improve welfare due to a reduction in the costs of decision errors and an improvement in deterrence effects. Furthermore, we noted that the (potentially negative) implications of legal certainty may have been exaggerated. These factors suggest that the welfare gains from adopting effects-based standards could well compensate their higher administrative costs and that, therefore, adopting effects-based standards can be justified for conducts that were previously treated by per se rules.

#### 2.2 The Role of the Substantive Standard (SS)

Where do the considerations examined above and the conclusions reached leave us? Although the above considerations suggest, assuming a welfarist substantive standard, that adopting effects-based standards would be justified, on the grounds of improving welfare, for many conducts that have traditionally been treated as object restrictions, the standards actually adopted remain close to per se and the extent of economic analysis applied by the vast majority of CAs today remains very low.36 This implies that the arguments concerning decision errors, deterrence effects, legal uncertainty and administrative costs, may not be the only, or even the most important, influences in choosing legal standards and the extent of economic analysis in CL enforcement. In practice, other factors may be very important. One is the substantive standard of the authority or the court.37

As noted in some detail in the Introduction, the SS adopted may not be that of consumer or total welfare, and this of course influences the extent of economic analysis and evidence in the assessment of potentially anticompetitive conducts. As explained, even if effects-based legal standards are adopted, the extent of economic analysis used, when the substantive standard is not welfarist,38 would be limited or very limited. To clarify this further we need to take the following into account.

Non-welfarist SS, or non-welfarist liability criteria, can differ from welfarist SS in two ways:

(a) A non-welfarist SS can be one of a continuum of criteria that need to be examined in order to form a judgement about the ultimate welfare criterion. Hence, for example, the criterion of "preservation of competition" or whether the type of conducts/market conditions under consideration have an "exclusionary effects", becomes part of the process of reaching a judgement based on the welfare criterion. However, in the case of the latter, it is necessary to additionally examine whether the conducts could have substantial efficiency effects that in

36There are exceptions to this, such as the US and Canada, but the statement does in fact reflect the reality in the vast majority of other jurisdictions.

37Generally, the CA will recognize, from case law, and adopt the substantive standard that is used by the Courts.

38Such as the preservation of undistorted competition which require that conducts do not make it more difficult for a rival to compete).

many cases might outweigh the potential exclusionary effects and thus increase consumer surplus and efficiency. We believe that the main difference in the liability standard applied in the EU and the US in recent years is of this type.

(b) A non-welfarist SS may be one related to "public interest concerns", which, as mentioned above, have been popular (perhaps increasingly so) in BRICS and developing countries. For example, the SS may focus on non-welfarist criteria such as inequality, employment or international competitiveness. These are not criteria that need to be examined when forming a judgement about the welfare criterion, i.e. they are distinct from the latter. CAs using these non-welfarist liability criteria can adopt per se or effects-based legal standards, in the sense we defined above,39 in order to reach a decision concerning how the examined conducts/market conditions affect the selected criterion. When a CA emphasises a non-welfarist SS of this type then, of course, the extent to which it will rely on competition-related economic analysis and evidence will be very limited.

Focusing below on the case of a type-A non-welfarist SS (N-WSS), this is expected to lead to a limited application of economic analysis and evidence, for two reasons: first, as already mentioned, even if effects-based legal standards are used, under a N-WSS the extent of economic analysis will be limited, compared to the case where a welfarist SS (WSS) is used; second, with a N-WSS the likelihood of the CA adopting a per se standard40 is higher than when the SS is welfarist. Below we explain why these statements are true. We assume that the N-WSS is that of "preserving competition" or whether the specific conduct "is likely to have exclusionary effects41".

To start with, provided allegations that a specific conduct violates the law, we need to start by specifying the general population of conducts to which the specific conduct belongs and, in many cases, the market conditions that are relevant for this type of conducts, according to competition law and precedents42—e.g. the conditions under which dominance exists. Given this population of conducts/market conditions43 we can consider and compare the following alternatives:

39Meaning that with per se standards we rely on making inferences about the effects of a specific conduct from what we already know about the effects of populations of similar conducts; with effects-based standards we do not rely on making such inferences and try to identify the effects by investigating the specific conduct in detail.

40With very limited use of economics.

41Here we interpret the term exclusionary effects as making it more difficult for rivals to compete. 42Strictly speaking, in the case of conducts for which a contextual analysis of market conditions is important, the per se rule is not a "strict per se" rule—the latter being based purely on a presumption

about the characteristics of the conduct. "Modified per se" is a more appropriate term for the case where market conditions are taken into account and it entails the population of conducts/market conditions where a presumption of illegality has to be made. Below we will refer simply to per se rules when considering either "strict per se" or "modified per se" rules.

43Tying-related conduct would be a good example. A number of alternative legal standards have been proposed for their assessment, ranging from per se (illegality) to full effects-based; see, Ahlborn et al. (2004) who favour an intermediate legal standard (structured rule of reason).

From the descriptions above, we first note that if the CA adopts a N-WSS, even if it chooses an effects-based standard (i.e. the above-mentioned alternative N-WSSEB) the extent of the economics applied would be limited relative to using an effectsbased standard under a WSS (i.e. alternative WSSEB). Since, with WSSEB, additional economic analysis will have to be applied, on top of that applied under N-WSSEB, in order to show that the specific conduct does not just have an exclusionary effect, but also reduces CS.

Second, we note that since for the general population of conducts/market conditions the probability of a negative presumed effect on exclusion is higher than that of a negative presumed effect on CS (because the former is a necessary but not a sufficient condition for the latter), we can say that the presumption of illegality is higher under the alternative A.2 (N-WSS—per se) than under the alternative A.1 (WSS—per se), so ceteris paribus, per se is more likely to be favoured under N-WSS. However, we need to examine this in more detail.

Note that under a WSS the CA may prefer WSSTEB to per se (alternative A.3 to A.1), because under the former the presumption of illegality is much greater (presumption of negative effect on CS is stronger for conducts that have exclusionary effects than for all conducts), given the quality (in terms of decision errors) of economic thinking and of models for establishing exclusionary effects under WSSTEB. Let us assume that this is the case.

However, under a N-WSS the CA may well prefer per se to N-WSSEB (i.e. alternative A.2–A.4) because under a per se legal standard the presumption of illegality is stronger with a N-WSS (than under WSS—per se), and the discriminatory quality of economic thinking and models for establishing exclusionary effects is the same under N-WSSEB (alternative A.4) as under WSSTEB (alternative A.3), as

44The alternative SS could be total welfare.

indicated above. Thus, under N-WSS the CA is more likely to choose per se than under WSS. Of course, this would tend to limit the extent of economic and evidence applied in enforcement when the CA uses N-WSS. Indeed, if under a WSS the CA were to prefer to adopt a WSSEB to a WSSTEB (as Rey and Venit (2015), believed should have been the case in the Intel case) then the reduction of the economics applied under a N-WSS (as that adopted in that case by the EU Court and the Commission DG COMP Legal Service) could be substantial.

#### 2.3 The Effect of Reputation on the Choice of Standards

Competition authorities are government or independent organisations that typically have a certain degree of freedom to choose among different possible courses of action. While they are concerned with the welfare benefits that their activities bring to society, they are concerned with how their activities affect their public image and reputation. This is consistent with the widely recognised fact that, in many cases, CAs operate under performance criteria that are not always related to the welfare effects of their enforcement activities.45

Recent work, by Katsoulacos (2017) and by Katsoulacos et al. (2016a, b) influenced by the work of Harrington (2011) and Schinkel et al. (2015), assumes that CAs maximise a utility function that depends both on a composite indicator of enforcement success and the welfare impact of the CA's decisions, given the legal standards on the basis of which these decisions are made. The enforcement success (and thus the utility) of a CA is affected negatively by the decrease in the number of cases that the CA opens and concludes (independently of whether the decisions concern infringements) and by the increase in the number of reversals of its infringement decisions by the courts of appeal. The CA's utility is affected positively by an increase in the welfare impact of its choices related to legal standards. A reputation-maximising CA, which does not take into account the welfare effect of its choice of legal standards, will not have incentive to adopt effects-based standards, which utilise more economic analysis and evidence, when this can lead to an increase in the likelihood that appealed infringement decisions will be annulled by the courts of appeal. On the other hand, welfare-maximising CAs will choose standards that are more effects-based and will be prepared to apply economic analysis and evidence to a greater extent than reputation-maximising CAs.

45The performance criteria used to assess the activities of CAs are extremely heterogeneous. On one side there is the experience of UK's OFT, which is subject to positive impact assessment in order to achieve a target of 5:1 (now 10:1) ratio of benefits to consumers relative to the cost to the taxpayers. On the other side, many authorities still use crude output indicators (e.g. the number of handled cases) or indicators of enforcement success (proportion of decisions supported by the courts) instead of welfare outcome indicators as important performance criteria. At the present, there is still no adequate design for a performance evaluation (Kovacic et al. 2011).

#### 3 A Practical Approach to Choosing Legal Standards that Minimise Decision Errors

Consider a CA (and court) that adopts a welfarist SS, which has to decide whether some conduct by a firm or group of firms violates CL. How should it choose the best legal standard to apply in assessing the conduct in order to minimise decision errors46?

We consider the CA deciding in several stages which standard is appropriate.

Stage 1 Verification and identification of the nature, object (or form) of the conduct; the CA undertakes an investigation that allows it to characterise fully the nature of the conduct.

As a result of this investigation the CA can locate the specific conduct, within a subset/subpopulation of conducts, with similar characteristics to the conduct that is alleged to violate the law, within a general category of potential anti-competitive conducts. Further, at this stage the CA is provided with or can obtain some basic information concerning market characteristics and can identify what established economic theory and available empirical evidence and case law suggest about the specific subpopulation of conducts identified. Based on what is learned in Stage 1, the CA can determine the frequency of (genuinely) harmful conducts bγ, the loss in welfare (negative harm) from falsely condemning benign conduct ( bhB), and the loss in welfare from not condemning harmful conduct bhH, for the subpopulation of conducts to which the conduct is found to belong, i.e. it can form a prior about the fraction of harmful and benign conducts in this subpopulation and the average harm across different potential market characteristics (or environments). ¼ bγbhH þ -b

Thus the CA determines the average harm from this subclass of conducts

2e \widehat{\phantom{a}} \widehat{\phantom{a}} \widehat{\phantom{a}} \text{(or \'en\'ron\'em\'en\'ens).}
$$\text{e average harm from this subclass of conductors}$$

$$\bar{h} = \widehat{\eta}\widehat{h}\_H + \left(1 - \widehat{\gamma}\right)\widehat{h}\_B \tag{1}$$

determining whether the subclass of conducts is presumptively legal or it is presumptively illegal:

presumptively legal (PL): h-< 0

presumptively illegal (PI): h-> 0

Also it can define indicators of the strength of the presumption of legality, sPL (illegality, sPI) as follows47:

46For the remainder of this section we will assume that the choice is made on the grounds of decision-error minimization; we will also neglect all the other considerations that influence this choice (which were examined above).

47See also Katsoulacos and Ulph (2009).

$$\text{Y. Kostousalacos}$$

$$\begin{aligned} s\_{PL} &= \frac{\left(1-\widehat{\gamma}\right)\left(-\widehat{h}\_{B}\right)}{\widehat{\gamma}\widehat{h}\_{h}} > 1\\ s\_{PI} &= \frac{\widehat{\gamma}\widehat{h}\_{h}}{\left(1-\widehat{\gamma}\right)\left(-\widehat{h}\_{V}\right)} > 1 \end{aligned} \tag{2}$$

$$s\_{PL} = \frac{\widehat{\gamma}\widehat{h}\_h}{\widehat{\gamma}\widehat{h}\_h} > 1 \tag{2}$$

$$s\_{PI} = \frac{\widehat{\gamma}\widehat{h}\_h}{\left(1 - \widehat{\gamma}\right)\left(-\widehat{h}\_B\right)} > 1 \tag{3}$$

At the end of Stage 1, the CA can reach a decision on the case without any further investigation, using a per se legality (PSL) standard (thus allowing the conduct), or a per se illegality (PSI) standard (thus disallowing the conduct). This could be appropriate if the strength of the presumption of legality or illegality are very strong, so by using per se the CA can satisfy its standard of proof for establishing its ultimate contention (there is very little risk of substantial decision errors that could justify the use of an effects-based standard that would aim to discriminate whether the conduct in question is benign or harmful). For example, if bγ is close to unity then this would be sufficient to make the strength of the presumption of illegality in Eq. (3) extremely large, something that would justify the use of a per se illegality standard (for example, this is the rationale for using this standard in the case of explicit horizontal price fixing). However, assume that the values of bγ, bhH, bhB are such that the CA does not

b

consider that the strength of the presumption of legality or illegality is sufficiently great to justify (without further analysis) the use of a per se standard—it expects that this could result in too many decision errors. In this case it would need to decide which standard to use by comparing the cost of the decision errors of the alternatives. We can define:

Costs of Decision Errors (CDE) ¼ Costs of False Convictions (CFC) + Costs of False Acquittals (CFA).

