Supplier damages and the umbrella effect of price cartels

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Msc. Thesis: Supplier Damages and the Umbrella Effect of

Price Cartels

Lennart Kroon 10676627

January 23, 2015

Abstract

In the history of cartel cases in the US and EU, claimants of cartel harm have mostly been purchasers. However, economic analysis shows that price cartels are likely to harm other parties in a production chain as well. The new directive for cartel damages recently adopted in the EU gives a basis for standing for suppliers to a cartel. As price increases and output reduction by the cartel go hand in hand, demand for input evidently drops. Suppliers are therefore damaged by the cartel through a loss in sales and possibly through lower prices as well. Also, the so-called ‘umbrella’ effect is currently a hot topic in EU competition policy. Victims of this umbrella effect claim that the non-colluding firms they purchased from, were able to set higher-than-competitive prices due to the anti-competitive behaviour of the colluding firms.

In this thesis, I analyze the magnitude of the umbrella effect, as well as the relative direct and indirect supplier harm, within a theoretical framework. I consider multiple scenarios and market settings which provides a decent guideline to assess the effects men-tioned above. The results show that, under certain conditions, both the umbrella and the supplier damages can indeed be quite substantial.

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1 Introduction

The perfect world in terms of economics is not one of blue skies and pearl white beaches. Rather, it is one where firms act competitively and markets are efficient. The current view on economics is that the former attains the latter, perfect competition implies an efficient allocation of resources. There are a lot of factors that could and in practice do distort such an ideal economic scenario. The number of competitors in a market being small and products being imperfect substitutes are among this long list. Competition authorities strive to a situation resembling the perfect economic framework as close as possible. However, most market characteristics are fixed and beyond the reach of authorities. Firms cannot be forced to enter a market in order to make it more competitive nor can authorities, for example, directly influence the pricing strategies of firms. Yet, it can be made easier for firms to enter a market by opposing actions that are intended to keep newcomers from entering the market and collusive market behaviour can be punished in order to deter price fixing by competitors. It is therefore the (anti-competitive) behaviour of firms that is the focus point of competition authorities.

The bulk of the cases that competition authorities have to deal with are either merger or cartel cases. A merger is a publicly announced proposal to merge two or more firms into one new entity. Numerous versions of mergers exist, think of horizontal and vertical mergers or joint ventures. The thing they have in common though is the fact that merger control by authorities is ex ante, a merger will only be carried out if it is approved by the competition authority in charge. In practice, a merger will be accepted if it is deemed not to have a significant anti-competitive effect or that the positive effects resulting from the merger outweigh these anti-competitive effects. Even though the decision to clear a merger might not always be straightforward, whether third parties are harmed by a merger is to a reasonable extent in the hands of competition authorities.

On the other side of the competition authority spectrum, cartel control is ex post. Private cartels are conducted in secrecy and after one is exposed, authorities have to decide on who to compensate for the harm inflicted by the cartel. In history there have been cases of public cartels as well, where cartels were encouraged by governments in order to increase efficiency and revitalize the economy.1 A cartel is a situation in which firms coordinate their market behaviour, aiming to extract wealth from other players in the economy. This coordinated behaviour frequently consists of price fixing or limiting production. Even though it is shown by Tuinstra et al. (2014) that under specific circumstances cartels can be welfare-enhancing, in general this is not the case.2 Nowadays, price cartels are therefore illegal per se in the US and the EU.

In the majority of the cases, cartel members coordinate their actions in order to raise the price level above the competitive level. Depending on the type of competition in the market, cartels can achieve this either by directly fixing prices - Bertrand competition - or controlling production - Cournot competition. Evidently, direct buyers from the cartel suffer since they have to pay more per unit of output and thus can generally buy less compared to the competitive case. However, depending on the structure of the market, these buyers might

1_{I will refer to ‘private cartels’ as ‘cartels’ hereafter since this is the type of cartel that is of interest for}

competition authorities

2

It is shown that incomplete cartels under Cournot competition can be welfare-enhancing. If the non-cartel members produce more efficient and expand production in reaction to limited production of the cartel, total welfare may increase while the cartel is still profitable.

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in turn react to these higher prices by raising prices for their respective consumers. The higher prices are ‘passed on’ to layers further down the production chain. On the other hand, since a price increase by the cartel is likely to go hand in hand with a decrease in quantity supplied by the cartel, suppliers might face lower demand for their input products and will be harmed by cartel actions as well. These suppliers might react by ‘passing up’ the cartel harm to their suppliers. A third effect that might arise in case of collusion is the so-called ‘umbrella’ effect. When firms acting in the same layer of a production chain produce perfect substitutes this effect is evident. A price increase by the cartel shifts demand to the substitutes of the non-cartel members. The firms supplying these substitutes face higher demand for their products and have the possibility to raise their prices along with the cartel. Consequently, by the same rationale as before, both suppliers to and buyers from these non-cartel members that are ‘under the cartel umbrella’ suffer indirectly from the actions of the cartel. The umbrella effect might also arise when products are imperfect substitutes, depending on the degree of substitutability.

The cartel effects described above have been investigated in previous literature. Especially passing-on effects have had quite some attention. Hellwig (2006) concludes that passing-on effects are irrelevant in assessing the true amount of cartel harm. In particular, he shows that for a direct purchaser from a cartel, potential gains from passing-on effects are exactly offset by the output effect that arises as the increase in the downstream price lowers demand. He uses a three-layer production chain - manufacturer, retailer, consumer - for his analysis. The same type of production chain is used by Basso and Ross (2010) but they allow for a degree of heterogeneity of products in their model. It is shown that as the downstream market gets less competitive, the more erroneous the direct overcharge measure of harm becomes - that is, the harm suffered by direct purchasers through higher cartel prices. Moreover, they claim that allowing standing to indirect purchasers does not lead to duplicative recovery of damages, as is often argued.

Han et al. (2009) extend the analysis on cartel effects to a broader setting. They consider a production chain with an arbitrary number of layers and a model with conjectural variations. This more general framework allows them to analyze the impact of certain cartel specifications such as location of the cartel in the production chain and type of competition. They find that the direct overcharge is a poor reflection of the true cartel harm. Regarding the harm to suppliers however, their model specifications and assumptions - constant marginal costs of production - imply that the price decreasing effect from reduced demand and the price increasing effect from reduced production exactly offset. Hence, it might be interesting to consider the effects on suppliers under different assumptions.

This is just a selection of the papers in which the passing-on effect has been studied, but in general the likelihood of passing-on effects is confirmed by the literature so far.3 On the other hand, the literature on supplier harm and umbrella effects is relatively limited. Inderst et al. (2013) show that significant umbrella effects will arise in a large number of market settings and that the amount of umbrella damages is strongly dependent on market characteristics such as the type of competition, the degree of product differentiation and the elasticity of demand and supply. Bueren and Smuda (2013) address the issue of damages to both direct and indirect suppliers to a cartel. They focus however on the legal aspect of supplier standing and possible quantification of harm and refrain from an extensive economic

3

See also Verboven and van Dijk (2007) and Kosicki and Cahill (2006) for example, who too have established the passing-on of cartel harm under varying model specifications

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analysis on damages.

The conclusion from previous literature is that the actions of a cartel are likely to percolate through to multiple layers in a production chain - upwards, downwards and even sideways. In this thesis I will focus on the relatively underexposed area of supplier harm and ‘umbrella’ damages and the magnitude of these cartel effects for a number of market settings. More specifically, I will compare the ‘overcharge’ to consumers caused by the umbrella effect to the overcharge of colluding firms. Also, I will compare supplier damages to total damages and investigate whether ‘traditional’ measures used to determine purchaser harm are appropriate to measure supplier harm. In section 2, I will briefly discuss the current legal framework regarding compensation for damages. The theoretical framework used to analyze umbrella and supplier harm will be introduced in section 3. In section 4, I will decompose cartel harm into specific cartel effects. Solutions of the model introduced in section 3 will be presented in section 5. Section 6 will be devoted to the results obtained from this theoretical analysis of cartel harm and in section 8, I will link these results to reality and state the conclusions regarding the significance of supplier and umbrella damages. Furthermore, I will provide some tests of robustness in section 7.

