Technical Appendix to Long - Term Contracts under the Threat of Supplier Default
نویسندگان
چکیده
Proof. (i) In a short-term contract, prices must be subgame perfect. Thus, it is easy to see that in the second period the buyer will o¤er the lowest prices that satisfy the participation constraints of the suppliers, i.e., p22 = 2 (c1) + d (d1) for supplier 2 and p s 12 = d1 + 2 (c1) for supplier 1 (since d1 is known at the end of the rst period). Recalling that the buyer must also incur a per unit switching cost of k if he decides to switch to supplier 2, we see that the buyer will switch suppliers if k + d (d1) < d1. Thus, in choosing the optimal rst period price, the buyer maximizes his total expected pro t,
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