CONCLUSIONS
Using the Cobb-Douglas production function and the cost minimization approach, we were able to find the optimal conditions for the cost function and plot the outcome relative to the quantity produced. As production increases, the minimum cost needed increases in a non-linear, exponential fashion, which makes sense given that Y (quantity produced) is in the numerator on the right-hand side of the cost function and positively related to the cost.
This was a fun exercise that made me think about the usefulness of the Cobb-Douglas production function, which I learned to optimize multiple times in my Economics courses. I was excited to find a pleasant utility for it using simulated data and will probably explore more exercises like this in the future.
REFERENCEs
I used a lot of resources to write this blog, which are provided below.
A site dedicated to the discussion of economics called EconomicsDiscussion.net was a great resource.
These papers were incredibly helpful in preparing the example in R:
Lin CP. The application of Cobb-Douglas production cost functions to construction firms in Japan and Taiwan. Review of Pacific Basin Financial Markets and Policies Vol. 5, No. 1 (2002): 111–128.
Larriviere JB, Sandler R. A student friendly illustration and project: empirical testing of the Cobb-Douglas production function using major league baseball. Journal of Economics and Economic Education Research, Volume 13, Number 3, 2012: 81-92
Hu, ZH. Reliable Optimal Production Control with Cobb-Douglas Model. Reliable Computing. 1998; 4(1): 63-69.
I encountered some issues regarding complex numbers in R. Fortunately, I found some great resources about it.
I found a great discussion about R’s calculation of exponents and “NaN” results and why complex numbers can mess up your math in R.
Another good site (R Tutorial: An Introduction to Statistics) explaining complex numbers in R.
John Myles White wrote a nice article about complex numbers in R.