L – Labor input which indicates the total number of labor that went into production.A – Total factor productivity it is a positive constant and is used to show the change in output that is not the result of main production factors.Y – Total production or output of goods.This production function equation is the basis of our Cobb-Douglas production function calculator, where:
The Cobb-Douglas production function formula for a single good with two factors of production is expressed as follows: We can compare the importance of the Cobb-Douglas production function to macroeconomics to the importance of the Pythagorean theorem to math. It was a cornerstone for macroeconomics and has been widely used, adopted, and improved since its inception. The Cobb-Douglas production function is known for being the first time a proper aggregate production function was estimated and developed to analyze whole branches of industry accurately. Paul Douglas formally presented the results in 1947. Over the years, the theory was improved and expanded using US census data and proved accurate for other countries as well. It is even more critical when you want to try to estimate industry-wide macroeconomic theories. Even when conducting small-scale research, you need a proper sample size to make your results statistically significant (see sample size calculator). The results they got very closely reflected American macroeconomic data at the time.Īlthough accurate, economists criticized the results for using sparse data. He wanted to show how they relate to each other and express this relation as a mathematical function.Ĭharles Cobb suggested using an existing production function equation proposed by Kurt Wicksell as a base, which Douglas and Cobb improved and expanded upon. Development of this production function started in the 1920s when Paul Douglas calculated estimates for production factors for labor (workers) and capital (here in a broad sense: money, buildings, machines).
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