Let there be K different vehicle type/vintage combinations (for example, old Sedan, new Sedan, old SUV, new SUV, etc.) that a household can potentially choose from (for ease in presentation, we will use the term “vehicle type” to refer to vehicle type/vintage combinations). It is important to note that the K vehicle types are imperfect substitutes of each other in that they serve different functional needs of the household. Let be the annual mileage of use for vehicle type k (k = 1, 2,…, K). Also, let the different vehicle types be defined such that households own no more than one vehicle of each type. If a household owns a particular vehicle type, this vehicle type may be one of several makes/models. That is, within a given vehicle type, a household chooses one make/model from several possible alternatives. Let the index for vehicle make/model be l, and let be the set of makes/models within vehicle type k, and let be the utility perceived by the household for make/model lof vehicle type k. From the analyst’s perspective, the household is assumed to maximize the following random utility function:
be the annual mileage 
be the set of makes/models 
be the utility perceived by the household for make/model l