In the case of per se, the CDE are:

CDEPSL ¼ CFAPSL ¼ bγbhH ð4Þ -

with a per se legality standard, and:

$$\begin{array}{rcl} \text{CDE} & = \text{CAI} & = \text{\textyen}\_{H} \\\\ \text{standard, and:} \\\\ \text{'} \text{CDE}^{\text{PSI}} = \text{CFC}^{\text{PSI}} & = \left(1 - \hat{\mathcal{\gamma}}\right) \left(-\hat{h}\_{B}\right) \end{array} \tag{5}$$

with a per se illegality standard:

The CA assessment must now move to the second stage.

Stage 2 Detailed identification of the characteristics of the market environment. At the end of Stage 2 the CA may make a decision using a modified per se standard subject to a significant market power (SMP) requirement. This is provided so that the investigation in Stage 2 will allow the CA to revise the values of γ and h. it is assumed that these (revised) values are γ, hH, hB.

The CA can re-determine the average harm and the strength of the presumption of illegality for these revised values of γ and h, and may decide whether it should use a (modified) per se rule subject to SMP (if for example the revised value of γ is very high, it would be justified in using a per se illegality rule on the basis of the strength of the presumption for the restricted subpopulation of firms with SMP). Using a (modified) per se standard subject to a SMP requirement is consistent with the practice of CAs throughout the world (including the US) prior to the mid-1990s, when dealing with a number of business practices undertaken by dominant firms (bundling, royalty rebates, exclusive contracts with distributors, etc.).

However, even in the presence of SMP the CA could well consider the presumption of illegality not high enough to justify the adoption of per se rules and may consider to use an effects-based standard to make its assessment, although this does not imply that the CA would necessarily move to full-blown rule-of-reason. This is the situation relating to the mentioned practices in the US (and some other countries, e.g. Canada and the UK) in the past two decades.

This suggests a third stage of analysis for choosing the appropriate legal standard.

Stage 3 Undertaking an effects-based assessment, which implies showing how, given the market environment, the specific conduct can generate social harm, on the basis of additional economic analysis, modelling and empirical evidence.48 The CA can only identify market characteristics and relate them and the characteristics of the conduct to harm by using economic analysis and evidence with certain errors. Whether or not an effects-based standard should be chosen turns on the comparison of the costs of the decision errors with those of staying with per se, and this requires comparing the strength of presumption of illegality (or legality) with the discriminatory quality of an effects-based economic analysis.

Assuming that if the CA adopts an effects-based (EB-type) standard, it considers that the economic models and evidence it can use for assessing the specific type of conduct will lead to the finding of a law violation with probability β, 0 < β < 1, therefore a finding of no-violation will emerge with probability 1 β. This compares to the CA deciding that there is violation in all cases under a per se illegality standard and deciding that there is violation in none of the cases under a per se legality standard. β is a probability that is much easier to understand and try to estimate (see below) than probabilities associated with the errors that the CA makes when it adopts an EB standard. Also it is important to introduce this probability to capture the intuition that when the conduct is presumptively illegal then the higher β is, the lower the cost will be of decision errors of the EB standard, for any given propensity of this standard to make errors,49 while oppositely, when the conduct is presumptively legal the lower β is, the lower the cost will be of decision errors of the EB standard for any given propensity of this standard to make errors.

Finally, assuming that the CA considers that the following hold, concerning errors in its decisions (to be discussed below):

48At this point we disregard the fact that the CA may choose a truncated or a structured effectsbased standard.

49And therefore, the more likely that the CDE of EB will be lower than the CDE of Per Se—see also comparison below.

At a minimum the discriminatory quality of an EB standard must be such that:

$$
\beta\_H > 1 - \beta\_B
$$

Although, as we will see below, this is not a necessary condition for the CDE of an EB standard to be lower than the CDE of per se standards.

The first thing to note is that the various probabilities are related by the following consistency constraint. For harmful cases:

$$
\beta \beta\_H + (1 - \beta)(1 - \beta\_B) = \chi \tag{6}
$$

and for non-harmful cases:

$$(1 - \beta)\beta\_B + \beta(1 - \beta\_H) = 1 - \gamma \tag{7}$$

These expressions make it clear that if the CA improves its ability to identify correctly harmful conducts, it will have improved its ability to correctly identify benign conducts. They can be used to express the value of βΗ(βΒ), which would satisfy the consistency constraint as follows, given β and γ and βΒ(βΗ):

$$
\beta\_H = \frac{\gamma - (1 - \beta\_B)(1 - \beta)}{\beta}. \tag{8}
$$

$$
\beta\_B = \frac{(1-\chi) - (1-\beta\_H)\beta}{(1-\beta)}.\tag{9}
$$

The CA can infer γ from the investigations it undertook in Stages 1 and 2, of the exact characteristics of the conduct and the characteristics of the market and firm (s) under investigation, and from all the available economic analyses and empirical evidence that is related to this type of conduct.

It can also infer β based on information from its past investigations of this type of conduct (with EB-type standards), and from information of investigations and decisions reached by other authorities worldwide; indeed, the latter is a standard practice used by CAs to examine what other authorities have done in similar cases. Note that given γ and β, the CA has to form judgment about either βΗ or βΒ, in order to infer the value of the other (given the consistency constraints).

From Eqs. (8) and (9), for βΗ 0 and βΒ 0:

$$(1 - \beta) + \beta \beta\_H \ge \chi \ge (1 - \beta)(1 - \beta\_B) \tag{10}$$

Or, given β and γ, for βΗ 0,

Considerations Determining the Extent of Economic Analysis and the... 149

$$
\beta\_B \ge \frac{(1-\beta)-\chi}{(1-\beta)}\tag{11}
$$

and for βΒ 0,

$$
\beta\_H \ge \frac{\gamma - (1 - \beta)}{\beta} \tag{12}
$$

#### Comparison of Costs of Decision Errors

The CDE of the EB standard is given by the following expression:

$$CEE^{EB} = CFA^{EB} + CFC^{EB} \tag{13}$$

so:

$$CDE^{EB} = (1 - \beta)(1 - \beta\_{\rm B})\gamma h\_H + \beta(1 - \beta\_{\rm H})(1 - \gamma)(-h\_{\rm B})\tag{14}$$

Let

$$m = \frac{h\_H}{(-h\_B)}$$

(i) By comparing the CDE under EB and per se we come to: for conducts considered to be presumptively legal (PL):

$$CDE^{EB} < CDE^{PSL}$$

iff:

$$q^{EB,PL} + \frac{1}{(1 - \beta\_H)} > \frac{(1 - \gamma)(-h\_B)}{\gamma h\_H} = \frac{(1 - \gamma)}{m\gamma} = s^{PL} \quad q^{EB,PL} = \frac{(1 - \beta)\beta\_B}{\beta(1 - \beta\_H)} \tag{15}$$

where qEB, PL is an indicator of the discriminatory quality of the EB standard under PL (ratio of the probability of not finding to the probability of finding that there is violation of competition law when the conduct is benign);

(ii) for conducts considered to be presumptively illegal (PI):

$$CDE^{EB} < CDE^{PSI}$$

iff:

$$q^{EB,PI} + \frac{1}{(1 - \beta\_B)} > \frac{\gamma h\_H}{(1 - \gamma)(-h\_B)} = \frac{\gamma m}{(1 - \gamma)} = s^{PI} \tag{16}$$

where

$$q^{EB,PI} = \frac{\beta \beta\_H}{(1 - \beta)(1 - \beta\_B)}\tag{17}$$

is an indicator of the discriminatory quality of the EB standard under PI (ratio of the probability of finding to the probability of not-finding violation when the conduct is harmful).

Results and Observations:

It is straightforward to produce simulations based on the above expressions, which would allow a CA to use the above formulas in practice, in order to decide which standard minimises decision errors. Here is an example.

Assuming that the CA believes that γ is likely to be around 0.6, and that hH is likely to be twice hB (m ¼ 2). The conduct is considered quite strongly presumptively illegal (authors addressing tying arrangements by dominant firms would consider lower values for γ—see Ahlborn et al. (2004); on the other hand, for RPM a much higher value may be appropriate50). The strength of the CA's presumption can be measured by s PI, which is s PI ¼ 3.

Assume also that given the information available to the CA (as mentioned above), it is believed that β ¼ 0.8.

From Eq. (8), for βB ¼ 0 the value of βH is βH ¼ 0, 5. As βB increases the value of βH increases, and βH ¼ 0, 75 when βB ¼ 1. From Eq. (16), we can see that EB is superior in CDE terms even for the lowest βB and βH values, βB ¼ 0 and βH ¼ 0, 5, so it is superior for all βB and βH values that are consistent with the "more objectively" identified values of β and γ.

If the strength of the PI is higher, e.g. γ ¼ 0.8, and β is lower, e.g. β ¼ 0.6, then for βB ¼ 0 the value of βH is βH ¼ 0, 666 and as βB increases the value of βH increases and βH ¼ 1 when βB ¼ 0, 5. Now with βB ¼ 0 and βH ¼ 0, 666, the CDE under EB are less than under per se; it is only when βB > 0, 2 and βH > 0, 8 that the CDE of EB become lower than those under per se. However, if β ¼ 0.9 then even with βB and βH values at the lowest end of the relevant ranges, the EB standard will have lower CDE than the per se standards.

The argument here is that if the CA can obtain the information and knowledge required to identify β, γ and m, then it can use these to examine for which ranges of βB and βH values the CDE of EB standards is lower than under per se. If these are "reasonable" in the sense that even at low βB and βH values in the relevant ranges the CDE is lower under EB, then the CA has a very strong case for using EB.

#### 4 Concluding Remarks

We have examined the factors influencing the choice of legal standards, and hence determining the extent of economic analysis and evidence applied in competition law enforcement, focusing on recent economic literature. We have emphasised the analytical and practical usefulness of viewing legal standards as a continuum between strict per se and rule-of-reason. We have suggested explanations of why the decisions of CAs in relation to the utilization of economic evidence may well diverge from social welfare-maximising decisions. We have emphasised the very significant, but still underexplored, role played by the choice of substantive standards on whether per se or effects-based legal standards are adopted, and on the extent that economic analysis is utilised. We have also proposed a practical methodology that can be used by CAs for identifying which legal standards minimise decision errors in the assessment of specific conducts.

50See for example Katsoulacos and Ulph (2009), Section V.

Acknowledgement The author is grateful to the participants of the International Conference on Institution Building of the Competition Authorities in South East Europe for many helpful comments and suggestions. The author is also grateful, for the helpful discussions on the subject of this article, to Svetlana Avdasheva, Svetlana Golovaneva, Joe Harrington, Frederic Jenny, Eleni Metsiou and David Ulph.

#### References

Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

## Three Economist's Tools for Antitrust Analysis: A Non-technical Introduction

Russell Pittman

#### 1 Introduction

The importance of economics to the analysis and enforcement of competition policy and law has increased tremendously in the developed market economies in the past 40 years. In younger and developing market economies, competition law itself has a history of 20–25 years at most—sometimes much less—and economic tools that have proven useful to competition law enforcement in developed market economies in focusing investigations and in assisting decision makers in distinguishing central from secondary issues are inevitably less well understood. While agencies and enforcers face a steep learning curve regarding these tools, companies and their attorneys and economic consultants are already using them to present agencies with sophisticated economic analyses purporting to demonstrate the lack of cause for concern regarding particular deals or practices.

