial-intelligence-anthropic-amodei.html">https://www.nytimes.com/2026/02/12/opinion/artificial-intelligence-anthropic-amodei.html</a>.
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<div id="ref-arnon2025projected" class="csl-entry" role="listitem">
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Arnon, Alex. 2025. <span>“The Projected Impact of Generative AI on Future Productivity Growth.”</span> Brief. Penn Wharton Budget Model. <a href="https://budgetmodel.wharton.upenn.edu/issues/2025/9/8/projected-impact-of-generative-ai-on-future-productivity-growth">https://budgetmodel.wharton.upenn.edu/issues/2025/9/8/projected-impact-of-generative-ai-on-future-productivity-growth</a>.
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