2 Competition Policy

In order to eventually formulate an advice on who to compensate for cartel harm, obtaining a clear insight in current competition law is a logic first step. In this section I will give a sketch of the present rules regarding cartel compensation and review cases that have shaped this juridical landscape.

2.1 US Competition Policy

Antitrust law in the US was formalized in the Sherman Antitrust Act in 1890 and extended by the Clayton Act in 1914. A much-quoted statement from this latter act is that “(. . . ) any person who shall be injured in his business or property by reason of anything forbidden in the antitrust laws may sue therefore (. . . ) and shall recover threefold the damages (. . . ).” Despite this seemingly noble proclamation, standing in cartel compensation claims have been quite restricted in the US.

One of the flaws in early US competition law was the fact that courts could only adjudi-cate interstate violations of the Sherman Act and therefore ‘local’ anti-competitive acts were outside the reach of US courts.4 Later, it was recognized that in a production chain, activi-ties in different layers are likely to be intertwined, which expanded the range of competition authorities’ legislation to violations on intrastate level.5 Nonetheless, it still took some years before US competition authorities took this final stance and a series of related appeals known as the “Shreveport Rate Cases” were an important landmark in this discussion.6

Related, in Mandeville Island Farms (1948), the court ruled that

4_{See for example United States v. E. C. Knight Co., 156 U.S. 1 (1895). The court decided that “the result}

of the transaction was the creation of a monopoly in the manufacture of a necessary of life” but ruled that it “could not be suppressed under the provisions of the Act” since the manufacturing was a local activity not subject to congressional regulation of interstate commerce.

5

Swift & Co. v. United States, 196 U.S. 375 (1905) established a “current of commerce” argument that allows intrastate violations to be punished if the industry where the violation took place is part of a larger, interstate chain of production.

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“the artificial and mechanical separation of ‘production’ and ‘manufacturing’ from ‘commerce’, without regard to their economic continuity, the effects of the former two upon the latter, and the varying methods by which the several processes are organized, related and carried on in different industries or indeed within a single industry, no longer suffices to put either production or manufacturing and refining processes beyond reach of Congress’ authority or of the statute.”7

This ruling furthermore seemed to imply that US competition law does take into account cartel effects on other layers in a production chain, be it upward layers or downward layers. The plaintiffs - beet growers - who were suppliers to a price cartel - sugar refiners - were given standing. However, this ruling is rather unique as in the majority of cases, standing was denied to suppliers to a cartel.

A leading case is Associated General Contractors (1983) in which the court laid the foun-dations for the ‘five factor test’, which should provide a guideline in determining whether a private firm has antitrust standing:8

(i) The nature of the plaintiff’s alleged injury; that is, whether it was the type the antitrust laws were intended to forestall;

(ii) (In)directness of injury from the act to plaintiffs’ alleged harm (iii) Speculative nature of the claimed damages

(iv) Risk of duplicative recovery

(v) The complexity of allocation of damages, due to conflicting claims by plaintiffs at dif-ferent levels of the production chain.

Supplier standing usually fails this test; it is often argued that harm to suppliers was caused by a ‘neutral’ aspect - the damages to the supplier being offset by cost savings of the cartel members - of the cartel agreement. Hence, allowing supplier standing would cause overdeter-rence. In other words, the harm to suppliers is merely a welfare transfer and is not related to welfare loss of consumers. It is doubtful whether this is indeed always the case.

Even though this five-factor analysis offers some sort of guidance, it is not waterproof and it can be broadly interpreted. US courts however have been fairly conservative in their interpretation. As for either indirect buyers or purchasers, there is generally no standing as a result of the indirectness argument. The passing-on (or passing-up in case of indirect suppliers) defence is denied under federal law following the verdicts in Illinois Brick (1977) and Hanover Shoe (1968).9,10 _{Neither is the umbrella effect commonly recognized by US}

courts and umbrella pricing victims have been denied standing under the five-factor test. That this test is open for interpretation is reflected by the odd case where umbrella victims have been allowed standing.11

Since US courts frequently point to the harshness of the trebling damages rule when denying standing to parties other than direct buyers or suppliers, the question whether the wrongdoer is severely punished seems to be of singular importance while the question whether

7

Mandeville Island Farms v. American Crystal Sugar Company 334 U.S. 219 (1948).

8

Associated General Contractors v. Carpenters, 459 U.S. 519 (1983)

9_{Illinois Brick Co. v. Illinois 431 U.S. 720 (1977).} 10

Hanover Shoe Inc. v. United Shoe Machinery Corp. 392 U.S. 481 (1968).

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the right parties are compensated for suffered harm and whether the compensation is in the correct proportion to the actual cartel harm seems irrelevant. This stance of US competition policy is expressed in the verdict of Illinois Brick, where the court concludes that “from the deterrence standpoint, it is irrelevant to whom damages are paid, so long as someone redresses the violation.” Of course, the former issue of deterrence should be an important focus point of competition authorities. However, foregoing on the second issue of appropriate ‘victim’ compensation might significantly distort markets. This can be illustrated by a simple example.

Consider two consecutive layers of a production chain and suppose that some of the suppliers make price agreements and succeed in raising the price of the whole market for a period of time but the cartel is exposed at some time in the future. Then ignoring umbrella pricing victims implies that only the firms that bought their input from the cartel firms have a right to claim compensation while they have suffered (approximately) the same damages as the firms that bought input from the non-cartel firms. This suggests an unfair treatment of firms in the downward layer.

An argument against the rationale of the example above is that the umbrella effect is speculative. As argued in Garabet (2000) :

“[A] wide range of factors influence a company’s pricing policies. Normally, the impact of a single change in the relevant conditions cannot be measured after the fact; indeed a businessman may be unable to state whether, had one fact been different...., he would have chosen a different price.”12

However, one can think of a great amount of markets where the assumption that the price of competitors is - one of - the key determinant(s) in setting prices is a fair one.

Moreover, Lave (2003) points out that the five-factor test is flawed as “the courts ei-ther assumed that umbrella standing does not present different issues from indirect-purchaser standing or they failed to fully appreciate what these new issues are”. He also finds, similarly to the conclusion of Han et al. (2009), that current compensation rules - focusing on the direct overcharge - underestimate the true harm inflicted by a cartel. Finally, he claims that - without umbrella standing - direct purchasers in markets with differentiated goods might not be optimally incentivized as potential plaintiffs are unsure whether they purchased from a colluding firm. If the cost of determining the extent of a cartel is high, (umbrella) victims might be discouraged to take legal action.

Admitted, the transition from economic theory to reality is not always a flawless one but ignoring certain economic phenomena just because they are not straightforward to prove seems rather myopic and unfair from a cartel victim’s point of view. Economic analysis such as provided in this thesis is therefore an essential step towards a more fair framework for cartel victims.

2.2 EU Competition Policy

In the EU, policy regarding anti-competitive practices are stated in article 101 of the Treaty on the Functioning of the European Union (TFEU), which was enacted in 2009.13 In EU

12

Garabet v. Autonomous Technologies Corp., 116 F. Supp. 2d 1159 (C.D. Cal. 2000)

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jurisdiction, price cartels fall under the so-called ‘hardcore’ restrictions. That is, they are illegal under any circumstances.

In contrast to the US, Europe has a relative brief history as it comes to private com-pensation claims for cartel damages. Similar to the statement in the Clayton Act regarding standing for cartel victims, the European Court of Justice (ECJ) concludes in Courage14:

“The full effectiveness of Article 85 of the Treaty and, in particular, the practical effect of the prohibition laid down in Article 85(1) would be put at risk if it were not open to any individual to claim damages for loss caused to him by a contract or by conduct liable to restrict or distort competition.”

In general the ECJ is less conservative as it comes to giving standing to cartel victims and has translated its words into deeds. This is especially reflected in the development of EU competition policy in recent years.