This paper presents a non-technical introduction to three economic tools that have become widespread in competition law enforcement in general and in the analysis of proposed mergers in particular: critical loss analysis, upward pricing pressure, and the vertical arithmetic. The first is used primarily in the context of horizontal mergers for both market definition and the analysis of potential competitive effects from the merger, while the second and third are used primarily in the analysis of potential competitive effects, the second in horizontal mergers and the third in vertical mergers. All three are discussed extensively by now in the economics and legal literature, so that an introduction inevitably gives inadequate attention to some corollaries and complexities.

R. Pittman

155

Antitrust Division, U.S. Department of Justice, Washington, DC, USA

Kyiv School of Economics, Kyiv, Ukraine

New Economic School, Moscow, Russia e-mail<EMAIL_ADDRESS>
This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2018

B. Begović, D. V. Popović (eds.), Competition Authorities in South Eastern Europe, Contributions to Economics, https://doi.org/10.1007/978-3-319-76644-7\_9

#### 2 Critical Loss Analysis

Critical Loss Analysis (CLA) was introduced in 1989 (Harris and Simons 1989) primarily as a tool for market definition in merger investigations and has been used extensively since then in the analysis of both product markets and geographic markets. Subsequently it began to be applied, with appropriate amendments, to the analysis of competitive effects of mergers as well, with a focus on the analysis of the unilateral effects of mergers in markets with differentiated products. We will consider the two applications in that order.

### 2.1 Critical Loss Analysis for Market Definition

The standard methodology for market definition in merger analysis begins with the "hypothetical monopolist test": whether "a hypothetical profit-maximizing firm, not subject to price regulation, that was the only present and future seller of ... [a set of products] likely would impose at least a small but significant and non-transitory increase in price ('SSNIP') on at least one product in the market ..." (U.S. Department of Justice and Federal Trade Commission 2010). Even the broad implementation of this test requires the analyst to make a number of detailed choices and assumptions—some of which will be considered later—but for now let us make the exercise more straightforward by assuming that the hypothetical monopolist is restricted to charging a single price to all potential customers. (Note that this is a conservative assumption, in that it renders the analysis less likely to satisfy the test, since we are restricting the ability of the hypothetical monopolist to set the prices of each good at its profit-maximizing level.)

Algebraically, we assume that industry profits are currently set as:

$$
\Pi\_0 = (\mathbf{P}\_0 - \mathbf{C})\mathbf{Q}\_0 \tag{1}
$$

where fixed costs are assumed sunk and irrelevant in the short term and marginal costs C are assumed constant, i.e. equal to average costs. The hypothetical monopolist of the industry would consider increasing price according to the following equation:

$$
\Pi\_1 = (\mathbf{P}\_0 + \Delta P - \mathbf{C})(\mathbf{Q}\_0 - \Delta \mathbf{Q}) \tag{2}
$$

and the critical issue is:

$$(\mathbf{P}\_0 + \Delta P - \mathbf{C})(\mathbf{Q}\_0 - \Delta \mathbf{Q}) \not\approx (\mathbf{P}\_0 - \mathbf{C})\mathbf{Q}\_0\tag{3}$$

Does the increase in profit from the price increase ΔP on the sales that remain outweigh the reduction in profit resulting from the loss of sales ΔQ? Simple algebra reveals the "critical loss" of output that would make the monopolist indifferent:

$$\frac{\Delta \mathcal{Q}}{\mathcal{Q}} = \frac{\Delta P/P}{M + \Delta P/P} \tag{4}$$

where M ¼ (P0-C)/P0, the existing price-cost margin. If the loss of sales ΔQ resulting from the increase in price ΔP is higher than that which satisfies this equation, the price increase would not be profitable.

Of course, if we knew the elasticity of demand for the product, we would know the ΔQ/Q that would result from a given ΔP/P, and no further analysis would be required to answer the market definition question. But let's assume that we are early in an investigation, without the data required for estimating such a parameter. Then the critical loss calculation described above serves to frame a very specific question: if price increases by a certain amount, how much would demand fall? And in particular, where would it "go"? Or, in the language of the CLA literature, now that we know the "critical loss", what would be the "actual loss"?

Consider now a hypothetical merger investigation, and the information that might be available early in the investigation to the analyst at the antimonopoly agency seeking to answer the market definition question.1 Suppose that the analyst has the following information, considered inexact but reasonably reliable.

Now suppose that firms W and X propose to merge, and our analyst wants first to analyze whether the product sold by these firms constitutes a relevant product market. Using the hypothetical monopolist test along with CLA, the question may be formulated as follows: would a hypothetical monopolist of this product raise prices by a SSNIP, say 5%?

Using the prices and costs of the merging firms shown in Table 1, and assuming that these represent the prices and costs of a hypothetical monopolist, we see that a price increase of 5% would equal \$2.50, so that the monopolist would gain \$2.50 on each unit still sold, but would lose \$50-\$30 ¼ \$20 on each unit sale lost. Thus ΔP/ P ¼ 5% and M ¼ \$20/\$50 ¼ 40%. Then the critical loss for determining whether the price increase would be profitable is ΔQ/Q ¼ 5/(40 + 5) ¼ 1/9 ¼ 11%. We therefore have the following question to investigate: if a hypothetical monopolist provider of this product raised price from \$50 to \$52.50, would sales be reduced by as much as 11%? And in particular—focusing on the demand side, as is the practice in US enforcement—to what other products might consumers of these products switch?

1 Examples of the use of critical loss analysis in US and EC merger investigations are presented in Langenfeld and Li (2001), O'Brien and Wickelgren (2003), Amelio et al. (2008), and Hüschelrath (2009).

The relevant product market question asks to what degree customers will substitute away from the product in response to the price increase. Are there other products that are imperfect substitutes for this product but would become more attractive following a price increase? If the product is a consumer good, are consumers likely to be highly sensitive to price increases and to reduce their purchases of this good, allocating more of their budgets to other consumer goods, whether close substitute goods or unrelated goods? If the product is a producer good, are the firms that use this product as an input into the production of other goods able to substitute other inputs in the production process, and/or will they suffer their own losses of sales if forced to "pass through" this price increase of an input?

This is the basic version of CLA. It does no more and no less than focus the attention of the analyst on the precise (or somewhat precise, as will be discussed) question of how much substitution away from the products in the provisional product market would be necessary to defeat a potential anticompetitive price increase, and thus whether this choice of provisional product market represents the state of competition in the world as it exists or whether the provisional product market must be expanded to include the next closest substitute to constitute an actual market.

Once having identified the relevant product, a similar analysis would be applicable to the definition of geographic markets. To test whether the area that includes only the four firms in Table 1 is a relevant geographic market, for example, observe that the critical loss of 11% of their collective sales of 243 units is 27 units. If the hypothetical monopolist that raises price from \$50 to \$52.50 would lose sales of fewer than 27 units to producers outside of that area, the test is satisfied. If it would lose more than 27 sales, the area must be expanded to include those rivals to which purchasers switched. A number of variations and complications to this simple story should be considered.

#### 2.1.1 Implicit Elasticities

In practice, the merging parties (and/or their lawyers and consultants) may argue that existing price-cost margins that look "high" suggest that a hypothetical monopolist would be unlikely to raise price much from its current level; after all, the argument may go, each unit lost in a reduction of output loses the entire existing margin—\$20 in our example—and the hypothetical monopolist would have to lose only a small amount of sales in order to regret its decision to impose a SSNIP.

However, as a theoretical matter, as Katz and Shapiro (2003), O'Brien and Wickelgren (2003), and Kaplow and Shapiro (2007) have pointed out, the estimated price-cost margin potentially contains information about the elasticity of demand facing the firms in the industry. According to the well-known Lerner Index, a profitmaximizing firm sets price where the price-cost margin equals the negative reciprocal of the elasticity of demand that it faces. In our example, the existing firms are earning profits of 40%, which implies a firm-level demand elasticity of -2.5.  Thus a high operating margin, which implies a critical loss sufficiently small that merging firms may argue that it is unlikely to be realized, at the same time implies a small actual loss, since only firms facing a demand curve with relatively low elasticity could set prices and margins so high.2 As Katz and Shapiro (2003) summarize it, "A high gross margin implies a small critical loss. But a high gross margin also tends to indicate a small actual loss."

#### 2.1.2 Cost Estimates: Marginal vs. Variable, Constant vs. Fixed

The profit maximization derivations on which both the CLA and the Lerner Index are based use the margin between price (or sometimes marginal revenue) and marginal cost to analyze the incentives of either individual firms or the hypothetical monopolist. In general, however, business firms do not calculate "marginal cost" in the ordinary course of business; rather, they usually calculate "variable cost", and though empirical analysts often use the latter as a proxy for the former, there are good reasons, both conceptual and practical, why the two are not likely to be identical.

First of all, from a pure measurement standpoint, Fisher and McGowan (1983) and Fisher (1987) demonstrate just how different the accountants' treatment of factors such as advertising, research and development, and other typical fixed costs can be from the economists' definitions. A separate measurement issue concerns the multiproduct nature of most firms; even the most careful business accounts may not be kept at the level of individual products.

Second, and more conceptually, as noted by Carlton and Perloff (2005) and Pittman (2009), true marginal cost as the first derivative of total cost includes at least implicitly a rental value of capital, and this term may become especially important as firm and/or industry production approaches capacity. An inquiry into the likely effect of a SSNIP that does not factor in the possibility of a rising marginal cost curve—which of course we observe in any intermediate microeconomics text may underestimate the attractiveness to the firm of reducing output, and therefore too quickly reject the proposition that a hypothetical monopolist would find it profitable to increase price and reduce output. Simons and Coate (2014) argue the related point that firms making decisions regarding profit maximization in the long term will not generally base their thinking on short run marginal costs, even if measured accurately.

Werden (2005) and Baumann and Godek (2009) also note that the issue is broader than just the distinction between (theoretical) marginal and (measured) variable cost. Even if marginal cost is measured accurately, by variable cost or otherwise, the assumption that it is constant over the range of output choices of firms and the

2 As the Horizontal Merger Guidelines point out in Sect. 2.2.1, a high operating margin may also be an indicator of existing coordination among the firms in the market.

hypothetical monopolist may need to be examined. Approaching capacity limitations may be one factor; another may be differences in costs across firms, such that the hypothetical monopolist might not only raise price but also reduce output asymmetrically, focusing on cancelling production shifts at more expensive plants or even closing them down. To the extent that these complications lead the analyst to underestimate the marginal cost savings of lost sales, a price increase by the hypothetical monopolist will appear less profitable.

#### 2.1.3 The SSNIP

As emphasized by Werden (2005, 2008), the details of the assumption of a SSNIP as usually practiced in the market definition exercise may be misleading in at least two ways, and these two may interact. First, the Guidelines ask whether a hypothetical monopolist would likely impose a SSNIP—a profit maximization question whereas the more common practice is to analyze whether the hypothetical monopolist could profitably impose a SSNIP—a break-even analysis. The latter interpretation has the distinct advantage of not requiring the analyst to make assumptions about the shape of the demand curve in the industry (Langenfeld and Li 2001), but it may affect the conclusion nonetheless.

In particular, a break-even analysis of a "small" price increase—say 5% or 10%, the usual choices—may miss the possibility that a firm or hypothetical monopolist facing customers with varying elasticities of demand might find it unprofitable to raise price by a small amount that keeps most customers in the market regardless of their elasticity of demand, but find it profitable to raise price a great deal more such that elastic demanders are priced out of the market while inelastic demanders pay the higher prices (Werden 2005, 2008). Rejecting the profitability of a small price increase can lead to a decision to expand the size of the provisional market, when examining the profitability of a larger price increase might lead to the conclusion that the original provisional market was correct after all.

