Umbrella damages and the passing-on defence in cartel damages claims

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University of Amsterdam

Umbrella damages and the

passing-on defence in cartel

damages claims

Master’s Thesis Economics

Markets & Regulation

July 15, 2018

Abstract: A prevailing type of unethical competition authorities face is the case of cartels. Cartels distort competition through engaging in price-fixing agreements or limiting production. As a consequence, firms competing with cartels in the same relevant market face higher demand, which leads to higher prices for the products produced by cartel outsiders. These price increases by the outside firms are the so-called ‘umbrella damages’. Since 2014, it is possible for umbrella firms to claim compensation from cartels for the suffered harm. In cartel cases, defendants can resort to the pass-on defence. However, umbrella effects may have implications for the degree of passing on and therefore also the pass-on defence. This thesis focuses on the relation between umbrella damages and the pass-on rate. First, I show what this relation is in case of Bertrand competition with differentiated goods. Further, I provide advice for defendants regarding whether it is still beneficial to use the pass-on defence taking the results into consideration. The results show that umbrella effects have a positive effect on the pass-on rate. If using a pass-on defence implies admitting that umbrella damages exist, the incentive for a defendant to use a pass-on defence changes. In every situation, the umbrella damage, together with the output effect, is larger than the pass-on effect. Using a pass-on defence is no longer beneficial.

Author

L.S. Waller (10329765)

Supervisor

Prof. Dr. M.P. Schinkel

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Statement of Originality

This document is written by Lily Waller, who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervi-sion of completion of the work, not for the contents.

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List of Figures

1 But-for price estimation . . . 14

2 Umbrella effects with Bertrand competition . . . 18

3 Effect of Monopoly market on direct purchasers . . . 19

4 Overcharge (A), pass-on effect (B) and output effect (C) . . . 20

5 The three-layer market of wholesalers, retailers and consumers . 22 6 Results pass-on caused by umbrella effect . . . 30

7 Pass-on effect caused by umbrella effect and umbrella effect . . . 31

8 Effect of umbrella effects on pass-on (θtotal) . . . 32

9 Results pass-on effect, output effect and umbrella damage . . . . 34

10 Results pass-on effect, output effect and umbrella damage . . . . 35

List of Tables

1 Results of the competitive Nash equilibrium . . . 25

2 Price results of wholesale market with cartel for M=5 . . . 28

3 Price results of retail market with cartel for M=5 . . . 28

4 Quantity results of retail and wholesale market with cartel for M=5 28 5 Decomposition of total harm with M=5 . . . 29

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1 Introduction

In an ideal economic world, markets act competitively and efficiently. How-ever, firms are incentivised to change their prices or quantities whenever this can increase their profit. Since in economic theory, firms act rationally, they constantly strive to obtain more profits. For this reason, they are continuously tempted to participate in illegal practices such as price-fixing agreements, abuse of dominance and exclusionary conduct. To prevent markets for this type of il-licit action, the United States and Europe have developed antitrust policy and regulation. The purpose of antitrust policy is to promote effective competition and protect the competitive process to maintain free competition in markets. Price setting must be characterised by undistorted competition (Motta, 2004). Authorities aim to protect consumers and promote ’consumer welfare’ and total welfare (Blair & Durrance, 2018). According to the EU’s competition rules, any individual or business that has suffered from harm due a breach of Article 101 or 102 of the Treaty on the Functioning of the European Union (TFEU) can claim compensation from the party that caused the breach (Oxera, 2009). Claimants are entitled to compensation for actual loss and for loss of reduced profit, including interest for the duration of the time when the damage occurred. The goal of compensation for harm suffered is to place the harmed party in the position in which it would have been if the infringement of Article 101 or 102 had not happened (European Commission, 2013).

A prevailing type of unethical competition authorities face is the case of cartels. A cartel exists when firms agree to coordinate their behaviour, aiming to increase their profit by extracting welfare from other players in the mar-ket (Bos, 2009). Cartels distort competition through engaging in price-fixing agreements or limiting production. The primary harm caused by cartels is that their victims must pay more for products than they would have done with-out a cartel agreement (Oxera, 2009). In addition, higher prices cause a de-crease in the volume purchased. According to economic theory, if a cartel is incomplete, these increased prices typically lead to a substitution away from the cartel insiders’ products to the substitute products of the cartel outsiders (Inderst, Maier-Rigaud & Schwalbe, 2014). Accordingly, firms competing with cartels in the same relevant market face higher demand, which leads to higher prices for the products produced by cartel outsiders. These price increases by the outside firms are the so-called ‘umbrella damages’. From the point of view that the harmed party must be placed in the position in which it would have been without the infringement, ‘umbrella damages’ should be included in the quantification of cartel damages. Undertakings that are active in a market, but outside a cartel, do not violate the prohibition of anticompetitive coordination when they adapt their prices charged to the increased demand caused by the cartels. Accordingly, these cartel outsiders do not violate Article 101 of the TFEU, which forbids price-fixing agreements.

In cartel cases, defendants can resort to the pass-on defence (Verboven & van Dijk, 2009). This defence implies the argument that purchasers of cartels may have passed on part of the overcharge to the downstream customers. If the

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downstream market is not perfectly competitive, firms are able to pass on part of the price increase (Hellwig, 2006). A pass-on defence can give a discount on this estimated price overcharge and is recognised by the European competition damage Law . This discount is based on the pass-on effect and adjusted for the volume effect. The magnitude of the pass-on effect and output effect has been investigated previously. Hellwig (2006) has focused on a market with an upstream cartel and a downstream market which is completely cartelised. He has found that the output effect offsets the pass-on effect for direct purchasers. Therefore, he has concluded that the pass-on defence is not relevant in case of a cartel claim. However, this conclusion appeared to be erroneous according to further literature. Basso and Ross (2010) have investigated harm caused by car-tels as a whole to both direct and indirect purchasers. They have concluded that if the harm is only based on the overcharge, there is an error that depends on the competitiveness of the downstream market. Verboven and van Dijk (2009) have showed that the discount and the price overcharge are positively correlated in a Bertrand industry, unless the customer operates in a fully monopolised mar-ket (a monopoly or a complete cartel). This makes it economically justified to adjust the overcharge with a discount rate that represent the pass-on effect and volume effect. They have utilised the degree of market power in the downstream market to estimate the justified discount rate on the price overcharge. Han et al. (2009) have found that the direct purchaser overcharge underestimates the true total harm that occur in all production layers. They have also concluded that the longer the vertical chain of production and the lower the chain where the cartel operates, the more problematic it is to rely on the direct overcharge. Existing literature regarding umbrella damages is limited. Inderst, Maier-Rigaud and Schwalbe (2014) have written an extensive report about the eco-nomic foundation of umbrella damages. This paper has been corrected by Holler & Schinkel (2017), who have found that umbrella effects increase with both a higher number of cartel members and a higher degree of substitutability. Blair & Durrance (2018) have written a paper about the economic explanation of umbrella damages. However, their analysis is limited and not based on game theoretical models. Most existing literature is written from a legal perspective. Accordingly, much can be investigated when it comes to umbrella damages.

