Inferring Competitor Pricing with Incomplete Information

We study how business customers make multi-product purchase decisions and how the distributors who sell those products can make inferences about their demand functions with incomplete information. The problem is that distributors rarely observe a competitor's price directly, and must infer competitor response indirectly from their own observations about customer purchases. In this research we propose that customers make their product orders by minimizing procurement costs. Using the first order conditions from this optimization problem we characterize the regions of the parameter space where consumers buy from each distributor. We use these conditions to estimate a model of purchase behavior that enables us to identify the likelihood of each consumer buying from the competitor versus a direct change in consumption patterns. Our proposed model is applied to a wholesale food distributor and we find widespread heterogeneity in purchase patterns. The empirical results shed light on the competitive elements of customer demand that cannot be studied with traditional reduced form response models. For example, we found that some costumers satisfy most of their requirement from one of their distributors, while others consistently split their demands across suppliers. Also, we found that price sensitivity of customers making most of their purchases with the focal supplier are less affected by the volume of purchases in previous periods. We expect this result to provide valuable information for vendors to negotiate prices with the customers. It allows the distributor to make efficient inferences about competitors in those occasions when competitor price is not directly observed.