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α: calibrated so average coauthorship-adjusted count equals average raw count
A firm sells a dangerous product to heterogeneous consumers. Higher consumer types suffer accidents more often but may enjoy higher gross benefits. The firm invests resources to reduce the frequency of accidents. When the consumer's net benefit function (gross benefits minus expected harms) is decreasing in consumer type, the firm contractually accepts liability for accident losses and invests efficiently. When the consumer's net benefit function is increasing in consumer type, the firm contractually disclaims liability and underinvests. Legal interventions, including products liability and limits on contractual waivers and disclaimers, are necessary to raise the level of product safety.