Monopoly pricing in vertical markets with demand uncertainty

Motivation Pricing decisions are often made when market information is still poor. While modern pricing analytics aid firms to infer the distribution of stochastic demand that they facing, data-driven price optimization methods impractical or incomplete if not coupled with testable theoretical predictions. In turn, existing models reason about response optimal prices changing characteristics without exploiting all available distribution. Academic/practical relevance Our aim develop a theory for and systematic comparison between different instances same under various forms knowledge corresponding distributions. Methodology We revisit classic problem monopoly uncertainty in vertical an upstream supplier multiple downstream competition arbitrary symmetric retailers. cases, falls who acts first sets uniform before retailers observe realized place their orders. Results main methodological contribution we express elasticity expected terms mean residual (MRD) function This leads closed form characterization points unitary maximize supplier’s profits derivation mild unimodality condition objective generalizes widely used increasing generalized failure rate (IGFR) condition. A direct implication markets can be ordered stochastically according MRD functions equivalently, elasticities. Using above, framework compare via rich comparative statics challenge previously established economic insights effects size, transformations variability on monopolistic prices. Managerial implications findings complement regarding provide useful making predictions advance movements.