considered in both ex ante and ex post versions. The subscripts xa and xp will show
which.
Ex ante net investment can be notated I(K,)__ and defined as identical to thrift flow —df(K,) or —Af(K,,). Its rate is the same as thrift rate -df or —Af . Ex post net
investment is actual growth K, or AK, /At asa flow, and g or AK, /(K,At) asa
rate. Free growth theory, supported by data wherever tested, predicts that thrift or ex ante net investment at the collective scale sacrifices cash flow (pure consumption) with no growth to compensate. My interpretation is that the optimum collective ex ante net investment rate is zero, or equivalently that optimum investment is current cost depreciation plowback from both factors. Then optimum
ex ante net investment becomes
I(K,).,,optimum=0, at the collective scale. (A9.3)
(Net) output Y at that scale is total capital growth (net investment of both factors) plus pure consumption. Here too we can distinguish ex ante output as pure consumption plus ex ante investment, while ex post output is pure consumption plus
ex post net investment. (9.3) gives
Y optimum = C, , atthe collective scale, (A9.4)
where Y_, is ex ante output.
Since (gross) investment equals net investment plus makeup for decaptalization,
while decapitalization equals pure consumption C, collectively by (A1.4a), we can
show [(K,,)_. optimum = C, as an alternate statement of (A9.4).
APPENDIX A: The Argument in Notation 3/7/16 21
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