This blog is a follow-up on my previous blog on wholesale contracts between Amazon.com and Hachette. In that blog, I showed, using game theory, that raising wholesale prices is in general not desirable if Amazon’s strategy is to sell e-books at a very small margin, given that supply chain profits are the lowest when the distributor’s profit margin is the smallest. Let us now explore the attractiveness of the agency model, which is the model that publishers try to promote.
As in my previous blog, let us assume that demand depends on both price and promotional effort, i.e., D(p,e)=a + b * e – p, in which a and b are parameters and let us assume that it costs the distributor e * e (that is e square) to exert e units of effort.
Under the agency contract, the distributor receives a percent of the price. Accordingly, the distributor’s profit is equal to a * p * D(p,e) – e* e. The first term is the commission rate, multiplied by the selling price and the demand. The second term is the cost of exerting promotional efforts. In contrast, the publisher’s profit is equal to (1 - a) * p * D(p,e), which corresponds to the price, net of the commission, multiplied by the demand. In the agency model, the distributor chooses only the promotional effort e, whereas it is the publisher who chooses the retail price p.
Similar to the wholesale price contract, the agency model leads to incentive conflicts. In particular, the publisher would like the distributor to exert as much promotional effort as possible so as to boost demand, whereas the distributor, who incurs the costs of such efforts, would most likely be happier with some intermediate level of effort.
However, and this is in contrast to the wholesale contract model, the incentives regarding the pricing decisions are more aligned with the agency model. In particular, the revenue of distributor’s profit, a * p * D(p,e), is aligned with the revenue of the publisher, (1 - a) * p * D(p,e). Hence, with the agency model, it is more likely that the parties would agree on the right pricing model. Yet, the distributor will not account for the implications of its pricing decisions on the distributor’s cost of effort, so some inefficiency may remain.
Despite better aligning the pricing incentives than with a wholesale contract, the agency model is not without tensions. Specifically, there will be some disagreement about the rate of commission. As shown in the chart below, the distributor’s profit (in red) is increasing in the commission rate, whereas the publisher’s profit (in green) is decreasing in the commission rate. Agency contracts will therefore be hard to negotiate.
It is interesting to note that the supply chain’s total profits (in purple), i.e., the sum of the distributor’s and the publisher’s profits, is maximized at some intermediate value of the commission. Intuitively, the commission rate should be sufficiently high to encourage the distributor to exert promotional effort, but sufficiently low to incentivize the publisher to set the right price. In the particular case where a=10 and b=0.8 (depicted above), the supply chain’s total profit is maximized when the publisher gives a commission of 80%. However, moving to such outcome may be difficult in practice, since the publisher’s profit is decreasing in the commission it gives to the distributor.
To sum up, the agency contract is a good alternative, because it better aligns the pricing incentives, but they are hard to negotiate. It is quite understandable that Amazon is not pleased with the current contractual terms, which set their commission at 30%. If publishers want Amazon to adopt an agency contract, they should perhaps give a higher commission to the distributor, to increase the distributor’s profit, and make the agency contract at least as appealing as the current wholesale contract. For instance, in the example above, in order to give the distributor at least the same profit under the agency model than under the wholesale contract (with w/p=50%), the commission rate a would need to be increased to 45%. This is the price publishers may have to consider paying if they want to take back from the distributors the right to make pricing decisions.