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?
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%
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.