The analyst who finds that the application of a break-even SSNIP leads to a rejection of the provisional market definition may therefore want to check the robustness of this result by asking whether there are customers of the product with significantly different elasticities of demand. Are there customers with demand so inelastic that selling to them only, at an even higher price, would be a profitable strategy for the hypothetical monopolist? At this point, of course, one is moving away from the appealing simplicity of the break-even test.

#### 2.1.4 Market Definition Is Not the Whole Story

It perhaps goes without saying—but we will say it—that market definition is not the whole story in merger analysis. In particular, market definition, especially as practiced in the US, is focused on the demand side—purchaser preferences and switching behavior. But in many investigations the supply side—including the strategic responses of rival firms—may also be important. In EU practice, some of this supply-side analysis is included in the market definition exercise, while in US practice most of it is subsumed under the rubric of the potential for entry by other firms into the product and geographic market.3

In our example, on the supply side the analyst would be asking questions like the following: Are there producers outside of the market that might reposition themselves (either in product or geographic space) such that customers could easily switch to new suppliers without losing much in the way of either utility or efficiency? Are imports (from other domestic geographic areas or from foreign companies) poised to enter the market, and are there good reasons like transportation costs, tariffs, or quotas that would limit the scope or scale of their entry? If these imported products are not being purchased by customers now, there may be good reasons why they would remain unpurchased even following a SSNIP.

#### 2.2 Critical Loss Analysis for Unilateral Effects Analysis

CLA is used not only in market definition but also in competitive effects (and especially unilateral effects) analysis. In this case the algebra of the derivation of the critical loss becomes a bit more complicated, and the introduction of an important new term is required.

In particular, let us return to the industry setting of Table 1, but now instead of analyzing whether it would be profitable for a hypothetical monopolist of the entire industry to increase price by a SSNIP, we analyze whether the merger of two firms, say firms W and X, would provide the merged firm with the unilateral incentive to increase its own price only. We will simplify the analysis by considering the question of whether it would be profitable to increase the price of the good produced by firm W only; clearly the merged firm would consider the profitability of increasing the price of the goods produced by both firms.

Before the merger, firm W sets prices according to the same profit-maximization principles as the hypothetical monopolist, according to Eqs. (1)–(4), above. Prices were increased until just the point at which the loss in sales—both to other firms in the market and to the rest of the economy—outweighed the benefits of higher prices. After the merger, however, some of the losses from a price increase for the product of firm W are newly internalized by the firm—they are "recaptured" by firm X, now under the same control as firm W. Thus we have a new factor in the calculations, the

3 See the Horizontal Merger Guidelines of the U.S. Department of Justice and Federal Trade Commission, August 19, 2010, at §4: "Market definition focuses solely on demand substitution factors, i.e., on customers' ability and willingness to substitute away from one product to another in response to a price increase or a corresponding non-price change such as a reduction in product quality or service. The responsive actions of suppliers are also important in competitive analysis. They are considered in these Guidelines in the sections addressing the identification of market participants, the measurement of market shares, the analysis of competitive effects, and entry."

diversion ratio DWX, the share of the sales of W that are lost as the result of a price increase for W that are "recaptured" by firm X (Willig 1991; Shapiro 1996, 2010).

Thus the profit-maximization question facing the merged firm as it considers whether and by how much to raise the price of good W is now:

$$\begin{array}{l} (\mathbf{P\_W} + \Delta \mathbf{P\_W} - \mathbf{C\_W})(\mathbf{Q\_W} - \Delta \mathbf{Q\_W}) + (\mathbf{P\_X} - \mathbf{C\_X})(\mathbf{Q\_X} + \Delta \mathbf{Q\_W} \mathbf{D\_{WX}}) \not{\gtrless} (\mathbf{P\_W} \\\ - \mathbf{C\_W})\mathbf{Q\_W} + (\mathbf{P\_X} - \mathbf{C\_X})\mathbf{Q\_X} \end{array} \tag{5}$$

where ΔQWDWX ¼ ΔQX.

As with Eqs. (3) and (4), this translates into the critical loss of quantity W for the merged firm to raise price on good W (Langenfeld and Li 2001; Hüschelrath 2009):

$$\begin{array}{l} \Delta \mathbf{Q\_W} / \mathbf{Q\_W} \lessapprox (\Delta P\_{\mathbf{W}} / \mathbf{P\_W}) / \left[ (\mathbf{P\_W} - \mathbf{C\_W}) + (\Delta P\_{\mathbf{W}} / \mathbf{P\_W}) - (\mathbf{P\_X} - \mathbf{C\_X}) \right] \\ \times (\mathbf{P\_X} / \mathbf{P\_W}) \mathbf{D\_{WX}} \end{array} \tag{6}$$

Comparing Eq. (4)—as interpreted for a single profit-maximizing firm premerger—and Eq. (6)—the calculation for the firm after merging with a competitor—shows that the difference is the last term in the denominator on the right-handside—and that because this is the subtraction of the product of three positive terms, it will tend to increase the size of the critical loss that would make a price increase unprofitable. Note also something that we will return to in the next section: the increase in the critical loss for good W following the merger—and thus the increase in the incentive of its producer to increase price—is a positive function of (a) the margin earned on the second good X, (b) the ratio of the price of the second good X to the first good W, and (c) the diversion ration of W to X—the percentage of sales of good W lost by a price increase that are recaptured by good X, now owned by the same firm.

#### 3 Upward Pricing Pressure

Upward Pricing Pressure (UPP) might be considered a first cousin to the use of critical loss in the analysis of the unilateral effects of a proposed merger, with, among other wrinkles, a more direct focus on the potential efficiencies of the proposed merger and whether they are likely to outweigh the loss of competition in the price-setting of the merged firm.

In the previous section of the paper, we abstracted from the distinction between homogeneous and differentiated products, assuming that all firms charged the same price but that a single firm had the option to charge a different price. In this section we abandon this abstraction and embrace the distinction between these two types of goods that was such an important part of the revised Merger Guidelines in 1992. As Shapiro (2010) discusses at length, while the 1982 and 1984 Guidelines focused on the danger that a merger among competitors would increase the likelihood of collusion—either explicit or tacit—in the more concentrated market, thus focusing implicitly on homogeneous products, the 1992 Guidelines added a second focus on the likelihood that a merger among competitors producing differentiated products would provide incentives for the merged firm to raise price unilaterally, regardless of the behavior of competitors in response.

Thus a new emphasis was placed on the degree to which competing products were close or distant substitutes to each other—a concept implemented in the term that we introduced in the previous section, the diversion ratio DWX between two firms W and X, the percentage of sales of good W lost in response to a price change for good W that are "diverted" to good X. A larger value for this diversion ratio DWX clearly suggested a merger that would be more troublesome from a competitive standpoint, ceteris paribus.

However, the 1992 Guidelines, along with the subsequent literature, simultaneously added a new focus on another term in the denominator of Eq. (6): the pricecost margin earned in the production of good X. If this margin were "high", especially vis-à-vis the margin earned in the production of good W, the merged firm would be quite happy for sales of W to be diverted to sales of X; not so much if the margin earned on the production of X were "low". Thus increased attention came to be focused on the product DWX(PX – CX), the value to the merged firm of sales of W that were diverted by the price increase for W to sales of X, a parameter termed the "Gross Upward Pricing Pressure Index" (GUPPI) from the merger (Farrell and Shapiro 2010a; Moresi 2010). A corresponding term was calculated and considered for the merged firm's incentive to increase the price of good X.

#### 3.1 How to Use GUPPI?

But how are we to interpret and use GUPPI? Any non-zero diversion from W to X accompanied by any non-zero margin on X would yield a positive value for GUPPI. One option would be to proceed with the CLA described in Sect. 2.2 above for the analysis of unilateral merger effects, plugging an estimated value for GUPPI into Eq. (6). Again, for an evaluation of the impact of the merger one would also perform the exercise in reverse, analyzing the incentives created by the merger for a unilateral increase in the price of X, taking account of recapture in the sale of W through the corresponding diversion ratio DXW.

A second option would be to use GUPPI to calculate the likely price impact of the merger directly, abstracting from any possible efficiencies from the merger. Farrell and Shapiro (2010b) and Hausman et al. (2011) provide formulas for doing so that rely on the assumptions of a linear demand curve and symmetric cross-price elasticities of demand along with estimated values for six parameters: the prices and margins for the two goods and the two diversion ratios.

For good W, the post-merger profit-maximizing price change equals the following:

$$
\Delta P\_{\rm W}/\text{P}\_{\rm W} = \left[\text{D}\_{\rm WX}(\text{P}\_{\rm X} - \text{C}\_{\rm X}) + \text{D}\_{\rm WX}\text{D}\_{\rm XW}(\text{P}\_{\rm W} - \text{C}\_{\rm W})\right] / \left[2(1 - \text{D}\_{\rm WX}\text{D}\_{\rm XW})\text{P}\_{\rm W}\right] \tag{7}
$$

and correspondingly for good X. Again, what the formula makes most clear is one of the most important additions of the 1992 Guidelines to the 1982 and 1984 Guidelines: a significant incentive to increase price post-merger requires not only significant diversion ratios but also significant operating margins on the good or goods to which demand is diverted.

Figure 1 shows makes this point graphically. A price increase for the first good moves out the demand curve for the second good. The "value of diverted sales" is the rectangle that represents the product of (a) the volume of diversion from the first good to the second and (b) the margin earned on the second. Only if both the base and the height of the rectangle are of non-trivial magnitudes is the area of the rectangle "large".

Finally, as demonstrated in Werden (1996), information on diversion ratios and margins may be used to estimate the merger-specific marginal cost reductions ("efficiencies") that would be required to counterbalance the upward pricing pressure generated directly by the merger and so create a situation of unchanged pricing incentives for the merged firm.

#### 3.2 GUPPI to UPP

A cousin of GUPPI is UPP, Upward Pricing Pressure, which adds estimates of postmerger marginal cost savings to the GUPPI calculations in order to calculate a measure of the "net" (of claimed or predicted efficiencies) incentives for the merged firm to increase prices. As suggested by Farrell and Shapiro (2010a) and then presented explicitly by both Farrell and Shapiro (2010b) and Schmalensee (2009), requiring now not only the assumption of linear demand curves but also estimates for the product-specific diversion ratios, prices and marginal costs, and claimed/ predicted reductions in marginal cost, the formula for merger UPP for good W is as follows:

$$
\Delta P\_{\rm W}/P\_{\rm W} = \left\{ \left[ 2\mathbf{D}\_{\rm WX}(\mathbf{P}\_{\rm X} - \mathbf{C}\_{\rm X}) - \mathbf{E}\_{\rm X} \left( 1 - (\mathbf{P}\_{\rm X} - \mathbf{C}\_{\rm X})(\mathbf{D}\_{\rm XW} - \mathbf{D}\_{\rm WX}) \right) \right] \right. \\
$$

$$
(\mathbf{P}\_{\rm X}/\mathbf{P}\_{\rm W}) + \mathbf{D}\_{\rm XW}(\mathbf{D}\_{\rm XW} + \mathbf{D}\_{\rm WX})(\mathbf{P}\_{\rm W} - \mathbf{C}\_{\rm W}) - \mathbf{E}\_{\rm W}[1 - (\mathbf{P}\_{\rm W} - \mathbf{C}\_{\rm W})(\mathbf{D}\_{\rm WX} - \mathbf{D}\_{\rm WX})]
$$

$$
$$

Again, there is a symmetric formula for the "upward pricing pressure" created by the merger for good X.

#### 3.3 The Diversion Ratio

Of course, a key requirement for making use of all these concepts is the estimation of diversion ratios. Unlike prices and (variable if not marginal) costs, these are not to be found in the account books kept by the companies. How, short of complex econometric estimation, might these be approximated by the competition agency analyst?

