Equation 5 · Part 14 · What the Machine Breakers Actually Wanted

change

\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}}

change

What this part means

Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.

Its job in the formula

Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.

Full expressionchangeArticle 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.

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.