Currently, a new directive that should help private parties to claim compensation for damages, is in the process of being implemented.15 Among other things, it presents a relative broad platform for standing for cartel victims. In particular - and this is where it deviates significantly from US competition law - it allows the passing-on defence - if it can be proved by the defendant.16 On the other side of the same coin, an indirect buyer has standing for legal action if he can prove both the fact that a cartel’s actions resulted in a overcharge for the direct purchaser and that “he purchased the goods or services that were the subject of the infringement, or purchased goods or services derived from or containing the goods or services that were the subject of the infringement”.17 Furthermore, standing is provided to suppliers of a cartel.18

A matter that is ignored by this directive is that of umbrella pricing. Nonetheless, it is currently a hot topic in the EU. The discussion on whether umbrella victims should have a right to legal action was flared up recently by the opinion of Advocate General Kokott of the ECJ in Kone (2014).19 This resulted in a verdict in favour of umbrella victims.20 The court states that “(...) a cartel can have the effect of leading companies that are not a party to it to raise their prices in order to adapt them to the market price resulting from the cartel, a matter of which the members of the cartel cannot be unaware. Market price is one of the main factors taken into consideration by an undertaking when determining the price at which it will offer its goods or services.” This statement is in direct opposition of the view adopted by US courts who claim umbrella effects to be merely speculative.

Even though the ECJ is starting to adopt cartel effects that are recognized by economic

14

Case C-453/99 Courage Ltd v Bernard Crehan and Bernard Crehan v Courage Ltd and Others. par 26. Note that Art. 85 of the Treaty of Rome is the predecessor of Art. 101 TFEU.

15

The Proposal for a Directive of the European Parliament and of the Council on certain rules governing actions for damages under national law for infringements of the competition law provisions of the Member States and of the European Union. COM(2013) 404, final was adopted on 17 April 2014 by the European Parliament and has been signed into law on 26 November 2014. The EU Member States need to have harmonized their legal systems with the new directive by 27 December 2016.

16

Article 12 of the Proposal for a Directive (...) on (...) damages (...).

17_{Article 13 of the Proposal for a Directive (...) on (...) damages (...).} 18

Article 14 of the Proposal for a Directive (...) on (...) damages (...).

19

Opinion of General Advocate Kokott delivered on 30 January 2014 (1), Case C-557/12, Kone AG and Others

20

Judgment in Case C-557/12 Kone AG and Others v ¨OBB-Infrastruktur AG, Court of Justice of the European Union, Press Release No 79/14, Luxembourg, 5 June 2014

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theory in its competition laws, there is still a gap between law and economics. Private claims in the EU have been limited as a result of a failure in recognizing and correctly quantifying cartel harm. A first and essential step to a more fair environment for cartel victims is to draw a clear picture that encompasses all effects resulting from a cartel under various market scenarios. This picture will be drawn in the following sections of this thesis.

3 The Model

In this section I will introduce the theoretical framework that allows me to investigate the possible effects of a cartel. I will build up the model as broad as possible as to capture a number of scenarios. From this relatively general framework I can focus on specific scenarios. This way, I will be able to draw strong conclusions and make recommendations regarding supplier and umbrella harm.

The foundation for the model will be the chain of production for a particular - unspecified - market, depicted in figure 1. It is a slightly modified version of the production chain used by Han et al. (2009). The chain consists of 3 layers, with layer k consisting of nk firms. In

layer 1, firms use a raw product to produce their output, which is used by layer 2 to produce the input for layer 3. In layer 3, products are sold to the end consumers. For now, let this technological process of transforming input to output be unspecified. The layer of interest is layer 3, where the retailers operate. Retailer i produces a differentiated end product xi and

sells it to the consumers. I assume furthermore that the products in all other ‘upstream’ layers are homogeneous. Let the consumer demand for end product i be represented by a singular - inverse - demand function p3,i x1, ..., xn3 of a representative consumer. The specification

and derivation of consumer demand will be presented in the next subsection. Within the framework presented above, I will investigate the effect of a cartel in the retailer layer, which allows me to focus on umbrella and pass-up effects.

Indirect Suppliers: Q1 Direct Suppliers: Q2 xi x1 xn3 Consumers Retailers Retailers

Figure 1: A 3-Layer Production Chain With Differentiated End Products

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consumers, in the case of layer 3. I assume that the upstream layers 1 and 2 are competitive wholesale markets, where a homogeneous product is produced. Given these assumptions it makes sense to assume Cournot competition in these markets. The structure of the model is then as follows.

Firms in layer 1 move first and determine their strategy they set an output quantity -given demand of layer 2. This results in a total market supply and corresponding market price. Given input price and given demand from the downstream layer, firms in layer 2 maximize profits and produce a specific optimal quantity of output to layer 3. Again, aggregating over all firms in layer 2 yields total market supply and corresponding market price. Finally, the firms in layer 3 set - depending on the type of competition - an optimal price or quantity. Hence, firms in consecutive layers move sequentially and furthermore, I assume that firms in the same layer move simultaneously.

Using concepts from the field of game theory, the model can be solved using backward induction. That is, given consumer demand, firm i from layer 3 will maximize its profits π3,i.

Since its profits depend on input prices, aggregating over all retailers yields an inverse demand function p2(Q2) for the product from layer 2. Given this inverse demand function, firms in

layer 2 maximize profits, resulting in an inverse demand function p1(Q1) for the product from

layer 1. Now, as the firms in layer 1 do not use input from other markets, the only variable costs that they face are the costs of converting the raw products into output. Given these costs and given the inverse demand function, firms in layer 1 maximize profits. This yields optimal output quantities q₁∗, total market supply Q∗₁ and market price p∗₁. Correspondingly, consecutive markets clear, giving equilibrium prices p∗₂ and p∗_3,i. Here, the superscript ∗ stands for competitive equilibrium values.

In order to work out a solution to this model, functional forms of the demand and cost functions are required.

3.1 Consumer Demand

The consumer demand function p(xi) is based on utility maximization of a representative

consumer:

max

x U (x0, x) s.t p · x = M − x0

The utility of a consumer U is a function of the end products x with corresponding prices p and M is the available budget. Also, x0 represents the num´eraire good. In other words, all

other products consumed that are not related to the products produced in the market that is scrutinized. The consumer observes prices p = [p1· · · pn3] and chooses, given his budget M ,

an optimal consumption bundle of end products x = [x1· · · xn3]

T

.

The corresponding Lagrangian is L = U (x0, x) + λ(p · x − M + x0) which gives the n3+ 1

first order conditions ∂L ∂xi = ∂U (·) ∂xi + λpi = 0, ∀i ∈ [1, ..., n3] and ∂L ∂x0 = ∂U (·) ∂x0 + λ = 0

To represent consumer utility I choose the utility function introduced by Bowley (1924).

U (x₀, x) = x0+ X i xi− 1 2 X i x2_i −γ 2 X i X j6=i xixj

The first thing to notice is the quadratic term −1₂P

ix2i. This implies that utility decreases

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functional form of consumer utility is captured in the term −γ₂ P

i

P

j6=ixixj. The parameter γ

measures substitutability and allows me to vary between fully heterogeneous products (γ = 0) and fully homogeneous products or perfect substitutes (γ = 1). Note that end products are symmetrically differentiated. That is, substitutability between any good x3,i and x3,j is the

same for all i and j, so that γ = 0 corresponds to retailers being monopolists. Utility decreases as substitutability increases. Hence, consumers care for product differentiation - they prefer having choice in consumption.

Utility maximization yields the following (inverse) consumer demand function.21

pi(x) = 1 − xi− γ n3 X j6=i xj xi(p) = 1 m1 − m2 (1 − γ)m1 pi+ γ (1 − γ)m1 n3 X j6=i pj With m1= 1 + (n3− 1)γ and m2 = 1 + (n3− 2)γ (1) 3.2 Cost Function

A second important determinant for the outcome of the analysis will be the cost function. Let me decompose various costs in order to formulate a sensible cost function.