A straightforward approach, often treated as a sort of default option, is to use the shares of competitors in a candidate or provisional market to estimate diversion ratios (Willig 1991; Shapiro 2010). In our numerical example outlined above, if we consider firms W, X, Y, and Z as the competitors in our candidate market, firms X, Y, and Z have 56%, 23%, and 21% respectively of non-W sales. Since these market shares reflect the preferences and choices of existing consumers in the market place, we might assume that those same preferences would drive diversion in these proportions in reaction to a price increase on good W. This approach is based on a number of assumptions (Willig 1991; Rybnicek and Onken 2016), including that we have an idea as to market definition—the latter a requirement that UPP analysis is designed in part to obviate (Farrell and Shapiro 2010a).

But there are often other good sources of information to guide the analyst in both evaluating the accuracy of market shares as indicators of diversion ratios and in judging how these estimates of diversion ratios might be adjusted to better reflect market realities. As Farrell and Shapiro (2010a) note:

The diversion ratio might be estimated using evidence generated in the merging firms' normal course of business. Firms often track diversion ratios in the form of who they are losing business to, or who they can win business from. Consumer surveys can also illuminate diversion ratios, as can information about customer switching patterns (p. 18, footnote omitted).

In particular, interviews with, and documents supplied by, customers of the firms may yield subjective but informative information as to the particular qualities of differentiated products that make each a closer or more distant substitute for others as well as objective reports of past switching events and their rationales. In the latter respect, "natural experiments" may be especially informative: when product W became temporarily unavailable because of labor or transportation problems, what did its usual customers do in response? These additional sources of information can allow the analyst to calculate diversion ratios from an independent source or to better evaluate the diversion ratios estimated via market shares.

Finally, any estimates based on the within-market shares of diverted sales may be tempered by the recognition that some of the demand for good W will leave the market entirely in response to a price increase—thus each firm-level estimate may be multiplied by a factor that reflects the "aggregate diversion ratio"—the "fraction of the units that would be lost by an individual firm that are retained by the hypothetical monopolist" (Farrell and Shapiro 2010b).

#### 3.4 The Limits of UPP and GUPPI

As noted above, both UPP and GUPPI may be used as indicators of the degree of competition likely to be lost from a merger; to provide a forecast of post-merger price increases by the merged firm; or to calculate the magnitude of merger-induced "efficiencies" necessary to remove the incentive for price increases following the merger. UPP and GUPPI, like critical loss analysis, are tools that focus attention on particular issues and factors that affect the profitability of a price increase by either a hypothetical monopolist (in market definition) or the merged firm (in unilateral effects analysis).4

That being said, it is also important to keep in mind that conclusions based on UPP and GUPPI—and CLA—are strongest when the analyst has also assessed the validity of the underlying assumptions as well as other questions not directly addressed by these tools. As one important example, none of these takes account of the possibility of the reactions of other firms to the possible price changes imposed by the merged firm. Such reactions could render the proposed merger either more or less harmful to competition and customers. For example, if competitors "accommodated" post-merger price increases by increasing their own prices, the merger harm

4 Baltzopoulos et al. (2015) discuss the use of UPP in five recent cases reviewed by Konkurrensverket, the Swedish Competition Authority.

would be increased. On the other hand, if competitors repositioned their products in order to be closer substitutes to the products of the merged firm, that could increase the diversion to rivals, reducing the incentive for price increases and the harm to competition from the merger (Pakes 2010; Cheung 2016).5

#### 4 The Vertical Arithmetic

Consider a proposed merger that is vertical rather than (or in addition to) horizontal. Consider, for example, a proposal by a manufacturer to purchase its supplier of a crucial raw material. How much should the antimonopoly agency be concerned about a loss to competition? In particular—though, as we will discuss below, the problem is potentially more general—how much should the agency be concerned about the potential for post-merger anticompetitive "foreclosure"—that is, the denial of access to important inputs to competing manufacturers?6

It is common in such a situation for competing manufacturers to contact the competition authority to express their concerns that if the raw material supplier comes under control of their manufacturing competitor, they will be discriminated against in supply in the future, whether with regard to price, service, or product availability. The reply from the merging firms will likely be that they would only be hurting themselves by treating a customer badly. How is one to evaluate the tradeoff that would face the newly merged, vertically integrated firm?

One analytical tool which could be presented to the competition authority by either party is a technique called the "vertical arithmetic" (Riordan and Salop 1995; Sibley and Doane 2002; CRA 2005; Moresi and Salop 2013).7 As with critical loss analysis and upward pricing pressure, the vertical arithmetic offers no magical

5 As Pakes (2010) also points out, there could also be post-merger repositioning by one or both of the merging firms, and this could either increase or decrease the harm to competition that would otherwise take place.

6 Of course, a proposed vertical merger could also raise the possibility of the foreclosure of access to downstream customers from an upstream competitor—what Riordan and Salop (1995) and Baker (2011) term "customer foreclosure". Or, as in the case analyzed by Baker, it could raise both issues simultaneously.

7 An interesting application was the analysis by Ofcom, the UK communications regulator, of the incentives of the British Sky Broadcasting Group to deny access to premium channels to its downstream competitors such as Virgin Media. For the Ofcom analysis, see especially https:// www.ofcom.org.uk/\_\_data/assets/pdf\_file/0014/40451/annex8.pdf; for the Sky responses see https://www.ofcom.org.uk/\_\_data/assets/pdf\_file/0022/36616/1\_sky.pdf and https://www.ofcom. org.uk/\_\_data/assets/pdf\_file/0021/50925/10\_sky\_annex\_7.pdf. Application in a case brought by the FCC, the US telecommunications regulator, regarding similar issues in the proposed Comcast/ NBCU merger is discussed in Baker (2011) and Baker et al. (2011), while application in a case brought by the Antitrust Division of the Justice Department, the proposed acquisition of the direct broadcast satellite assets of the News Corporation and MCI by Primestar, is discussed in Salop et al. (1998) and Rubinfeld (2000).

#### Fig. 2 A vertical merger

solutions, but it can be useful in focusing the competitive analysis on particular questions and issues.

Consider then a steel manufacturer A that is proposing to acquire its supplier of iron ore, as in Fig. 2. Assume that "steel" constitutes an antitrust product market; if the two firms both produced, say, "cold rolled steel", we would want to examine competition and foreclosure issues in that narrower potential product market instead or in addition to the broader one.

Let M1 equal the percentage profit margin earned by the iron ore company in its sales to steel manufacturers A and B (we assume equal margins for sales to the two customers) and M2 equal the percentage profit margin earned by steel manufacturers A and B in their sales to their own customers (also assumed equal across the two firms). Next we introduce IB, the sales of iron ore to steel manufacturer B—A's rival—and DBA, a downstream diversion ratio, the share of any sales of steel lost by steel manufacturer B that is recovered by steel manufacturer A (i.e., that would be recovered by the newly integrated firm after the merger).

Now consider the incentives of the newly integrated firm A in dealing with its steel manufacturer rival B. If the integrated firm refuses to supply iron ore to steel manufacturer B, it loses IBM1, its variable profits on those sales. However, from any steel sales diverted from the disadvantaged firm B to integrated firm A it gains DBAIB(M1 + M2), the variable profits both upstream and downstream of the increased steel sales by A.

If DBA ¼ 0—if the none of the lost steel sales of firm B are recaptured by firm A—then the only result of A's decision to deny access to iron ore to B is the loss of its upstream variable profits IBM1—clearly an unprofitable strategy. On the other hand, if DBA ¼ 1—if all of the lost steel sales of firm B are recaptured by firm A then the gains and losses upstream cancel each other out, and the integrated firm would gain downstream variable profits IBM2 from its decision to deny access to iron ore to B—clearly a profitable strategy. The breakeven point for the integrated firm's decision to deny access to its non-integrated rival is the point where DBA ¼ M1/ (M1 + M2)—if A gains less than this fraction of B's lost sales, foreclosure is unprofitable in this example.

The importance of the variable margins at the two stages of production is quickly apparent. If the iron ore firm has been earning a very large margin on its sales to steel manufacturers—if M1 is high, especially relative to M2—then a vertical foreclosure strategy looks unlikely: the diversion ratio DBA would have to be very high to make such a strategy work, ceteris paribus. On the other hand, if the steel manufacturer A earns a very large margin on its sales to steel customers—if M2 is high, especially relative to M1—then a vertical foreclosure strategy looks more likely: even a small DBA can make the strategy work.

So we are back to the importance of a familiar pair of figures: margins and a diversion ratio. We discussed both the usefulness and imperfections of measured firm margins in the previous section. As in that section, we next face the question of how to estimate the diversion ratio—again, in this case, the share of steel sales lost by steel manufacturer B that would be recaptured by its competitor steel manufacturer A.

As with the discussion of the use of diversion ratios in the analysis of upward pricing pressure, a first, default approximation is to use the firms' shares of the sales of steel. Maintaining the assumption that steel constitutes a product market, if firm A has 50% of the market and firm B 20%, then a first approximation of the diversion ratio of sales from B to A would be 50/(100 - 20) ¼ 0.625. We could then, as earlier, discount this figure by the percentage of B sales that might leave the steel market entirely were B to cease being a supplier—likely a small number.

At that point we would consider other factors that might render A's market share either an over- or an underestimate of this diversion ratio. If A's current capacity utilization in steel manufacturing is very high, it might not be able profitably to take over much of B's sales. If other rival steel manufacturers have plenty of excess capacity, they might be more aggressive in taking the diverted sales themselves. (Of course, we should also consider the possibility that the integrated firm would foreclose their iron ore supplies.) Similarly, there may be steel imports that are not currently in the market but could potentially be available to customers of B.

The investigation of these types of questions may inform the analyst's estimate of the relevant diversion ratio. Then this estimated ratio may be combined with the two margin estimates to reach a more informed analysis as to the potential of anticompetitive input foreclosure from the vertical merger. Going further, Moresi and Salop (2013) introduce several variants on GUPPI that may be used in the analysis of vertical mergers—vGUPPIs.

Finally, we should emphasize that the vertical arithmetic, like critical loss analysis and upward pricing pressure, does not answer all questions. Perhaps most importantly, we have not considered the possibility that foreclosure might not only disadvantage B and advantage A but also lead to a rise in the price of the downstream good, steel; the analysis presented above is thus conservative in its evaluation of the incentives for the merged firm to engage in foreclosure (Baker et al. 2011; Moresi and Salop 2013). We have not considered the possibility that other current or potential suppliers of iron ore might step in to supply B, thus rendering a foreclosure strategy ineffective in harming B in the first place. (This reminds us of the broader point that vertical mergers are likely to be harmful to competition only in the presence of significant market power at both levels.) We have also not considered the likelihood that there are other, more refined anticompetitive strategies available to the vertically integrated firm than the rather crude instrument of absolute input foreclosure (Moresi and Salop 2013). The vertical arithmetic outlined in this paper is only one of many tools that the analyst employs in assessing foreclosure incentives and effects.

#### 5 Conclusion

Critical loss analysis, upward pricing pressure, and the vertical arithmetic are three investigative tools that have come into widespread use in the enforcement of competition law within the last two decades, reflecting the increased role played by economic analysis in competition policy and law enforcement. Their value resides not so much in their ability to answer enforcement questions by themselves as in their usefulness in isolating certain important issues to be addressed and questions to be answered by the investigator and the decision maker. Furthermore, experience suggests that debates concerning whether they are applicable to a particular investigation as well as which assumptions inherent in their use are or are not satisfied may be as informative as the outcomes of the use of the tools themselves.

The enforcement agency analyst who is adept at using these tools will be well prepared not only for his or her opportunity to educate decision makers, tribunals, and courts as to the most important issues and questions regarding an investigation, but also for the presentations and arguments of the companies and their attorneys and economic consultants who come before the agency to urge their own point of view.

Acknowledgment The author is grateful for comments on this presentation from colleagues at the Antimonopoly Committee of Ukraine and participants in the Conference on Institution Building of the Competition Authorities in South-East Europe (Belgrade, June 2016) and on a previous draft of the paper from Xiaoling Ang, Beth Armington, Tim Brennan, Jim Foster, Rui Huang, Atsuko Izumi, Šarūnas Pajarskas, and Steven Salop. The views expressed do not purport to reflect the views of the U.S. Department of Justice.

