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As companies outsource more product design and manufacturing activities to other members of the supply chain, improving end-product quality has become an endeavor extending beyond the boundaries of the firms' in-house process capabilities. In this paper, we discuss two contractual agreements by which product recall costs can be shared between a manufacturer and a supplier to induce quality improvement effort. More specifically, we consider (i) cost sharing based on selective root cause analysis (Contract S), and (ii) partial cost sharing based on complete root cause analysis (Contract P). Using insights from supermodular game theory, for each contractual agreement, we characterize the levels of effort the manufacturer and the supplier would exert in equilibrium to improve their component failure rate when their effort choices are subject to moral hazard. We show that both Contract S and Contract P can achieve the first best effort levels; however, Contract S results in higher profits for the manufacturer and the supply chain. For the case in which the information about the quality of the supplier's product is not revealed to the manufacturer (i.e., the case of information asymmetry), we develop a menu of contracts that can be used to mitigate the impact of information asymmetry. We show that the menu of contracts not only significantly decreases the manufacturer's cost due to information asymmetry, but also improves product quality.