with Evan L. Porteus
Abstract
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.