The Cobb Douglas technology

In growth theory it is often assumed that countries have a common technology describing national output. The technology frequently takes the Cobb Douglas form Y=A.L^alpha.K^(1-alpha), where L is labour, K is capital, and A and alpha are constants.

The Cobb Douglas has some properties which make it reasonable, like if you increase the labour and capital by a certain percentage, the output increases by the same percentage. I've never been convinced that this is its main selling point. Rather, taking logs gives

ln Y = ln A + alpha ln L + (1-alpha) ln K

So it could be painted as the first order approximation to any function expressing ln Y as a function of ln L and ln K, plus a condition on the coefficients. I'd drop the condition (and thus sacrifice the Cobb-Douglas form whilst keeping the multiplicative shape), replacing (1-alpha) by a free constant since there are many circumstances where the coefficients would not sum to unity. Any production function which uses only capital and labour omits other important factors influencing output - such as education or the existence of market networks - and mobilising labour and capital may influence them to such an extent that better than proportionate returns are obtained. When I was looking at the expansion of economies after conflict and attempting to explain their commonly unparalleled rapidity of growth, I considered Y=A.L.K as a possible short term production function.