#### References

Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

# Pricing Benchmark in Market Definition: Theoretical Background and Practical Application

Siniša Milošević, Jelena Popović Markopoulos, Jelena Grahovac, and Aleksandra Ravić

#### 1 Introduction

The aim of this paper is to demonstrate the practical application of quantitative tests in the process of delineating relevant markets. The paper provides an application and comparison for four mutually complementary tests that are based on product price movements over time. Following the example of three products, the paper seeks to examine the empirical verification of the initial hypothesis that two out of the three selected products belong to the same relevant market.

The manner in which the relevant market is defined sets the estimated market shares and market power of business entities, hence precisely setting relevant market boundaries represents a precondition for further investigation of competition conditions in the given market.

The concept of the relevant market, as used in competition law, differs from the concept of the market as an economic category, and is predominantly narrower when compared. For example, business entities predominantly define the market as geographical territory where they sell their products, or even the whole industry sector to which they belong (European Commission 1997). On the other side, positive legal regulations governing the protection of competition perceive the relevant market vis-à-vis two, mutually complementary dimensions—the product dimension and the geographic dimension. This means that in each process of determining the relevant market, its scope is set by the assortment of products, on the one hand, and the geographical area where such assortment is sold, on the other.

The Law on Protection of Competition of the Republic of Serbia adopted the definition of the relevant market as applied in the European Union. The relevant

S. Milošević (\*) · J. P. Markopoulos · J. Grahovac · A. Ravić

Serbian Commission for Protection of Competition, Belgrade, Serbia

e-mail<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
B. Begović, D. V. Popović (eds.), Competition Authorities in South Eastern Europe, Contributions to Economics, https://doi.org/10.1007/978-3-319-76644-7\_10

product market represents a set of goods or services that consumers and other users consider interchangeable in terms of their characteristics, common purpose and price, while the relevant geographic market is defined as the area in which business entities are involved in the supply or demand, and in which the same or similar conditions of competition apply, appreciably different from the conditions of competition in neighbouring areas.

The paper consists of seven sections. The introduction defines the concept of the relevant market and presents the structure of the paper. The overview of different methodological approaches to defining the relevant market is given in the second part, while the third part presents the theoretical foundations of price-based tests. The following fourth part of the paper provides an overview of European Commission practice in the application of price tests. The fifth, and at the same time, the main part of the paper is dedicated to the practical application of price tests. The conclusion gives the summary of the paper's findings.

#### 2 The Methodological Approach to Defining the Relevant Market

The key concept, on which the definition of relevant market is based, is the concept of interchangeability, i.e. demand-side substitution. In addition to demand substitution, the process of defining the relevant market may also require investigation of the possibility of supply substitution, which is beyond the scope of this paper. Different methodologies are used for investigating the possibility of demand substitution and, by extension, of defining the relevant market, while application of a specific one will depend on factors such as the nature of products for which the relevant market is determined and data availability. The actual procedure for defining the relevant market is case-specific, hence it may occur (although it is not common) that in some cases two products belong to the same relevant market, while in others they constitute two separate relevant markets.

Assessment of the relevant market primarily implies carrying out a qualitative assessment, followed by a quantitative one. The qualitative assessment of the relevant market represents the first step in the process of determining the relevant market. It refers to the logical assumption of the relevant market definition or other potential definitions, later tested by applying quantitative methods.

It is intuitive that chocolate prices will not be sensitive to changes in motor vehicle prices, because they are products that significantly differ in terms of characteristics, as well as in terms of usual purpose, thus under no circumstance can these two products constitute a single relevant market. Without qualitative analysis, significantly more time would be required to determine a relevant market. Therefore in practical terms, the pool of possible relevant market definitions is narrowed by carrying out the qualitative analysis.

The presence of similarity between the characteristics and the intended use of products indicates the existence of so-called functional substitution between them (Davis and Garces 2010). However, from the standpoint of competition, functional substitution is not sufficient, but it is significantly important to merit a look at the product prices, in addition to their characteristics and purpose. Therefore, for the mutual substitution of products, all three factors—product characteristics, intended use and price—are of equal importance. This is precisely the reason why in competition cases it is often necessary to carry out certain quantitative tests, in order to define relevant market, as precisely as possible. Quantitative assessment implies the use of different tests, based on time-series of observed product prices, in order to confirm or refute assumptions made during the qualitative assessment of the relevant market.

The hypothetical monopolist test, also called the "small but significant and non-transitory increase in prices" (SSNIP) test, is the best known and most common method for determining the relevant market. The methodological approach in defining the relevant market in the form of a hypothetical monopolist test was first introduced by the US Department of Justice in the Merger Guidelines, in 1982, while in 1992 became part of the joint Horizontal Merger Guidelines of the US Department of Justice and the Federal Trade Commission. In the EU, the hypothetical monopolist test was used for the first time in the Nestlé/Perrier case (No. IV/M. 190, 1992), and has been officially recognised in the Notice on the definition of the relevant market for the purposes of Community competition law, published by the European Commission in 1997. Modelled after the European Commission, the Office of Fair Trading of the United Kingdom included the hypothetical monopolist test for the first time in the market definition procedure in 1999.

The purpose of the SSNIP test is to identify the narrowest group of products (or geographic area) where the hypothetical monopolist could profitably implement the small (5–10%) but significant and more permanent (up to 1 year) price increase of its own product. The relevant product market question asks to what degree customers will substitute away from the product in response to the price increase (Pittman 2017). The procedure is basically iterative in nature and starts by identifying the closest substitutes for the observed product, progressively adding new products—potential substitutes, up to the point when shown that a price increase would be profitable for the hypothetical monopolist producing all products in a market defined in such manner. The test formulated in such way has a quantitative character, but its primary role is to offer a conceptual framework for analysing the nature of competition between products and services, and for assessing the competitive pressure on the potential relevant market (NERA 2001).

Despite the general consensus that the hypothetical monopolist test provides an appropriate analytical framework for defining the relevant market, its implementation is not always straightforward (Froeb and Werden 1991). In a situation in which there is no data on price elasticities, in order to see if and when the hypothetical monopolist would be able to profitably increase prices of its own products, it is necessary to assess the profit at different levels of product prices. This requires an assessment of cost function, or a rather heroic assumption that all average costs are the same. Because of limited data availability for the estimate of the hypothetical monopolist's cost function and difficulties in determining "competitive" price level subject to the assumed 5–10% increase, the test in effect is often reduced to a qualitative experiment and a not too formal econometric test that is rigorously implemented in all cases.

Reviewing the significance of the relevant market definition's concept and accepting new approaches in order to overcome information-related limitations, is based on the premises that the market definition is not an objective per se and does not necessarily have to be the first step in analysing competition conditions in all cases. Although there is still no universally accepted test for determining the boundaries of the relevant market (Kaplow 2013), the practice in recent years has increasingly turned towards information-wise less demanding tests, which exclusive rely on analysing (most often of available) data on prices. These tests are based on the logical premise that if two products belong to the same (relevant) market, their prices will move in similar manner over time.

#### 3 Theoretical Foundations of Price-Based Tests

Horowitz (1981) and Stigler and Sherwin (1985) were among first to define the relevant market based on identifying similarities in product price movement over time. The authors depart from the idea that price-led arbitrage will disable diverse price dynamics in different price areas, if such areas belong to same relevant market. Four mutually complementary tests stand out among most utilised tests that are based on prices of goods and services, whose practical application will be the subject of this paper: the correlation test, the Granger causality test, the stationarity test (unit root test), and the cointegration test.

# 3.1 Price Correlation Analysis

Price correlation analysis is based on the assumption that prices of products that are close substitutes move together, i.e. that exists a strong mutual correlation. It can be considered that products i and j belong to the same relevant market if there is a correlation between movements in their prices (Stigler and Sherwin 1985). For example, if the price increase of product i occurs, instead of product i consumers will purchase a substitute, product j, whose price remained unchanged. The increase in demand for product j will lead to that product's price increase, hence causing the existence of a positive correlation in price movement of product i and product j. As demonstrated, the price correlation analysis includes comparison of two price series that can be performed over time, in the case of time-series, or spatial comparison, in the case of structural series.

In other words, there are limits to which product prices may diverge within the same relevant market, because the demand-side substitution or supply-side substitution always bring them back to the equilibrium level. Therefore, we should expect that movements in prices of all products in a particular relevant market are correlated over time. The price correlation analysis demonstrates the strength of these links, i.e. the degree to which two price series are related. If a price of one product limits the price of another product, which is characteristic of affiliation to the same relevant market, both price movements must demonstrate similar patterns.

The correlation coefficient ranges from þ1 (when two price series move together perfectly) to -1 (when two price series move in perfectly opposite directions). A high and significant correlation coefficient close to unity may indicate that the two candidate products belong to the same relevant market. A low or insignificant correlation coefficient may indicate that two candidate products do not belong to the same relevant market.

Price correlation analysis is subject to a number of limitations. A high correlation coefficient may suggest that markets should be widely defined when in fact the correlation is spurious. Spurious correlation occurs when two series seem to be correlated but actually are not. On the other hand, a low correlation coefficient may lead to a narrow market definition when in fact the two price series are related but subject to significant random disturbance that breaks up such correlation. Also, no unique criterion exists to determine whether a correlation is large enough. Despite these limitations, price correlation analysis can provide useful information for relevant market definition, if it is applied and interpreted appropriately.

# 3.2 Stationarity Test

If two products belong to the same relevant market, then limitations exist in terms of corridors within which their price movement may diverge. In that sense the unit root test, i.e. stationarity test, is used for investigating whether two products belong to the same relevant market (Forni 2004). If two products belong to the same relevant market, shocks that increase single product price against the other product will have a temporary effect. Substitution will occur, demand for the more expensive product will decrease, while demand for more affordable product will increase. The decline in demand for the more expensive product will cause its price to drop, while on the other side, the more affordable product's price increase will occur due to the increased demand for that product. In those conditions product prices always return to the long-term equilibrium level. For that reason the time-series of relative prices, i.e. the quotient or difference between prices of the first and the second product is always stationary, if such products belong to the same relevant market.

# 3.3 Cointegration Test

Using similar logic to when implementing the unit root test, investigating whether two products belong to the same relevant market may also be performed by applying the cointegration test. Two non-stationary time-series are said to be cointegrated if their linear combination is stationary. If the cointegration test demonstrates that price movement series for two products are cointegrated, then those products belong to a single relevant market, and vice versa (Coe and Krause 2008).

# 3.4 Granger Causality Test

Correlation in some cases may be spurious: the result of coincidence and not of a causative link between the observed occurrences, meaning that two products may belong to different relevant markets, yet have a high level of interconnectivity in terms of their price movement over time. For example, due to the strong correlation of prices of the two with the third product, indisputably out of the market. On the other side it may occur that no significant correlation between the observed products' price movements exists, but that they nevertheless belong to the single relevant market. This occurs when price alignment happens with a certain time-lag. This means that it takes a certain time following one product's price increase for the prices of its substitutes to increase as well. In this case, the correlation between price movements will be approximately equal to zero even though the products are a very close substitutes.

For those reasons the need arose for the Granger causality test, aimed at determining the existence of causality between prices of two products (Slade 1986). This test was named after Clive Granger, winner of the Nobel Prize in Economics (Engle and Granger 2003). The use of the concept of the Granger causality in competition law inquiries can be illustrated with reference to market definition. The intuition behind the test is obvious and based on a very simple idea: would it be possible to advance prediction of a single product price movement if we don't only look at the time-series of that product price movement, but also include in the analysis the time series of other product prices (Bishop and Walker 2010)? The first step is to fit a regression curve, by using the least squares method, to the time-series of the first product prices based on several shifts, i.e. lags. The second step is to add the timeseries of the second product, also with several lags. Then we ask is the explanation for the first product price movement better if, in addition to those prices, we also include other product prices. The common statistical tests are used for enacting a ruling of "better" or "not better" explanation. Comparison between the mean squared errors is performed most frequently. If the explanation is "better", it improves the ability of predicting the first product price movement. In such a situation, the second product price is the cause of the first product price.

