Why is the Cobb-Douglas production function so popular? As relatively novice quantitative analyst/ Cost analyst, Ive been asked to estimate the level of a given organizations productivity more than once, and then forecast for the next couple of periods. The place I work at is a relatively small non-profit (around 30 people) dedicated to food bank donation distribution and volunteer solicitation, so Im not sure if firm size has something to do with this.

Most of the time I've been asked for specific units and not percentage changes or elasticities, so I'm forced to present one of two production functions.


$$f(x_1,...,x_n)=\Sigma_{i=1}^n\beta_i x_i$$
$$f(x_1,...,x_n)=\gamma \min(x_1,...,x_n)$$


Yet when I read  economic literature I see the cobb douglas (or some variation of it like the stone-gerry)  being used all the time. 

I know it has the property of mathematically showing diminishing returns to scale for a single factor of production, however Im having difficulty seeing it in my line of work. Is it a production function exclusive to manufacturing of real goods?
As you hint at in your question, the real underlying reason (in my opinion) behind the C-D production function's popularity is mathematical convenience. The fact that the sum $\alpha + \beta$ is a nice, intuitive representation of "returns to scale" is very convenient.

I think of its use as similar to the use of exponential or power utilities in mathematical finance. Unrealistic? Perhaps, but oh so friendlier to work with.