1 research outputs found
Monopoly Pricing in a Vertical Market with Demand Uncertainty
We study a vertical market with an upsteam supplier and multiple downstream
retailers. Demand uncertainty falls to the supplier who acts first and sets a
uniform wholesale price before the retailers observe the realized demand and
engage in retail competition. Our focus is on the supplier's optimal pricing
decision. We express the price elasticity of expected demand in terms of the
mean residual demand (MRD) function of the demand distribution. This allows for
a closed form characterization of the points of unitary elasticity that
maximize the supplier's profits and the derivation of a mild unimodality
condition for the supplier's objective function that generalizes the widely
used increasing generalized failure rate (IGFR) condition. A direct implication
is that optimal prices between different markets can be ordered if the markets
can be stochastically ordered according to their MRD functions or equivalently
to their elasticities. Based on this, we apply the theory of stochastic orders
to study the response of the supplier's optimal price to various features of
the demand distribution. Our findings challenge previously established economic
insights about the effects of market size, demand transformations and demand
variability on wholesale prices and indicate that the conclusions largely
depend on the exact notion that will be employed. We then turn to measure
market performance and derive a distribution free and tight bound on the
probability of no trade between the supplier and the retailers. If trade takes
place, our findings indicate that ovarall performance depends on the interplay
between demand uncertainty and level of retail competition