University of Amsterdam
MSc Economics: Markets & Regulation
Master’s Thesis
Towards Fair Compensation for Consumers: A
Compensating Variation Method
Author:
Martijn Mouw
Supervisor: Prof. Dr. M.P. Schinkel
Abstract
In this thesis it is argued that the current compensation measurement for con-sumers in antitrust cases is incorrect. The focus of the European Commission (EC) is mostly on deriving the total overcharge and neglects the deadweight loss (DWL) part of the damage done to consumers. The Compensating Variation (CV) is found to be the correct measurement for compensating consumers after a price increase caused by an antitrust violation. The CV has not been implemented as the stan-dard measurement in antitrust cases due to several quantification and legal issues. In addition, conditions on the use of a (aggregated) demand function cause extra complications. A numerical example on two methods that allow the calculation of the CV, starting with only a known demand function, shows that the calculation is possible. The numerical approximation method by Breslaw and Smith (1995) is the most feasible method to implement and accurately estimates the CV when compared to the exact method byHausman(1981).
Keywords: Antitrust, Compensating Variation, Consumer Compensation JEL: D11; D12; K21; L41
Acknowledgements
I would like to express my gratitude to my supervisor Maarten Pieter Schinkel for the useful discussions and critique through the learning process of this master thesis. Furthermore, I would like to thank Eelko Ubels, Jan Tuinstra and the user Torsten from Mathworks.com for their help on coding with MATLAB. Lastly, I am profoundly grateful to Suzanne Stevens for setting the initial steps towards this research with her BSc thesis (Stevens,2013). Errors and opinions remain mine.
Statement of Originality
This document is written by Martijn Mouw who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document are 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 supervision of completion of the work, not for the contents.
Contents
1 Introduction 5 2 Theory 8 2.1 Class-action lawsuits . . . 8 2.2 State of affairs . . . 10 2.3 Critique . . . 12 2.4 Potential measures . . . 15 2.4.1 Marshallian vs. Hicksian . . . 15 2.4.2 EV/CS/CV . . . 17 2.5 Incorporation issues . . . 20 2.5.1 Legal issues . . . 20 2.5.2 Quantification issues . . . 20 3 Methodology 22 3.1 Potential Methods . . . 22 3.1.1 Hausman . . . 243.1.2 Breslaw & Smith . . . 27
3.2 Use with caution . . . 29
3.2.1 Integrability conditions . . . 29
3.2.2 Aggregated demand conditions . . . 30
3.3 A ’Real’ Case . . . 35
3.3.1 Demand function estimation . . . 35
3.3.2 Application of methods . . . 40
4 Conclusion & Discussion 45 5 Appendices 51 5.1 Appendix A . . . 51
List of Figures
1 The area of total overcharge and deadweight loss underneath a demand
curve . . . 12
2 A graphical explanation of the but-for price estimation . . . 13
3 Marshallian & Hicksian demand curves . . . 16
4 The OVC, CS and CV for various price changes . . . 43
List of Tables
1 Welfare losses with different methods . . . 412 Comparison between Marshallian and Hicksian measurements . . . 42
1
Introduction
Today’s world seems to focus more and more on fairness. From a cry for attention towards racism during the 88th Academy Awards in 2016 with #OscarSoWhite1 to a more direct form of action with Iceland becoming the first country to enforce equal payment of men and women in 20182. The increasing attention for fairness is also present in the antitrust world. In the 21st century, after cases such as Courage Ltd v. Bernard Crehan3 and Manfredi v. Lloyd Adriatico Assicurazioni SpA4, it has been accepted that also individuals can claim compensation after infringements of articles 101 or 102 TFEU5 (Maier-Rigaud, 2014). In 2014, Margarethe Vestager, European Union (EU) commissioner in charge of competition policy, said that:
“We need a more robust competition culture in Europe. So I am very glad that the Council has now also formally approved the Directive on antitrust damages actions. I am very pleased that it will be easier for European citizens and companies to receive effective compensation for harm caused by antitrust violations”
This was after the implementation of Directive 2014/104/EU of the European Parlia-ment and of the Council of 26 November 2014 on certain rules governing actions for damages under national law for infringements of the competition law provisions of the Member States and of the EU. Apparently, until 2014 it had not been easy for citizens to effectively claim compensation for antitrust violations. After being harmed by an antitrust violation it would be unfair if claiming compensation would be difficult and ineffective, especially if that could potentially benefit the violator itself. Thus, after Di-rective 2014/104/EU, one would expect that victims of violations could be more often fairly compensated. However, nothing could be further from the truth.