There are three kinds of relations in reference to the Granger causality. If we test the existence of causality between the prices of products X and Y, it is plausible that:

If two products X and Y belong to the same relevant market, it can be expected that the prices of product X cause the prices of product Y, and vice versa.

#### 4 Summary of Case Studies

In its practice up to present, the European Commission has used price-based tests mainly for the purpose of defining the relevant market when examining proposed mergers. In the case of Nestlé/Perrier (1992), the price correlation analysis was used for the first time to define the relevant product market. In its merger notification, Nestlé defined the relevant product market as non-alcoholic beverages market, including bottled source water and soft drinks. The European Commission departed from the assumption that bottled source waters represent a distinct relevant market from soft drinks. Additionally, the assessment of the proposed merger considered whether there is a separate market for sparkling and flavoured waters within the wider, bottled water market. Based on the results of the correlation analysis, which demonstrated the high correlation between the prices for two types of bottled water and low correlation coefficients between bottled waters and other non-alcoholic beverages, the relevant market was defined as the bottled source waters market.

In the case of Gencor/Lonrho (1997), following the determining of a high correlation coefficient between the prices of gold and platinum, and due to indications of related "false correlation", the European Commission applied the cointegration test. This test demonstrated that long-term correlation between the prices of the selected product categories was nonexistent, i.e. the that prices of platinum, rhodium, palladium, silver and gold, have a tendency to move irrespectively of other(s), so that it can be reasonably assumed that this represents the case of separate relevant product markets.

In the case of UPM-Kymmene/Haindl (2001), based on the price correlation coefficient, the European Commission determined that two type of magazine printing papers, so-called wood-free coated paper (WFC) and wood coated paper,1 make

1 Such are Super Calendered (SC) and Coated Mechanical Reels (CMR), including Light Weight Coated (LWC), Medium Weight Coated (MWC) and Heavy Weight Coated (HWC) paper.

two separate relevant markets. Namely, the determined correlation coefficient was below 0.55, which constituted an insufficient argument for classifying all types of printing papers in the same relevant market. On the other hand, price correlation between certain types of wood coated papers was also tested, thus validating the determined correlation coefficient between the Light Weight Coated (LWC) paper and Super Calendered (SC) paper at 0.85, which indicates that both types of wood coated papers belong to the same relevant market.

In the case of CVC/Lenzing (2001), by applying the correlation analysis, the European Commission determined that it was not only viscose and lyocell fibres that constituted separate relevant markets, but that viscose fibres and fibres made of other materials, such are cotton, polyester and polypropylene, also did not belong to a single relevant market. Namely, the correlation coefficients between prices of viscose fibres and other fibres ranged from 0.04 for natural fibres, i.e. cotton-made fibres, to above 0.06 for polypropylene fibres from the lower price category, 0.24 for polypropylene fibres from the higher price category, 0.39 for polyester fibres from the lower price category, all the way up to 0.44 for polyester fibres from the higher price category. This European Commission opinion was completely contrary to the view of the parties to the concentration that all textile fibres, artificial (cellulose and synthetic) and natural, constitute the same relevant market.

In the case of Ryanair/Aer Lingus (2003), a price-correlation analysis was used to complement other evidence in determining the relevant geographic market. The takeaway from this example is that there is no agreed level or threshold that defines whether series move sufficiently together for two products to belong to the same relevant market. A partial, but generally accepted, response to this critique is the use of benchmarking techniques. As a benchmark against which to compare other correlations, one can use the correlation coefficient between the prices of two series that one is willing to state on a priori grounds are in the same relevant market. In this case the average correlation on six routes operated both by Aer Lingus and Ryanair was used as a general benchmark. According to this approach, the correlation coefficients of individual routes that were above the average correlation of 0.69 were used as a first indication that the merging parties are close competitors on these routes.

In the case of Arsenal/DSP (2009), the European Commission applied the price correlation and stationarity tests in order to define the relevant geographic market. Contrary to the view of the parties to the concentration that the relevant market in geographic terms was the global market, the European Commission concluded, based on the low correlation coefficients between continents and absence of stationarity of relative prices, that Europe, Asia, and North America represent separate geographic markets.

#### 5 Practical Application of Price-Based Tests

We will demonstrate the practical application of price-based tests on the example of analysis of monthly time-series data relating to prices of three products, two different brands of edible sunflower oil and diesel fuel, in the Serbian market, during a 4-year period (2012–2015). For further ease of use, the products will be marked as A, B, and C, with C being diesel fuel. Each data-series had 48 observations. The prices of all three products were deflated using appropriate indexes.

Departing from the basic legal requirements in determining the relevant market (characteristics, common purpose, and price), already in the first step taken, it was noted that based on the criteria of characteristics and purpose, products A and B belonged to the same market, while product C represents the second, considerably different and separate market. Further empirical analysis dealt with the price movement of these three products with the aim of verifying whether products A, B, and C, whose retail prices move at approximately identical level, belong to the same relevant market. In addition to that, the purpose of the empirical work was to obtain an answer as t the existence of causality of the price of product A against products B and C, and if any, whether the causalities were unidirectional- or bidirectional in nature.

First, we will examine the graph presentation of time-series data of prices related to products A, B, and C. Already at first glance, such visual representation suggests that the prices of products A and B demonstrate similar dynamics, while the price of product C has a considerably different trend (Fig. 1).

Fig. 1 Movement of observed prices

# 5.1 Price Correlation Test

Further investigation analysed the correlation between those three data-series. The values of correlation coefficients and associated probabilities are presented in the form of Table 1.

Correlation analysis demonstrated a high and statistically significant correlation coefficient between products A and B (0.94), while the correlation coefficients of product C against products A and B have a negative sign, demonstrating low values (-0.17 and -0.14, respectively), and are not statistically significant.

The obtained results suggest that products A and B belong to the same relevant market, while product C belongs to another relevant product market, therefore confirming the preliminary conclusion reached based on the qualitative assessment of the relevant market, by analysing the characteristics and purpose of these products. The correlation analysis results should be interpreted with caution, particularly in situations when not all observed time series are stationary. Consequently, it is recommended to combine correlation analysis with other price movement tests.

# 5.2 Stationarity Test (Unit Root Test)

Next we implemented another price-based test, by investigating the stationarity of the time-series of relative prices, related to products A, B and C, whereas the relative prices are expressed as a difference in price between two products (Fig. 2).

Based on the graph presentation, already prima facie it can be concluded that the time-series of relative prices of products A–B is stationary, while the time-series of relative prices of products A–C, and B–C are non-stationary, which we will verify by applying the unit root test.

Firstly, we will test the stationarity of time-series by using the Augmented Dickey-Fuller (ADF) test, followed by the Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test. Although in principle they lead to the same conclusions, the tests differ in the null hypothesis. Namely, the ADF test departs from the hypothesis on the presence of a unit root (lack of stationarity), while the KPSS test tests the null hypothesis that the time-series is stationary.

Table 1 Results of the price correlation test

\*Significant at p 10%

\*\*Significant at p 5%

\*\*\*Significant at p 1%

Fig. 2 Movement of product price differences

Table 2 Results of the ADF stationarity test for products A and B

\*\*Significant at p 5%

\*\*\*Significant at p 1%

By applying the ADF test to the time-series of relative prices of products A and B, we get the result as indicated in Table 2.

Based on the ADF t-statistic, which is below the critical value for all significance levels, we can reject the null hypothesis on the presence of a unit root, hence we concluded that the time-series of relative prices relating to products A and B is stationary.

Now we tested the stationarity of the time-series of relative prices of products A and C (Table 3).

The table demonstrates that the t-statistics is in the area of accepting the null hypothesis for all significance levels, hence we conclude that the time-series is not stationary. The identical result is also achieved when we apply the test to the timeseries of relative prices of products B and C (Table 4).

By testing the stationarity of time-series of relative prices relating to products A, B and C, using the ADF unit root test, we concluded that products A and B belong to the same relevant market, while product C constitutes the separate relevant market.

By applying the KPSS test we arrive to almost identical conclusions, hence below, for illustration purposes, we will give only the result of testing the stationarity of the time-series of relative prices of products A and B (Table 5).

The critical value (0.352) is located in the area of acceptance of the null hypothesis, for significance levels of 1% and 5%, while the null hypothesis is practically located in the margins of the critical area, for the significance level of 10%. Based on the abovementioned, we conclude that the time-series is stationary.

# 5.3 Cointegration Test

The test that we have used in order to draw conclusions on the determination of observed products against the same or different relevant markets is the cointegration test. The purpose of this test is to investigate whether the linear combination of two (non-stationary) time-series is stationary, from which it is concluded whether products belong to the same relevant market.

In order to investigate whether the time-series are cointegrated, it is primarily necessary to estimate the regression equations for each pair of products (three equations in total), then to create the residuals and test whether the time-series of the residuals are stationary, by using the unit root test. Therefore, the cointegration test is actually reduced to testing the presence of a unit root in the residuals, obtained by estimating the regression equations, by using the ordinary least squares method.

The result of the stationarity testing of the residuals obtained through the assessment of the regression equation of the A-B product time-series is presented in Table 6.

Based on the calculated value of the ADF t-statistics and associated probability, and comparing it against the critical values for different significance levels, we conclude that the null hypothesis on the presence of a unit root is rejected, i.e. that the time-series is stationary, which suggests that products A and B belong to the same relevant market.

For the estimated regression equation of the time-series of products A and C, and the related resulting residuals, we obtain a different result (Table 7).

The calculated value of t-statistic is not statistically significant and it is located in the area of accepting the null hypothesis for all significance levels, thus we cannot reject the null hypothesis on non-stationarity. Accordingly, we conclude that products A and C do not belong to the same relevant market. The identical result is also obtained if we test the stationarity of residuals obtained by estimating the regression equation of the time-series of products B and C, which is demonstrated in Table 8, thus we conclude that those products belong to different relevant markets.

# 5.4 Granger Causality Test

Bearing in mind that the previous test confirmed that products A and B belong to the same relevant product market, further examination referred to the causality of the price movement of these three products. The Granger causality test is applied to examine whether the time-series of product A prices causes the time-series of

Table 9 Results of the Granger causality test

\*Significant at p 10%

\*\*Significant at p 5% \*\*\*Significant at p 1%

product B and C prices, and if causality exists, whether it is unidirectional or bidirectional.

The causality analysis is preceded by a statistical analysis of the model from the aspect of the optimal number of lags. A single lag is included in the model, and the following results are obtained (Table 9):

The determined values of the Granger causality test and associated probability (p < 0.05) demonstrate that when testing the causality of products A and B, the null hypothesis on the absence of causality is rejected, thus it is concluded that the price movement of product A is caused by the price movement of product B, and vice versa.

On the other hand, in the case of product sets C-A and C-B, the null hypothesis on the absence of causality in the price movement relating to the observed products cannot be rejected (p > 0.05), which additionally increases the previous finding that product C does not belong to the relevant product market to which products A and B belong.

This result is consistent with the conclusions reached in all three previously applied price tests, as well as with the initial assumption based on the qualitative analysis of products' characteristics and intended use. Various brands of edible sunflower oil constitute a relevant market that is different and separate from the market to which diesel fuel belong.

#### 6 Conclusion

The definition of the relevant market is one of the most fundamental concepts upon which all crucial issues of competition policy are based. Defining the relevant market is a widely applicable analytical framework that represents an initial step when analysing competition conditions and investigating potential infringements of competition. Properly determined boundaries of the relevant market enable identification of the market structure and market participants, as well as assessment of the competitive pressure that they face from one another.

There is a wide range of different methods and techniques that can be applied when assessing the relevant market, starting from the qualitative, which are based on product characteristics and their intended use, to the quantitative, which are based on the hypothetical monopolist test and price-based tests. Which of the methods will be implemented depends on the conditions under which the determination of relevant market is performed and on available data.

Tests that are based on the monitoring of time-series of product price movements are used when it is not possible to collect data for conducting other, more complex and information-demanding tests, such as the SSNIP test. Scientific papers published during last two decades and provide an abundance of examples of practical application of price-based tests, while the European Commission has used them extensively since 1992 in defining the relevant market, when assessing proposed concentrations.

