SS 7 - TFP and Constant returns to scale

mikecocos…
you’ve got to take a look at the book brother. “A” = growth in TFP
 
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.
 
CFALEB Wrote:
——————————————————-
> DFW can you please tell me what page exactly?
> thx
Q is on pg 176
 
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.
 
You must log in or register to reply here.
Back
Top