• Fixed Costs: First of all, there will be costs that do not - directly - depend on production. Think of costs for maintenance of machinery and such. Let these costs be summarized by the parameter ak,i.

• Input Costs: In the production chain introduced above, firms use products from the previous layer as input. Therefore, part of the costs for firm i in layer k are the input costs; the price pk−1 times the amount of input needed xi,k−1. Let me introduce an

efficiency parameter ξk,i that describes the technology process of firm i in layer k, i.e.

qk,i = ξk,ixi,k−1. Hence, ξk,i indicates how efficient a firm uses input to create output

and can basically be any positive number. Suppose that differences in efficiency within a layer are minimal. That is, let me assume that ξk,i= ξk, for all firms in layer k.

• Production Costs: Lastly, apart from the input costs, the process of production will incur costs. Let these costs be summarized by ck,i(qk,i) = bk,iq_k,iνk, with bk,i, νk > 0. The

parameter νkis the ‘shape’ parameter. For 0 < νk < 1, the cost function is concave. For

νk = 1, it is linear and for νk> 1 it is convex. A concave cost function corresponds to

decreasing marginal costs, whereas a convex cost function implies increasing marginal costs. Both situations can occur in reality, depending on how a product is created. In general, a product that is created by a relative large amount of human labour yields decreasing productivity and thus increasing marginal costs, whereas marginal costs may be decreasing due to economies of scale. Hence, νk is market-specific and I assume that

it is the same for all firms within a layer.

Collecting terms, the cost function for firm i from layer k is:

Ck,i

qk,i, pk−1

= ak,i+ pk−1xi,k−1+ ck,i(qk,i) = ak,i+ pk−1

qk,i

ξk

+ bk,iq_k,iνk

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and the marginal cost function: M Ck,i qk,i, pk−1 = ∂M C(·) ∂qk,i = pk−1 ξk + νkbk,iq_k,iνk−1

Given a specification for consumer demand and for the cost function I can work towards a solution of the model. I assume that all firms are profit-maximizers. Furthermore, I assume that all markets clear in equilibrium - all demand is satisfied. The maximization problem of a retailer depends on the type of competition in the market - Bertrand or Cournot. In the Bertrand case, firms set prices and take quantity as given. In the Cournot case, it is the other way round and firms maximize profits by setting their output quantity. Generally, in markets with a large amount of competitors with a limited degree of product differentiation, the firms are ‘price takers’. This is due to the fact that pricing above the market price would scare off customers, since they have sufficient alternatives.

Bertrand competition is typical for oligopolistic markets, markets with a small amount of competitors who have enough market power to set their prices independently from competi-tors. I will investigate profit maximization under both types of competition.

3.3 Bertrand Competition between Retailers

Under the assumption of Bertrand competition, retailers set prices in order to maximize profits and take prices set by the competing firms as given. Assume without loss of generality that fixed costs, ak,i= 0 for any k and i.22 The corresponding maximization problem for firm

i from layer 3 is:

max p3,i π3,i = max p3,i x3,i(p3) p3,i− p2 ξ3 − c_3,ix3,i(p3)

The n3 corresponding first order conditions for these maximization problems are :

x3,i(·) + " p3,i− p2 ξ3 − ∂c3,i x3,i(·) ∂x3,i # ∂x3,i(·) ∂p3,i = 0

This set of n3 first order conditions constitute a system of equations which implicitly give

the reaction curves of the retailers, given input price p2. Solving this set of equations gives

equilibrium retailer prices as a function of input price p2. From this, using equation (1),

equilibrium output can be obtained as a function of p2. Correcting for the efficiency parameter

and aggregating over the n3 retailers yields the demand function Q2(p2) for the wholesale

market of layer 2. This demand function needs to be inverted to obtain the desired inverse demand function p2(Q2). From here on, this process of backward induction becomes easier as

upstream products are homogeneous. Homogeneity of products also makes the assumption that firms compete on quantity a fair one. If a wholesaler raises its price above the market price, customers will switch to the product of a competitor. At the top of the production chain, firms in layer 1 face the inverse demand function p1(Q1). Since these firms do not use

output from another layer, the first order condition for a firm i in layer 1, given Cournot competition, is:

22

In assessing cartel effects I will look at the difference between competitive and collusive outcomes. Fixed costs will then simply drop from the difference-in-profit equations.

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p1(Q1) + q1,i ∂p1(Q1) ∂Q1 ∂Q1 ∂q1,i − ν₁b1,iq1,iν1−1 = 0 (2)

Here, let εk,i = _∂q∂Q_k,ik be a conjectural variation term. That is, εk,i describes how firm i of

layer k thinks that the market supply reacts to a change in its own supply. It is a measure of the market power of a firm. Let εk,i = 1 for the rest of this analysis, which corresponds

to the classic Cournot conjecture. Solving (2) yields optimal q∗_1,i, Q∗₁ and consequently p∗₁, in terms of the model parameters. Finding equilibrium quantities, prices and profits in all other layers is now straightforward.

Looking at the demand function defined in (1), someone with some mathematical and economic intuition might expect the retailer price reactions to be positive (as pi and pj have

opposite sign). That is, the reaction of a retailer to a price increase by a competitor is to increase its price as well. In the next section, this is shown to be true. Furthermore, it is shown that elasticity of retailer prices to the input price is positive. Hence, increasing input prices lead to higher retailer prices.

3.4 Cournot Competition between Retailers

Cournot competition is the situation where output is the strategic variable. In other words, firms take prices as given and maximize profits by setting an optimal output quantity. Al-though Bertrand competition is typical for a retailer market with differentiated products, I will also consider Cournot competition in the retailer market.

The maximization problem for a retailer i, given Cournot competition, is:

max x3,i π3,i = max x3,i x3,i p3,i(x3) − p2 ξ3 − c3,i(x3,i)

This gives corresponding first order conditions :

p3,i(·) − p2 ξ3 + x3,i ∂p3,i(·) ∂x3,i −∂c3,i(·) ∂x3,i = 0

These equations correspond to the output reaction curve and solving this set of n3 linear

equations yields equilibrium output as functions of the input price p2. Again, adjusting for

efficiency and aggregating over all retailers gives Q2(p2), the demand function for layer 2.

From this point, solving the model is similar to the Bertrand case.

Retailer cross-output elasticity can be expected to be negative using economic and math-ematical intuition (xiand xj in (1) have the same sign). Output reduction by a retailer yields

to output expansion of competitors as residual demand increases.23 Elasticity of retailer output and input prices is negative as higher production costs leads to retailers producing less.

3.5 Collusion

The goal of this thesis is to investigate the effects of a cartel. It is therefore important to exactly pin down what happens in terms of the model if firms collude. Suppose retailers i

23

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and j form a cartel. In terms of the model, they will maximize their aggregate profits. That is, in case of Bertrand competition:

max p3,i,p3,j π3,i+ π3,j = max p3,i,p3,j x3,i(p3) p3,i− p2 ξ3 − c_3,ix3,i(p3) + x3,j(p3) p3,j− p2 ξ3 − c_3,j(x3,j p₃) (3)

Equation (3) gives two first order conditions and the only additional term, compared to the competitive case for retailer i is

∂x3,j(·) ∂p3,i p3,j− p2 ξ3 − ∂c3,j x3,j(·) ∂x3,j Therefore, if ∂x3,j(p3)

∂p3,i = 0 for any colluding firms i and j, there will be no effect on the

equilibrium of the model. Under the assumption of ‘Bowley’ consumer utility: ∂x3,j(p3)

∂p3,i

= γ

(1 − γ)m1

So it becomes immediately clear that for γ = 0, collusion in layer 3 will have no effect. This is in line with economic intuition as in that case, end products are not substitutable and all retailers operate on isolated, monopolized markets. Hence, collusion does not change the competitive equilibrium.

The additional term in case of Cournot competition will be

x3,j

∂p3,j(x3)

∂x3,i

= γx3,j

Again, for γ = 0 the retailer market corresponds to n3 seperated monopolies and a cartel will

not change the market equilibrium.

