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Published equation contexts

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

Why this formula appears here

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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LL

Symbol L

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

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (1)

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

Equation 1 · Labour & Technology

What the Machine Breakers Actually Wanted

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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.…

Meanings in this article

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