productivity rate = “os = constant, (4.7a)

implying output productivity rate = “os = constant, (4.7a) capital assuming again that acceleration is nonzero. This shows how to find the position of capital in the sequence led by output, and how to test between free growth and thrift theories. The market-valued capital denominator in (4.7) and (4.7a), and the consumption numerator in (4.7), can be taken directly from national accounts data collected at the Piketty-Zucman website. The output numerator in (4.7a) can be constructed as consumption plus current change in market-valued capital. By (4.7), free growth theory (Mill’s idea) predicts a roughly constant consumption/capital ratio, even in accelerations and decelerations and reversals. Then capital acceleration would lag alongside consumption acceleration while output led alone. Thrift theory makes the opposite prediction ofa roughly constant output/capital ratio, so that output and capital would lead together while consumption lagged alone. There is no need to measure and test both indexes, as either is defined as one less the other. My charts and tables track the free growth index. They confirm free growth theory in all countries and periods. Defining Free Growth and Thrift (4.2) through (4.7a) defined the free growth and thrift indexes, but not free growth or thrift themselves as flows. Since I will use those terms often, I’d better clear that up now. Define free acceleration = productivity gain = gaininrateofreturn, and thrift acceleration = thrift gain = drop in cash flow rate, so that those sets of terms become interchangeable. Then (4.5a) can be put as Chapter 4 Mill’s Idea 1/11/16 15 HOUSE_OVERSIGHT_011006