Question

Need assistance with this economics problem please.

Suppose Rachel can hire a trainer for thirty sessions. The total benefit of hiring a trainer is given the function B(S) = 154S - 3S^2 and the total cost is given the function C(S) = 2S + 3S^2.

A. If Rachel were an economist, how many sessions would she buy? Explain.

B. Suppose the gym decides to charge Rachel a one-time no refund service fee of $25 for access to the new member work out area. If Rachel were an economists, how many sessions would she buy? Explain.

Answer 1

Net benefit (NB) = B(S) - C(S) = 154S - 3S² - 2S - 3S² = 152S - 6S²

(A)

Optimal number of session is obtained when NB is maximized.

NB when maximized when dNB/dS = 0

dNB/dS = 152 - 12S = 0

12S = 152

S = 12.67 ~ 13 (Considering integer value for number of sessions)

(B)

Since the $25 is a fixed cost which does not impact marginal net benefit (= dNB/dS), optimal number of sessions remains the same at 13.