Are prices higher under an agency model than a wholesale pricing model?

[This post is wonkish. If you prefer to read such things in pdf form, this note is available here.]

This is the question floating around with regard to the DOJ’s investigation into eBook pricing. There are suggestions that it will result in a move back from the agency model to the wholesale pricing model for eBook pricing. The basic economics of the situation suggest that this is a bad idea and, given the discussion, I figured that I would just write down a simple model to explore the issue. This model is based on Gans (2012). Note that the model here predicts what it predicts. If Amazon, for example, is charging less under wholesale pricing there is more going on (e.g., subsidisation of device sales) but this basic model is designed to reflect what is likely to occur in the long-run when such things are less likely to be important.

Suppose that the (inverse) demand for an eBook is given by P = a – Q where P is the price consumers pay for an eBook and Q is the quantity they purchase. eBooks are assumed to cost nothing to distribute to consumers who have devices. Gans (2012) explores the consumer’s choice to purchase a device as well but this will not be considered here.

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).


Gans, Joshua S. (2012), “Mobile Application Pricing,” Information Economics and Policy, 24(1): 52-59;

5 thoughts on “Are prices higher under an agency model than a wholesale pricing model?

  1. I’m still wondering why the agency model seems to being passively accepted by retailers. From what I understand of anti-trust law, it is illegal for a manufacturer to dictate the retail price of a product (thus they give “manufacturer’s suggested retail price). For physical goods it’s well established that the retailer can sell for any price desired. As far as I know that also applies to software, whether sold as a physical package or via downloads.

    So it seems odd that there are arguments that publishers are colluding to set prices. The mere fact that a single publisher sets a required retail price would seem to be open to a pretty simple challenge.

  2. Does it matter if the demand function isn’t linear? I think one of the major points at the time was that the 9.99 price was critical value which spurred a lot of sales. I would think that the demand for ebooks is not liner in price, would that change your conclusion?

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