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:
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
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.