# Analyzing Household Brand Switching: A Stochastic Model

In a recent study, Kahn, Morrison and Wright showed that for exponentially
distributed interpurchase times (of individuals), the household choice process
approaches a zero-order process as the number of individuals in the household
increases, even though the purchasing behavior of each individual is first
order. We show that their result holds for any arbitrary interpurchase-time
distribution that has a density over some interval. Thus, additional support is
provided for their conclusion that the empirically observed zero-order choice
behavior at the household level may not convey much information about
individuals' choice behavior. We also derive a general formula that determines
exactly the degree of dependence between two successive household purchases for
any given family size and (well-behaved) interpurchase-time distribution.