 This topic has 11 replies, 5 voices, and was last updated Apr177:46 pm by ykilstein.

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Up::13
Hi @sophie, i’m sure you could help me with this.
What is the formula for capital deepening?
Calculate the capital deepening from the given data:
nominal growth in GDP (%)
real growth in GDP (%)
growth in TFP (%)
growth in hours worked (%)
growth in labour productivity (%)From what I gathered it’s [growth in labour productivity] – [growth in TFP]
but why?





Up::2
Hi @vincentt, capital deepening is the increase in capital (K) to labour (L) ratio that brings a movement along (to the right of) the productivity curve.
So let’s take a look at the the production function: Y = AK^Î± L^(1Î±)
Let’s transform that equation to get K/L (capital deepening): Y/L = A(K/L)^Î±** PS – I couldn’t get superscript to work somehow, so take ^ as sign for superscript. Hope it’s not confusing.
So if you apply a neat math operation called “first difference of log” (not important for CFA exams), you can transform this relationship to a % change one:
% change in Y/L [output per labour or labour productivity] = % change in A [TFP] + % change in Î±(K/L) [capital to labour ratio]
Hence that’s how you get the “capital deepening” (or change in capital to labour ratio) formula.

Up::2
@sophie yup i use ^ for power functions as well so that’s fine.
I’ll probably give you the table:
Which country has demonstrated the largest contribution to labour productivity growth from capital deepening?
Because there isn’t any ‘capital’ given, though i got the right answer, but i couldn’t come up with a figure to show why.







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