The new economics of loss leaders

Chen and Rey show an additional intuitive reason for loss leading: screening. Imagine there are two goods, A and B. Large stores sell both, while specialty or discount retailers sell only B, with unit costs cLA, cLB and cSB; the specialty retailer has a cost (or quality) advantage in B. Let consumers dislike shopping, with a heterogeneous cost of shopping for shopper i of s(i) for each store they patronize. Let consumers have homogeneous unit demand (vA>cLA and vB>cLB) for both A and B. If only the large store exists, it can’t screen by shopping cost, so it just sets a uniform price for the bundle of goods A and B to maximize profit; this means that those with low shopping costs will earn some rents since I keep the price low enough that even high shopping cost folks buy. If, on the other hand, the specialty retailers exist, the large store can sell B at below cost, keeping the combined price of A+B the same as before. This ensures that the large store continues to extract full rent from the high shopping cost buyers, and allows full extraction of willingness to pay for good A from low shopping cost buyers (who now visit both stores).

The authors prove that whenever the large retailer finds it worthwhile to price such that at least some shoppers buy both A and B at the large store, then that store will loss lead with B. As long as the distribution of shopping costs is sufficiently high, the large store earns higher profits when they face small store competition than under monopoly, since the small store can be used to screen for shopping costs, and hence for willingness to pay. This flavor of result is general to having only one competitor rather than a competitive fringe of small firms, as well as other loosened assumptions. Banning loss leading increases total social welfare as well as consumer surplus; those who shop at both venues are made better off, as are those who have shopping costs just too high to make shopping at both venues worthwhile, while every other consumer and the large firm earn the same surplus.

From A Fine Theorem, here is more.


The model is defective in two points:

1) While small/specialty stores may have lower retail prices on good B, it is unusual for them to have a lower wholesale cost. Thus, the large store can loss-lead good B without actually losing much.

2) Manufacturers and distributors are big players in the game, but are completely absent from the model. Determination of whether good B is actually sold at a loss is complex to the point of being unknowable. Details of promos, SPIFFS, racking fees, rebates, and a host of other channel manipulation activities are not completely known within any of the firms involved.

Given these 2 defects, I don't see how the authors can assert that banning loss leading increases total social welfare.

Right, one big problem is the assumption that "banning loss leading" is done in a perfect fashion; i.e., that banning loss leading only results in preventing loss leading where the smaller/specialty store actually has a lower wholesale cost and the bigger store is losing, and doesn't result in competitor complaints of "loss leading" where the bigger store actually has lower costs and isn't losing money. Banning a larger retailer that has lower costs from economy of scale, etc. from offering prices that reflect that is clearly inefficient.

How many of the trade "dumping" complaints are cases where the foreign competitor is actually offering something below cost, and how many of them are complaints from a higher cost competitor? That could be one guide as to the efficiency of such regulation.

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The authors prove that whenever the large retailer finds

No, no they didn't. To the extent they "proved" anything, they proved that under assumptions A, B, C, D...their model works. The only way their model can be said to have proven anything in "the real world" is if their assumptions are essentially correct and they didn't leave out any relevant variables. It takes a certain sort of arrogance to assume no relevant variables were left out.

This attitude of models "proving" something is a major blind spot I see time and time again. Bob Knaus is correct; they really haven't come close to including all variables in their model. Instead they seem to have dropped their keys in the proverbial darkness and decided to over to a streetlight to see what they can find.

I don't mean to pick on the authors of the study; it happens all too often.

I also don't mean to say that their model is worthless; pioneering a new line of thought is always helpful, at least so long as it is taken with the approriate grains of salt needed to make it palatable.

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Crap, sorry about the all-italics post. This site really needs a "review submission" button.

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For some, perhaps even many, s(i) < 0.

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What is special about s(i)=0? The heterogeneity is the important thing.

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This only makes sense if the large retailer has a monopoly on A.
If the large retailer raises cLA in order to compensate for lowering cLB, many low-shopping-cost consumers will seek another outlet to purchase A, so you're not really going to extract full willingness to pay from them.

