Consider the problem of gym attendance as presented in this chapter, where Jamie perceives the value of attending the gym to be

where x_n is the monetary value to Jamie of experiencing the n_th single attendance event at the gym, p is the price paid once every six months, δ is the monthly rate of depreciation, t is the number of months since the last payment was made, n is the number of times Jamie has attended the gym since paying, including the attendance event under consideration, and p_y(n) is the price Jamie considers fair for attending the gym n times. Suppose that the cost of gym membership is $25. Further, suppose Jamie considered the value of attending the gym n times in a six-month window to be

Also, suppose that Jamie considers the fair price for a visit to be $4, so the transaction utility is equal to

Payments depreciate at a rate of δ = 5. Determine the number of visits necessary in each of the six months in order to obtain a positive account. How much time would have to pass before only a single visit could close the account in the black?

Transcribed Image Text:

- po (n)+v,(-po +p,(n)) it'