Since 2014, it is possible for umbrella firms to claim compensation from car-tels for umbrella harm suffered due to increased prices in the EU. However, the fact that cartel members are liable for umbrella damages may have implica-tions for the pass-on defence. The degree of the pass-on effect is dependent on the degree of competition in downstream markets (Hellwig, 2006). The more competitive the downstream layer is, the less able firms are to pass-through over-charges. The amount of competition in downstream layers is also dependant on the magnitude of umbrella damages. Downstream firms are only able to pass-on a certain rate of price increases caused by cartels if markets are not perfectly competitive. When firms in upstream markets form partial cartels and cartel outsiders increase their prices under the umbrella of a cartel, the purchasers of both cartel insiders and outsiders are affected by price increases. Otherwise, without umbrella pricing, there would be a larger difference in the input prices

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between the purchasers of cartelised firms and the purchasers of cartel outsiders, resulting in a comparative advantage for the purchasers of cartel outsiders. If this were the case, cartel purchasers would be less able to increase their prices after input prices increase due to the cartel . In conclusion, downstream markets would be more able to pass on damages when umbrella damages exist. Accord-ingly, by claiming that claimants passed on a certain amount of damages, cartels may recognize that umbrella damages exist. This would be the case if it is not possible to pass-on damage when umbrella effect does not exist. Consequently, defendants could call for an umbrella claim when using the pass-on defence. If the umbrella claims are larger than the benefits from using a pass-on defence, there come be a turning point when it is no longer beneficial for defendants to use the pass-on defence. However, the relation between umbrella effects and pass-on effect never have been investigates before. Therefore, a question arises regarding what the effect of the magnitude of umbrella damages is on the de-gree of the pass-on effect. My thesis contributes to the existing literature on the relation between umbrella damages and pass-on effect. Thereby, this thesis is based on game-theoretical behaviour. I aim to show this relation. Therefore, I focus on the following research questions:

1. What is the relation between the umbrella damage and the pass-on rate? 2. what factors affect the magnitude of the relation between umbrella damage

and pass-on defence depend?

3. Does the fact that umbrella claimants can claim for compensation change the incentive to use the pass-on defence?

The more competitive the downstream layer is, the less able firms are to pass-through overcharges. The degree of competition in downstream layers is also dependent on the magnitude of umbrella damages. The smaller umbrella effects are, the larger the comparative advantage of firms who buy from umbrella firms compared to firms who buy from cartelised firms. Therefore, I expect that umbrella damages have a positive effect on the degree of pass-on effects of the overcharge caused by a cartel.

Section 2 discusses the history of the cases of how liability for umbrella dam-ages has arisen. Thereby, I explain the differences between the United Stated and the European Union regarding this subject. Section 3 is about the pass-on defence. Similarly, I also explain the differences between the US and the EU with respect to the pass-on defence. In Section 4, I provide a short introduction to cartel damage estimation. Section 5 explains the economic background for incomplete cartels, umbrella damages and pass-on effects. Section 6 illustrates the methodology I use for this thesis. Section 7 shows the results for a com-petitive market in a pre-cartel situation, and Section 8 shows the results for a market with a partial cartel. In Section 9, I decompose the overcharge, pass-on effects and output effects. Section 10 extensively explains the relation between the umbrella effect and the pass-on effect, according to the results of this the-sis. Section 11 gives advice for defendants in cartel damage claims regarding whether to use the pass-on defence. Finally, Section 12 concludes the thesis.

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2 Legal standing regarding umbrella damages

2.1 Umbrella damages in the EU

In Kone (2014), a discussion arose whether cartelists should be held liable for umbrella damages (Schreiber & Savov, 2014).1 _{A subsidiary of the Austrian}

Federal Railways, ÖBB Infrastruktur Aktiengesellschaft, claimed compensation from the cartel members, including umbrella damages. The Kone case arose due to the elevator and escalator cartel, which had been recognised by the ECJ in 2007.2 Seven producers colluded since 1980s for the production of eleva-tors and escalaeleva-tors (Peralta, 2016). In the period when the cartel was active, ÖBB Infrastruktur bought from third parties who may have benefited from the cartelised prices. However, the Oberster Gerichtshof (the Supreme Court of Austria) decided that the loss caused by the umbrella effects could not be at-tributed to the members of the cartelised firms. According to the court, the necessary causal link was not present in Austrian law. The Oberster Gericht-shof requested for a preliminary ruling concerns the interpretation of Article 101 TFEU, that Court of Justice of the European Union (CJEU) must decide whether national law, which legally excludes any liability for umbrella damages, must be set aside because of the rights granted under Article 101 of the TFEU. In the Courage and Crehan (2001) case, the judgment by the CJEU was explic-itly that ’any harmed individual can claim for compensation’.3 _{According to EU}

law, national rules cannot jeopardize the functioning of the TFEU. The ECJ stated explicitly that private enforcement of EU competition law must follow the rules of the treaties which emphasise the duties to all economic agents who enter a market (consumers, firms, authorities etc.).4 Therefore, the CJEU de-cided in June 2014 that the EU right granting full compensation includes losses caused by the increased prices of the non-cartelised firms. In AG Kokott’s opin-ion, in the EU, ’functioning markets characterised by undistorted competition are in themselves an asset beyond all cost-benefit considerations’.5 _Overall,

the court clarified that, based on economic behaviour, the link between price increases by cartelised firms and price increases by cartel outsiders cannot be ignored. Therefore, the court decided that cartel members can be held liable for umbrella damages that result from manipulation of the market. The Kone decision implies that national laws must ’specifically take into account the ob-jective pursued by Article 101 of the TFEU, which aims to guarantee effective and undistorted competition in the internal market and, accordingly, prices set on the basis of free competition’ (Peralta, 2016). The ECJ concluded that, to prove a direct causal link, the cartel does not have to be the single cause of damages: rather, it is sufficient that the cartel is a co-originator of the umbrella

1_{Kone and others v. ÖBB-Infrastruktur, C-577/12, EU:C:2014:1317, (2014)} 2_{Case COMP/E-1/38.823, PO/Elevators and Escalators (C(2007) 512 final)} 3_{Courage and Crehan,C-453/99, EU:C:2001:465. (2001)}

4_{Judgment of the Court of Justice (ECJ), Francovich, Joined Cases C-6/90 and C-9/90}

(19 November 1991)

5_{Opinion of Advocate General Kokott in Case C-557/12 Kone AG and Others v. OBB}

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damages. Regarding the harm resulting from umbrella damages, the court spec-ified three conditions that must be proven by the claimant in order to have the right of compensation (Schreiber & Savov, 2014):

1. the market price was increased due to the cartel

2. the claimant suffered harm due to the increased prices, and

3. the cartelised firms must have been able to foresee the harm caused by the umbrella effects

Courts now must decide whether umbrella damages were likely to occur and decide whether the defendants were able to foresee this. As pointed out by Advocate General this question is redundant because a cartel will only be in-troduced if the cartelised firms believe their profit will increase compared to the profit without a cartel . This will only be the case a cartel’s competitors raise prices as well (Monti, p.467). According to AG, when competitors do not increase their prices and undercut the cartelised prices to obtain a larger market share, cartel agreements would me less profitable.

2.2 Umbrella damages in the US

The starting point in the United States and the European Union regarding losses is not different: ’any individual’ (EU) and ’any person’ (US) who suffered from harm may claim for compensation.6 _{However, the United States has a different}

point of view regarding compensation to claimants for umbrella damages. Where the EU largely emphasises on arguments favoring liability for umbrella claims, appeared the US to point out the importance of efficient law systems. Courts in the US are incoherent, some allow claimants to claim for umbrella losses, and some do not. In the US, it is permitted to have different rules regarding umbrella damages among different circuits. In contrary, the CJEU has EU wide rules regarding liability. By denying divergence, the CJEU hinders ’forum shopping’ in the EU (e.g., choosing the court with the largest likelihood of a favorable judgment) (Monti, 2014) .

