SS 7 - TFP and Constant returns to scale

mikecocos… you’ve got to take a look at the book brother. “A” = growth in TFP

I will, later tonite… I’m at work…

mikecocos is right imho. Equation 1 above is not the growth rate of TFP, it is TFP in monetary terms. TFP need not be zero. Its the growth rate in TFP that is 0. for example consider TFP is 5, Capital is 12 and Labor is 23. You would replace all those in the output equation. Whereas if we want to calculate growth rate in GDP you assume TFP stays the same because of consant returns to scale. Therfore growth rate in TFP is 0. then you would only add growth rate in labor and capital respectively multiplied by 1-alpha and alpha. Now consider this: Volume 3, Page 135: “If we assume that the production function exhibits constant returns to scale (i.e. a given percentage increase in capital stock and labor inputs results in an equal percentage increase in output), we can substitute Beta = (1 - alpha) in Equation 1.” They say percentage increase. This is growth rate of K and L. the only way the above sentence can hold true is if percentage change in TFP is zero. or else a 15% increase in L and K together, and knowing that beta is 1-alpha would result in a rate of growth in GDP different than 15%: 15% * alpha + 15% (1-alpha) = 15% If you add any percentage of increase in TFP to above the equation cannot hold. So it only holds if change in TFP is 0.

I see. A Yank. Well, let me know. Maybe I’m reading it wrong.

See question & solution for 2a in cfai reading 24. According to this, you add tfp even with constant returns to scale. I got messed up by Schweser too but corrected myself when working the eoc ?s.

you can argue till the cows come home, TFP is the 'ish IMO.

DFW can you please tell me what page exactly? thx

CFALEB Wrote: ------------------------------------------------------- > DFW can you please tell me what page exactly? > thx Q is on pg 176

you down with TFP? yeah you know me!

As per the Cobb-Douglas equation Y = A . K^alpha . L^beta Constant return to scale means A is a constant. When you take Log on both side followed by a partial derivative of both sides (calculus 101), you get (delta Y) / Y = (delta A) / A + alpha . (delta K) / K + beta . (delta L) / L Now constant return to scale implies delta A = 0 and the growth equation reduces to (delta Y) / Y = alpha . (delta K) / K + beta . (delta L) / L Also, alpha and beta always add up to 1, constant return to scale or not. economically speaking, constant return to scale simply means that factors other than labour and capital (think technological innovations) do not magnify production to a level higher than what could be expected.

CFASniper- Your growth equation makes sense to me. I took a look at the CFAI text yesterday and there is an example in their curriculum that doesn’t exclude TFP in the growth calculation though. I think CFA got it wrong as the definition of constant returns doesnt make sense if you add a TFP growth component. I wrote them an email yesterday, making that point. Suggest you do the same if you feel likewise.

CFA got it wrong? It’s the CFA way or the highway as far as this test is concerned. If they are preaching one way in the book, don’t expect to see them drift far from it from the actual test guideline answers. You guys make a compelling point, though I still feel that if CFAI had it the way they did in the text, then that’s the approach that should’ve been taken.

CFAsniper, this is exactly what I wrote above. This is my understanding of the CB function since university. I think I will send an email to CFAI. Even though they had an example where they did not exclude TFP it makes no sense to add it. Constant returns to scale means no growth from productivity. You canno expect productivity to grow each year at a given percentage. Its a growth equation.

guys, I think it’s meaningless - CFA has published their curriculum for many months, with no errata on this. If you thought the formula was wrong then, why not bring it up to them before the exam? The point is, the CFA way is that constant returns to scale means beta = 1 - alpha, and is defined by a given % increase in capital stock and labor input results in an equal % increase in output. There are footnotes on page 135 that discuss the Solow residual, which is the reverse engineering of the formula, but can change and thus should be given in a problem. For the purposes of the CFA exam, constant return to scale does not mean TFP = 0. TFP is a plug factor that is used to attribute that portion of an economy’s growth that is not directly attributable by capital stock and labor input.

I still don’t get it

I think the CFAi textbook explains it well

If you’re going to act smug about it, at least get the terminology correct. It’s not partial, it’s total. And it’s not a derivative; it’s a differential. And it’s not even truly a differential; it’s only an approximation: you’re using _delta_s, not _d_s. And, finally, it’s not calculus 101; functions of several variables are generally covered in a third-semester calculus class.

That’s not what constant returns to scale means.

Again, you’re incorrect. The definition of constant returns to scale implies that

α + β = 1.

Constant returns to scale means that if you keep TFP constant, an increase in labor of a given percentage and an increase in capital of that same percentage gives you an increase in output of . . . you guessed it! . . . that same percentage. For this to be true, α + β must equal 1. TFP certainly can vary, so ΔTFP needn’t be zero; it’s simply that the term constant returns to scale explains what happens when ΔTFP = 0.

If α + β < 1, you have decreasing returns to scale; if α + β > 1, you have increasing returns to scale.

I wrote an article on the Cobb-Douglas production function that may be of some help here: http://financialexamhelp123.com/cobb-douglas-production-function/.

^ The Legend responds… and nails it as always…Thanks Majician…Flawless majic at work

Thanks for this info - I think Schweser should revise this section to be clearer on this. As part of your explanation - what determines the components of the α + β = 1 equation. Meaning what actually is α and β, who decides their values, and do they change as well?

Still not clear after reading the cfai books