Partial derivatives economics question

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SUMMARY

The discussion focuses on computing the expression KY'(K) + LY'(L) for the function Y = AK^a + BL^a, where Y'(K) represents the partial derivative with respect to K. The correct computation yields KY'(K) + LY'(L) = aY, confirming the book's answer. The partial derivative Y'(K) is derived as Aak^(a-1), highlighting the role of constants A and B in the expression. Participants clarify the distinction between constants and variables, aiding understanding of the problem.

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If a and b are constants, compute the expression KY'(K) + LY'(L) for Y = AK^a + BL^a

Y'(K) means partial derivative with respect to K by the way. The answer in the book is KY'(K) + LY'(L) = aY

I'm not sure what they did or what they're asking :/
 
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It's pretty straightforward. I'll do the first one for you. We have $y_k=Aak^{a-1}$ (because the other term doesn't have a $k$ since it's the partial derivative), and $y_k$ denotes the partial derivative respecto to $k.$

Try the other one and substitute.
 
Krizalid said:
It's pretty straightforward. I'll do the first one for you. We have $y_k=Aak^{a-1}$ (because the other term doesn't have a $k$ since it's the partial derivative), and $y_k$ denotes the partial derivative respecto to $k.$

Try the other one and substitute.

Thanks! I get it now, was confused on whether the A and B were variables or not. Thanks!
 

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