CFA CFA Level 2 Capital Deepening?

Capital Deepening?

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    • Avatar of vincenttvincentt
      Participant
        • CFA Level 3
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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?

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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.

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

      • Avatar of vincenttvincentt
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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?

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

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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.

        • Avatar of vincenttvincentt
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            • CFA Level 3
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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.

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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).

          • Avatar of vincenttvincentt
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              • CFA Level 3
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              that clarifies some of my doubts! Damn economics! thank god is only 1 item set [-O<

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              :)) now you’ll ace it!

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

            • Avatar of vincenttvincentt
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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 :))

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