← All parts of this equation

Equation 7 · Part 8 · The Jagged Frontier Fallacy: Deconstructing Harvard's Canonical AI Productivity Study

subtraction

Y=(∫01y(s)σ−1σ ds)σσ−1,Y = \left( \int_{0}^{1} y(s)^{\frac{\sigma-1}{\sigma}} \, ds \right)^{\frac{\sigma}{\sigma-1}},
subtraction

What this part means

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

Its job in the formula

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

The passage around this formula

Let total output Y be produced by combining a continuum of specialized tasks s ∈\in [0, 1] according to a constant-elasticity-of-substitution production function: Y=(∫01y(s)σ−1σ ds)σσ−1Y = \left( \int_{0}^{1} y(s)^{\frac{\sigma-1}{\sigma}} \, ds \right)^{\frac{\sigma}{\sigma-1}}. where each task y(s) can be performed by labor or by an automated system if that task falls within the feasible automated set A\mathcal{A} . Under Hulten’s theorem, the first-order aggregate TFP cost savings from automating a subset of tasks is bounded by the expenditure share of the automated tasks multiplied by the average unit cost reduction:

Read this part in the article →

Learn the underlying idea

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

Open the illustrated addition and subtraction in an equation guide →

Sources cited in the article section

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