Summary: Online Supplement
Dynamic Pricing of Limited Inventories when Customers Negotiate, by Chia-wei
Kuo, Hyun-soo Ahn and Goker Aydin
A. Proofs of Results in Section 4
Proof of Lemma 1
We first prove that, for a given p t-1(y), b , Jt(p, c, y) is strictly unimodal in c for c
[t-1(y), p]. To do so, we prove the following claims: (i) Jt(p,c,y)
c c=t-1(y)
0, (ii) 2Jt(p,c,y)
c2 < 0
whenever Jt(p,c,y)
c = 0, and (iii) Jt(p,c,y)
c c=p
0.
The first and second derivatives of Jt(p, c, y) (given by (4)) with respect to c are
Jt(p, c, y)
c
= q f(c)(t-1(y) - c) + (1 - ) F
p - (1 - )c

Source: Aydin, Goker - Department of Operations and Decision Technologies, Indiana University Bloomington

Collections: Engineering