levfings:
S2000magician:
CFASniper:
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) . . .
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.
CFASniper:
. . . 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
Again, you’re incorrect. The definition 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/ .
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?
Alpha and beta are, respectively, the output elasticities of labor and capital, much like price and income elasticities of demand that you had at Level I. I’m sure that they’re estimated using regression analysis on a ton of data. what determines them will be things like the skill of the workforce, the education of the workforce, the level of technology (though, as mentioned above, not the change in technology; that’s another factor), and so on. They will, of course, change over time, and will be different in different economies.
I don’t have the CFA curriculum, so I don’t know how they presented it.
How can anyone possibly dispute the CFA cobb douglas function. Its probably on every official and unofficial mock in the world, and the textbook.
Nope: they’re not wrong. Constant returns to scale implies that α + β = 1.
Noticed the same thing while studying. Schw does it differently from CFAI. I chose to ignore Schw.
system
June 13, 2014, 3:37pm
#47
so are A and B always constant? Give me an example when they would change Mr. Magician?
Of course they’re not constant.
They’ll change with a change in technology (TFP). Beta will likely increase when technology improves.
They’ll change with a change in the productivity of the workforce. Alpha will likely increase with an increase in the productivity of the workforce.
But labour inputs would also change TFP?
Yes, potentially.
In short, it’s complicated.
system
June 13, 2014, 4:24pm
#51
^
yea magician that will be cfai explanation as well. Their way or the highway.