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Equation 5 · Part 4 · Selection Accounting: The Price Equation Runs the Economy

Symbol β

dzˉdt∣selection=β Var⁡s(z)\frac{d\bar z}{dt}\Big|_{\text{selection}} = \beta \, \operatorname{Var}_s(z)
β\beta

What this part means

never a constant of nature.

Its job in the formula

β is an input to the expression that computes the quantity on the left.

Where the article explains it

What the paper adds is a discipline on β\beta : because realized market selection acts on profitability rather than on physical output alone, per Foster, Haltiwanger, and Syverson’s finding that price and physical productivity pull in opposite directions across surviving plants [ 14 ] , β\beta is never a constant of nature.

The passage around this formula

…2 states an economic reading of Fisher’s fundamental theorem of natural selection [ 2 ] : dzˉdt∣selection=β Var⁡s(z)\frac{d\bar z}{dt}\Big|_{\text{selection}} = \beta \, \operatorname{Var}_s(z). The selection component of the growth rate of mean log productivity equals a selection-intensity coefficient β\beta times the share-weighted variance of log productivity across firms. The qualitative move is not new: Metcalfe applied Fisher’s principle to competing firms under replicator dynamics in the 1990s [ 4 ] , and Andersen used Price’s equation itself, by name, to split economic change into…

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Sources cited in the surrounding passage

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