A proof of Euler's theorem

A proof of Euler's theorem - ECON 200 Macroeconomic Theory...

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ECON 200 Macroeconomic Theory Before proving the claim that in a competitive economy with an aggregate CRS production function, the payments to factors of production equal total output, recall from multivariable calculus that the total derivative of a function such as is given by 1ÐDß AÑ .1 œ .D  .A `1 `D `A where I have assumed that all the required derivatives exist. Recall now that if the production function has constant returns to scale, we can write ]œJÐO ßP Ñ -- - ß P Ñ for any As this is an identity in we may different both sides of the expression ! Þ with respect to and retain the equality. Differentiating the LHS we have - .Ð ] Ñ . œ] - - . To differentiate the RHS use the result on total derivatives to write
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