CFA CFA Level 2 Capital Deepening?

Capital Deepening?

  • This topic has 11 replies, 5 voices, and was last updated Apr-17 by ykilstein.
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  • vincentt
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    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?

    Sophie Macon
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    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^α L^(1-α)
    Let’s transform that equation to get K/L (capital deepening): Y/L = A(K/L)^α

    ** 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 α(K/L) [capital to labour ratio]

    Hence that’s how you get the “capital deepening” (or change in capital to labour ratio) formula.

    vincentt
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    @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.

    Sophie Macon
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    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
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    @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?

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

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

    Sophie Macon
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    :)) now you’ll ace it!

    Sarah
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    @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.

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

    Alta12
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    @vincentt wouldn’t 5-10% mean that it can be up to 2 item sets?

    ykilstein
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    @alta12 It would, but it won’t be.

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