Bargains and Rip-offs, continuum of types

Let us suppose consumers have imperfect information about prices. A consumer can pay s to learn where the deals are. But consumers are heterogenous in their cost to learn information. This Heterogeneity is captured in a CDF, F(s), which is defined as the proportion of consumers with cost less than s.

In addition, we have additional simplifying assumptions such as homogeneity in willingness to pay, and unit demands on the demand side. On the supply side, we have zero profit and a U shaped average cost curve.

The models gives us the possibility of price dispersion. Zero profit and profit maximization tells us that there are two prices possible, the efficient monopoly price and the low price, which is equal to average cost of minimum efficient scale.

The equilibrium features s*,  consumers with F(s*) will choose to pay, i.e. choose to be informed about the ‘bargains’ out there. The bargain hunters get the low price, while all the others, the ‘uninformed’, pay the highest they are willing to pay.

There are three possibilities.

1. smallest s >maximum net consumer surplus. the proportion of consumers that would find it worthwhile to be informed is zero (i.e., the smallest s would make utility negative). No one becomes informed, and the price is the highest possible.
2. s*=0. Here, the proportion of people who might be informed is high enough such that everyone wants to get informed so there is only one price in equilibrium, the low price.
3. Price dispersion. Some stores set a low price, attracts F(s*) proportion of consumers. The rest of the consumers stay, decide not to be informed.

Price Dispersion

Price dispersion is when different sellers offer different prices for the same good in a given market. Its different from third-degree price discrimination, where a seller offers a good for different sellers for different groups of buyers. It is also different from geographical price dispersion, as in the failure of the Law of One Price across cities and countries.

I imagine a good in a city (say, soap), that sells for different prices in different stores at a given point in time. The theoretical approach is that there is imperfect information among consumers about where to find the lowest price good.

An early attempt at this is by Diamond (1977, “A Model of Price Adjustment” JET). Given that every consumer is the same [preferences] and each buyer knows only the price in one shop, and there as many shops as there are buyers. Everyone has a cost to learn about prices in other stores sequentially (imagine calling one new store, one store at a time, a process called sequential search). The Nash Equilibrium is no price dispersion, and each store charges a monopoly price. At this point, it becomes obvious. If everyone is the same, each has the same reservation price, say r, the highest price at which a buyer buys the product. Each store knows this and sets p=r. Each buyer knows this, and thus know that is no price dispersion, and does not bother to learn other store’s prices.

It is clear from the above that to achieve NE where there is dispersion, you have to exploit not only imperfect information, but also some kind of heterogeneity in seller and buyers, or both. An example is Varian (1980, A model of sales, AER). He assumes there are informed consumers and uninformed consumers, the relative proportions in the population are exogenous. The result is a mixed strategy in prices. Stores randomize because there is no dominant strategy — if all stores sold at the same price, it would be profitable to undercut your competiton and attract the informed buyers. The presence of uninformed buyers pushes stores to sell at a high price.

The next step is to endogenize the decision for consumers to inform themselves or other prices. Varian’s model can be interpreted as two groups of consumers, one with high search costs and one with low search costs. A paper by Burdett and Judd (1983, Equilibrium Price Dispersion, Econometrica) argues that even  with all consumers with a small, positive search cost, price dispersion can still exist.

Who owns Price information?

According to big retailers, they do. This shows that the internet (or information, more generally) hasn’t tamed price dispersion.

Online Price Dispersion

Its time to get back to work. A few weeks ago, “A Competive Model for Online Price Dispersion” was presented at the Business School.

They motivate their paper with the observation that even in online markets, prices for identical goods are different. To explain this, they rely on vertical differentiation. Firms (here firm 1 and 2) are differentiated by brand name recognition and service quality. They later find that these two factors explain much of the price variation in their data.

More interestingly on a theoretical level, their model allows for a negative relationship between price and service quality. Consider the case where firm2 is less recognized than firm one and offers less service than firm1. As Firm 2 offers more service, firm 1 and 2 become more similar and some customers who like good service are now more attracted to firm 2.

Thus the key variable here is the marginal consumers: If there are alot of these service-sensitive people [or for the few that are there, they are willing to pay alot for service], the more likely it will be that its worth fighting over them.  Hence,  a more heterogenous population in the service dimension is key for this to happen.

However, the authors rightly contend that this adverse price effect should never be observed in [a static] equilibrium. Firms figure out that this effect will happen and will lower their service to eliminate the price effect. Does the fact that they find this in their empirical results mean that these are non-equilibrium results [whatever that means]. At any rate, the authors don’t discuss this admittedly more philosophical issue, content as they are in just explaining the empirical result.

My lesson here is that a well-specified vertical differentiation model can generate reasonable results on price dispersion. I would like to apply this to other markets.