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Economists have found that a good approximation of value added production fucntion 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?

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