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I am trying to solve the following problem as described here: https://www.adb.org/publications/total-factor-productivity-testing-growth-models (pages 4-5) http://digamo.free.fr/macombie98.pdf (pages 165-166)

It all starts with this accounting identity:

accounting identity

The equation is transformed so that it can be expressed in growth rates of the corresponding variables. If we suppose that a is a constant and that both w and r grow at constant exponential rates, we can integrate the iquation and it should yield this:

$$ Y_t = A_0 \exp (\lambda t)L_t^a K_t^{1-a} $$

Does anybody know the exact steps taken while integrating the growth-rates-form equation?

Thank you

Adam
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You appear to be wanting to integrate $A \exp(\lambda t)L^a_tK^{1-a}_t$. That depends strongly on exactly how $L^a_t$ and $K^{1-a}_t$ depend on t and I could not find that in your links.

Henry Lee
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user247327
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  • Perhaps this helps: http://college.holycross.edu/RePEc/eej/Archive/Volume31/V31N3P427_445.pdf (page 433) – Adam Apr 28 '21 at 12:51
  • I believe we are supposed to apply this rule of integration ∫(u′/u)dt=ln|u|+C but I might be wrong – Adam Apr 28 '21 at 12:53
  • similarly to here... https://math.stackexchange.com/questions/919432/integral-respect-to-time?rq=1 – Adam Apr 28 '21 at 13:05