Suppose you decide to hire a clerk to help you with completing a project you hav

Question

Suppose you decide to hire a clerk to help you with completing a project you have been assigned to complete. The total benefit function you expect to derive expressed as a function of number hours of help you get is given by B(H) = 475H - 22.5H2 and the cost function is given by C(H) = 100 + 15H2. The corresponding marginal benefit and marginal cost functions are given by MB(H) = 475 - 45H and MC(H) = 100 + 30H.

a. What is the best choice of hours that will maximize your total benefit?

b. What is your total benefit?

c. What will be your net benefit?

Explanation / Answer

a) Total benefit will be maximized at the point where: MB = MC

    475 - 45H = 100 + 30H

75H = 375

H = 375 / 75 = 5 hours

b) Total Benefit = 475H - 22.5H2

                         = 475(5) - 22.5(5)2

                         = 2375 - 562.5

                         = $1812.5

c) Net benefit = Total Benefit - Total Cost

                      = 1812.5 - (100 + 15H2)

                      = 1812.5 - (100 + 15(5)2)

                      = $1337.5

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