Selling to the Newsvendor: An Analysis of Price-Only Contracts

TLDR

The base model assumes a worst‑case scenario where wholesale prices may fall below the optimal level due to various factors, providing a conservative benchmark for supply‑chain performance. The study investigates how a manufacturer’s wholesale‑price‑only contract influences retailer behavior and explores factors that may cause the manufacturer to set a price below the profit‑maximizing level. The authors impose a mild distributional restriction that makes the manufacturer’s optimization tractable and analyze how retailer forecasting ability and bargaining power affect wholesale‑price decisions. The results show that larger markets raise both profit and sales, but the wholesale price is sensitive to market growth and relative variability; lower coefficient of variation raises the wholesale price, boosts manufacturer profit share and system efficiency, yet can severely hurt retailer profitability.

Abstract

We consider a simple supply-chain contract in which a manufacturer sells to a retailer facing a newsvendor problem and the lone contract parameter is a wholesale price. We develop a mild restriction satisfied by many common distributions that assures that the manufacturer's problem is readily amenable to analysis. The manufacturer's profit and sales quantity increase with market size, but the resulting wholesale price depends on how the market grows. For the cases we consider, we identify relative variability (i.e., the coefficient of variation) as key: As relative variability decreases, the retailer's price sensitivity decreases, the wholesale price increases, the decentralized system becomes more efficient (i.e., captures a greater share of potential profit), and the manufacturer's share of realized profit increases. Decreasing relative variability, however, may leave the retailer severely disadvantaged as the higher wholesale price reduces his profitability. We explore factors that may lead the manufacturer to set a wholesale price below that which would maximize her profit, concentrating on retailer participation in forecasting and retailer power. As these and other considerations can result in a wholesale price below what we initially suggest, our base model represents a worst-case analysis of supply-chain performance.