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Equation 1 · Part 2 · What the Machine Breakers Actually Wanted

Symbol w

Δln⁡w  =  Δln⁡ ⁣(YL)  +  Δln⁡sL\Delta \ln w \;=\; \Delta \ln\!\left(\frac{Y}{L}\right) \;+\; \Delta \ln s_{L}
ww

What this part means

the real wage, Y/L output per worker, and sLs_L labour’s share of value added.

Its job in the formula

w is part of the quantity the equation computes from the expression on the right.

Where the article explains it

where w is the real wage, Y/L output per worker, and sLs_L labour’s share of value added.

The passage around this formula

…resume growing in line with productivity, with factor shares stabilising [ 8 ] . The gap between output per worker and the real wage is an accounting identity once the labour share is admitted: Δln⁡w  =  Δln⁡ ⁣(YL)  +  Δln⁡sL\Delta \ln w \;=\; \Delta \ln\!\left(\frac{Y}{L}\right) \;+\; \Delta \ln s_{L}. where w is the real wage, Y/L output per worker, and sLs_L labour’s share of value added. Productivity growth is necessary for durable wage growth but not sufficient for it: the second term can absorb the first for decades. Allen’s contribution is to show that in Britain it did.

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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