The original paper on the Cobb-Douglas Production Function is found here. A hearty thanks to Tim Schilling at MV=PQ for this paper. This paper comes at a time when I'm analyzing the returns to education using the same model. It's interesting to observe that the original function took L^.75 and K^.25 inferring that the returns are greater to labor. If this same model is applied to education, I think it can generally be said that the greatest growth potential is in the humans using the kapial. So just giving a computer to a kid who could care less is equivalent to giving me a power tool. In my hands, a power tool is a dangerous thing. As Emerson said, I think, "What lies before us is nothing compared to what lies within us." This function confirms this cliche about teaching.
I read in a Malcolm Gladwell article or book, that it takes 10,000 hours to become an expert on a subject. To me this infers that learning is a nonlinear function and subject to diminishing marginal returns. In my opinion, this quote shows that learning is gradual where the most returns come at the beginning. I also believe that there are diminishing marginal returns to kapital too. How many, books on Algebra does a kid need? Or how many ways does a student need to share information on the Internet?
I believe that the new tools of education both enhance education and heighten students learning. I just believe that kids are kids and are the same kids that I grew up with where it took hours and hours of hard work to learn and learning approximated the production function Y=AL^.75K^.25. Now to learn partial derivatives so I can prove it.