Answer to Question #145202 in Microeconomics for Rathete Lefaladi

Question #145202
A firm's production function is given by Q= L2e^-0,01L

Find the value of L that maximizes the average product of labour
1
Expert's answer
2020-12-06T18:05:43-0500

The average product of labour is:

"APL = Q\/L = L\u00d7e^{-0.01L}."

APL is maximized if APL'(L) = 0, so:

"(L\u00d7e^{-0.01L}) ' = e^{-0.01L} - 0.01L\u00d7e^{-0.01L} = e^{-0.01L}\u00d7(1 - 0.01L) = 0,"

L = 100 or

"e^{-0.01L} = 0", which has no roots.


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