Equation 16 · The Jagged Frontier Fallacy: Deconstructing Harvard's Canonical AI Productivity Study
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol pi_s
p is part of the quantity the equation computes from the expression on the right.
Symbol c_L
is one of the signed contributions combined to compute the quantity on the left.
Symbol s
s is part of the quantity the equation computes from the expression on the right.
Symbol c_draft
raft occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Symbol c_audit
udit occurs above the fraction bar. The numerator is divided by the entire denominator below it.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subtraction
Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.
subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
Numerator: c_L(s) - [c_draft(s) + c_audit(s)]
The complete quantity above the fraction bar.
Denominator: c_L(s)
The complete quantity below the fraction bar; it must be nonzero for this division.
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.
What the article says around this equation
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: . 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.
Sources cited in the surrounding passage
These citations give research context. Read each source to check which claims it supports.
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