A Flexible Demand Model for Complements Using Household Production Theory

According to household production theory, consumers buy inputs and combine them to produce final goods from which they derive utility. We use this idea to build a micro-level model for the quantity demanded by a consumer across product categories. Our model proposes an intuitive explanation for the existence of negative cross-price effects across categories and can be estimated on purchase data in the presence of corner solutions and indivisible packages. We find that, even when reusing the same functional form as some previous models of demand for substitutes, our model can accommodate very different patterns of consumer preferences from perfect complementarity to no complementarity between goods. We estimate the model on purchase data from a panel of consumers and find that it yields a better fit than a set of benchmark models. We then show how the demand system estimated can be used to increase the profitability of couponing strategies by taking into account the spillover effect of coupons on demand for complementary categories and by manufacturers to make decisions regarding the size of packages by taking into account cross-category consumption. We also use the model to simulate demand under a shift in the proportions used in joint consumption, which could be stimulated via marketing efforts.