Constructing Demand Curves from a Single Observation of Bundle Sales

Abstract

Firms typically require multiple sales observations under varying prices to understand how the demand for their items respond to price. In this paper, our partner online retailer is faced with the problem of reconstructing demand curves when only a single point on each curve has been historically observed. We show how a second point on each curve can be extracted from the sales of their discounted bundles, after which we help them estimate linear demand curves for their items. We perform this extraction by fitting a multi-item valuation model from the bundle pricing literature, introducing a new iterative procedure for solving this fitting problem. Our extraction process reveals a new insight on the relationship between an item's relative frequency of bundle sales vs. the steepness of its demand curve around its current price. We validate this insight on the data provided by our partner firm.

Keywords: bundling, valuation learning, revenue management