Relational Contracts and Optimal Buy-Back Price

Abstract

In Chap. 4, we considered a contracting problem where two firms interact repeatedly on the basis of a QF contract. In particular, the long-term buyer-supplier relationship was geared towards quality improvement and allowed for informal adaptations of contract parameters. The goal of the analysis was to determine an optimal relational contract specifying optimal policies for supplier and buyer. In this chapter, we shall keep the previous setup, but replace the QF contract by a buy-back contract. That is, we consider a price-based returns mechanism instead of a quantity-based one. The objectives are to identify an optimal relational contract for this setting, to examine the effect on the optimal buy-back price, and to lay the ground for the comparison of QF and buy-back contract in the context of relational contracting.

Consider a two-firm supply chain where supplier and buyer contract on the basis of a buy-back contract with relational aspects influencing buyer-supplier interactions. Figure 5.1 describes the sequence of events. Suppose that the two firms negotiate a formal buy-back contract at the beginning of the business relation. This long-term contract specifies that the buyer purchases Q units for the price w _b per unit at the start of the period and may return up to Q units at the end of the period for a refund of b per unit. Also note that this contract is court-enforceable. In the course of their business relationship, buyer and supplier both induce effort for quality improvement. But their efforts for quality are unobservable and uncontractible. To induce effort from the supplier’s side, the buyer holds out the prospect of reducing the buy-back price. In addition, the buyer can offer a supplementary transfer payment. Unlike the parameters of the formal buy-back contract, these promises are informal and cannot be enforced by court.