Two-stage supply chain pricing strategies with reference price effect

¹ School of Business, University of Shanghai for Science and Technology, Shanghai 200093, P.R. China
² School of Intelligent Emergency Management, University of Shanghai for Science and Technology, Shanghai 200093, P.R. China

^* Corresponding author: feipan@usst.edu.cn

Received: 28 July 2024
Accepted: 28 September 2025

Abstract

Products sold to the market typically traverse the introductory and maturity stages. During maturity, retailers often raise prices to capitalize on expanding market demand. However, consumers commonly regard the first-stage price as a psychologically acceptable reference point. When the second-stage price exceeds this threshold, they tend to perceive it as unfair, leading to a decrease in demand. Conversely, a price decrease strategy can leverage the reference price effect to stimulate purchases. This study investigates optimal two-stage supply chain pricing under dynamic market expansion with the reference price effect. We develop a Stackelberg game model involving a manufacturer and a retailer, analyzing both centralized and decentralized decision-making to explore how the reference price effect affects pricing, profit allocation, and supply chain coordination. The main findings are as follows: (1) Under centralized decision-making, moderate market expansion prompts second-stage price decreases to mitigate reference price effect’s negative impacts and stimulate demand; substantial expansion enables a price increase strategy to exploit reference price effect for higher unit profitability; (2) Decentralized decision-making with reference price effect exacerbates double marginalization. Moreover, manufacturers’ first-stage wholesale prices are independent of reference price effect, while second-stage wholesale prices decrease as it strengthens; (3) To achieve supply chain coordination, a two-part tariff contract with fixed fees across two stages is proposed, effectively aligning incentives and enhancing profits across varying market expansion scenarios. Numerical analyses further identify parameter regions for optimal price strategies, quantify the reference price effect’s profit-impact thresholds, and sensitivity analysis of key parameters.