The US Court of Appeals for the Third Circuit decided that the economic causation between infringement caused by cartel members and prices that un-dertaking parties outside the cartel charge is too complex to prove with suffi-cient certainty (Franck, 2015). The court stated further that compensation for umbrella damages would burden the court with excessive economic complexity because any proof given would, at best, be highly conjectural. Several courts have affirmed this opinion. The Ninth Circuit expressed the following skepticism about estimating umbrella damages (Blair & Durrance, 2018, p.244);

“Under an umbrella theory, the result of any attempt to ascertain with reasonable probability whether the nonconspirators’ prices re-sulted from the defendants’ purported price- fixing conspiracy or from

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numerous other price considerations would be speculative to some de-gree ... Not only would we be required to speculate that plaintiffs were injured solely as the result of umbrella pricing, but also we would be required to sanction complex judicial inquiry into the pricing deci-sions of sellers remote from plaintiffs”.

3 Legal standing regarding pass-on defence

3.1 Pass-on in the EU

The principle of pass-on effects became first evident by the CJEU in Ireks-Arkady (1979) (European Commission & RBB Economics, 2016).7 _{In Courage}

and Crehan (2001), the ECJ clarified that infringements of the Treaty gives standing to indirect claimants because the judgment by the CJEU was explicitly that ’any harmed individual can claim for compensation’(Verboven & van Dijk p.462). As a result of this decision, the European Commission (EC) emphasised the importance of a passing-on defence. Therefore, the EC wrote its Green Paper in 2005 about damage actions including a disquisition on the pass-on defence. It is important to note that the EC also emphasises the output effect which follows from a pass-on defence. Thereafter, in 2008, the EC published a White Paper, where the EC clarified the standing to claim damage for all parties and it allows defendants to use the pass-on defence. As mentioned previously, if a pass-on defence is used, the discount on the overcharge must be corrected by the output effect. If a claimant receives compensation for the complete overcharge, while the claimant had passed on a certain degree of the overcharge, the claimant would receive more than the harm suffered. Therefore, the court clarified that the claimant should not be unjustly enriched. On 26 November 2014, the damages directive was implemented (bron jaremba lalikova). In appendix A, all rules can be found concerning the pass-on defence. The specific rule about the passing-on defence can be found in Appendix A, paragraph (e & g ).

However, the CJEU has stated that estimating the exact pass-on effect can be difficult because price setting behaviour is subject to many different influences. Further, defendants must prove the pass-on defence by showing what indirect purchasers would have done without the cartel. They must show that prices would have been lower without an overcharge. To estimate what the situation would have been for the harmed party without an infringement, a construction of the ‘counterfactual scenario’ is needed. Some form of estimation is necessary because counterfactual prices and quantities are not directly observable. Finally, the CJEU has noted the importance of the volume effect. The loss of profits due to cartels can be dismantled into three different effects (Verboven & van Dijk p.458):

1. the price overcharge (e.g., the increased price due to the cartel).

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2. the pass-on effect (e.g., to what extend the increased price is passed-on to the downstream indirect customer), and

3. the output effect or volume effect (e.g., the reduction of sales due to the price increase)

The national court’s analysis must also include the negative effect of the pass-on effect pass-on the amount of sales of the claimant, and thereby the reductipass-on in profit. To successfully utilise the pass-on defence, a defendant must show that the damage compensation based on the overcharge would unjustly enrich the claimant (European Commission & RBB). The rule about the output-effect can be found in Appendix A(f ).

3.2 Pass-on in the US

The first case where direct purchasers could claim compensation for the over-charge due to a cartel agreement was in Chattanooga Foundry (1906) (Han et al., 2009, p.2).8 _{The present situation concerning pass-on defence is originated}

by three important cases. First, in Hanover Shoe (1968), the Supreme Court rejected the passing-on defence (Hellwig, 2006).9 _{The Court required in this}

case that, in order to establish a pass-on defence, the defendant must proof three requirements: first, the defendant must prove that the claimant increased prices due to the cartel, second, that the claimant did not decreased output due to the increased prices and, third, that the claimant wound not have had increased their prices regardless of the existence of the cartel. The rejection in Hanover Shoe was based on the fact that indirect purchasers were dispersed, and therefore offenders might be punished too lightly if the pass-on defence was allowed to reduce the claim. Thereby, the court decided that dividing damages among different levels of the supply chain was exceedingly complex and would make the process less efficient and effective. Therefore, in 1968, the US Supreme Court denied the existence passing on damages because it would be too difficult to estimate damages along different chains of the distribution channel (Euro-pean commission & RBB, 2016). Second, in Illinois Brick (1977), the Supreme Court continued with the same way of reasoning.10 _{The Court denied standing}

to indirect purchasers under US federal antitrust law to claim damage from the defendants. This rejection was based on the fact that the ‘pass-on defence’ had already been rejected in Hanover Shoe. Thereby, the Court decided that direct overcharge is more representative than the indirect overcharge. In the decade after the decision in Illinios Brick, there was a lot of criticism about this deci-sion. Third, in ARC America Corp. (1989), the Supreme Court decided that indirect purchasers could claim compensation and their standing was recognised (Kosicki & Cahill, 2006). 11

8_{Chattanooga Foundry & Pipe Works v. Atlanta, 203 U.S. 396 (1906).} 9_{Hanover Shoe, Inc. v. United Shoe Machinery Corp., 392 U.S. 481 (1968).} 10_{Illinois Brick Co. v. Illinois, 431 U.S. 720 (1977)}

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Defendants are not permitted to use the pass-on defence as a matter of Federal Law, therefore the pass-on defence is usually analysed in the context of indirect purchaser cartel damage actions. These are known as ‘class actions, which implies that a purchaser brings a claim on the behalf of the whole class with a similar situation who allege they are also affected by the cartel. The court’s justice will be the same for the entire class. This class action litigation results in a key difference between the US and the EU competition law.

4 Quantification methods

This section shows a short overview of the possible methods to quantify damages. These methods also can be used for estimating umbrella damages. Economists have developed a wide range of methods to quantify damages. To estimate what the situation would have been for a harmed party without an infringement, a construction of the ‘counterfactual scenario’ is needed. Some form of estimation is necessary because the counterfactual prices and quantities are not directly observable. Oxera (2009) and the European Commission (2013) provide exten-sive quantification guides with practical methods to estimate harm caused by an infringement of Articles 101 and 102 of TFEU.

