Supplement to "Responsible Sourcing in Supply Chains"

In this document, we analyze two alternative assumptions from the model discussed in the main text: heterogeneous base valuations for the product (§1) and a salvage value less than the production cost (§2). 1 Heterogeneous Base Valuations In this section, we allow consumers ’ base valuations for the product to be uniformly distributed on the interval [vl, vh], independent of consumer type (socially conscious or non-socially conscious), where V = vh vl is defined as the width of the consumer valuation distribution. Socially conscious consumers are assumed to have homogenous, additive willingness-to-pay for responsibility equal to r, i.e., a socially conscious consumer with base valuation v 2 [vl, vh] is willing to pay v + r 2 [vl + r, vh + r] for a responsibly sourced product. Our goal is to demonstrate that two of our key results from the main paper continue to hold under this alternative assumptions, specifically: 1. An increase in consumer WTP for responsibility or the size of the socially conscious segment can lead to a decrease in responsible sourcing and an increase in risky sourcing 2. Mechanisms penalize the buyer such as increased detection probability, increased consumer willingness-to-punish, and increased penalties always lead to more responsible sourcing and less risky sourcing. We refer to these as results 1 and 2 throughout this document. We first derive the firm’s optimal profit under each of the four sourcing strategies discussed in the main text of the paper, and then we confirm the two key results listed above. In what follows, we focus on interior solutions (i.e., points at which the optimal price lies in the interior of the consumer valuation distribution’s support); boundary solutions are similar to the case of homogenous consumer valuations (i.e., if the optimal price is the lower bound of the consumer valuation