Economists have found that a good approximation of value added production ntion is given by Y=TFP*(K^alpha)*(L^-alpha)
TFP is Total factor Productivity
K is capital stock
L is quantity of labor used
alpha is a paramater around 1/3.
How is value added defined? Why don't intermediate inputs enter this production function?
I presume the exponent on L is (1-alpha). This would make your production function a Cobb-Douglas -- very traditional in econ literature.
Value added is defined by your value added fuction which is determined by a mix of labor and capital inputs.
I'm not sure what you mean by your second question. Are intermediate inputs embodied in your K capital input?
Value added is a measure of economic productivity that represents the increase in the value of goods and services that occurs at each stage of production. It is calculated by subtracting the value of intermediate inputs from the total value of output. In other words, value added represents the contribution made by labor and capital to the final product.
In the given production function, Y = TFP * (K^alpha) * (L^(1-alpha)), intermediate inputs do not enter the production function explicitly. This is because the production function assumes that the inputs of labor (L) and capital (K) are used independently to produce the final output (Y), without explicitly considering the intermediate inputs.
However, it is important to note that in reality, intermediate inputs play a crucial role in the production process. Intermediate inputs are the goods and services that are used up or transformed in the production process before the final product is produced. These inputs include raw materials, components, energy, and other intermediate goods purchased from other firms.
While the given production function does not explicitly incorporate intermediate inputs, it assumes that these inputs are implicitly captured in the overall productivity measure, Total Factor Productivity (TFP). TFP represents the portion of output not explained by the inputs of labor and capital alone, and it includes factors such as technological progress, managerial efficiency, and the overall state of the economy. TFP is essentially a measure of the efficiency and effectiveness with which inputs are used in the production process.
So, even though the production function does not explicitly include intermediate inputs, the impact of intermediate inputs is indirectly captured through the TFP term.