Manufacturer-Retailer Contracting Under an Unknown Demand Distribution

We consider a manufacturer introducing a new product into a distribution channel and examine what wholesale price should be charged. The setting in many ways is simple. The channel is abbreviated with the manufacturer selling directly to the retailer. The contract is also simple, merely a flat wholesale price. Demand is stochastic but independent and identically distributed in each period. Complications arise from two additional assumptions. First, neither party knows some parameter of the demand distribution. The system evolves informationally as the channel has more experience with, and information about, the product. Second, we assume unmet demand is both lost and unobserved, so only sales data are available. The autonomous retailer’s stocking level consequently dictates the rate at which the channel acquires information. The manufacturer’s pricing policy, in turn, influences the retailer’s actions. We explore how the wholesale price evolves as beliefs are updated in a Bayesian fashion. Pricing is driven by the precision of information and not the size of the market. In particular, we show that the manufacturer charges a lower price following a stockout than after an exact observation. That is, she prices more aggressively following a signal of relatively weak demand (unsold stock) than after a signal of strong demand (empty shelves). The apparent anomaly is explained by relating the precision of information to the number of observed stockouts and the elasticity of retailer orders to the precision of information; stockouts are less informative, and an uncertain retailer is relatively price sensitive.