Explore BrainMass
Share

Explore BrainMass

    Production Function and Total Product of Labor

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    See the attached file for further details.

    A firm's production function is given by:
    Q= Le^-0.2L

    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.

    © BrainMass Inc. brainmass.com October 9, 2019, 9:18 pm ad1c9bdddf
    https://brainmass.com/economics/production/production-function-total-product-labor-180157

    Attachments

    Solution Preview

    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 ...

    Solution Summary

    A neat and step-by-step solution to determine the production function and total product of labor.

    $2.19