Also, there seems to be an assumption that cLB > cSB, otherwise, the low-shopping cost consumers will shop at the large retailer for both, and gain increased utility by reducing their (albeit small) shopping costs.

In real life what happens is that one large retailer offers a loss leader on B, the other one doesn't (and has a lower price for A), and the low-shopping cost consumer goes to both stores and gets B at the loss leader price and A at the regular price.

Their model specifically seems to be grocery stores, where they compare the big retailers with lots of SKUs to chains like Aldi or Trader Joe's that have smaller stores and smaller number of product offerings, mostly under private label.

In reality, though, Trader Joe's doesn't offer just "the basics," they offer a number of unusual and gourmet foods, which change regularly, making it difficult for the larger retailer to practice this strategy consistently, particularly if many small retailers can pick and choose which product to offer, as you note.

(As well, larger storefronts are also free to explore private label efficiencies while still selling a larger selection of other goods; such a strategy has worked well for Wegmans.)

What I've observed is that the smaller and discount retailers are actually MORE likely to offer loss leaders than the big retailers, possibly for this reason. Trader Joe's is well known to have their cheaper wines (Two Buck Chuck), and coffee, but once you're in the store you get sucked into buying thing like frozen acai berry pastries at $10 a box, and cashew butter. So it's really Trader Joe's that have the monopoly on A (unusual products), and are offering a loss-leader on wine.
The same thing is true of my local "discount" grocery store. They have cheap produce and the best loss-leaders, but their regular prices for meat, dairy, and packaged/canned goods is noticeably higher. However, they do have a large "international" foods section so if I want something like Mexican Coke or authentic queso fresco, I'll go there.

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In real life what happens is that one large retailer offers a loss leader on B, the other one doesn’t (and has a lower price for A), and the low-shopping cost consumer goes to both stores and gets B at the loss leader price and A at the regular price.

The other thing that happens in real life, as you imply, is that there's one small retailer that only sells A, and another small retailer that only sells B, and if the large retailer tries to raise the price of A or B then the low shopping cost consumer goes to whichever specialist store is appropriate.

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I think the observation about pricing is correct, but the observation about total welfare is wrong.

It's an empirical question that has been answered in some studies of the effect of miniumum mark up and sales below cost statutes: basically, what the research finds is that in states which have minimum markup laws (limiting the ability of a large retailer to discount on say, milk or gasoline) what you find is a proliferation of small and pop stores, gasoline, and liquor stores selling at higher prices compared to states which do not have minimum markup and sales below cost statutes. In other words, prices are lower than in states where there are no such laws, even though there are fewer smaller vendors.

There is sometimes a mistake in equating the number of competitors with total welfare. (If you want to do your own study, you can use the census of retail trade establishments data and research state laws...good project for someone to replicate as the studies I am aware of are from the 70s).

I think you make an excellent point here. What I suspect that happens is that minimum markup and sales below cost statutes tend to be, as actually, implemented, different from the theoretical perfect model in the paper. They're used against larger retailers who are selling things cheaper than the smaller competitors due to higher efficiency, not just selling at a loss. It's difficult to verify if something is really being sold as a loss, but easy to just see that "you're selling it for less than the little guy," so the latter tends to be used as prima facie evidence of the former.

As well, I think that in reality the alternative isn't just "big stores selling A and B while little stores sell only B," but "big stores selling A and B while some little stores sell only A and other little stores sell only B." Under that alternative, this model breaks down.

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And those with more time than money can shop the sales, with a pro-poor impact :)

I'm glad to not have to waste my time (and taste buds) shopping the sales, although I still throw a decent dose of frugality into my search for quality food.

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In addition to the good point of cLB not being larger than cSB, it also seems to me that the assumption of unit demand (not sure if it is in the paper, I've only read the blog post) is a big driver of the result. It completely negates Varian's point that price discrimination is welfare enhancing if overall demand goes up...

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