There are three different groups of methods which can be used for car-tel damage estimation; comparator-based, financial-analysis-based and market-structure-based (Oxera, 2009). A comparator-based approach uses data that are external to the cartel to estimate the counterfactual scenario. There are three different comparator-based approaches; a cross-sectional comparison (compar-ing the cartel variables with a different geographical/product market), time-series comparisons (comparing the variables before, during and after the cartel period) and the ‘difference-in-difference’ approach (a combination of the two above; comparing the change of price before, during and after a cartel against the change in a comparable non-cartelised market). Financial-based methods use the financial performance of the cartel members or the harmed party as a starting point. Another method includes the cost-based method (European Commission, 2013). The cost-based uses the production costs of the cartelised product in combination with a mark-up for a reasonable profit margin to esti-mate the counterfactual scenario. Market-structure-based approaches refer to Industrial Organisation theory. Based on theoretical models and assumptions, counterfactual scenarios can be assessed. By identifying the most representa-tive models that fit the relevant market, insight can be given how a certain market works and what the counterfactual price would have been. Each esti-mation method has different strengths and weaknesses. Which method suits best for a given case depends on different circumstances and the kind of data that is required of available. For example, an advantage of methods comparing over time, is that because is uses data from the same geographical and product market, demand characteristics, degree of competition and market structure is more comparable than with other geographical of product markets. However, the disadvantage is that the effect of the cartel before, during and after has not

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only been caused due to the infringement.

According to the EC, the definition of a relevant product market is a market which include all products and services which can bee seen as interchangeable or substitutable by a consumer with respect of the prices, use of the product and the characteristics. A well known method to estimate what the relevant market is, is the small but significant nontransitory increase in prices (SSNIP) test (Davis & Garcés, 2010, p.201). This test is based on the idea that a market where products within one market do not face significant influences from changes in prices from products of another market. Most jurisdictions look at whether a price increase of 5-10% for at least one year is profitable for a hypothetical monopolist. If it is not profitable, it means that there must be at least one substitutable good excluded from the relevant market and then the relevant market has been taken too narrow. Than the SSNIP test must be done again for a wider range of relevant products.

To estimate in what position the harmed party would have been, one can estimate the but-for price (European Commission, 2013). The but-for price is the estimated price that would have prevailed without the cartel agreements. It is impossible to estimate with complete certainty what this but-for price would have been without the infringement. Therefore, but-for price estimation always relies on certain assumptions and approximations. Once the but-for price has been estimated, a comparison with the actual price is necessary to quantify the harm caused by a cartel. A standard method to measure harm caused by cartels in a price-fixing agreement is to estimate the overcharge on the purchases that were actually made. Formally, the overcharge is represented by (Blair & Durrance, 2018);

4 = (Pa− Pbf)Qa (1)

Where a refers to the actual price and quantity and bf to the but-for price. In direct cartel damage estimation, it is possible to estimate the overcharge by running a reduced-form regression of explanatory variables (demand and cost factors) that affect the price level but which are not affected by the cartel (Davis & Garcés, 2010). Graphically, the difference between the but-for price and the real price looks as follows:

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Figure 1: But-for price estimation (source: European Commission, 2013, p.29)

Two well-known method to estimate the but-for price are the dummy variable approach and the forecasting approach (European Commission, 2013). The dummy variable approach is a comparison of the average price before-and-after the cartel period with the average price during the cartel period. It is possible to estimate the overcharge by running a reduced-form regression of explanatory variables (demand and cost factors) that affect the price level but which are not affected by the cartel (Davis & Garcés, 2010). A dummy variable must be included in this regression which is 1 for the time period that the market is in a cartel and 0 otherwise. The coefficient of the dummy variable captures the overcharge (the unexplained increase in price) caused by the cartel. A key assumption of the dummy variable approach is that the coefficients are constant over time and not affected by the cartel. A dummy variable regression looks as follows:

pt= α + γ ∗ Cartelt+ β1∗ Costst+ β2∗ Characteristicst+ t

Where Carteltis the dummy variable and a vector of demand and cost factors

that are correlated with the price but not depended on the cartel are included. γ is the amount of overcharge for a given time period.

Considering umbrella damages, there are two different methods to use the dummy variable approach to estimate the but-for price for the umbrella firms. First, the regression can be run on the whole relevant market, including the car-tel insiders and outsiders. The coefficient of the dummy variable would equal 1 for all time periods that the market is in a cartel, for both the cartelists and

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the non-cartelists. This coefficient would capture the total effect of the cartel on the price. One disadvantage of this method is that if there is a significant difference in behaviour of the cartelists and the non-cartelists, the damage for the cartel claimants could be underestimated and the damage for the umbrella claimants could be overestimated. To estimate whether there is sufficient evi-dence to indicate significantly distinguishable behaviour between the cartelists and non-cartelists, one can include an interaction term with a cartel dummy and the alleged cartelists (e.g. Cartel ∗ Conspirator). If this coefficient is statisti-cally not significant it would reveal that the cartelists and non-cartelists do not have distinguishable different behaviour regarding their price setting strategy. Second, the same regression can be used to estimate separately what the over-charge is for the cartelists and for the non-cartelists. These overover-charges could be compared to see whether the price increase is similar or different.

The main difference between the forecasting approach and the dummy vari-able approach is that in the forecasting approach only data is used from com-petitive periods. With this data, the but-for scenario will be estimated based on the features during the competitive periods. A disadvantage of this method is that less data is used compared to the dummy variable approach and if there is not enough before-and-after data available, the data may be insufficient to forecast.

There are multiple reasons why it is difficult to incorporate umbrella damages into cartel damage estimation (Blair & Durrance, 2018). This may include the need for a complex damage estimation procedure, the fear of duplicative damage awards, the speculative aspect of the damage and the fear of over-deterrence. Nonetheless, according to EU law, quantifying umbrella damages is particularly important because they are directly caused by cartels and no arguments have been presented why umbrella effects should not be legitimate for damage claims (European Commission, 2013). From a legal perspective, the likelihood of proving umbrella damages with a high degree of certainty appeared to be difficult, specifically concerning the causal link between anti-competitive conduct and umbrella damages (Peralta, 2016).

5 Economic foundation

In the subsequent section, I decompose the economic foundation of the harm caused by a cartel. I begin with an explanation of why cartels are stable. This is followed by how direct purchasers and purchasers from umbrella firms are harmed. Lastly, I provide an explanation of the economics of passing on damages. In general in cartels cases, firms typically increase their prices to increase joint profits. Due to the price increase, purchasers of a cartel pay higher prices than they would have done without a cartel agreement. The increased prices also cause a decrease in quantity sold because some consumers decide not to purchase anymore.

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5.1 The Economics of incomplete cartels

An incomplete cartel is one in which not all firms in the relevant market are members of a cartel. In a relevant market with an incomplete cartel, cartel members leave a part of the demand for the cartel outsiders. An incomplete cartel is stable when its members earn increased profit compared to the situation without a cartel agreement (Bos, 2009 pp.12-13). Stable cartels may face two distinct problems: a coordination problem and an incentive problem. A coordi-nation problem includes problems with accomplishing an agreement regarding the content of the agreement (e.g., bargaining problems). An incentive problem includes incentives to members to deviate from cartel agreements. According to previous real-world studies, the primary reason that cartels are not stable relates to coordination problems that arise from difficulties with bargaining be-tween members (Levenstein & Suslow, 2004). Accordingly, to maintain a stable cartel, two conditions are necessary. First, cartels must be internally stable, implying that it would not be profitable for cartel members to stop colluding. Mathematically:

πc(k) ≥ πo(k − 1) (2) Second, cartels must be externally stable, implying that it would not be prof-itable for outside firms to join cartels. Mathematically:

πo(k) ≥ πc(k + 1) (3) If both conditions hold true, a cartel is said to be stable.

Incomplete cartels exist in all standard oligopoly models, except for a Bertrand competition market with homogeneous goods. In this case, if a cartel is incom-plete, outsiders drive prices down to marginal costs. Accordingly, the cartel is not sustainable, and no cartel effects or umbrella effects will exist. In case of product differentiation, lower prices of cartel outsiders do not drive prices down to marginal costs. Even if the outsiders’ prices are lower, they may leave some demand to the cartel members (Bos, 2009 p. 29).

