How to Optimize Buyer Information
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How to Optimize Buyer Information

IGIER VISITING STUDENT LAURE ANIQUE REPORTS ON THE RECENT IGIER POLICY SEMINAR WITH STEPHEN MORRIS (MIT)

The rise of the internet and the digital economy highlighted the central role that data plays in our economy. Nowadays, consumers leave a trail of evidence on their likes and dislikes, which can be exploited by firm to offer products that better fit buyers’ needs – or capitalize on this information and increase profits. The growing relevance of data collection has compelled sectors to participate into some form of buying, selling and exploitation of the information available. As prof. Stephen Morris pointed it out during his IGIER seminar on “The Optimality of Coarse Menus”, the thriving influence of information will induce more predictive work integrated with information theory in order to reach a better understanding of a world where data has become a central part.
 
In such new light, what can we say of firms’ behavior with respect to the collected data and their offer to customers? Morris provides an answer to this question by developing a model combining contract design and information design. The model is set up as follows; we have a monopoly seller that sells a vertically differentiated good, i.e. the same good declined in different quality levels. The seller commits to a “public menu”, that is a list of different quality levels and their associated price. This set of pairs forms a “menu”, from which buyers choose which combination best fits their needs. Furthermore, the menu is said to be “public” as it is available for all; this implies that third-degree price discrimination is not possible, that is the seller applies the same price to all consumers for each quality level. Buyers do not know their “value”, that is they do not know their preference for quality of said product. On the other hand, the seller has access to information about the buyers’ value and can commit to a rule that transmits this information to the buyers through a recommendation rule, that is a “signal”.
 
This model’s set up is justified by the structure of our digital economy. First of all, sellers are well-informed about buyers’ value through data gathering and analysis. In particular, prof. Morris assumes that the buyer knows nothing while the seller has access to full information. While such assumption is rather extreme, it can be a good representation of the current digital economy, especially if the seller can only customize recommendations, not prices. Moreover, the assumption that the menu is public is realistic, as this represents the business model of many sellers, such as Amazon who applies the same price to all customers for every given good, but also because it is easy for the consumer to look at the menu under other identities.
 
This model can be expressed as an optimization problem, where the monopolist chooses a signal and a menu that maximize its profits, subject to the individual rationality and incentive compatibility constraints; while the individual rationality constraint ensures that the consumer is better off participating in the transaction rather than staying out of it, the incentive compatibility one ensures that the buyer is better off choosing the value recommended rather than another one in this menu. From there, Morris finds that the seller’s problem becomes the expectation of the allocation rule and the information that maximize total surplus, defined as the value of the buyer minus the cost of seller, minus information rent, that is what the buyer extracts from the contract.
 
Solving this problem led to two conclusions; first of all, the optimal menu is finite and the recommendation rule is increasing in type. This means that the menu offered by the seller has a limited number of quality levels, and that buyers who obtain a greater value from the quality of the item are recommended a higher quality. In particular, prof. Morris finds that the corresponding signal to the optimal menu, that is the optimal recommendation rule, is finite monotone partitional, meaning that the recommendation rule pools buyers into a countably finite number of groups. Each group is recommended a specific quality level, and higher quality levels are suggested to groups with higher types of buyers.
 
The second result highlighted by prof. Morris is that the seller will choose a single item menu, that is the seller will offer only one quality level, if the marginal cost function is convex and if the distribution of buyer types satisfies a “weak right tail condition”, meaning that it is a single peaked with concave decreasing component distribution. Under these conditions, the seller will not exploit the available information to offer differentiated qualities, as it is more profitable to pool all buyers together and offer only one type of quality. 
 
These results may appear surprising, as one could intuitively think that it is in the seller’s best interest to exploit the available information to extract as much as value as it can from the consumer. In fact, when pooling buyers, Morris finds that there are two effects that work against each other. The first effect is the reduction of the total surplus from the loss in buyers’ value. As less goods are offered to consumers, some types of buyers have to choose an option that would not have been the optimal choice had they been offered a continuum of quality levels instead. Hence, these types of buyers are not obtaining all the value they could, and total surplus decreases. The second effect is the decrease in information rent, that is the value buyers extract from the contract. Since buyers are given less information about their type, as the recommendation rule is given for a pool of buyers instead of for a specific buyer, the information exploited by the buyers is decreased. Morris finds that the later effect outweighs the former, that is the decrease in information rent is greater than the decrease in total surplus. Hence, pooling increases the monopolist’ profits, and as such it is in the seller’s interest to group buyers by offer a limited number of quality levels and not exploit all the information available. 
 
These findings underlined by prof. Morris’ work are of crucial importance as they highlight a mechanism through which the available information floating around is not exploited by sellers in order to make efficiency gains. In particular, the variety of items offered is reduced in order to achieve higher profits and lower information rents. The relevance of such findings is even more heightened in a market where data’s importance is magnified, as it offers a new understanding on how the availability of information to firms affects the social welfare, but also as it opens the door to new approaches to understand an economy where data plays a central role.
 

by Laure Anique
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