Explore BrainMass
Share

Explore BrainMass

    marginal cost function for reducing pollution

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

    Appalachian Coal Mining believes that it can increase labor productivity and, therefore, net revenue by reducing air pollution in its mines. It estimates that the marginal cost function for reducing pollution by installing additional capital equipment is
    MC = 40P
    Where P represents a reduction of one unit of pollution in the mines. It also feels that for every unit of pollution reduction the marginal increase in revenue (MR) is
    MR = 1,000 - 10P
    How much pollution reduction should Appalachian Coal Mining undertake?

    © BrainMass Inc. brainmass.com October 10, 2019, 1:45 am ad1c9bdddf
    https://brainmass.com/economics/regression/marginal-cost-function-for-reducing-pollution-348037

    Solution Preview

    The installation of additional capital equipment will reduce pollution and increase the labor productivity..But look at the additional cost...It is not offsetting the benefit So fix the level of pollution reduction in an optimal manner...The optimal value P is Marginal cost = marginal revenue

    Set MC = MR and solve for P

    MC = 40P MR = 1000 -10P

    That is 40P = 1000-10P

    Take -10 p to that side... 40P + 10P = 1000

    50P = 1000

    P = 1000/50

    P = 20

    Chapter 3, Applied Problem 4
    Twentyfirst Century Electronics has discovered a theft problem at its warehouse and
    has decided to hire security guards. The firm wants to hire the optimal number of security guards. The following table shows how the number of security guards affects the
    number of radios stolen per week.

    Number of security guards Number of radios stolen per week
    0 ............................. ............................. 50
    1 ............................. ............................. 30
    2 ............................. ............................. 20
    3 ............................. ............................. 14
    4 ............................. ............................. 8
    5 ............................. ............................. 6
    a. If each security guard is paid $200 a week and the cost of a stolen radio is $25, how many security guards should the firm hire?
    b. If the cost of a stolen radio is ...

    Solution Summary

    The installation of additional capital equipment is advised in this case. References are also provided to further validate the findings.

    $2.19