Question

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

Find the value of L that maximizes the average product of labour

Answer 1

The average product of labour is:

$APL = Q/L = L×e^{-0.01L}.$

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

$(L×e^{-0.01L}) ' = e^{-0.01L} - 0.01L×e^{-0.01L} = e^{-0.01L}×(1 - 0.01L) = 0,$

L = 100 or

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