Now suppose at any time a cartel C of any size nc₃ can arise, given that it is profitable, and only one cartel formation can arise at the same time. The colluding firms will maximize joint profits which results in reaction curves, which are a function of the non-colluder prices and price of input. The reaction curves of the non-colluding firms are similar to the competitive case. Solving these reaction curves now gives rise to a new equilibrium. In the same way as before, inverse demand functions pc_k(Qk), (k = 1, 2), for the products of upstream layers

can be found and eventually, equilibrium quantities q_k,ic , prices pc_k and profits π_k,ic . Here, the superscript c stands for equilibrium values under collusion. Finally, the change in profits πc_k,i− π_k,i∗ can be obtained for all firms in the production chain as well as changes in all other variables of interest such as prices and output quantities (recall that the superscript∗denotes competitive equilibrium values). A final step is to decompose these effects.

4 Decomposition of Harm

Collusion at the retailer level is likely to affect all firms and consumers in the production chain introduced in section 3. In order to investigate the magnitude of cartel harm and how these damages manifest, it is useful to decompose cartel harm. This decomposition will be similar to the one in Han et al.(2009). However, as the structure of the model is different I will have to introduce some new terms.

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4.1 Supplier Damages

In the model introduced in the previous section, the competitive equilibrium profits of a direct supplier are π_2,i∗ = q_2,i∗

p∗₂− p∗1

ξ2

− c2,i(q2,i∗ ) and total direct supplier profits are Π∗2 =

Q∗₂ p∗₂−p∗1 ξ2 −Pn2 i=1c2,i(q ∗

2,i). Typically, higher-than-competitive prices and output reduction

by the cartel go hand in hand. Part of the output reduction of the cartel will be compensated by non-colluding competitors expanding output. However, in toto, total output of the market where the cartel emerges will generally decrease. Evidently, this causes the demand for the input supplied by the firms of layer 2 to decrease and consequently the inverse demand function p2(Q2) to shift inward to pc2(Q2).24 The equilibrium input price under collusion can

then increase, decrease or remain unchanged, depending on the cost structure of suppliers.25 Total cartel harm to direct suppliers, ∆Π2 = Πc2− Π∗2, can be decomposed similarly to

the purchaser harm decomposition of Han et al. (2009)

∆Π2 = Qc2 pc₂− p∗₂+Q c 2 ξ2 p∗₁− pc₁+ " (QC₂ − Q∗₂) p∗₂−p ∗ 1 ξ2 + n2 X i=1

c2,i(q∗2,i) − c2,i(qc2,i)

# = µ2+ ρ2+ β2 Where • µ₂ = Qc₂pc₂−p∗ 2

: Undercharge Effect. This is the change in profits due to the change in output price and is caused by the shift of the inverse demand function p2(Q2). Without

the cartel actions, the suppliers would have been able to get a price of p∗₂ rather than pc₂ for the supplied quantity Qc₂. The sign of the undercharge effect depends on how the upstream price reacts to the decrease in demand and can, in general, be positive, negative or zero.26 • ρ₂ = Qc2 ξ2 p∗₁− pc 1

: Pass-up Effect. The amount of damages passed on to the indirect suppliers. It is caused by the shift of the inverse demand function p1(Q1). In the

competitive situation, the direct suppliers would have paid p∗₁ rather than pc₁ for their demanded input from layer 1, Qc₁= Qc2

ξ2. • β₂ = (Qc₂− Q∗₂)p∗₂−p∗1 ξ2 +Pn2 i=1

c2,i(q∗2,i) − c2,i(qc2,i)

: Output Effect. The change in profits resulting from the decrease in Q2 demanded by the retailers. The term p∗2−

p∗1

ξ2, is

the competitive profit-margin on one unit of output. The first part then represents the loss in profits resulting from the decrease in sales and is always negative. The second part represents the savings in production costs resulting from the decrease in sales and is typically positive.27 The net output effect can therefore be positive, negative or zero

24

For a graphical example, see Appendix B.

25_{It is shown in section 5.2 that if suppliers have linear shaped cost functions, there will be no change in}

input prices. An increase in input prices might occur if suppliers have concave shaped cost functions.

26

See fn. 25

27

The sign of the second part depends on the cost functions of the suppliers. If firms have asymmetric cost functions, total production costs might be higher in the cartel case. For example, if firms with concave-shaped cost functions produce more in the new cartel equilibrium. However, if direct suppliers are symmetric and hence production of Q2 is equally divided among the suppliers, it is fair to assume that producing less

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depending on the magnitude of the loss in sales and the decrease in production costs.

Similarly, total damages to indirect suppliers can be decomposed

∆Π1 = Qc1 pc₁− p∗₁+ " (Qc₁− Q∗₁)p∗₁+ n1 X i=1

c1,i(q∗1,i) − c1,i(qc1,i)

#

= µ1+ β1

The first thing to note here is that the undercharge of indirect suppliers is equal to the pass-up of direct spass-uppliers in absolute value, ρ2 = µ1. Furthermore, there is no pass-up effect for

indirect suppliers which makes sense as there is no upstream layer to pass cartel harm on to.

4.2 Retailer Profit Decomposition and the Umbrella Effect

In the situation where a cartel limits production and achieves higher prices for their products, the competing non-cartel members might profit along with the cartel. If there is some degree of substitutability between the products of the cartel and the product of a non-cartel member, costumers may switch to the product of the non-cartel members as a reaction to the higher cartel prices. A non-cartel member faces a change in its inverse demand function. The stronger substitutes the products are, the stronger this change. As a reaction to the altered demand function, a non-cartel member might increase its price. This effect is called the ‘umbrella’ effect as non-colluding firms can raise prices ‘under the umbrella’ of the cartel. An essential determinant of the price response of non-colluders is the substitutability parameter γ, introduced in section 3.1. If γ = 0 there will be no price effect in the Bertrand case, as discussed in section 3.5. If 0 < γ < 1, this so-called ‘umbrella’ price effect will be a fraction of the cartel price. This also implies that, as non-colluder price increases are smaller than cartel price increases, the demand for the products of the non-colluding firms increases. Hence, competitors of the cartel firms profit in two ways from the existence of a cartel, both through the ‘umbrella’ price effect and through an increase in residual demand. Combining these two effects, non-colluding firms might benefit even more than the actual colluding firms. This raises questions about the stability of incomplete cartels. The matters of profitability and stability of cartels will be analyzed and discussed in sections 6.3 and 6.4.

The change in profits of an individual colluding retailer i can be decomposed as follows

∆π_3,ic = xc_3,i pc_3,i− p∗_3,i+x c 3,i ξ2 p∗₂− pc₂+ " (xc_3,i− x∗_3,i) p∗_3,i−p ∗ 2 ξ3 +

c3,i(x∗3,i) − c3,i(xc3,i)

# = OC_ic+ ρc_3,i+ β_3,ic Here • OCc i = xc3,i

pc_3,i− p∗_3,i: Cartel Overcharge. The overcharge that consumers have paid if a retailer cartel arises and thus the increase in profits of a colluding caused by the higher-than-competitive price. In the competitive case, consumers would have paid a price p∗_3,i rather than pc_3,i for the amount xc_3,i. Total cartel overcharge is simply Pnc3

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• ρc 3,i = xc 3,i ξ2 p∗₂ − pc 2

: Input Cost Effect. The change in input costs caused by the reduction in input demand. The sign depends on how the input price reacts to a decrease in demand and can generally be positive, negative or zero.28

• βc

3,i= (xc3,i− x∗3,i)

p∗_3,i−p∗2

ξ3

+c3,i(x∗3,i) − c3,i(xc3,i)

: Output Effect. The net change in profits resulting from the decrease in sales. As x∗_3,i> xc_3,i, the first part will be negative. This also implies that the second part is generally positive.29 Hence, the sign of the net output effect is ambiguous and can be positive, negative or zero.

