Ijoined the TSE in September 2013 as an Assistant Professor. Although my research interests are reasonably broad, I mainly work on theoretical industrial organisation. An area of special interest to me is consumer search. Imagine there is a particular product that you wish to buy: for example, a book or a grocery item. According to the canonical textbook model, you know precisely which firms sell that product, and how much they charge. Armed with this information, you purchase it at the lowest price avail- able. Firms price aggressively in order to persuade you to buy the product from them. Unfortunately few real-world markets work like this. For example, most consumers are poorly-informed about prices. Usually consumers can only learn about prices by visiting websites and wandering around stores - both of which are time-consuming, and therefore costly.
One might conjecture that if the cost of gathering addi- tional prices is small - as for example might be the case online - this imperfect consumer information would make little difference. Surprisingly, economic theory suggests that this conjecture is false. This is the conclusion of the well-known “Diamond Paradox”, named after the Nobel laureate Peter Diamond. To gain some insights into how search costs affect equilibrium prices, consider the follow- ing simplified model. Suppose there are two symmetric firms which stock the same product. Consumers have heterogeneous valuations for this product, distributed on an interval [a, b]. In order to learn a retailer’s price (and then buy its product), consumers must incur a search cost s > 0. How should consumers optimally behave in such an environment? To begin with, consumers must form a belief about how much each firm is charging. To simplify mat- ters, let us suppose that both firms are expected to charge the same price pe. Consumers whose valuation exceeds pe + s expect to earn positive surplus, and therefore search one ran- domly selected retailer; other consumers believe that search is not worthwhile, and stay at home. How should the firms in this market behave? These firms are free to choose any price they like - in particular, they are under no obligation to charge pe. There are two separate cases of interest. Firstly when pe + s > b the expected price is so high that no consumer searches. Firms face zero demand, and are therefore indifferent about what price to charge. As a result any pe > b - s constitutes an equilibrium, in a trivial sense. Secondly when pe + s ≤ b the expected price is sufficiently low that some consumers do search. The problem here is that once a consumer enters a store or visits a website, she reveals that her valuation exceeds pe + s. Moreover her search cost is sunk - if she decides that she wants to buy from the other retailer, she must incur an additional s.
Consequently if consumers expect a price pe, each retailer can charge pe + s and still sell to every consumer who searches it. Equivalently, it is not rational for consumers to expect a price that satisfies pe + s ≤ b. The only possible outcome of the game is the first one, in which consumers expect high prices and therefore do not search. Hence we have a paradox. Perfect information leads to strong competition and low prices; small amounts of imperfect information lead to high prices and market breakdown (1).
This paradox is an important and intriguing result. Several authors have suggested ways to weaken it. One class of mod- els attacks the problem from the consumer side. For example, consumers might plausibly learn several prices during a single search (Burdett and Judd 1983). Alternatively, some consum- ers may enjoy shopping around and comparing prices (Varian 1980, Stahl 1989). In both cases, firms have an incentive to set relatively low prices, in an attempt to win business from the better-informed consumers. Another class of models attacks the Diamond paradox from the firm side. Essentially the paradox arises because firms cannot commit not to ‘hold up’ consumers ex post with a high price. Therefore if firms can inform consumers about their price via advertising, they can guarantee consumers some surplus (Wernerfelt 1994, Anderson and Renault 2006). However, an important point is that papers within this literature have traditionally made the (implicit) assumption that firms sell only one product.
My research on this topic seeks to relax the assumption of single-product retailers. From a practical point of view, most firms do sell a wide range of products. Moreover, consumers frequently buy several items in one shopping trip. From a theoretical point of view, allowing firms to stock multiple products can also overcome the above ‘no search problem’. Intuitively this is because in the single-product case, only consumers with a high valuation decide to search, so retailers exploit this and charge a high price. However, in the multi- product case, somebody with a low valuation on one product may search because she has a high valuation on another. This weakens a firm’s incentive to hold-up consumers: when increasing one of its prices, it loses demand from consumers who like the product a little, but who are primarily shopping for something else. As such, it is possible to construct an equilibrium where consumers have correct expectations about each retailer’s prices, and still find it optimal to search. Once we have this equilibrium, we are potentially able to answer several other interesting questions. For example, when consumers have search costs, what are the advantages to a retailer from stocking a wider range of products? How do pric- ing incentives change when a firm sells more products? Some retailers send out adverts, containing information about the prices of a small proportion of their total product range. How much can consumers learn from these adverts? For example, if a firm offers a good deal on one product, should consumers expect the firm to raise the prices of its other goods?
