CFAI reading 14 question 8.
I wonder
(*) why correct answer to EOC question 8 is A (Country A)? I would say that there is not enough data provided to answer this question and the answer may be A or C depending on shares of capital in GDP for countries A and C.
(*) is capital deepening = (% change in capital-to-labour ratio) or (% change in capital-to-labour ratio) * (share of capital in GDP)?
As I understand capital deepening is dk/k (% change in capital-to-labour ratio) and is not a*dk/k (share of capital in GDP)*(% change in capital-to-labour ratio).
Therefore I expected the formulas for capital deepening for question 8 to be:
(1) dy/y = dA/A + a*dk/k (from equation 6 in reading 14)
therefore
(2) dk/k = (dy/y - dA/A) / a
(capital deepening = % change in labor productivity - % change in TFP) / (share of capital in GDP)
But in the answer to question 8 assumed formula is:
(3) capital deepening = dy/y - dA/A (capital deepening = % change in labor productivity - % change in TFP). Therefore by capital deepening authors understand a*dk/k. But I never see “share of capital in GDP” mentioned in definitions for capital deepening.
If I use formula (2) for answering question 8 then correct answer will be dependent on a (share of capital in GDP) which we don’t have directly but can assume that a is much less for country C than for country A. And if we assume that share of capital in GDP for country A = 2*share of capital in GDP for Country C then the answer to question 8 becomes country C.