Cobb-Douglas

[archived_user]

The Schweser text states:
Empiricial studies suggest it is reasonable to assume constant returns to scale, any given change in capital or labor (for example, from 2% to 3% or 5% to 6%) has a linear effect on output.
I thought capital and labor both have diminishing returns to scale due to the elasticity of capital and labor which sum to 1. Can someone clarify this?

 

[archived_user]

Cobb-Douglas is constant to scale.

 

[archived_user]

Linear doesn’t mean 1:1 increase. For example, if alpha = 0.4, if capital increased from 2% to 3%, we would expect output to increase by 0.4 * (3% - 2%), or 0.4%

 

[archived_user]

I_Got_It wrote: Linear doesn’t mean 1:1 increase. For example, if alpha = 0.4, if capital increased from 2% to 3%, we would expect output to increase by 0.4 * (3% - 2%), or 0.4%

But it does mean that the slope is constant, which is inconsistent with diminishing marginal returns.

 

[archived_user]

The original function is Y = A KalphaLbeta => Alpha and Beta are different.
After that, they assume constant returns to sale, substitute Beta = Alpha -1 and take the natural logarithm of both sides to get the growth formula. Therefore, in the exercise, it is always assumed constant returns to scale.

 

[archived_user]

bqh9 wrote: The original function is Y = A KalphaLbeta => Alpha and Beta are different.

Unless α = β = 0.5.

bqh9 wrote: After that, they assume constant returns to sale, substitute Beta = Alpha -1 and take the natural logarithm of both sides to get the growth formula. Therefore, in the exercise, it is always assumed constant returns to scale.

I believe that you mean β = 1 − α.

 

[archived_user]

Mark