Optimal payment scheme when the supplier's quality level and cost are unknown

When procuring a product from a supplier, a buyer faces the problem of designing a payment scheme to screen the supplier's quality level and cost. We explore an instalment payment (contract) consisting of an initial payment to the supplier as soon as the product is put in use, followed by a deferred payment that is contingent upon the product in normal operation within a certain period. We find that when the high quality supplier has a higher cost than the low quality supplier, and the suppliers' financing costs are lower than a certain threshold, the optimal instalment payment has two options: an initial-payment-only option preferred by the low quality supplier and a deferred-payment-only option preferred by the high quality supplier; otherwise, the optimal contract degenerates into an initial-payment-only option. Thus, our research complements past work on moral hazard where no initial payment is proposed. Moreover, we show that the buyer has an incentive to assist with the supplier's financing. Finally, we compare the instalment payment with the rental contract and show that when the supplier's financing cost is low or the quality difference among different supplier types is small, the rental contract is more likely to be preferred by the buyer than the instalment payment.