A similar decomposition applies to non-colluding retailers

∆π_3,inc = xnc_3,i pnc_3,i− p∗_3,i+x nc 3,i ξ2 p∗₂− pnc₂ + " (xnc_3,i− x∗_3,i) p∗_3,i−p ∗ 2 ξ3 +

c3,i(x∗3,i) − c3,i(xnc3,i)

#

= OC_inc+ ρnc_3,i+ β_3,inc

The total umbrella overcharge,Pn3−nC₃

i /∈C OCinc, is typically positive.30 The input cost effect

for non-colluders can again be positive, negative or zero, depending on the cost structure of the suppliers. Also, x∗_3,i < xnc_3,i implies that the first term of the non-colluder output effect will be positive. Consequently, the second term will typically be negative. Again, the sign of the net output effect can be negative, positive or zero. Also note that the sum of the input cost effects, PnC3

i∈Cρc3,i+

Pn3−nC3

i /∈C ρnc3,i, is equal - in absolute value - to the total undercharge of

the direct suppliers µ2, as Pn

C 3 i∈C xc 3,i ξ3 + Pn3−nC3 i /∈C xnc 3,i ξ3 = Q c 2. 4.3 Consumer Damages

Using the ‘Bowley’ utility function introduced in section 3.1, consumer utility in the compet-itive case is.

U∗(p, x) = M − n3 X i=1 p∗_3,ix∗_3,i+ n3 X i=1 x∗_3,i−1 2 n3 X i=1 x∗_3,i2 + γ n3 X i=1 n3 X j6=i x∗_3,ix∗_3,j ! Here, I substituted x∗₀ = M −Pn3 i=1p ∗

3,ix∗3,i. Consumer damages can now be decomposed

as follows.

∆U =X

i∈C

xc_3,ip∗_3,i− pc_3,i+X

i /∈C

xnc_3,ip∗_3,i− pnc_3,i+X

i∈C

p∗_3,ix∗_3,i− xc_3,i+X

i /∈C

p∗_3,ix∗_3,i− xnc_3,i

+X i∈C " xc_3,i− x∗_3,i−1 2 xc_3,i2 − x∗_3,i2 # +X i /∈C " xnc_3,i− x∗_3,i−1 2 xnc_3,i2− x∗_3,i2 # + γ 2 " _n₃ X i=1 n3 X j6=i x∗_3,ix∗_3,j − n3 X i∈C xc_3,i _X j∈C\{i} xc_j+X k /∈C xnc_k − n3 X i /∈C xnc_3,i _X j /∈C\{i} xnc_j +X k∈C xc_k # = −T OCc− T OCnc_{+ ζ + τ + θ} 28 See fn. 25 29

This depends on the cost functions. However the assumption that producing less costs less seems a fair one.

30

There are however cases where the umbrella overcharge is negative, that is, non-colluders set lower-than-competitive prices as a response to the cartel. See section 6.1 for more details.

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The various decomposed effects here, are: • T OCc₌P i∈Cxc3,i pc_3,i− p∗ 3,i

: Total Cartel Overcharge. The sum of overcharges of all colluding firms. It corresponds to the loss in available budget for the numeraire good x0. Its sign is positive as evidently, pc_3,i > p∗_3,i. That is, the total cartel overcharge

causes consumer utility to decrease.

• T OCnc ₌P

i /∈Cxnc3,i

pnc_3,i− p∗_3,i: Total Umbrella Overcharge. The sum of overcharges of all non-colluding firms, caused by the umbrella price effect. Its sign is typically positive.31 Hence, the total umbrella overcharge causes consumer utility to decrease.

• ζ =P i∈Cp ∗ 3,i x∗_3,i− xc 3,i +P i /∈Cp∗3,i x∗_3,i− xnc 3,i

: Budget Effect. The change in budget for the numeraire good caused by the change in consumption. As xc_3,i < x∗_3,i, the sign of the first term will be positive and as xnc_3,i > x∗_3,i, the sign of the second term will be negative. However, as total output by the retailers decreases in case of a cartel, the net budget effect will be positive.32

• τ = P

i∈C

"

xc_3,i − x∗_3,i− 1₂xc_3,i2 − x∗_3,i2 # +P i /∈C " xnc_3,i − x∗_3,i+ 1₂ xnc_3,i2 − x∗_3,i2 # : Consumption Effect. The change in utility caused by the change of consumption bundle. Its sign is ambiguous.

• θ = γ₂ " Pn3 i=1 Pn3 j6=ix ∗ 3,ix∗3,j− Pn3 i∈Cxc3,i P j∈C\{i}xcj+ P k /∈Cxnck −Pn3 i /∈Cxnc3,i P j /∈C\{i}xncj + P k∈Cxck #

: Variation Effect. The change of utility caused

by the change in composition of the consumption bundle. Depending on whether the variation in consumption increased/decreased in the collusive equilbrium, its effect is positive/negative.

4.4 Measure of Cartel Harm

Competition authorities have to draw a line in assessing to what extent a cartel is responsible for the loss in profits throughout the production chain. This is where the decomposition of the previous subsection comes into play. In practice, the cartel overcharge is used to measure cartel harm to purchasers. To answer the question of how significant the harm caused by the umbrella effect is, I will consider the fraction of the cartel overcharge to the total overcharge

OCc_i OCc

i+OCinc. In answering my second question, I will take a look at the fraction of supplier

damages to supplier damages. In other words, I will consider the fraction of ‘upstream’ harm to ‘downstream’ harm, U H_DH. If the harm to direct and indirect suppliers is indeed deemed significant, another question arises; how should this harm be measured in practice? An apparent choice of tool would be to use the supplier equivalent of the overcharge, the undercharge. I will investigate to what degree the (indirect) undercharge is able to capture the harm to suppliers. More specifically, I will take a look at the fraction µ1+µ2

µ2+β1+β2. The

results can be found in section 6 and 7.

31

Again, see section 6.1 for details on the ‘negative’ umbrella effect.

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5 Model Solution

In the following subsections, I will present the model solutions for the competitive and cartel cases. In order to obtain closed-form model solutions, I first need to make a few assumptions. First of all, I consider two types of cost functions, linear (ν = 1) and quadratic/convex (ν = 2) shaped cost functions. Furthermore, I assume that all firms within one layer are symmetric.33 This last assumption also implies that in the competitive equilibrium, all firms within a layer set the same optimal price or quantity. Also, any colluding firms will set the same optimal cartel price and non-colluding firms will set the same non-collusion price in equilibrium. All derivations can be found in Appendix C.

5.1 Equilibrium Upstream Markets

Given either linear or quadratic cost functions of the firms in layer 3, a linear inverse demand function for layer 2 will arise. Let this inverse demand function be given by p2(Q2) = A−BQ2.

Furthermore, I assume Cournot competition in the upstream markets and ∂Qk

∂qk,i = 1, for

k = 1, 2. In the framework of this thesis the only things for upstream firms that will change in case of collusion in layer 3, are the values of A and B. I can therefore derive a general upstream solution, given A and B.

Lemma 5.1. The symmetric equilibrium in upstream layers 1 and 2, in case of quadratic cost functions (ν = 2), is:

p∗₁= ξ2A h 2b1n2+ ξ22 2b2+ (n2+ 1)B i 2b1n2+ (n1+ 1)ξ22 h 2b2+ (n2+ 1)B i q₁∗= n2ξ2A 2b1n2+ (n1+ 1)ξ22 h 2b2+ (n2+ 1)B i p∗₂= Ah2b1n2+ 2b2ξ22(n1+ 1) + ξ22B(n1+ n2+ 1) i 2b1n2+ (n1+ 1)ξ22 h 2b2+ (n2+ 1)B i q₂∗= n1ξ 2 2A 2b1n2+ (n1+ 1)ξ22 h 2b2+ (n2+ 1)B i

It might be interesting to investigate how (indirect) supplier harm will be affected by the cost structure of the upstream firms. Therefore, I also derive the general solution for the case where all upstream firms have linear cost functions (ν = 1).