In the quantification guide for antitrust damages it is stated that compensation includes not only the actual loss suffered but also the loss of profit (European
Commis-1www.twitter.com/hashtag/oscarsowhite 2
www.bbc.co.uk/bbcthree/article/253d8b3e-1891-43ab-8848-4a5110bda171
3Case C-453/99, Courage v. Crehan, 2001 E.C.R. I-6297 4
Joined cases C-295/04 to C-298/04, Manfredi v. Lloyd Adriatico Assicurazioni SpA, 2006 ECR I-6619
5
sion,2013). This arose due to the fact that purchasers could buy less products because of a higher price. It is clear that if these purchasers intended to use these products for their own commercial activities, they would miss out on profits because of the price increase. What is less clear is that, when these purchasers are final consumers, if the loss of profit part of compensation also applies to them. Final consumers will not use bought products for commercial activities, but they would also miss out on ’profits’ in the form of utility. Since Directive 2014/104/EU states that victims have the right to claim full compensation for harm done by antitrust cases, one would expect that these final consumers would also be compensated fully. Even when it comes to their loss of utility due to higher prices.
However, a recent article by Rosenboom, Kocsis, and Mulder (2017) states that the current compensation method understates that the actual damage incurred and that it is still unclear how to compensate consumers for their losses caused by antitrust violations. In addition, the article argues what the correct compensation measurement could be, but does not give a definitive correct method with guidance on how to derive this. With the global trend towards fairness, an unfair compensation methodology seems rather odd. A correct methodology for compensation would be a significant contribution towards fairer compensation in private damage claims. This thesis aims to fill this gap by finding a solution to the problem. There are several important questions to answer before a correct method can be proposed:
1. What is the current measurement of antitrust damage claims and why is this understating true damage?
2. What should be the correct measurement and why is this not implemented?
3. How is the correct measurement derived and is the implementation feasible in antitrust cases?
These questions shall be answered on the basis of a price increase caused by an antitrust violation that is affecting final consumers.6 A cartel is a violation of article 101 TFEU
6
Naturally, there are forms of antitrust violations which are profoundly complex such that a method-ology could not be applied. However, the aim is that for cases in which consumer prices are increased, it should be feasible to apply a correct method.
and is defined by the European Commission (EC) as: “a group of similar, independent companies which join together to fix prices, to limit production or to share markets or customers between them”.7 In a price cartel two or more firms could set prices higher than they would have set if they were competing without an agreement on price setting. Another violation is abusing a dominant position by a firm and is a violation of article 102 TFEU. The EC defines this as: “A company can restrict competition if it is in a position of strength on a given market. A dominant position is not in itself anti-competitive, but if the company exploits this position to eliminate competition, it is considered to have abused it”.8 This can be through, for example, charging unreasonably high prices.
The thesis is structured in the following way. In section2 the theory behind the topic is discussed. This is done in order to answer the first two important question mentioned before. The increasing importance of the matter is explained. Followed by the current EC methodology and the critique on this methodology. It concludes by showing what is regarded as the correct measurement along with the drawbacks of implementation. In section3the methodology behind the ’correct’ method is discussed. Various potential methods are described along with various conditions that should hold in order for them to be applicable. Then, with a hypothetical case of a price increase, it is shown that it is feasible to derive the fair compensation for consumers. This thesis concludes in section4by summarizing the findings and discussing what the shortcomings are and what could be included in potential further research.
7
www.ec.europa.eu/competition/cartels/overview/index en.html
8
2
Theory
In this section the theory behind the problem of unfair compensation is discussed. Sec-tion2.1explains the importance towards a correct methodology because of the increasing number of class-action lawsuits. In section2.2the current state of consumer compensa-tion with antitrust violacompensa-tions is discussed. Seccompensa-tion 2.3gives an overview of the critique on the current methodology of the EC by scholars. Section 2.4describes the potential measures for full compensation of consumers. Section2.5concludes by describing what the incorporation issues are of the most preferred method from the fourth subsection
2.1 Class-action lawsuits
The situation of cartel damages for purchasers is discussed intensively for the last decades and, while new findings and opinions arise on the topic occasionally, it is not a leading-edge subject in competition policy. On the contrary, the situation of cartel damages for consumers has not been discussed as heavily. There are several reasons why this is the case. One is that, unlike firms, consumers are not required to hold on to the receipts of a purchase and often forget or throw away this proof of purchase. Resulting in the inability to prove that they were harmed by a cartel. Along with the digitization this problem was more easily solved but still consumers faced obstacles to compensate their loss. Mainly the high value of the costs compared to the relatively low potential compensation could cause consumers not to consider a lawsuit. These costs could consist of litigation costs, psychological costs, time and effort costs and knowledge barriers (Laitenberger & Smuda, 2015; Lehne, 2012; R¨uggeberg & Schinkel, 2006). Allowing for the aggregation of many individual lawsuits, a so called class-action lawsuit, would reduce many of these costs and lead to a more cost-effective case and consequently a higher number of (successful) class-action lawsuits.9 Thus, a class-action lawsuit seems as a beneficial tool for consumers to claim damage compensation.
