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Equation 7 · Part 11 · The Jagged Frontier Fallacy: Deconstructing Harvard's Canonical AI Productivity Study

Starting index or lower bound: 0

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}},
00

What this part means

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

Its job in the formula

0 appears in the bound of this integral. The bound states where the repeated operation starts, ends, or which values it includes.

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:

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Learn the underlying idea

Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

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Sources cited in the article section

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