What follows is probably more of a discussion on price discrimination and countercyclical prices than almost anyone is interested in, so I’m putting most below the fold.

Arnold Kling weighs in again on price discrimination, clarifying his theory of Black Friday discounts and explaining how it can apply to Cyber Monday discounts as well. Arnold has previously responded to my theory of price discrimination by arguing that “the key issue here is that the cost of many products is dominated by overhead costs, and marginal costs are close to zero”, and so a wedge between mc and p may be a necessary and welfare improving. He also argues that because marginal costs do not decline in my cost based theory of black friday, it’s not a traditional microeconomic story.

My cost-based explanation for black friday discounting would be consistent with a simple rule-of-thumb pricing, but I agree with him that that is not a traditional microeconomic story. In the age of Wal-Mart I don’t find simple rule-of-thumb pricing to be a satisfactory theory of firm pricing.

However, another way that an economies of scale model could generate lower prices is if the number of competitors changes in high demand periods. While actual entry and exit is obviously unlikely, there may be effective entry and exit into new product markets by firms on Black Friday due to the exogeneously high demand. According to Warner and Barksy (more on this paper later), “there may be economies of scale or scope of the retailer…Large orders may receive quantity discounts from the manufacturer, or at least have lower per-unit shipping costs. There is an important overhead component to the employment of salespeople…[E]ntry and exit from niches in product space does appear to be a reasonable response to changes in temporary profit opportunities. In this manner, prices may be driven down in period when average selling cost is low.” I do agree with Arnold, however, that this is not a fully satisfactory theory for Black Friday.

Arnold’s theory of Black Friday price discrimination, and of retail sales in general, is that stores offer random discounts to attract price sensitive customers who are willing to wait, while regularly charging a higher price on every other day to customers who are not willing to wait. Some stores end up having random sales on the same day, e.g. Black Friday, as a competitive equilibrium in this model. In addition, Black Friday may have arisen as one of these equilibria because the crowds serve as an additional mechanism to keep price-insensitive shoppers, i.e. the regular shoppers, away.

Arnold’s theory seems like a decent enough explanation to me, it’s probably better than the simple cost-based explanation I offered, and it is a standard price discrimination story going back to, I believe, Hal Varian. However, a better explanation for Black Friday discounts can be found in the literature on countercyclical prices, which is when, counter to textbook economic theory, prices decrease during periods of higher demand.

In this paper, Chevalier, Kayshap, and Rossi (CKR) argue that there are three leading models that can explain the phenomenon: a model of cyclical elasticity of demand, a model of counter-cyclical collusion, and a model of advertising by multi-product firms.

Arnold’s theory is most similar to the cyclical elasticity of demand model, in that it relies on heterogeneous demand elasticities. This model is different from Arnold’s model, however, because it doesn’t assume two kinds of shoppers, and the Black Friday sale date is not an equilibrium result of random discounts. Rather, discounts are offered on Black Friday because of exogeneously high demand, and not vice-versa. This cyclical elasticity of demand model is elaborated on in a paper on holiday and weekend discounts by Warner and Barksy. They explain the large sales on Black Friday as one case of a general model that also explains the fact that prices of consumer goods fall as the week goes on in the Pre-Christmas season. The weekday discount can be in figure X below, which they estimated from a dataset of retail prices.

In fact, as seen in figure 12, part of the Black Friday discounts, which they call the “Thanksgiving Effect”, is explained by a normal Pre-Christmas season friday sales effect.

This type of price discrimination discounting is clearly different then the random sales price discrimination offered by Arnold. The discounts are very non-random, and are determined by days of the week and exogenous increases in demand caused by holidays.

CKR offers two more models of holiday discounts. The second model of price discrimination, the tacit collusion model, argues that the price dispersion is caused by collusion between retailers, and the fact that returns cheating on the collusive agreement are greater in high demand periods.

The third model focuses on strategic advertising and imperfect information. In this model consumers don’t know what prices are until they arrive at the store, at which point consumers’ travel costs are sunk, and so firms can charge a higher than marginal cost price. Firms advertise low prices on, and discount, higher demand items. The implication of this model is that at high demand times retailers will discount the highest demand goods. This model is part of a broad class of loss-leader models, which include equilibria with firms advertising on a subset of items; a much more realistic result.

CKR uses an impressive dataset of grocery store retail prices and wholesale prices to empirically test the three competing models of countercyclical prices during peak demand periods, including Christmas and Thanksgiving. What they find is that people are in fact not more price sensitive during times of high demand, like Black Friday, which contradicts the heterogeneous demand based models, like Arnolds, and supports the loss-leader based model.

Overall, I’m having a hard time pinning Black Friday on a single theory, despite the empirical evidence in favor of the loss-leader model put forth by CKR, and the evidence from Warner and Barsky that Black Friday is part of a general non-random pattern of weekend and holiday discounts. This is because there are features of the random sales model put forth by Arnold that explain aspects of Black Friday that the other theories do not; namely the seemingly purposeful secrecy of some sale items. On Black Friday information about what will be on sale and where is often not publicly announced, and can only be found by searching the web for leaked info. This is inconsistent with the advertising version of the loss-leader model of CKR, and consistent with the random sale theory put forth by Arnold.

In the end, Black Friday discounts may be the result of multiple mechanisms acting in tandem, with several theories capturing part of the truth. However, the best empirical evidence I have seen provides evidence against the heterogeneous demand models, including the one Arnold presents.

[UPDATE: For some reason this post originally included two or three copies of the writing below the fold. This has been corrected]