Buyback Contracts with a Stochastic Demand Curve

Abstract

We explore buyback contracts in a supplier-retailer supply chain where the retailer faces a price-dependent downward-sloping demand curve subject to uncertainty. We formulate the problem as a supplier-led Stackelberg game and derive explicitly the equilibrium contract parameters along with the corresponding retail price and order quantity−all as functions of the demand curve uncertainty level. We examine the value of buyback and assess its impact on the supply chain’s efficiency. We find that in equilibrium (i) Pareto-improvement can be attained using buyback only at an intermediate uncertainty level, (ii) the supply chain’s efficiency is maintained at 75% of the optimal channel profit regardless of the uncertainty level, (iii) the retailer orders more only at an intermediate uncertainty level, (iv) the supplier need not change the equilibrium wholesale price associated with the corresponding deterministic demand curve and only needs to adjust the buyback price in response to the uncertainty level, and (v) the end consumers do not benefit from buyback regardless of the uncertainty level. We derive insights and managerial implications of the theoretical results.

Keywords: Supply chain management, marketing interface, buyback contract, stochastic demand curve

JEL Classification: C02, M11, M31, L11, C61, B23, C15, C10, C4, M20, C73