Josh Gans gives a handy benchmark model where the answer is no.

MODEL 1: Wholesale PricingSuppose 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: AgencyUnder 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

ConclusionRegardless 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).

## 4 comments

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April 12, 2012 at 7:39 am

PLWSure.. for a monopoly ebook seller. Repeat this analysis for N>1 retailers. If you stick with price-setting, 2 will suffice. Of course, that’s exactly the issue.

April 12, 2012 at 9:05 am

jeffI think that the platform gives the retailers monopoly power. So I wouldn’t use a Bertrand model for price setting retailers.

April 12, 2012 at 10:06 am

PLWI guess I don’t understand, then. I thought the justification for the agency agreement in the first place was “ruinous competition” (lol) from Amazon and Barnes and Noble Online. Who’s the monopolist?

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