Josh Gans gives a handy benchmark model where the answer is no.
MODEL 1: Wholesale Pricing
Suppose that a book publisher charges a price of p to a retailer. Then, based on this, the retailer sets a price to consumers of P and earns (P – p)(a – P).
In this case, the retailer’s optimal price is:
P* = (a + p)/2
Given this, the publisher’s demand is Q = a – P* or Q = (a-p)/2. The publisher chooses p to maximize its profits of pQ which results in a price of p* = a/2. This implies that the final equilibrium price under the wholesale pricing model is:
P* = 3a/4
MODEL 2: Agency
Under an agency model, the publisher sets P directly while the retailer receives a share, s, of revenues generated. The publisher, thus, chooses P to maximize its profits of (1-s)PQ. This generates an optimal price of:
P* = a/2
Regardless of s, the price under the agency model is lower than the price under a wholesale pricing model. The reason is that the agency model avoids double marginalization. The comment here does not reflect other effects arising from ‘most favored customer’ clauses that can apply in both wholesale pricing and agency models and are discussed further in Gans (2012).