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Summary: Online Supplement
Appendix A - Proofs for Sections 3 and 4.1
Proof of Proposition 1: Let µR1 and µR2 denote the mean reservation prices for customers
who are in the target and non-target segments of the regular product, respectively. Similarly,
define µP1 and µP2 to be the mean reservation prices for customers who are in the target
and non-target segments of the promotional product, respectively. Then, we have
E(X) = qR1µR1 + qR2µR2
and
E(Y ) = qP1µP1 + qP2µP2.
We also have
E(XY ) = qR1
0
0
xyfR1(x)(11fP1(y) + 12fP2(y))dxdy
+ qR2
0
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