Price discrimination under online–offline competition (2023)


Third-degree price discrimination may be socially desirable without an increase in total output in an oligopoly with potential entrants (Armstrong and Vickers, 1993, Jorge and Pires, 2013), differential production costs (Galera and Zaratiegui, 2006), or markets that differ in costs (Chen et al., 2021). This work is motivated by the online–offline debate on whether online price discrimination should be allowed.1 Online social platforms and data mining technology allow firms to capture the digital trails of their customers and set up differential prices accordingly.

We ask when and whether online price discrimination is socially desirable under online–offline competition. Consider an online firm that engages in price competition with one local offline firm in each of two separate markets with unequal sizes. The online firm has the advantage of extracting personal information (such as zip code information) to enact discrimination between the two markets. Online transactions suffer a distaste cost but enjoy a lower unit cost.

We find that online price discrimination is socially desirable when the intensity of online–offline competition is strong (represented by a large online–offline cross-demand parameter), even though the total online and offline outputs are unchanged due to our linear demand setting. This is because the cross-demand effect dominates the output-misallocation effect. Unsurprisingly, the total consumer surplus is worse under online discrimination. However, online discrimination is beneficial to the online firm and benefits (harms) the offline firm in the large (small) local market. Alternatively, in the case of a uniform-pricing chain store, online discrimination is always socially undesirable.

Among the other recent studies on price discrimination, Dobson and Waterson (2005) showed the possibility that allowing differential prices is not profitable for the chain-store but increases the consumer welfare. Jorge and Pires (2013) and Armstrong and Vickers (2019) explored the case with captive customers who only buy from specific sellers. Tremblay (2019) analyzed a situation in which implemented first-degree price discrimination can be Pareto superior to uniform-pricing without receiving a consumer backlash. Our study also reinforces the importance of emerging online competition studies by Liu et al. (2006), Loginova (2009), and Guo and Lai (2017).

Section snippets

The model

Suppose there are two separate local markets (1 and 2), where each has one offline firm selling a differentiated product to the local residents and one online firm selling a product to both markets.2 Assume that the online and offline demand for the differentiated products in market i are respectively Dio=aib(pio+λ)+γpi and Di=aibpi+γ(pio+λ), i=1,2,

Online price discrimination and social welfare

Whether online price discrimination benefits firms’ profits, consumer surplus, and social welfare is shown as follows:

Proposition 1

When online price discrimination is allowed: (1) discrimination is welfare-superior to non-discrimination if and only if the cross-demand parameter is large. That is, SW˜>SW iff γ>2(21)b0.8284b. (2) Consumer welfare is always worse. (3) Online firms benefit and the total profit of offline firms increases. However, discrimination benefits the offline firm in a large local

Chain stores

Now, consider the offline markets served by a chain-store firm with a total profit π1+π2. If this chain store is allowed to set offline discriminatory prices, the previous analysis applies. If the chain store can only set a uniform price, we have a different welfare comparison for online discrimination. The chain store firm maximizes its profit by (π1+π2)|p2=p1/p1=0. Online price discrimination always worsens social welfare, since SW˜SW=(a1a2)2/(16b)<0. This is because the cross-demand


Online price discrimination can be welfare-improving under an online–offline competition framework, in which an online firm engages in Bertrand competition with a local offline firm in each separate market, even though the total output remains unchanged. Our policy implication of online price discrimination is that it would be valuable to examine whether the online–offline cross-demand parameter is sufficiently large to override the traditional misallocation effect.

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