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A firm's production function is given by:
Find the value of L which maximizes the TOTAL PRODUCT of labor. In obtaining this result ensure that you:
(a) Derive the first-order condition for the firm's product maximization.
(b) Verify that, at the critical point, the second-order sufficient condition holds.
(c) Check that average product equals marginal product at the critical point.
Q = L e^-0.2L
(a) dQ/dL = L (-0.2 e^-0.2L) + e^-0.2L
= e^-0.2L (-0.2L + 1)
For Q to be maximum, dQ/dL = 0
Therefore e^-0.2L (-0.2L + 1) = 0
This gives -0.2L + 1 = 0
-0.2L = -1
L = 5
The critical point is L = 5.
(b) d^2Q/dL^2 = e^-0.2L (-0.2) + (-0.2L ...
A neat and step-by-step solution to determine the production function and total product of labor.