Is Cobb-Douglas the only output function corresponding to a competitive economy?
Let $a+b&lt;1,\;\; a,b&gt;0$.  Pay the factors of production their marginal product:

$$rK = \frac {aQ}{K} K= aQ,\;\;\ wL=\frac {bQ}{L} L=bQ$$

So total payments to factors of production will be

$$rK +wL = aQ + bQ = (a+b)Q &lt; Q$$

And the question is: who gets the rest of the output that has been produced?