The COBB-DOUGLAS Production Function
I suggested in class that the Cobb-Douglas production function was a good approximation to the U.S. Economy because the share of GDP that is appropriated by capitalists was, over the long run, constant at about 30%, whereas the share appropriated by workers was constant at about 70%. This is shown for the period 1929-1999 (notice that, over the short run, the shares move a little -for example, the labor share increased a lot during the great depression, as capitalists lost a lot of income, but over the long run, they remain fairly stable). This suggests that the capital share, (which we called alpha in class) is about 0.3.
Here is a picture that supports my claim:
Source: Pikety and Saez, NBER Working Paper, 2001.