Cost pass-through and inverse demand curvature in vertical relationships with upstream and downstream competition

•We study vertical relationships with upstream and downstream competition.•Arbitrary numbers of manufacturers and of retailers are allowed.•The retailer's markup relative to the manufacturer's markup is characterized.•It is expressed by cost pass-throughs at the wholesale and the retail levels.•It can be also expressed in terms of the inverse demand curvature.

This paper provides two characterizations of the retailer's markup relative to the manufacturer's markup in vertical relationships with homogeneous manufacturers and homogeneous retailers. We first show that retailer's relative markup is equal to the ratio of the retail pass-through to the wholesale pass-through, multiplied by the number of manufacturers relative to the number of retailers. We then provide its expression in terms of the inverse demand curvature.