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. In many markets, manufacturers do not sell directly to consumers but distribute products through decentralized channels; wholesalers and distributors take possession of the goods before retailers offer them to customers. When the links of the distribution chain are independent firms, a manufacturer must bundle her product with a contract governing channel transactions. Contracting within a distribution channel has received considerable attention within economics (e.g., Spengler, 1950; Mathewson and Winter, 1984; Tirole, 1988, provides a survey) and marketing (e.g., Jeuland and Shugan, 1983; Moorthy, 1987). Both fields emphasize the impact of the contractual form on total channel profits and their division. Both generally presume a known deterministic demand curve. Issues of inventory or stochastic demand are ignored. In the operations management literature, researchers have examined schemes that lower a supplier’s ordering and inventory costs in an economic order quantity setting. Monahan (1984) and Lee and Rosenblatt (1986) suggest quantity discounts to alter buyer’s ordering patterns. Weng (1995) shows that quantity discounts alone will not maximize channel profits. Pasternack (1985) considers both inventory and stochastic demand; his retailer faces a classic, single period newsvendor problem for a known demand distribution. He proves that channel profits are maximized when the manufacturer offers a returns policy. Here, we study a manufacturer who launches a new product in an uncertain environment and then dynamically adjusts the wholesale price as information is revealed. The manufacturer deals directly with a self-interested retailer who holds stock in anticipation of demand and sells the product at a fixed retail price. Demand is stochastic with all realizations independently and identically distributed, but neither party knows some parameter of the demand distribution. Both gain information about that parameter by observing sales. Thus, despite stationary demand, the demand distribution appears different in each period because estimates of the unknown parameter change. The system evolves informationally as the channel gains experience with the product. Further, we assume that unmet demand is both lost and unobserved. Beliefs about the demand distribution are updated based on observed sales. As sales data provide only a lower bound on realized demand when the retailer stocks out, the autonomous retailer’s stocking decision dictates the rate at which the channel acquires information. The manufacturer’s pricing policy, in turn, influences the retailer’s actions.