Modeling indivisible demand

Disaggregate demand in the marketplace exists on a grid determined by the package sizes offered by manufacturers and retailers. Although consumers may want to purchase a continuous-valued amount of a product, realized purchases are constrained by available packages. This constraint might not be problematic for high-volume demand, but it is potentially troubling when demand is small. Despite the prevalence of packaging constraints on choice, economic models of choice have been slow to deal with their effects on parameter estimates and policy implications. In this paper we propose a general framework for dealing with indivisible demand in economic models of choice, and we show how to estimate model parameters using Bayesian methods. Analyses of simulated data and a scanner-panel data set of yogurt purchases indicate that ignoring packaging constraints can bias parameter estimates and measures of model fit, which results in the inaccurate measures of metrics such as price elasticity and compensating value. We also show that a portion of nonpurchase in the data (e.g., 2.27% for Yoplait Original) reflects the restriction of indivisibility, not the lack of preference. The importance of demand indivisibility is also highlighted by the counterfactual study where the removal of the smallest package size (i.e., 4 oz) mainly results in nonpurchase in the yogurt category instead of switching to larger package sizes.