5.2 The Economics of umbrella damages

In contrast to the legal difficulty of proving the causal effect between the in-fringement and umbrella effects, the economic causality is more straightforward. Inderst, Maier-Rigaud and Schwalbe (2014) have conducted an extensive eco-nomic analysis on how cartel outsiders respond to cartels. This analysis has been corrected and extended by Holler and Schinkel (2014). Four situations can be considered, namely: Bertrand competition with homogeneous and differ-entiated goods and Cournot competition with homogeneous and differdiffer-entiated goods. In the subsequent paragraph, I provide a short overview of how strategic cartel outsiders respond to these four situations.

First, as explained in Paragraph 5.1, umbrella effects do not occur in the case of Bertrand competition and homogeneous goods if umbrella firms are not capacity-constrained. This is because all demand will divert to umbrella firms

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if cartel insiders increase their prices, and prices will drive down towards com-petitive level. Second, in the case of Bertrand competition and differentiated products, umbrella effects do occur. In this situation, prices are strategic com-plements: the optimal response for a cartel outsider is to raise their price as well (Inderst, Maier-Rigaud & Schwalbe, 2014, p.749). The price increase is given by the slope of the best-response functions. Incomplete cartels, in this situation, always increase the profitability of the cartel members (Bos, 2009 p.30). The degree of product differentiation is an important determinant for the magnitude of umbrella effects. The magnitude of the demand that spills over from cartel members to cartel outsiders becomes larger as products become more homoge-neous. Consequently, umbrella effects become more pronounced as good become less differentiated. Thereby, the magnitude of umbrella effects also depends on the market coverage of a cartel. If there are only a small number of firms inside a cartel, a smaller part of the demand spills over to each cartel outsider when prices increase. Consequently, price increase by the umbrella firms are less pro-nounced if the market coverage is small. To illustrate how cartels and cartel outsiders respond, see the following figure:

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Figure 2: Umbrella effects with Bertrand competition (source: Inderst, Maier-Rigaud & Schwalbe, 2014, p.750)

In Figure 2, the two best-response functions are drawn for two symmetric firms in a pre-cartel situation. The Nash-equilibrium can be found at the inter-section of the two best-response functions. If one firm is in a cartel, the cartel firm increases its price and therefore, the best-response function shifts upwards. The new equilibrium prices now can be found by the intersection of the best-response function of the cartel outsider and the new best-best-response function of the cartel insider. The cartel effect is given by the difference between pmand p. The

umbrella effect is given by the difference between p0and p. As seen in Figure 2,

the cartel effect is larger than the umbrella effect, and the effects depend on the slopes of the best-response functions. Third, another standard oligopoly model is quantity competition (Cournot). Salant et al. (1983) show that outsiders’ profits increase due to cartels. Thereby, their profit increases more compared to the increased profit of cartel members. This happens because, in the case of ho-mogeneous products, outsiders benefit from higher market prices in combination with an increase in quantity. In cartel agreements, cartels reduce their quan-tity and accordingly increase their prices to increase their profit. In a Cournot

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setting, quantities are strategic substitutes (Inderst, Maier-Rigaud & Schwalbe, 2014, p.751): if cartel firms decrease their quantity, the best response for cartel outsiders is to increase their outputs and take advantage of the extra demand caused by a cartel. The increase in output of cartel outsiders is not sufficient to offset the decrease in output by the cartelised firms. Therefore, both cartel insiders and outsiders have increased prices.

5.3 The Economics of pass-on

First, before examining the pass-on effect, consider a market where the pur-chasers of a cartel do not pass on any of the harm. Suppose that a cartel agrees to sell at the monopoly price instead of the competitive price (P = M C).

Figure 3: Effect of Monopoly market on direct purchasers (Source: Graph drawn by the author based on Hellwig (2006), p. 7)

The effects of the cartel agreement are illustrated in Figure 3. The downward sloping demand curve shows the relation between price and quantity. In this situation, the increased profit (e.g., producer surplus) for a cartelised firm is equal to the grey rectangle. However, the price increase also causes a deadweight loss, which is equal to the grey triangle. The decrease in consumer surplus is equal to the deadweight loss plus the grey rectangle. In conclusion, since the increase in profit is smaller than the decrease in consumer surplus, the total welfare change due to the cartel agreement is negative.

Now, consider a market where the direct purchasers can pass on a certain amount of the harm. As mentioned previously, the total amount of harm can

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be decomposed into three different effects, namely: overcharge, pass-on effect and output effect.

Figure 4: Overcharge (A), pass-on effect (B) and output effect (C) (Source: Graph drawn by the author based on European Commission & RBB

Economics, 2016, p.10)

As shown in Figure 4, the harmed party sustains a profit decrease due to the illegal price increase of c1− c0. The profit of the direct purchaser is decreased

by Area A (overcharge). To minimise the negative effect of the marginal cost increase, direct purchasers may increase their own prices to pass on part of the overcharge. Area B illustrates the pass-on effect. Passing on the overcharge cre-ates a profit increase due to the price increase of the direct purchaser from p0

to p1. However, because the prices are increased for indirect purchasers, some

decide to no longer buy the product, which results in decreased profit. This decreased profit is equal to Area C . To prove that the claimant would unjustly be enriched, Area C must not outweigh the effect of Area B. The only situation in which the direct overcharge is an accurate measure of the harm is when Area B is exactly equal to Area C. In conclusion, the damage caused to the claimant by an increase in input prices is composed of three different terms:

Damage = Overcharge − passingonef f ect + volumeef f ect

From a theoretical perspective, the pass-on effect, among others, depends on the type of competition that is assumed in a market (European Commission & RBB

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Economics, 2016, p.57). In the case of homogeneous goods industries, where competition focuses on prices, the competition may be very intense. Therefore, all sales go to the lowest cost firm, and charging higher prices than others is not possible in these markets. In the case of quantity competition, the competition represents a less intense rivalry. Given the nature of Cournot competition, a single market price is determined and the passing on of harm must influence that single market price. The industry-wide degree of pass-on depends on three primary factors, namely: the degree of competition, the change of output due to marginal cost change and the elasticity of inverse demand. In the case of product differentiation in both Bertrand and Cournot worlds, firms have some degree of market power and therefore can pass on a certain amount of the overcharge. In this thesis, I focus on the degree of passing on harm in Bertrand competition with product differentiation.