Using an example of three products, we have demonstrated the practical implementation of price-based tests in the procedure of determining the relevant market. The performed tests and the results obtained aimed to empirically verify the initial hypothesis that different brands of edible sunflower oil belong to the same relevant market, while diesel fuel represents the separate relevant market. All four utilised tests confirmed the preliminary position obtained in the qualitative analysis, based on which we concluded that diesel fuel belongs to the separate relevant market, i.e. that it does not belong to the relevant market to which edible sunflower oil belongs.

This paper has addressed the issue of how price correlation and other price-based tests can be applied for a given data set of average monthly retail prices of two brands of edible sunflower oil and that of diesel fuel, over a 4-year period. However, the initial selection of products was done in a way that made the results of a preliminary qualitative analysis rather intuitive, and these were in a later stage confirmed by quantitative testing. It would be interesting to see how well the obtained benchmarks fits into another, similar data set, for example, by applying the same techniques to test the hypothesis that all edible oils (olive oil, palm oil, coconut oil, etc.) constitute the same relevant market.

Acknowledgement The authors are grateful to Dr Miloje Obradović, President of Serbian CPC, for his helpful comments and support and Prof. Zorica Mladenović and Prof. Aleksandra Nojković from the University of Belgrade, Faculty of Economics, for their helpful comments and inputs.

#### References

Bishop S, Walker M (2010) The economics of EC competition law: concepts, application and measurement. Sweet & Maxwell, London Case: ARSENAL/DSP, COMP/M.5153 (2009)

Case: CVC/Lenzing, COMP/M.2187 (2001)

Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

## The Rationale for Using the Classic Cournot Mechanism in Merger Control

Bojan Ristić

#### 1 Introduction

This paper aims to theoretically establish, justify and show the possibilities for the application of the classic quantity competition model within industries where firms before they start with the price competition, are required to choose some level of capacity. It is a model developed by French mathematician and economist Augustin Cournot in the nineteenth century, which can be considered as a reduced (short) form of such a two-stage game.1

The inspiration for this topic comes from the need to perform a more significant inflow of economic theory into the domain of horizontal merger control, which can be of assistance to authorities in charge of competition protection in gathering evidence for cases that they investigate. This is a particular area of competition protection policy, where the unilateral effects of horizontal mergers (hereinafter, mergers or concentrations) on the conditions of competition in the relevant market are determined ex-ante. Accordingly, a judgement is made whether the merger should be approved or blocked, and under what terms. Thus, a theoretical framework would be developed for the right application of the stated economic model. We hope that the mentioned authorities (hereinafter, commissions) would, therefore, gain a valuable tool for determining the short-term merger effects. The application of this model is considered especially useful for the horizontal merger simulation method.

This paper does not aim to suggest the perfectness of the tool it offers. On the contrary, it should be regarded only as complementary analytics which clarifies or questions other evidence, gathered by traditionally present analyses used by the commissions. First of all, we refer to the definition of the relevant market and the

B. Ristić

1 See Cournot (1897).

Faculty of Economics, University of Belgrade, Belgrade, Serbia e-mail<EMAIL_ADDRESS>
consequential judgement based on market shares and measures of market concentration.

Mergers can cause two types of adverse effects on competition. Those are the mentioned unilateral effects, which are in the focus of this paper, and the coordinative effects, which can be the subject of some further analysis. In any case, it is important to differentiate between the two.

The coordinative effects stem from the fact that concentration, by its nature, decreases the number of market players, thus increasing the market concentration, also raising the possibility for a cartel to be created and to endure.2

The focus of this chapter will be, as already mentioned, on the unilateral effects that exclusively refer to the entity created by horizontal merger. European legislation sees the dominant market position as an indicator of the possession of market power. In that sense, gaining a dominant position is considered as motivation for firms to obtain and strengthen their market power through such steps, at the expense of the consumers, rival companies and suppliers, which is considered to be an abuse of the dominant position. Thereby, to prevent the occurrence of such abuse, since it assumes already violated competition conditions, it is the task of the commissions to predict the unilateral merger effects.

The starting point is that unilateral effects are exclusively connected to the participants of the concentration, but not to their rivals. In this sense, these effects could formally be defined by applying the Nash equilibrium concept, which is at the heart of the Cournot model.3

This chapter consists of two connected and rounded parts. First, it is necessary to discuss the circumstances within which the Cournot model can be considered as a good approximation of reality. Therefore, there is a need to also consider its existing role in the domain of merger control. Second, having discussed and chosen the competition model, we will offer a short algorithm for its application in merger simulations.

It is worth emphasising once more that the foremost purpose of these parts is to indicate the economic philosophy behind the carried-out analysis to the young commissions (without sufficient experience, expertise and other resources necessary for carrying out merger control). The general aim is to indicate the possibilities of making positive breakthroughs towards an increase in the quality of the economic analysis that is being performed, which would decrease decision-making errors of the first and second kind, which are an inevitable part of this sphere of competition policy.

2 For the definition of the coordinative effects see Begović and Pavić (2012, p. 97).

3 See Werden and Froeb (2008, pp. 45–46).

#### 2 The Rationale for Cournot Mechanism

The practice of this type is shaped by oligopoly theory, which lies at the very heart of the industrial organisation. The limitations inevitably faced in practice must be taken into account when considering the importance and the limits of the particular role of this economic theory. Practice is restricted by rigorous legislative norms (e.g. the short time-frame for collecting evidence), scarce resources (quantity of staff, accumulated knowledge, and insufficient financial funds), as well as limited availability of data needed to carry out the analysis. Because of this, it is logical to implement those economic tools, which under the given circumstances, reduce the space for making the stated errors.

A perfect simulation would assume that the applied competition model is fully compatible with the characteristics of the relevant market. In other words, there should be as many different game modes as there are different markets. However, economic theory does not differentiate an infinite number of competition mechanisms. Also, the limits of merger control practice can lead to a simplified appearance of reality, through the assumption of Cournot or Bertrand competition, depending on what is considered the key strategic variable—quantity or price. The approximation of reality always carries the risk of making a wrong decision. This is something that the authorities must be aware of when choosing the adequate set of instruments for the analysis.

It is evident that the possibility of mistake cannot be eradicated since forecasting social process outcomes always comes with a dose of unexplained variability. The interest of the authorities should be to minimise those possibilities by using sophisticated economic tools, which they are capable of implementing. On the other hand, another limiting factor must be taken into consideration: judges do not like "black boxes" containing evidence, which is something that the application of complex economic theories might resemble. Of course, this is the case when the analysed merger case gets its day in court.

By offering an answer to why the Cournot model of quantity competition should be applied, it is implicitly assumed that this model represents a good approximation of the market game within which a merger is taking place. Is this actually the case and when? The answer to this question has at least two components. First, the dilemma which competition model should be applied depends on the decision which strategic variable is considered to be crucial for the analysed market. Most often these variables are quantities and prices. However, firms use both strategic variables in their business. The Kreps and Scheinkman (1983) model (hereinafter, KS model) is proof that the outcome of the strategic interaction in which the firm would first choose its capacities and later engage in price competition with the aim to employ capacities, creates an outcome which coincides with the outcome of the Cournot model. That is why it is wise to use the Cournot model, and not the Bertrand model, in the circumstances described by the KS model. Second, it is a fact that merger control practice significantly relies on the Cournot model when establishing the relationship between the indicators of market structure (e.g. the number of firms within the industry, their market shares, and measures of market concentration) and the indicators of market performance (e.g. the Lerner index). Both of these reasons should be discussed in detail, as follows.

#### 2.1 Cournot Mechanism as the Reduced Form of the Two-Stage Competition

According to available literature, it appears that as far as simulations are concerned, the question of choosing a competition model is still insufficiently explored. Typically, without going into detailed argumentation, it is pointed out that for homogeneous products the Cournot model of competition should be applied, while for the differentiated products the focus should be on the Bertrand model. A transparent approach to this issue can be found in influential papers, such as Werden and Froeb (2008), and Budzinski and Ruhmer (2009). By this simple division of authorities between the two models, it is implicitly presumed that in the case of homogeneous products the dominant strategic variable is quantity, while in the case of differentiated products it is price.

However, this division seems too strict in the case of limited capacities, where prices and quantities can be the variables of a single two-stage game, with the outcome which fits the classic Cournot model. Moreover, it turns out that in certain circumstances this result can be valid, for both the markets of homogeneous and of differentiated products.

The KS model was devised on the basis of the seminal Edgeworth (1925) model and the model that was later developed by Levitan and Shubik (1972), which introduce exogenously limited capacities into price competition. It introduces capacities limitations into price competition, but as an endogenous firm's decision. By making capacities endogenous within the frameworks of price competition, both variables, prices and quantities, are put in the context of one game, with the conclusions being fairly attractive to the topic of this paper. Namely, the price competition which precedes the firms' decisions regarding capacities will in certain circumstances have as a result the outcome of the Cournot model. This result significantly affirms the role of Cournot's competition as a tool for short-term predictions, which is exactly the case with merger simulations. In other words, it represents a theoretical basis for the application of the Cournot model, as its reduced form.

Therefore, the KS model assumes that the firms choose their capacities during the first period, while in the second period, starting from chosen capacities, they choose prices that will fully engage those capacities. It is assumed that the production for inventory is not possible. Once chosen, the capacities are binding for the firms, which introduces into the model the assumption of a significant leap in the marginal costs for every unit produced above capacity. The KS model proves that in the circumstances of limited capacities if firms believe that the result of the price competition will be such, regardless of the chosen capacities, pricing policy will fully engage them. As a result, firm's supply will be found at the intersection of the Cournot's reaction functions.4 The example of homogeneous products duopoly originally proves this result, with the assumption of a negative slope demand function, non-decreasing marginal costs of production, and marginal costs of capacities. Also, the so-called efficient rationing rule is applied, which assumes that the lower price firm, up to the level of its pre-committed capacities, will serve the customers with the highest willingness to pay, while the more expensive one will be faced with residual demand, which excludes those customers. This rule maximises the consumers' surplus since the lower price is always achieved by the customers with the highest willingness to pay.5

To illustrate the rationale behind the KS model, similar as in Shy (1998), a simple example of two symmetrical firms, which participate in this two-stage game (firms 1 and 2) will be used. The inverse market demand is linear and given by the form p ¼ a q, where q ¼ q1 + q2 and a > 0. The per unit costs of capacities for both firms are constant at the level c^1 ¼ c^2 ¼ c^ > 0, while a > b. On the other hand, the per unit production costs are also constant and equal to zero, up to the level of installed capacities, i.e. c1 ¼ c2 ¼ c ¼ 0, and are infinite for every unit above that level.6

Differing costs of capacities and costs of production is an important characteristic of the two-stage KS model. While the costs of production are crucial for the second game period and the selection of price, the total costs (costs of capacities increased by the costs of production) are essential for the selection of capacities in its first period. The costs of capacities are a function of the level of installed capacities, where every unit of capacity enables the production of one unit of output. If the firm does not intend to generate inventories in equilibrium, nor to have unengaged capacities, but to always use them for the measure of intended production, it seems realistic to expect that qi ¼ ki. This continual following of the capacities with quantities can lead to the conclusion that the per unit capacity costs c^ can be characterised as per unit production costs (c), which is not the case. The per unit production costs refer to the second game period. Thus, they are not directly connected to the decision concerning capacities if production is maintained within their limits. On the other hand, even related to capacities construction, total

4 For the technical details of this complex model, which most certainly surpass the scope of this paper, see Kreps and Scheinkman (1983). For a rather intuitive interpretation see Shy (1998, pp. 112–115).

5 For a detailed discussion of logic of efficient rationing see Davidson and Deneckere (1986), and Tirole (1988, p. 213).

6 The assumption on zero costs of production is in accordance with the original interpretation of the KS model. Kreps and Scheinkman (1983) state that with slight complications in the proof, the conclusions of their model would not change even for non-zero production costs. The infinity of the capacity costs for every overrun unit secures their perfect rigidity. Maggi (1996) has shown that even without the perfect rigidity, the same conclusions, as in the standard KS model, can be reached.