A Model for Mixed Decision Variables : Modeling Subscription versus Ownership of Consumer Goods

The decision to rent or own is prevalent in many consumer decisions, including what to wear, what to watch and what to read. A challenge to firms pricing these products is understanding whether renting, or having access through a subscription, is considered complementary to, or acts as a substitute to owning the product. The challenge in modeling access by subscription versus ownership is that the subscription decision is discrete whereas the ownership decision can take on positive quantities other than one. We propose a mixed discrete/continuous direct utility model, and associated estimation algorithms, for assessing the economic relationship between renting and owning and find support for their complementary nature in two conjoint studies involving music and videos. We explore the degree to which profit maximizing prices are dependent on correctly assessing whether goods are substitutes or complements