6 Methodology

To show the relation between the umbrella effect and the pass-on effect, a few assumptions must be made. Several determinants influence the magnitude of the umbrella effect: type of competition (Bertrand/Cournot), cartel market coverage, degree of product differentiation of traded goods in the market, and whether outside firms behave strategically or non-strategically (Inderst, Maier-Rigaud & Schwalbe, 2014). If products are homogeneous, as explained previ-ously, no umbrella effects and no cartel effects occur. Therefore, the question of the magnitude of umbrella damages only exists when there is at least some degree of product differentiation and some customers who do not switch easily. In case of differentiated products, the magnitude of price increases by umbrella firms depends on the amount of demand diverted from cartelised firms to um-brella firms. The higher the degree of product differentiation is, the smaller the amount of demand diversion and the smaller the price increases by umbrella firms become. Thereby, in most markets, it is more realistic to assume that some degree of product differentiation exists (Blair, Durrance & Wang, 2016 p.408). Without some degree of product differentiation in the upstream mar-ket, it would not possible to form a partial cartel since competition between a cartel and an outsider in a Bertrand setting would drive prices down to marginal cost. If products are sufficiently differentiated, it may result in a stable cartel (Bos, 2009). According to Oxera’s quantifying antitrust damages paper (2009), if goods are differentiated, Bertrand competition is more appropriate compared to Cournot competition. Therefore, I assume that the firms compete regarding prices and that products are differentiated. Thereby, to simplify my model, I assume that all firms in the same layer have symmetric marginal costs prior to the cartel and linear marginal costs. Based on the Shubik (1980) linear demand function, I demonstrate the relation between the behaviour of umbrella firms and the direct claimants. I use the Shubik-Levitan demand function, as given

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by Deneckere & Davidson (1985): qi(p1, ..., pN) = V − pi− γ(pi− 1 Npi− 1 N N X j=1 pj) (4)

V refers to a demand scale parameter, n refers to the number of symmetric firms and γ ≥ 0 stands for the degree of product differentiation (γ = 0 implies uncorrelated goods and γ → ∞ implies homogeneous goods).

Figure 5: The three-layer market of wholesalers, retailers and consumers

Figure 5 displays the model I use in my thesis. From this point forward, I refer to Layer 1 as ‘wholesalers’, Layer 2 as ‘retailers’ and Layer 3 as ‘con-sumers’. Layer 1 consists of N wholesale firms where M out of N firms form a price fixing cartel. To calculate how the wholesalers maximise their profit, I assume in this model that the per firm quantity of the retailers (qri) is equal

to the per firm quantity of the wholesalers (qwi). Thereby, I assume that there

are ten firms wholesalers and each wholesaler sells to its own retailer. It is not possible for retailers to buy from other wholesalers than its own (e.g., no crossing-over). The wholesale firms sell their products as input for retailers and therefore I assume that the price of a wholesale firm is equal to the marginal costs of the retail firm who buys from that specific wholesale firm. Therefore, in case of a cartel, firms in the retail layer differ in their marginal costs

Layer 1: The pre-cartel price of the wholesalers, pw0, can be calculated by

maximising each profit function individually, assuming the firms are symmetric. In a cartel situation, M out of N firms form a cartel together, and therefore they maximise joint profits. Accordingly, they increase their prices compared to the pre-cartel situation. The optimal response for cartel outsiders is to in-crease their prices as well. The degree to which cartel outsiders can inin-crease their prices depends on the degree of product differentiation and the market coverage of the cartel. The cartel effect is the difference between the pre-cartel prices and the cartel prices of the cartelised firms. The umbrella effect is the difference between the prices of the outside firms in a cartel situation and the symmetric competitive prices.

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Layer 2: The pre-cartel price of the retailers, pr0, can also be calculated by

maximising each profit function individually, assuming the firms are symmetric. Whereby the marginal costs is determined by the prices of the wholesalers. In a cartel situation, M out of N retail firms buy from cartelised firms and N minus M firms buy from cartel outsiders. The retailers who buy from the cartelised firms are the parties harmed directly by the cartelised firms and suffers directly from the overcharge caused by the cartel. As explained above, in case of in-complete cartels, cartel outsiders increase their prices under the umbrella of the cartel. Therefore, retailers who buy from cartel outsiders suffer indirectly from the cartel. If there is no perfect competition in the retail layer, and firms have some degree of market power, it is possible for the second layer to pass-through some of the price increase to the final consumers.

Layer 3: The end consumers will respond according to Shubik demand.

Layer 1 moves first and determines its price, pwi, given the demand of the

down-stream layer. As mentioned previously, the per firm demand in the updown-stream market is equal to the per firm demand of the downstream market in pre-cartel situation. Layer 2 moves next. Given the input price, pwi, and the Shubik

de-mand function, the retailers maximise their profits and determine their prices, pri. The fact that the Shubik demand function is maximised in two different

layers causes double marginalisation. This model can be solved via backward induction. I assume horizontally competitive firms move simultaneously.

7 The pre-cartel solution with Shubik demand

This section demonstrates the results of a competitive market in a pre-cartel situation. As previously mentioned, I solve the model via backward induction. Therefore, I start with maximising the profit of the retailers. If the prices of the retailers are known, the prices for the wholesalers can be calculated. Firms maximise their profit according to the following Shubik demand:

qri(pr1, ..., prn) = V − pri− γ(pri− 1 Npri− 1 N N X j=1 prj) (5)

In this thesis, I assume the intersect term V is equal to 10. I assume there are 10 firms in the upstream market and 10 firms in the downstream market (N = 10). The marginal costs of the upstream firms is equal to 1 (c = 1).

7.1 The pre-cartel retail market equilibrium

I begin with retailers maximise their profit. This profit for firm i can be ex-pressed as:

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where pwi is the input price per product. In a symmetric, competitive

equilib-rium, retailers maximise their profit, and the Nash equilibrium can be found by assuming symmetry and deriving the best response functions of each firm. Max-imising the retailers’ profit with respect to the retailers’ price gives the following first-order condition (FOC):

∂πri ∂pri = 10 − 2pri− 2γpri+ γ 5pri+ γ 10 n X j=1,j6=i prj+ pwi+ γpwi− pwiγ 10 = 0 (7)

In this equation, the sum is the sum of the prices of all other firms except for firm i. This sum can also be written asPn

j=1,j6=iprj = (N − 1)pj. Substituting

this into the FOC (7) and applying the symmetry assumption that the price of all retailers is equal to each other pri= prj= p∗rigives the Nash equilibrium for

retail firms in a pre-cartel equilibrium and depends on the input prices pwi.This

gives the following expression:

p∗_ri= p∗_r0=V N + pw(N + γ(N − 1))

2N + γ(N − 1) (8) As expected, the price of the retailers is decreasing with the number of firms and the degree of substitutability. Substituting V = 10 and N = 10 in the equation (8) gives:

p∗_ri= p∗_r0=100 + pw0(10 + 9γ)

20 + 9γ (9)

7.2 The pre-cartel wholesale market equilibrium

In this section I show how to derive the Nash equilibrium for the wholesale market. The firms in the wholesale market maximise their profit according to the same demand as the retail market. Substituting the retail equilibrium price (9) into the demand function (5) gives the demand function for a given wholesale firm. This demand function can be found in Appendix B(a). Maximising the profit function (Appendix B(b)) w.r.t the price of a wholesale firm gives the FOC for the wholesalers. The FOC can be found in Appendix B(c) Solving this FOC gives the following Nash equilibrium for the wholesale market in the pre-cartel situation:

p∗_wi= p∗_w0=110 + 108γ + 8, 1γ

2

20 + 27γ + 9γ2 (10)

Filling in different degrees of substitutability into the Nash-equilibriums (9) and (10) gives the following results:

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Quantity (qw0= qr0) Wholesale price (pw0) Retail price (pr0)

γ = 0, 1 2,449 5,300 7,551

γ = 1 3,906 4,038 6,094

γ = 10 7,563 1,681 2,437

γ = 100 8,911 1,000 1,089

Table 1: Results of the competitive Nash equilibrium

As expected, the price of retailers and the price of wholesalers decreases with γ. This can be interpreted as stating that the more homogeneous the product is, the lower the price is. This follows naturally from the fact that demand diverts more easily due to a price increase if a product is more homogeneous (e.g., consumers are more indifferent between products). Consequently, the quantity increases in γ. Thereby, due to double marginalisation, the price of retailers is always higher than the price of wholesalers.

