Explore BrainMass
Share

Explore BrainMass

    Cost-Benefit Analysis: Known Cost & Benefit Functions

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

    Suppose a firm faces the total benefit function:

    B(Q) = 18Q - Q^2
    and the total cost function:

    C(Q) = 2 - 2Q +Q^2

    a. What quantity should the firm select?
    b. What is the amount of total benefits, total costs and total net benefits at the selected quantity?
    c. If the first term in the cost equation changed from 2 to 5, how would that impact the solution you provided above in part (a)?
    d. Explain the impacts in part (c) regarding the change to the optimal output quantity. How do you unambiguously know the quantity selected is the "optimal" one?

    © BrainMass Inc. brainmass.com October 10, 2019, 4:59 am ad1c9bdddf
    https://brainmass.com/economics/cost-benefit-analysis/cost-benefit-analysis-known-cost-benefit-functions-487008

    Solution Preview

    a) To find the optimum quantity, you have to find the Marginal Benefit (MB) and Marginal Cost (MC) functions. The maximum net benefit occurs when MB = MC.

    B = 18Q - Q^2
    MB is the derivative of B:
    MB = 18 - 2Q

    C = 2 - 2Q + Q^2
    MC is the derivative of C:
    MC = ...

    Solution Summary

    This is a detailed, step-by-step solution that calculates a firm's optimal Quantity when its Benefit and Cost functions are both known. The correctness of the solution is demonstrated by a spreadsheet.

    $2.19