J’s car buying policy is to always buy a new car, repair all breakdowns that occur during the first T time units of ownership, and then junk the car and buy a new one at the first breakdown that occurs after the car has reached age T .

Suppose that the time until the first breakdown of a new car is exponential with rate λ, and that each time a car is repaired the time until the next breakdown is exponential with rate μ.

(a) At what rate does J buy new cars?

(b) Supposing that a new car costs C and that a cost r is incurred for each repair, what is J’s long run average cost per unit time?