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Discussion Paper

No. 2009-25 | May 06, 2009
On the Effects of Selective Below-Cost Pricing in a Vertical Differentiation Model


We analyse the effects of predation in a vertical differentiation model, where the high-quality incumbent is able to price discriminate while the low-quality entrant sets a uniform price. The incumbent may act as a predator, that is, it may price below its marginal costs on a subset of consumers to induce the rival’s exit. We show that the entrant may adopt an aggressive attitude to make predation unprofitable for the incumbent. In this case predation does not occur and the equilibrium prices are lower than the equilibrium prices which would emerge in a contest of explicitly forbidden predation. Moreover, we show that when the incumbent may choose whether to price discriminate or not before the game starts, if the quality cost function is sufficiently convex, there always exists a parameter space on which the incumbent prefers to commit not to price discriminate.

JEL Classification

D43 L12 L41

Cite As

Stefano Colombo (2009). On the Effects of Selective Below-Cost Pricing in a Vertical Differentiation Model. Economics Discussion Papers, No 2009-25, Kiel Institute for the World Economy. http://www.economics-ejournal.org/economics/discussionpapers/2009-25


Comments and Questions

Anonymous - Generalizations
May 10, 2009 - 08:37

The paper deals with an interesting issue and provides very convincing arguments to show the predatory potential of price discrimination in the framework of a vertical differentiation duopoly. It also shows that an entrant may use sufficiently aggressive pricing to prevent the incumbent from predatory pricing of his product which ...[more]

... in its turn may force the incumbent to commit to uniform pricing in order to avoid such a war.

Although I like the paper and its overall approach to such a policy-relevant issue, I would like to point out that some of the assumptions adopted raise serious concerns about the validity of the results as a guide for real-world policy-making.

1. Quality exogeneity: In most cases, the issue of quality choice is a central one in the vertical differentiation literature. In fact, in the context of an incumbent-entrant duopoly, the quality chosen by the entrant is an important aspect of his strategy when entering into the market. How would these results change (especially, considering the implications of quality choice for the timing of the whole game)?

2. Generality of assumption on consumer preferences: The support of consumer preferences ("taste for quality parameter" ranges between 0 and 1) is bound below from 0. We know that if we adopt an alternative interval ranging from theta to theta+1 and we consider the critique by Wauthy (J.Ind.Econ, 1996) the "interior pricing" equilibrium described in Tirole (1988) may be abandoned in favor of "corner pricing" by the low quality firm, setting its price equal to the lowest valuation of its product in the market (p_L=theta·s_L). In this case, the maximum differentiation principle is substituted by an interior equilibrium, involving positive qualities adopted by both firms (making this a critical issue, should the author wish to extend his analysis to an endogenous quality framework as suggested in my first comment).

3. Technology of quality improvements: The author assumes that quality improvements affect variable costs. An equally relevant strand in the vertical differentiation literature (see, for example, Lutz, Lyon, Maxwell, J.Ind.Econ. 2000) assumes that quality affects fixed costs of production. When choosing one approach or the other, an author should be aware of its consequences on the generality of the results. In fact, recently, Liao (Bull.Eco.Res., 2008) has shown that under fixed costs of quality improvements Tirole's (1988) interior pricing totally disappears in favor of Wauthy's (1996) corner pricing, with all the aformentioned conseqences on the (missing here) quality choice stage.

4. Timing of the game and firms' strategy spaces: Despite a footnote (5) on the choice of each firm's move timing, the author's choice of the two firms' strategy spaces are far from sufficiently motivated. For example, when referring to other papers on asymmetric roles in price discrimination models, we should remember that asymmetry here is double. Becasue one of the two firms is AT THE SAME TIME: 1) entrant, 2) low quality, 3) first mover AND 4) exogenously restricted to uniform pricing. It is obvious that there are are more (asymmetric) combinations than the one considered here and the author should motivate his choice and briefly discuss the consequences of some plausible alternative assumptions. Just to mention a plausible alternative, why not letting the entrant price-discriminate too? It seems to me that this could be relevant for a firm "fighting to survive" against a price-discriminating rival.

Overall, this is a very useful and competently performed analysis on a very interesting issue, which can be easily used as the basis for a more general approach to the role of pricing policies in the determination of market structure.

Stefano Colombo - Reply to generalizations
May 12, 2009 - 09:41

see the attached file

Anonymous - Referee Report
May 14, 2009 - 14:06

Referee Report on:

"On the effects of selective below-cost pricing in a vertical differentiation model"

The author analyses the effects of predation in a vertical differentiation model, where the incumbent faces the entry of a low-quality firm. He shows that the entrant may adopt an aggressive attitude to ...[more]

... make predation unprofitable for the incumbent.

Main Comments

Entry Commitment. The entrant commits to enter the market without knowing the incumbent’s price. It is surprising that the entrant commits to enter at time 0 and later it leaves the market if it obtains non-positive profits.
The author assumes that the entrant sets price before the incumbent and says that it is according to the traditional price discrimination literature. However, he does not quote papers that make this assumption. In Liu and Serfes (2005), firms simultaneously set prices.

Other Comment

• In Introduction, the author quotes the paper Bolton et al., 2000. However, this paper does not appear on references

Stefano Colombo - Reply to Referee Report 1
May 16, 2009 - 17:26

See the attached file

Anonymous - Reply to Author`s Reply
May 29, 2009 - 13:01

see attached file

Stefano Colombo - Reply to Reply to Author`s Reply
June 04, 2009 - 10:08

See the attached file

Anonymous - Referee Report
June 22, 2009 - 08:27

see attached file

Stefano Colombo - Reply to second referee
June 24, 2009 - 14:23

See the attached file

Stefano Colombo - Revised version
June 30, 2009 - 17:20

I attached a revised version of the paper, which takes into account suggestions and criticism by the anonymous reader and the two anonymous referees.

In my previous replies I have already answered separately to each comment I received. In what follows I indicate where in the revised version of ...[more]

... the paper one may find the most relevant corrections suggested by the reader and the referees.

Comments by the anonymous reader:

Points 1&2: see section 5 in the revised version
Point 3: see footnote 3 in the revised version

Comments by the first referee:

Point 5: see p.7 in the revised version
Point 10: see p.6 in the revised version
Point 11: see p.8 in the revised version

Comments by the second referee:

Point 1: see section 2 and 3 in the revised version
Point 2: see section 3 in the revised version
Point 4: section 5 of the previous version has been dropped from the revised version (see also footnote 4 in the revised version)