CFA CFA Level 2 Capital Deepening?

# Capital Deepening?

• Author
Posts
• vincentt
Participant
• CFA Level 3
14

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?

• 5

@vincentt I am an economics major and I am hating this stuff. And I think in some point in time before CFA I actually liked economics.

• 5

@alta12 It would, but it won’t be.

• vincentt
Participant
• CFA Level 3
3

@sophie i think that make sense now.

Because I couldn’t find that formula in the book as it was given in a different form (G instead of labour productivity or Y/L).

So is Y/L equivalent to GDP output by labour which is just part of the whole GDP as there’s technology and capital?

• 3

Yes, Y/L = GDP output per labour. It’s just dividing the classic output equation with L.

• 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^(1-Î±)
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.

• vincentt
Participant
• CFA Level 3
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.

• 2

Country A @vincentt.

Did you read my derivation above? It proves that it’s growth in labour productivity less growth in TFP = growth in capital to labour ratio (another name for capital deepening).

• vincentt
Participant
• CFA Level 3
2

that clarifies some of my doubts! Damn economics! thank god is only 1 item set [-O<

• 1

:)) now you’ll ace it!

• 1

@vincentt wouldn’t 5-10% mean that it can be up to 2 item sets?

• vincentt
Participant
• CFA Level 3
0

i hope so thanks again @sophie u’re a star! ðŸ˜€ @diya now I wouldn’t look that bad to dislike economics :))