Lemma 5.2. The symmetric equilibrium in the upstream layers, in case of linear cost

func-33_{Firms are symmetric in the sense that b}

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tions (ν = 1), is: p∗₁ = ξ2(A − b2) + b1n1 n1+ 1 q∗₁ = n2 ξ2(A − b2) − b1 (n1+ 1)(n2+ 1)ξ₂2B p∗₂ = ξ2A(n1n2+ n1− 1) + n2(ξ2b2+ n1b1) (n1+ 1)(n2+ 1)ξ2 q∗₂ = ξ2(A − b2) − b1n1 (n1+ 1)(n2+ 1)ξ2B

Note that in case of linear costs in the wholesale markets, the equilibrium prices are independent of B, the variable part of the inverse demand function. As in most scenarios, the intercept A will not change in case of a cartel, consequently there will also be no effect on upstream prices.34 Hence, I obtain the same result as found by Han et al.(2009).

Proposition 5.3. If (indirect) suppliers have linear cost functions, a retailer cartel will not affect supplier prices.

5.2 Competitive Retailer Equilibrium

Assuming symmetric retailers in layer 3 and given, respectively, quadratic and linear costs, the symmetric competitive Bertrand equilibrium in layer 3, given input price ¯p2, is:

Lemma 5.4. Given quadratic cost functions (ν = 2), the symmetric competitive Bertrand solution is: p∗₃ ¯ p2 = E2+ m1m2 ¯ p2 ξ3 E2+ m1m2 x∗₃ ¯ p2 = m2 E2+ m1m2 h 1 −p¯2 ξ3 i π₃∗p¯2 = m2E1 (E2+ m1m2)2 h 1 −p¯2 ξ3 i2 ABQ= ξ3 BBQ= ξ₃2 h E2+ m1m2 i m2n3 where: m1(γ, n3) = 1 + (n3− 1)γ m2(γ, n3) = 1 + (n3− 2)γ E1(γ, n3, b3) = m1(1 − γ) + b3m2 E2(γ, n3, b3) = m1(1 − γ) + 2b3m2

34_{In the scenarios under scrutiny, retailers are assumed to be symmetric. In case of asymmetry, the intercept}

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Given linear cost functions (ν = 1), the symmetric competitive Bertrand solution is: p∗₃ ¯ p2 = [1 − γ + m2( ¯ p2 ξ3 + b3) m2+ 1 − γ x∗₃ ¯ p2 = m2 m1 h1 −p¯2 ξ3 − b3 m2+ 1 − γ i π₃∗p¯2 = m2(1 − γ) h 1 −p¯2 ξ3 − b3 i2 m1(m2+ 1 − γ)2 ABL= ξ3(1 − b3) BBL= m1ξ23 h m2+ 1 − γ i m2n3

The type of competition, Bertrand or Cournot, can be expected to have a significant influence on the market equilibrium. Suppose that the firms in layer 3 take prices as given and compete on output quantity. In this case, the symmetric competitive Cournot equilibrium is:

Lemma 5.5. Given quadratic cost functions (ν = 2), the symmetric competitive Cournot solution is: p∗₃p¯2 = 1 + 2b3+ m1 ¯ p2 ξ3 1 + 2b3+ m1 x∗₃ ¯ p2 = 1 1 + 2b3+ m1 h 1 −p¯2 ξ3 i π₃∗p¯2 = 1 + b3 (1 + 2b3+ m1)2 h 1 −p¯2 ξ3 i2 ACQ = ξ3 BCQ= ξ₃2 h 1 + 2b3+ m1 i n3

Given linear cost functions (ν = 1), the symmetric competitive Cournot solution is:

p∗₃ ¯ p2 = 1 + m1( ¯ p2 ξ3 + b3) 1 + m1 x∗₃ ¯ p2 = 1 − ¯ p2 ξ3 − b3 1 + m1 π∗₃p¯2 = (1 − ¯ p2 ξ3 − b3) 2 (1 + m1)2 ACL= ξ3(1 − b3) BCL= ξ₃2h1 + m1 i n3

Comparing equilibrium prices the following results can be obtained, where the subscripts BQ and BL indicate Bertrand competition with quadratic and linear costs respectively and the subscripts CQ and CL indicate Cournot competition with quadratic and linear costs respectively.35

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Proposition 5.6. For a given input price ¯p2, equilibrium prices are higher if retailers have

linear costs, p∗_BL> p∗_BQ and p∗_CL> p∗_CQ. Also, comparing equilibrium prices in the Bertrand and Cournot case yields:

p∗_BQ < p∗_CQ iff p¯2 < ξ3 and p∗BL< p ∗

CL iff p¯2 < ξ3(1 − b3)

As the demand function is linear, the results for the equilibrium outputs are evident

x∗_BQ> x∗_BL, x∗_CQ> x_CL∗ , x∗_BQ > x∗_CQ iff p¯2< ξ3 and x∗BL> xCL∗ iff p¯2 < ξ3(1−b3)

5.3 Cartel Equilibrium

Suppose a cartel C is formed in layer 3 consisting of nc₃ retailers, nc₃ ∈ {2, 3, ..., n₃}. The colluding firms act as one firm and set a cartel price pc₃ that maximizes joint profits. The non-colluding firms set their price independently and thus have the same reaction function as in the competitive case.

Lemma 5.7. Given quadratic cost functions, the cartel Bertrand solution is:

pc₃p¯2; · = (1 − γ)hX_BQc + Y_BQc p¯2 ξ3 i ΩBQ xc₃p¯2; · = (1 − γ)m C 1W1 ΩBQ h 1 −p¯2 ξ3 i pnc₃ p¯2; · = (1 − γ)hX_BQnc + Y_BQnc p¯2 ξ3 i ΩBQ xnc₃ ¯ p2; · = (1 − γ)m2W2 ΩBQ h 1 −p¯2 ξ3 i Ac_BQ= ξ3 BcBQ= ξ₃2ΩBQ (1 − γ) nc₃mC₁W1+ (n3− nc3)m2W2

Given linear cost functions, the cartel Bertrand solution is:

pc₃ ¯ p2; · = X c BL+ YBLc ( ¯ p2 ξ3 + b3) ΩBL xc₃ ¯ p2; · = m C 1(m1+ m2) m1ΩBL h 1 −p¯2 ξ3 − b3 i pnc₃ ¯ p2; · = X nc BL+ YBLnc( ¯ p2 ξ3 + b3) ΩBL xnc₃ ¯ p2; · = m2(m1+ m C 1) m1ΩBL h 1 −p¯2 ξ3 − b3 i Ac_BL= ξ3(1 − b3) BcBL= m1ξ32ΩBL nc₃m1(mC₁ − m2) + n3m2(m1+ mC₁)

Here, the X,Y and Ω.are terms consisting of parameters associated to the retailer market.

An overview of all these parameter ‘bundles’ can be found in Appendix A2.

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Lemma 5.8. Given quadratic cost functions, the incomplete cartel Cournot solution is: pc₃p¯2; · = X c CQ+ YCQc ¯ p2 ξ3 ΩCQ xc₃ ¯ p2; · = 2 + 2b3− γ ΩCQ h 1 −p¯2 ξ3 i pN C₃ p¯2; · = X nc CQ+ YCQnc ¯ p2 ξ3 ΩCQ xN C₃ ¯ p2; · = 2 + 2b3+ γ(n c 3− 2) ΩCQ h 1 −p¯2 ξ3 i Ac_CQ= ξ3 BCQc = ξ₃2ΩCQ n3 2 + 2b3+ γ(nc3− 2) − γnc 3(nc3− 1)

Given linear cost functions, the incomplete cartel Cournot solution is:

pc₃p¯2; · = X c CL+ YCLc ( ¯ p2 ξ3 + b3) ΩCL xc₃ ¯ p2; · = 2 − γ ΩCL h 1 −p¯2 ξ3 − b3 i pN C₃ ¯ p2; · = X nc CL+ YCLnc( ¯ p2 ξ3 + b3) ΩCL xN C₃ ¯ p2; · = 2 + γ(n c 3− 2) ΩCL h 1 −p¯2 ξ3 − b3 i Ac_CL= ξ3(1 − b3) BCLc = ξ₃2ΩCL 2n3 1 − γ + γnc₃(n3− nc₃+ 1)

Again, the X,Y and Ω. are terms consisting of model parameters and can be found in

Appendix A2.