Significant progress in answering these questions can be made using the following model. Suppose there are two firms, each of which sells the same n products. Consumers regard these products as independent, and would like to buy one unit of each. Valuations for each of the products are drawn independently from an identical distribution. As before, assume that consumers must incur a cost s > 0 in order to travel to a retailer and learn about its prices. In addi-tion, suppose that some consumers are ‘loyal’ to a particular store (and will only shop there), whilst others are ‘non-loyal’ and are happy to shop wherever they think they can get the best value for money. The move order of the game is then as follows. In the first stage, the two firms simultaneously choose their prices. They also have the opportunity to pay an advertising cost, and inform consumers about one of their prices. At the second stage, consumers observe adverts (if any) and form expectations about the prices being charged by each retailer. Consumers then choose between staying at home, or searching one of the two firms. Non-loyal consumers then have the opportunity to search the other firm if they wish. Consumers observe the actual prices being charged by the firms they have searched, and then make their purchases.
As a benchmark, first suppose that neither retailer chooses to advertise (for example because the cost of doing so is prohibi- tively large). As discussed above, whenever the firms’ product ranges are sufficiently broad, there exists an equilibrium in which consumers search. Moreover, this equilibrium is symmetric: firms charge the same prices, and therefore all consumers search at most once. We can also prove that when the firms stock more products, they charge lower prices on each individual product. Intuitively, a small retailer is searched by a relatively small group of consumers, who have high valuations on many of its products. A large retailer, on the other hand, offers many more products on which positive surplus can be earned. As a result, a larger retailer is searched by a larger number of consumers, who on average have a lower valuation for any individual product. Larger retailers should therefore charge lower prices, because they endogenously attract consumers who are more price-sensitive.
Now suppose that a retailer sends out an advert, containing the price of one of its products. Consider a thought experiment in which the firm exogenously varies the level of its advertised price. Notice that as the advertised price falls, some new consumers who like the advertised good decide to search. Since they were not previously searching, these additional consumers must have relatively low valuations. Therefore, anticipating this, the firm finds it optimal to also reduce its unadvertised prices in order to sell more products to these new searchers. Therefore consumers (rationally) expect a positive rela- tionship between a firm’s advertised and unadvertised prices. This happens even when products are completely independent and unrelated.
Finally, consider how firms choose their overall advertising strategy. Assuming the advertising cost is not too large, we can prove that a firm optimally behaves in the following way. Sometimes it charges a high ‘regular price’ on each product and does not advertise. Other times it advertises a low price on one randomly selected product. The discount on that product is also random and drawn from a distribution. Intuitively a firm must randomise in all three dimensions, otherwise its rival might be able to guess and undermine its promotional strategy. In light of the positive relationship between advertised and unadvertised prices, randomness in advertised prices generates (from an ex ante perspective) randomness even in the prices of products which are not being advertised. As such, price dispersion is a robust feature of the model. Overall then, even a relatively simple model can gen- erate quite rich predictions about how retailers should choose their pricing and advertising strategies when consumers face search costs.
 See Diamond (1971) and Stiglitz (1979). When individual consumers have elastic (rather than unit) demands, firms end up charging the same price as a monopolist. In this alternative setting, consumers do search and the market does not break down. Nevertheless the equilibrium price is still very different from the full-information case.
Anderson, S. and Renault, R. (2006) Advertising Contentí, American Economic Review 96(1), 93-113.
Burdett, K. and Judd, K. (1983): Equilibrium Price Dispersioní, Econometrica 51(4), 955-969.
Diamond, P. (1971): A Model of Price Adjustmentí, Journal of Economic Theory 3, 156-168.
Stahl, D. (1989): Oligopolistic Pricing with Sequential Consumer Searchí, The American Economic Review 79(4), 700-712.
Stiglitz, J. (1979): Equilibrium in Product Markets with Imperfect Informationí,
The American Economic Review 69(2) Papers and Proceedings, 339-345. 4
Varian, H. (1980): A Model of Salesí, The American Economic Review 70(4), 651- 659.
Wernerfelt, B. (1994): Selling Formats for Search Goodsí, Marketing Science 13(3), 298-309.