ECON 200Macroeconomic TheoryBefore proving the claim that in a competitive economy with an aggregate CRSproduction function, the payments to factors of production equal total output, recall frommultivariable calculus that the total derivative of a function such as is given by1ÐDß AÑ.1 œ.D .A`1`D`Awhere I have assumed that all the required derivatives exist. Recall now that if theproduction function has constant returns to scale, we can write]œJÐOßPÑ---ß PÑfor any As this is an identity in we may different both sides of the expression!Þwith 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
This is the end of the preview. Sign up
access the rest of the document.