6 Results

In this section, I will provide answers to the questions raised in the introduction of this thesis. How significant are umbrella and supplier damages and is the undercharge an appropriate measure for supplier damages? I will also address the issues of cartel profitability and stability in sections 6.3 and 6.4, respectively. Results will be presented graphically using a standard parameter configuration. These standard parameter values can be found in Appendix A.3. I will assume that (indirect) suppliers have quadratic cost functions unless stated otherwise.

6.1 Umbrella Damages

As colluding retailers set a higher-than-competitive price, the response of non-colluders is typically to increase prices in the slipstream of the cartel firms, the so-called ‘positive umbrella’ effect. This can be seen in figure 2.

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Figure 2: Non-colluder and colluder price increases compared. The solid lines depict colluder price increase pc

i − p∗i and the dashed lines non-colluder price

increase pnc_i − p∗_i. Also, the blue-colored lines are in case of a cartel size of 90% (18/20) and the red-colored lines for a cartel size of 50% (10/20).

0 0.2 0.4 0.6 0.8 1 −0.05 0 0.05 0.1 0.15 γ 0 0.2 0.4 0.6 0.8 1 −0.05 0 0.05 0.1 0.15

(a) Bertrand Competition, top-left corre-sponds to quadratic-shaped retailer costs and bottom-left to linear-shaped retailer costs

0.2 0.4 0.6 0.8 1 −0.05 0 0.05 0.1 0.15 γ 0.2 0.4 0.6 0.8 1 0 0.1 0.2

(b) Cournot Competition, top-right corre-sponds to quadratic-shaped retailer costs and bottom-right to linear-shaped retailer costs

First of all, it can be seen that there is only a small quantitative difference between the quadratic and linear costs cases here. In general, prices are lower if retailers have linear cost functions. Also, if products are weak substitutes, a surprising result is obtained.

Proposition 6.1. The umbrella price effect can be both positive and negative. Non-colluding competitors of the colluding firms set lower-than-competitive prices if products are weak sub-stitutes (γ is low). This negative umbrella effect occurs if, roughly γ ≤ 0.05.

This results might seem strange at first but there is actually an easy explanation for this phenomenon.

For retailers, two external factors influence their price level, prices set by competitors, p−i and the input price ¯p2. The price increase by the colluding firms make the price of

non-colluders go up, the degree of this price response depending on γ. On the other hand, in toto, output by retailers will decrease due to the action of the cartel. This evidently forces the demand for input to decrease and consequently the input price ¯p2.36 This second effect causes

the price of a non-colluding retailer to decrease. Typically, the second effect is outweighed by the first effect but for small γ it may be the other way around and a ‘negative umbrella’ effect arises. Note also that this negative umbrella effect can only occur if retailers buy input from the same wholesale market. For example, in the light of the KONE elevators case that

36

The price reaction to the decrease in demand is in general unambiguous as discussed in section 4. However, as I assume here that wholesalers have quadratic costs, the input price will decrease in reaction to the decrease in demand. If wholesalers have linear costs, there will be no effect on input prices (see section 5.1) and in case of a concave shaped wholesaler cost function, the input price might increase as a result of the decrease in demand.

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sparkled the discussion on the umbrella effect, cartel actions might have caused the price of, for instance, steel to decrease. If there is a large degree of differentiation of elevators (γ is small), then in theory, prices of non-colluding elevator-producing firms might have decreased as the effect of lower input (steel) costs outweighed the price-increasing effect of the cartel. Even though the negative umbrella effect occurs only in a small region of γ, it is important to keep in mind that the umbrella effect can be both positive and negative.

One of the questions of interest is how indirect harm in the form of an umbrella overcharge relates to direct harm, which is measured in practice by the cartel overcharge. Figure 3 shows the fraction of the cartel overcharge to the total overcharge.

It can be seen here that if γ is small, the cartel overcharge is an accurate measure of the total overcharge as its fraction of the total overcharge is close to 1. However, as product substitutability increases and as the cartel size increases, the cartel overcharge becomes less accurate, even to a point where it is less significant than the umbrella overcharge. That is, it constitutes less than half of the total overcharge. Again, this seems a strange result at first as from figure 2 it can be seen that the umbrella price effect on non-colluding firms is at a maximum as large as the price increase of the colluding firms. However, part of demand for the goods produced by the cartel switches to the goods produced by the non-colluding firms as a result of the price difference between the colluding and non-colluding firms. This result is even stronger in the Cournot case as non-colluding firms profit on the one hand from the scarcity created by the cartel through higher prices - especially the closer substitutes products are - and on the other hand take over part of the output that is cut off by the cartel to create this scarcity. Again, this raises questions about the stability of cartels. This issue will be addressed in sections 6.3 and 6.4.

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Figure 3: Relative cartel and umbrella overcharge compared. Illustration of the fraction OCic

OCc

i+OCinc against cartel size in percentage. The solid, dashed and

dotted lines correspond to, respectively, γ = 0.05, 0.50 and 0.95.

20 40 60 80 0 0.5 1 1.5 Cartel Size in % 20 40 60 80 0 0.5 1 1.5

Note also that the fraction of cartel overcharge can be larger than 1 for small γ. This is caused by the ‘negative’ umbrella effect, discussed earlier in this subsection. In those cases, the cartel overcharge slightly overstates total purchaser harm as the price increase by the colluding firms triggers a price decrease of its competitors.

In conclusion, the overcharge caused by umbrella pricing is indeed quite significant, even more so in the case of Cournot competition. The closer substitutes products are and the larger the size of the cartel, the larger the share of the umbrella overcharge in the total overcharge.

6.2 Supplier Damages

As price increases by the cartel and output reduction are intertwined, suppliers might suffer both from a decrease in sales and a decrease in output prices - the ‘undercharge’ - as can be seen from the decomposition in section 4.37 _{In order to assess how significant collusion}

by retailers affect the direct and indirect suppliers, I will look at the proportion of supplier damages in total damages. Hence, a first step is to define total harm. Two main viewpoints can be distinguished when defining total harm, a ‘government’s’ and a ‘victim’s’ point of view. From the government’s perspective, if extra profits gained by the cartel offsets the damages to all other parties involved, a cartel is good as total welfare increases. However, victims will argue that including profit gains will understate total cartel damages. As the latter point of view is generally more in line with the view of competition authorities, I will exclude retailer profits from total damages.

37

Two cases are considered here; ν = 1 and ν = 2. In the former case there will be no undercharge and in the latter case there will be.

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Figure 4: Upstream vs. Downstream Harm, Quadratic Costs Wholesalers.

Illustration of the fraction U H_DH against γ. The solid, dashed and dotted lines correspond to a cartel size of, respectively, 10%, 50% and 100%.

0.2 0.4 0.6 0.8 0.25 0.35 0.45 γ 0.2 0.4 0.6 0.8 0 1.25 2.5

0.2 0.4 0.6 0.8 0.25 0.35 0.45 γ 0.2 0.4 0.6 0.8 0.4 0.6 0.8

Figure 5: Upstream vs. Downstream Harm, Linear Costs Wholesalers.

Illustration of the fraction U H_DH against γ. The solid, dashed and dotted lines correspond to a cartel size of, respectively, 10%, 50% and 100%.

0.2 0.4 0.6 0.8 0.048 0.052 0.056 γ 0.2 0.4 0.6 0.8 0.2 0.35 0.5

0.2 0.4 0.6 0.8 0.048 0.051 0.054 γ 0.2 0.4 0.6 0.8 0.1 0.13 0.16

Supplier damages and the umbrella effect of price cartels

Msc. Thesis: Supplier Damages and the Umbrella Effect of

Price Cartels

Contents

1

Introduction

2

Competition Policy

3

The Model

4

Decomposition of Harm

5

Model Solution

6

Results