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.