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Equation 7 · Part 2 · The Jagged Frontier Fallacy: Deconstructing Harvard's Canonical AI Productivity Study

Symbol y

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}},
yy

What this part means

y is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

y is one of the signed contributions combined to compute the quantity on the left.

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

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

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