8 Cartel solution with Shubik demand

This section demonstrates the results of the asymmetric cartel equilibrium. Now, M number of firms in the wholesale layer form a partial cartel. In the following, for Layer 1, I denote the per firm profit, price, quantity and marginal costs of the cartelised wholesalers as, respectively, πwci, pwci, qwci and c. I

denote the per firm profit, price, quantity and marginal costs of the umbrella wholesalers as, respectively, πwui, pwui, qwui and c. M out of N firms in the

wholesale market form a cartel. Consequently, there are N − M umbrella whole-sale firms. I assume that the marginal costs of umbrella wholewhole-salers are equal to those of the cartelised wholesalers. I also assume that cartelised wholesale firms maximise their joint profits. They behave similarly to merged firms. Cartels prohibit members from acting individually; therefore, cartelised firms collude their prices symmetrically.

For Layer 2, I denote the per firm profit, price, quantity and marginal costs of the retailers who buy from the cartel as, respectively, πrci, prci, qrci and

pwci. I denote the per firm profit, price, quantity and marginal costs of the

retailers who buy from the umbrella wholesalers as, respectively, πrui, prui,

qrui and pwui. Accordingly, the cartel retailers and the umbrella retailers have

asymmetric marginal costs. As each retail firm buys from its own wholesale firm, and the total number of wholesalers and retailers are equal, M retail firms buy from a cartelised wholesaler and (N − M ) retail firms buy from an umbrella wholesaler.

8.1 The cartel retail market equilibrium

First of all, the prices of umbrella and cartel retailers can again be determined through backward induction. These firms again maximise their profits according

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to demand as given by equation (5). Cartel retailers and umbrella retailers now maximise the following profit functions, respectively:

πrci(prc1, ..., prcM, pru1, ..., pru(N −M )) = (prci− pwci)qrci (11)

πrui(pru1, ..., pru(N −M ), prc1, ..., prcM) = (prui− pwui)qrui (12)

The optimal price of retailers is dependent on their own prices and the prices of all other retail firms. The sum of all other firms for an umbrella retailer is the following: N X j=1 j6=i prj= M prci+ (N − M − 1)prui (13)

Similarly, for cartel retailers, the sum of all other firms constitutes the following:

N

X

j=1 j6=i

prj= (M − 1)prci+ (N − M )prui (14)

Substituting equation (13) into the FOC (7) for umbrella retailers gives the following FOC : ∂πrui ∂prui = 10 − 2prui− 2γprui+ γ 5prui+ γ

10(M prci+ (9 − M )prui) + pwui+ γpwui −pwuiγ

10 = 0 (15)

Solving this equation for prui gives the best response function for the umbrella

retailers:

p∗_rui= 100 + pwui(10 + 9γ) + γM prci

20 + γ(9 + M ) (16) Similarly, by substituting equation (14) into the retailers’ FOC for cartel retail-ers gives the following best response function for the cartel retailretail-ers:

p∗_rci=100 + pwci(10 + 9γ) + γ(10 − M )prui

20 + γ(19 − M ) (17) As shown in (16) and (17), the best response function of cartel retailers is de-pendent on the best response function of umbrella retailers, and vice versa. Substituting the best response functions of each into the other’s gives the equi-librium price for cartel retailers and umbrella retailers, respectively:

p∗_rci =(20 + γ(9 + M ))(100 + (10 + 9γ)pwci) 400 + 560γ + 171γ2 + γ(10 − M )(100 + (10 + 9γ)pwui) 400 + 560γ + 171γ2 (18) p∗_rui= (20 + γ(19 − M ))(100 + (10 + 9γ)pwui) 400 + 560γ + 171γ2 + γM (100 + (10 + 9γ)pwci) 400 + 560γ + 171γ2 (19)

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8.2 The cartel wholesale market equilibrium

To demonstrate how I derive the prices for the cartelised firms in the wholesale market, in this section, I illustrate this in detail for M=5. First, I derive the FOC for umbrella wholesalers. As previously mentioned, the quantity of an umbrella wholesale firm is equal to the quantity of an umbrella retail firm. However, the quantity of the umbrella firms may differ from the quantity of the cartel firms. Substituting equation (13) into demand function (5) provides the demand function for a given umbrella retail firm in a situation with a partial cartel in the wholesale market. This demand function is given in Appendix C(a). Because retail firms sell all their input, demand for the umbrella wholesaler is the same as for the retailer. By substituting the cartel (18) and umbrella (19) retail equilibrium prices, as derived above, into the demand, the demand as a function of the wholesale prices is given. The demand equation for umbrella wholesalers can be found in Appendix C(b). Umbrella firms maximise their profit function according to this demand. The FOC for umbrella wholesalers can be found in Appendix C(c). Solving the FOC gives the following best-response function:

pwui = γM (10 + γ + γM )(100 + (10 + 9γ)pwci) ((10 + 9γ)(400 + 560γ + 171γ2₎₎ −c(1100 + 1080γ + 81γ 2_{)(−20 + γ(M − 19))} ((10 + 9γ)(400 + 560γ + 171γ2₎₎ (20)

At this point, it is important to note that the FOC for the cartel firms does change because it maximises the aggregate profit of all cartel membersPM

m=1πm.

Cartel members maximise their profit with respect to the pwci. The FOC

there-fore changes to the following:

∂PM k=1πk ∂pwci = ∂πm ∂pwci + M X k=1 k6=m ∂πk ∂pwci (21)

Because cartels maximise the aggregate profits of all members, the individual price of a single member appears in the FOC via the other profit functions. Therefore, the FOC changes to the one derived previously (21). The part that changes can be substituted by the following:

M X k=1 k6=m ∂πk ∂pwci = γ 10(M − 1) (20 + γ(9 + M ))(100 + (10 + 9γ)) 400 + 560γ + 171γ2 (pwci− c) (22)

Substituting (22) into (21) the wholesalers’ FOC gives the FOC for a cartelised wholesaler. This FOC can be found in Appendix D(d). By solving this equation, applying the symmetry assumption pwci = p−wciand substituting c = 1, M = 5

and the best-response function for umbrella wholesalers (20) into the solution of the FOC, the price and quantity of cartel wholesalers and umbrella wholesalers can be calculated for different degrees of product differentiation. The results are the following:

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Wholesale price cartel (pwci) Wholesale price umbrella (pwui) Umbrella effect pwui−pw0 pwci−pw0 γ = 0, 1 5,442 5,359 41,55% γ = 1 4,855 4,428 47,56% γ = 10 2,472 2,137 57,65% γ = 100 1,201 1,150 75,83%

Table 2: Price results of wholesale market with cartel for M=5

Retail price cartel (prci) Retail price umbrella (prui)

γ = 0, 1 7,622 7,581

γ = 1 6,593 6,385

γ = 10 3,084 2,924

γ = 100 1,283 1,259

Table 3: Price results of retail market with cartel for M=5

Quantity cartel (qrci= qwci) Quantity umbrella (qrui= qwui)

γ = 0, 1 2,376 2,421

γ = 1 3,303 3,719

γ = 10 6,116 7.876

γ = 100 7,517 9.941

Table 4: Quantity results of retail and wholesale market with cartel for M=5

As one can see in Table 2, 3 and 4, the price of the retailers and the price of the wholesalers is again decreasing with γ. Both wholesale prices and umbrella prices are increased compared to the pre-cartel situation. As expected, the umbrella effect is increasing with γ. This is due to the fact that demand divert away from the cartel more easily if products are more homogeneous. Therefore, umbrella firms face a higher demand increase due to the cartel when γ is higher and therefore are better able to increase prices as well. As a result of the higher prices, the cartel firms’ quantity sold is decreased compared to the pre-cartel situation. The quantity sold for the umbrella firms is decreased for lower degrees of substitutability (γ = 0.1 and γ = 1) and increased for higher degrees of substitutability (γ = 10 and γ = 100) compared to the pre-cartel situation. Following the same approach, the results can be calculated for M 6= 5.

