# SS 7 - TFP and Constant returns to scale

Sch states that growth in total factor productivity (TFP) is zero when constant returns to scale are present. If that’s the case than in this formula Change in Y / Y = Change in A/ A + alpha x change in k/ k + (1-alpha) change in L/L Change in A / A will be zero. If that’s the case than in all the problems growth in TFP should be zero? Yet in all the problems TFP is added in to labor and capital. Can anyone clarify? thanks

I think schweser is wrong on this. “Constant returns to scale” == “alpha+beta =1 in the formula”.

what do you mean? formula is additive. DeltaA/A is 0… but there is still DeltaK/K * alpha + delta L/L * (1-alpha) which have some values. Can you give an example to show what you mean? I do not use schweser, so if you are posting something from there - I need the full question. thanks

cpk123 Wrote: ------------------------------------------------------- > what do you mean? > > formula is additive. > DeltaA/A is 0… but there is still DeltaK/K * > alpha + delta L/L * (1-alpha) which have some > values. > > Can you give an example to show what you mean? > > I do not use schweser, so if you are posting > something from there - I need the full question. > > thanks There is no particular question, just the way this “constant returns to scale” is presented is confusing in Schweser. CFAI text, does not go beyond stating, that if we assume constant returns to scale, we can substitute Beta = 1- alpha. CFAI does not say Change in TFP has to be zero.

If schweser stated change in tfp should be zero, as deriv mentions above - they are wrong. constant returns to scale just means alpha + beta = 1. If labor goes up, in some form capital comes down… (or vice versa). – and this is consistent with cfai.

If constant returns to scale is present (and it always is in CFA) the same percentage change in K and L will result in the same percentage change in Y. That’s what they say about it.

Makes sense. Thanks guys, Another place where relying on Just Schweser can cause trouble.

onelasttime Wrote: ------------------------------------------------------- > Makes sense. > > Thanks guys, Another place where relying on Just > Schweser can cause trouble. Tread lightly with the Schweez

in economics, constant returns to scale just means that there aren’t any kinks. for example, if you need one worker to make one chair, you’ll need two workers to make two if you DIDNT have constant returns to scale, adding another worker would result in 3 chairs being made. in terms of the cobb-douglas, i believe that means that as you add k or l, your alpha and (1-alpha) don’t change for all levels of k and l

dude. constant returns to scale is one sentence and footnote in CFAI. just memorize the a and (1-a) variables in the KL of YAKL

Just read this thread and am annoyed. I remember answering a question in a schweser practice exam that excluded growth in TFP becasue of the constant returns to scale assumption, which I suspect is wrong. I should have known better.

zoya Wrote: ------------------------------------------------------- > in economics, constant returns to scale just means > that there aren’t any kinks. > for example, if you need one worker to make one > chair, you’ll need two workers to make two > > if you DIDNT have constant returns to scale, > adding another worker would result in 3 chairs > being made. > > in terms of the cobb-douglas, i believe that means > that as you add k or l, your alpha and (1-alpha) > don’t change for all levels of k and l +1

Damn Schweser!

oh wow, glad I didn’t buy schweser this year. I thought CFAI materials on this new stuff were solid. EOC’s did a good job hammering it home. i agree w/ CPK and others here- const returns to scale wouldn’t mean TFP needs to be zero.

i am gonna go home and check my notes tonight but i am fairly certain schweser botched this. fml…

+1

TFP ROCKS!!!

I’m pretty sure constant returns to scale means TFP IS zero. if schweser stated that then they are perfectly correct about it. Actually the way some of you guys explain the meaning of constant returns to scale (CRS) to prove TFP is not zero is the exact reason why it is. If you assume CRS and you agree that a given percentage change in capital and labor would produce the same percentage change in GDP because of CRS, then TFP is 0. this means that thare no gains in productivity when you add workers or machines and the addition in workers and capital would only result in the same addition to GDP implied by the previous workers/machines used. That is, if you add one worker and one machine, they would produce the exact same output as a unit of worker or machine already present before the addition. Whereas if TFP was not constant, adding one worker would result in a higher increase in GDP because there is one more worker AND he has a higher productivity rate. Bottom line, if you are calculating growth in GDP using the CB function and you assume CRS (which is more realistic), you cannot assume that the productivity and efficiency in machines will grow at a constant rate of 5% for example each year. You are only adding workers and machines but the productivity cannot increasing each year by a given rate. it is constant and therefore the growth rate in TFP is 0. this is why you exclude it from the equation. I might be wrong but this was my understanding of CB function before Level III. one last thing: it is both logical and realistic to assume a given growth rate in labor and machines each year because of people reaching working age and growth in population and growth in business spending on capital. but it is irrealistic to assume an economy can acheive a constant rate of productivity EACH year. growth in TFP is caused by major inventions like the internet or something that really boosts efficieny every year.

Yeah but the equation you listed above isn’t an output growth equation. Not sure if: “a given percentage increase in capital stock and labor inputs results in an equal percentage increase in output” can be true if you add a TFP growth component to the function.