Guillaume Roels
This is a follow-up on my previous blog post. At the core of the negotiation between Hachette and Amazon lies the choice of contract, between the following two types:
- The wholesale contract, according to which the publisher sells each unit at a pre-agreed wholesale price and the distributor is free to set the price, typically twice the wholesale price.
- The agency contract, according to which the retail price is set by the publisher and the distributor receives a commission—typically 30%.
The wholesale price contract was the traditional contract used between book publishers and brick-and-mortar retailers. However, since Amazon started pricing e-books at a low price, sometimes even below cost, publishers have pushed distributors for taking back the right to set the retail prices, and this led them to them develop the agency model. Apple seemed to have been one of the early adopters of the agency model when it made some concessions with the book publishers to sell their content through its iBook store.
There has been a lot of research on supply chain contracting in the field of operations management in the last fifteen years using game theory, and I would like to share an academic perspective on the issue in this blog and an upcoming blog.
To generate some insight, let’s ignore the price-dumping effects for simplicity, and let’s consider only one product. Suppose that demand (D) depends on the distributor’s effort (e) and the retail price (p). Specifically, assume a linear demand D(p,e)=a + b * e – p, in which a and b are parameters, respectively representing the base demand and the demand sensitivity to price. The distributor’s promotional efforts consist of everything that Amazon is currently not doing for Hachette, namely promoting the book, expediting shipments, etc.
Suppose that there are no variable costs (since we are talking about e-books), and that it costs the distributor e * e (that is, e square) to exert e units of effort. That is, it costs more to exert high effort. If you exert 1 unit of effort, it costs you $1, but if you exert 2 units of effort, it costs you $4. For simplicity (and realism), I will assume that b<2, i.e., that demand is not too sensitive to effort, which guarantees that the optimal effort is finite.
Under the wholesale price contract, the distributor must pay w per unit. Accordingly, the distributor’s profit is equal to (p-w) * D(p,e) - e * e. The first term in this equation is the distributor’s profit margin, multiplied by the demand, and the second term is the (negative) cost of effort. On the other hand, the publisher’s profit is equal to w * D(p,e). Under the wholesale price contract, both the retail price and the promotional effort are chosen by the distributor to maximize its own profit.
Note that the pricing and promotional effort decisions that maximize the distributor’s profit may not be the same as the ones that maximize the publisher’s profit. In particular, when the wholesale price w is fixed, the publisher would like the distributor to price as low as possible and exert as much promotional effort as possible so as to increase demand D(p,e). The distributor, in contrast, will be quite reluctant to doing so since high promotional efforts are costly or low prices would eat up its margins. Hence, there is an incentive conflict, which explains why Amazon and Hachette cannot agree on the contractual terms.
Consider the now the choice of wholesale price: On the one hand, the publisher would like to set the wholesale price as high as possible so as to obtain a high profit margin on each book. On the other hand, the publisher anticipates that, if the wholesale price is high, the distributor would then exert less promotional effort (since its profit margin would be too small to be worth it) and would price the product too high (so as to still preserve some profit margin). Ultimately, these low promotional efforts and high prices would lower demand, and would therefore negatively affect the publisher. The publisher must then find the right balance between setting a wholesale price sufficiently low to lead the distributor to make pricing and effort decisions to boost demand and setting the wholesale price sufficiently high to earn some profit margin on each product sold to the distributor.
The chart below (when a=10 and b=8) illustrates those dynamics: The publisher’s profit (in green) is maximized at some intermediate wholesale price. The distributor, obviously, prefers when the wholesale price is zero since its profit (in red) is maximized when w=0.
It is interesting to note that the total supply chain profit, that is, the sum of the publisher’s and the distributor’s profits, is larger when the wholesale price is smaller. Hence, if the parties want to create more value (relative to the base case where the distributor’s profit margin, w/p, is equal to 50%), they would need to consider lowering the wholesale price. The graph above shows that, while the distributor would certainly be happy with a lower wholesale price, the publisher will in general not agree, since the publisher’s profits would then decrease.
The graph also shows that, if the distributors were to raise their wholesale prices to prevent Amazon from charging too low retail prices, i.e., if w/p increases, less value would be created in the supply chain. While it may be beneficial for publishers to raise w so that w/p is greater than 50%, i.e., so that Amazon’s profit margin becomes less than 50%, it is up to a certain point (60% in this example), since beyond that, Amazon will not have the right incentives to boost demand. Moreover, Amazon’s profit reduction would be so large that less added value would be created in the supply chain.
Overall, this simple analysis suggests that wholesale contracts are inevitably associated with incentive conflicts. Moreover, raising wholesale prices to preempt distributors from charging too low retail prices will in general destroy value in the supply chain. Instead, the publishers may want to investigate reducing their wholesale prices, and collaborating with distributors to capture some of this added value.
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