Equation 11 · Selection Accounting: The Price Equation Runs the Economy
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the same headcount and wildly different. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Under the empirically common case where productivity dispersion does not systematically favor large or small firms, that variance collapses to a clean statement: the noise in the selection term scales with the Herfindahl-Hirschman concentration index, an antitrust yardstick every industrial economist already computes as the sum of squared market shares, and the index’s reciprocal is the economy’s effective population size in exactly Wright’s population-genetic sense — the size of an idealized equal-share population that would generate the same drift. A hundred equal firms and one firm with half the market plus two hundred sharing the rest can have the same headcount and wildly different …
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Under the empirically common case where productivity dispersion does not systematically favor large or small firms, that variance collapses to a clean statement: the noise in the selection term scales with the Herfindahl-Hirschman concentration index, an antitrust yardstick every industrial economist already computes as the sum of squared market shares, and the index’s reciprocal is the economy’s effective population size in exactly Wright’s population-genetic sense — the size of an idealized equal-share population that would generate the same drift. A hundred equal firms and one firm with half the market plus two hundred sharing the rest can have the same headcount and wildly different .
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