Welfare Implications of Product Functionality and Multipurchasing-with Jong Jae Lee (under revision)
[ABSTRACT] This paper studies the socially optimal levels of product functionality and multipurchasing in the same environment that Anderson, Foros, and Kind (2017) demonstrate how multipurchasing arises in equilibrium when consumers on the Hotelling line gain from having access to different product functionalities. We show that the social optimum requires multipurchasing if the value of consumption is nonnegative for every consumer. This is because multipurchasing may increase consumption beyond the size of the consumer population, thereby creating additional social welfare gains that cannot be realized under single-purchasing. Moreover, we show that the social optimum requires higher levels of multi-purchasing and product functionalities than the equilibrium levels. For the parameter values that guarantee the existence of an equilibrium, the efficient outcome requires complete multipurchasing, which no non-trivial equilibrium fails to achieve. Moreover, as in equilibrium, the social optimum requires both firms to include the same level of product functionalities but to produce a higher level of functionalities because the social planner takes account of the positive externality of including product functionalities on the inframarginal consumers.