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πs=cL(s)−[cdraft(s)+caudit(s)]cL(s)≪0.40\pi_s = \frac{c_L(s) - [c_{\text{draft}}(s) + c_{\text{audit}}(s)]}{c_L(s)} \ll 0.40

Why this formula appears here

When applied to the Harvard BCG findings, Acemoglu’s macroeconomic framework reveals why the study’s 40% performance gains cannot be translated linearly into organizational throughput: πs=cL(s)−[cdraft(s)+caudit(s)]cL(s)≪0.40\pi_s = \frac{c_L(s) - [c_{\text{draft}}(s) + c_{\text{audit}}(s)]}{c_L(s)} \ll 0.40. Using rigorous baseline accounting across the United States economy, Acemoglu estimates that generative artificial intelligence will affect no more than 4.6% of total tasks over a ten-year horizon, producing an aggregate TFP increase of less than 0.71% cumulatively over a decade (approximately 0.07% annually) [ 2 ] . The breathless projections of 40% corporate workforce expansion derived from micro-task consulting studies collapse when subjected to rigorous general-equilibrium accounting.

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cdraftc_{\text{draft}}

Symbol c_draft

cdc_draft occurs above the fraction bar. The numerator is divided by the entire denominator below it.

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cauditc_{\text{audit}}

Symbol c_audit

cac_audit occurs above the fraction bar. The numerator is divided by the entire denominator below it.

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cL(s)−[cdraft(s)+caudit(s)]c_L(s) - [c_{\text{draft}}(s) + c_{\text{audit}}(s)]

Numerator: c_L(s) - [c_draft(s) + c_audit(s)]

The complete quantity above the fraction bar.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

πs=cL(s)−[cdraft(s)+caudit(s)]cL(s)≪0.40.\pi_s = \frac{c_L(s) - [c_{\text{draft}}(s) + c_{\text{audit}}(s)]}{c_L(s)} \ll 0.40.

Equation 16 · AI Economics & Systems

The Jagged Frontier Fallacy: Deconstructing Harvard's Canonical AI Productivity Study

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

When applied to the Harvard BCG findings, Acemoglu’s macroeconomic framework reveals why the study’s 40% performance gains cannot be translated linearly into organizational throughput: πs=cL(s)−[cdraft(s)+caudit(s)]cL(s)≪0.40\pi_s = \frac{c_L(s) - [c_{\text{draft}}(s) + c_{\text{audit}}(s)]}{c_L(s)} \ll 0.40. Using rigorous baseline accounting across the United States economy, Acemoglu estimates that generative artificial intelligence will affect no more than 4.6% of total tasks over a ten-year horizon, producing an aggregate TFP increase of less than 0.71% cumulatively over a decade (approximately 0.07% annually) [ 2 ] . The breathless projections of 40% corporate workforce expansion derived from micro-task consulting studies collapse when subjected to rigorous general-equilibrium accounting.

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