Online Appendix to “Nonstationary Relational Contracts with Adverse Selection”
نویسنده
چکیده
Lemma A1: If a contract {wt} is self-enforcing, then there is another self-enforcing contract {w′ t} such that: (i) w′ t is nondecreasing in t, (ii) the no-shirking conditions, Ut − U1 ≥ ĉ for all t ≥ 2, do not bind for any t ≥ 2, (iii) firms’expected (discounted) profits are the same under two contracts, V1 = V ′ 1 . Proof. The proof is by construction. We show it in several steps. Step (1) (construction of a new contract). Suppose that a self-enforcing contract {wt} decreases (strictly) from tenure period i to i + j, and are nondecreasing elsewhere. (The proof for {wt} decreases strictly more than one place is essentially the same). First, define w′ i as the following:
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