The Cobb-Douglas function has many applications in economics; from being a well-behaved preference in microeconomics to a production function in macroeconomics. It is named after Paul Douglas, an American Congressmen who was researching labour and capital shares and asked Charles Cobb, a mathematician, for help in formulating this into a function. In this article we will explore its use as a production function.
In its simplicity, a CD (Cobb-Douglas) function is just a function. A function, in mathematical jargon, transforms an input into a single output: it is a one-to-one mapping. For example Y=2X is a simple function. X is the independent variable and Y is the dependent variable, because Y is determined by whatever the value of X is. [...]