Setting price or quantity: Depends on what the seller is more uncertain about

We consider a seller with uncertain demand for its product. If the demand curve were certain, then setting price and setting quantity would be equivalent ways to frame the seller’s problem of choosing a profit-maximizing point on its demand curve. With uncertain demand, these become distinct sales mechanisms. We distinguish between uncertainty about the market size and uncertainty about the consumers’ valuations. Our main results are that (i) for a given marginal cost, an increase in uncertainty about valuations favors setting quantity whereas an increase in uncertainty about market size favors setting price; (ii) keeping demand uncertainty fixed, there is a nonmonotonic relationship between marginal costs and the optimal selling mechanism (setting price or quantity); and (iii) in a bilateral monopoly channel setting, coordination occurs except for a conflict zone in which the retailer’s choice of a selling mechanism deviates from the coordinated channel selling mechanism.