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9 Overcharge and pass-on and output effects

This section demonstrates how the results of the overcharge, pass-on effect, pass-on generated by umbrella effect, and output effect are calculated. Again, I illustrate the approach for M=5. Now that the cartel equilibrium prices and quantities are known for retail and wholesale firms, the overcharge and pass-on effect and output effect can be calculated. The total harm for a retailer is equal to the difference in profit before and after a cartel agreement. One can see in Appendix E that the separation of the three effects can be shown as the following:

dπ = (pwci− pw0)qrci− (prci− pr0)qrci+ (pr0− pw0)(qr0− qrci) (23)

The first part ((pwci−pw0)qrci) is equal to the overcharge caused by the increased

prices of wholesale cartel insiders, the second part ((prci− pr0)qrci) is equal to

the pass-on effect caused by the increased prices of retailers who buy from the cartel and the last part (pw0)(qr0− qrci)) is equal to the output effect caused by

the decreased output sold due to the increased prices of the retailers who buy from the cartel. As shown in Appendix F(c), the part of the pass-on effect that is caused by umbrella damages can be calculated with the following formula:

θumbrella=

∂θtotal

∂pwui

× (pwui− pw0)

Where θtotalis the total pass-on effect and θumbrellais the pass-on effect caused

by umbrella effect (hereafter umbrella pass-on).

For M = 5 the change in profit of the cartel retailer is the following:

Overcharge Pass-on effect Umbrella

pass-on % Output effect γ = 0, 1 0,337 -0,169 -0,0175 10,38 0,164 γ = 1 2,699 -1,648 -0,872 52,91 1,240 γ = 10 4,838 -3,957 -2,485 62,80 2,094 γ = 100 1,586 -1,458 -1,151 78,97 0,138

Table 5: Decomposition of total harm with M=5

As one can see, the overcharge, pass-on effect and output effect are the largest for intermediate degrees of substitutability (γ = 10). This is in agreement with the findings of Deneckere & Davidson (1985). They have found that in mergers, the profit for umbrella firms as well as cartel firms is the highest for intermediate degrees of substitutability. Therefore, the overcharge, pass-on effect and output effect are also the largest in this case.

Following the same approach as in section 8.2, the same results can be cal-culated different numbers of cartel members (M 6= 5). In the following figure,

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the results of the umbrella effect proportionally to the cartel effect is plotted against the pass-on effect caused by umbrella effect proportionally to the total pass-on effect. The results as calculates in table 2 and 5 are shown in Figure 6 for M=2 to M=9. 20 40 60 80 100 20 40 60 80 100 pwui−pw0 pwci−pw0 θumbrella/θtotal M=2 M=3 M=4 M=5 M=6 M=7 M=8 M=9

Figure 6: Results pass-on caused by umbrella effect

The magnitude of umbrella effects proportional to cartel effects is shown on the x-axis, and the pass-on effect caused by the umbrella effects proportional to the total pass-on effect in shown on the y-axis (both in percentages). The lowest square in every line plot is γ = 0.1, the second γ = 1, the third γ = 10 and the fourth γ = 100. As expected, umbrella effects increase with γ for every M. Thereby, in almost all cases, the umbrella effect increases with M. However, it is interesting to note that with γ = 10 and γ = 100, the umbrella effect proportional to the cartel effect decreases with M if M is larger than 5. This contradicts the findings of Holler (2016), who conducted a similar analysis for a market with only two layers, where the cartel sells directly to end consumers. Figure 6 also shows that for lower cartel coverages, the part of the pass-on effect that is caused by umbrella effects approaches 100%. If it is approximately 100 %, it would not be possible for cartel retailers to pass on any part of the harm if umbrella effects did not occur.

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10 Relationship between umbrella damage and

pass-on effect

In this section, I illustrate an elaborate response to the question of what the relationship between umbrella damage and pass-on effects is. Now, to focus purely on the relation between umbrella damage and pass-on, in the follow-ing figure, both umbrella effect proportional to cartel effect (blue) and pass-on caused by umbrella proportional to total pass-on (red) are plotted against γ with percentage on the y-axis and γ on the x-axis. 12

1 10 100 0 20 40 60 80 100 γ P er centag e

Blue: umbrella effect proportionally to cartel effect: pwui−pw0

pwci−pw0

Red: pass-on caused by umbrella proportionally to total pass-on: θumbrella

θtotal

Figure 7: Pass-on effect caused by umbrella effect and umbrella effect

Now, one can see that the slopes of the pass-on graphs are steeper compared to the slopes of the umbrella graphs for lower degrees of substitutability (γ < 10), and the slopes are more similar for higher degrees of substitutability (γ > 10). This means that the effect of umbrella damage on pass-on effect is probably larger for higher γ. This can be seen because the umbrella effect proportional to the cartel effect (pwui−pw0

pwci−pw0) rises faster than the pass-on caused by umbrella

damage proportional to the total pass-on effect when γ < 10. This is not the case when γ > 10. I proof this with the hypothetical situation, holding everything constant, and only changing the price of the umbrella wholesalers (and thus the umbrella effect changes by the same amount). To do this, the equation for θtotal in Appendix F(a) is used. The results are shown for different degrees of

substitutability in the following graphs:

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Figure 8: Effect of umbrella effects on pass-on (θtotal)

Figure 8 shows the effect of the umbrella effects (x-axis) on the magnitude of the pass-on effects (y-axis), with the hypothetical situation of holding everything else constant and changing only the price of the umbrella wholesalers. At the bottom right side of the x-axis, pwui is equal to the highest pwci for a market

with certain γ, as calculated in Section 8.2. This is because otherwise the effect of pwui on pass-on is shown when the price of the umbrella firms is larger than

the price of the cartelised firms (e.g., negative umbrella effects), which does not appear to happen in the model of this thesis. These figures show that umbrella effect has a positive effect on the pass-on effect in all cases. This can be seen because the slopes are positive in all situations. In addition, the relation between umbrella effect and pass-on effect appears to be quadratic in all cases. These results also show that the higher γ is, the larger the magnitude of the first derivative (f0(pwui) > 0) is (e.g., the larger the change in pass-on due to change

in umbrella effect). Accordingly, these graphs confirm that the effect of the umbrella effect on the pass-on effect is more pronounced in more homogeneous markets. These figures also show that the lower M is, the lower the pass-on effect is but the higher the magnitude of the derivative is. This means that the lower the market coverage of the cartel is, the more pronounced the effect of a change in umbrella effect is on pass-on effect. However, in this model, it is not

Umbrella damages and the passing-on defence in cartel damages claims

University of Amsterdam