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Equation 1 · Part 4 · What the Machine Breakers Actually Wanted

Symbol L

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

What this part means

L occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Its job in the formula

L occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

Allen’s analysis of the same period gives the mechanism a name. Across 1760–1913 he finds a two-stage evolution of inequality in which, over the first half of the nineteenth century, “the real wage stagnated while output per worker expanded”, the profit rate roughly doubled, and profits’ share of national income rose at the expense of labour and land; only after mid-century did real wages 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.…

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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

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