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Equation 16 · Part 12 · The Jagged Frontier Fallacy: Deconstructing Harvard's Canonical AI Productivity Study

Denominator: c_L(s)

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.
cL(s)c_L(s)

What this part means

The complete quantity below the fraction bar; it must be nonzero for this division.

Its job in the formula

cL(s)c_L(s) is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

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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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.