3/2/2024 0 Comments Cobb douglas exampleIf we are given values for K,α,L,β (our independent variables) then we can calculate a value for output, our dependent variable. In this form we have used CD as a production function. We could make our function Y=2X + 5, or Y=XZ so Y is now a function of two variables.Ī Cobb-Douglas Function takes the form of Q=K αL β where Q=output, K=capital, L=labour, and alpha and beta are used to represent input shares of capital and labour respectively. ![]() We can make our function more complex by adding different variables, or operators. Because we have been given an input (X=2) and we have a single output (Y=4) then Y=2X can be described as a function. If we say that X is 2 then Y has to be 4. X is the independent variable and Y is the dependent variable, because Y is determined by whatever the value of X is. A function, in mathematical jargon, transforms an input into a single output: it is a one-to-one mapping. In its simplicity, a CD (Cobb-Douglas) function is just a function. ![]() In this article we will explore its use as a production function. 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. ![]() The Cobb-Douglas function has many applications in economics from being a well-behaved preference in microeconomics to a production function in macroeconomics.
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