Equation 5 · Part 17 · What the Machine Breakers Actually Wanted

Starting index or lower bound: I

\Delta \ln L \;=\; \underbrace{\eta \, \Delta \ln Y}_{\text{productivity}} \;-\; \underbrace{\int_{I}^{I+\Delta I} s(x)\,dx}_{\text{displacement}} \;+\; \underbrace{\int_{N}^{N+\Delta N} s(x)\,dx}_{\text{reinstatement}}

I

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

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

Full expressionStarting index or lower bound: IArticle meaning

The passage around this formula

Written schematically, the change in labour demand decomposes as $\Delta \ln L \;=\; \underbrace{\eta \, \Delta \ln Y}_{\text{productivity}} \;-\; \underbrace{\int_{I}^{I+\Delta I} s(x)\,dx}_{\text{displacement}} \;+\; \underbrace{\int_{N}^{N+\Delta N} s(x)\,dx}_{\text{reinstatement}}$ . where tasks are indexed by x , s(x) is the value-added share of task x , I is the automation frontier below which capital performs the task, N is the upper edge of the task space where new tasks appear, and $\eta$ scales the induced demand from higher output. The expression is illustrative of the structure rather than a reproduction of any published estimating equation; the substantive claim it encodes is that the sign of $\Delta$ $\ln$ L is not determined by the size of $\Delta$ I alone.

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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

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