In recent years, the attention to the legal situation of consumer cartel damage claims increased. The EC published a green paper about this topic in 2005 which
ad-9This could also have a deterring effect for collusion due to the awareness of firms for potential
damage claims, which could off-set the increasing number of class-action lawsuits (though the latter will most likely have a smaller effect).
dressed the difficulty for consumers to bring in damage claims individually and raised the question if and how there should be special procedures for collective claims. In the follow-up white paper in 2008 it is stated that “there is a clear need for mechanisms allowing aggregation of the individual claims of victims of antitrust infringements”, showing that indeed there should be special procedures available. Furthermore, there have been consumer associations that addressed the issue. The European Consumer Consultative Group (ECCG) wrote a report in 2010 containing the opinion that “col-lective redress mechanisms to be available in all sectors where consumers interests are affected”. Directive 2014/104/EU, trying to ease the legal process for victims, shows that the EC is, by then, still concerned about the matter. It is not merely institutions that are aware of the problem since scholars also have their say in the matter. Lait-enberger and Smuda (2015) state that the current competition law in the EU is not in favor of class-action lawsuits. Clearly, the legal situation of collective consumer claims is a problem that has not been solved.
In addition, the report of the ECCG includes a different quote that could have attracted even more attention towards the subject than the previously mentioned issues: “innovative and practical solutions to the calculation of damages are needed to replace the often impossible task of calculating the exact loss”. Apparently there are more issues than merely the legal problems of the bringing in of claims from consumer groups. Calculation problems could lead to an under or overstatement of the ’fair’ compensation for consumers. In the situation where many consumers are involved in a class-action lawsuit a small over or understatement can already have large implications for the total damage not being compensated to consumers. Along with the upward sloping trend of class-action lawsuits (Basso & Ross, 2010) this indicates the importance of a correct framework for the calculation of the exact loss by consumers. First an overview of the current situation and the critique needs to be clear. Secondly, the correct measurement and its complications need to be analyzed in order to determine whether a different method is at all feasible.
2.2 State of affairs
After the Green Paper in2005, the White Paper in2008and the opinion by the ECCG in 2010, the Directorate-General for Competition (DG COMP) of the EC drew up a Draft Guidance Paper in2011. This paper was meant to guide and support courts with insights into the damage that can be caused by violations of the EU antitrust articles 101 and 102. Furthermore, it contains guidance on the methods and techniques available in 2011 to calculate the damage caused by infringements. The draft was preparatory work for a final quantification of harm guide that was published by the EC in 2013and was accompanied by a directive proposal on the rules of action for damages by antitrust violations for member states of the European Union (EU). This proposal was an earlier version of Directive 2014/104/EU that became active on 26 December 2014. Member states of the EU were required to implement the directive in their national legal system no later than 27 December 2016. Including a recommendation by the EC for member states to include collective redress mechanisms for consumers, the main motive for the directive was to “ensure that anyone who has suffered harm caused by an infringement of competition law by an undertaking or by an association of undertakings can effectively exercise the right to claim full compensation for that harm from that undertaking or association”. The document contains several comments to the right of full compensation. First, full compensation should make sure that a victim will be in the same position that he would have been in if the violation had not taken place. Second, overcompensation is not allowed. The quantification guide from 2013, which is the latest EC guide available to courts, should explain to courts the method to calculate the full compensation for victims.
In order to calculate the full compensation, the quantification guide should make clear what the actual harm done to victims is. In the first paragraph is stated that: “compensation includes reparation not only for actual loss suffered (damnum emergens), but also for loss of profit (lucrum cessans) and the payment of interest”.10 ’Actual loss’ is the reduction in an individual’s assets and ’loss of profit’ represents an increase in an
10This judgment was based upon the judgment by the European Court of Justice (ECJ) in the Manfredi
case in 2006, which was a class-action lawsuit, thus showing the priority of the EC to offer effective methods for collective claims after the Green Paper in 2005
individual’s assets, that would have occurred if the violation did not take place, which did not happen. Figure 1 shows the graph that is used in the guide to show the harm done when prices increase. Part A of Figure1 represents the actual loss part of the full compensation definition. In competition policy this harm based on the price increase is often referred to as the ’total overcharge’. The total overcharge is the increase in the price during the anti-competitive regime, which is the actual ’overcharge’, times the quantity bought at the prices during the anti-competitive regime. Part B of Figure
1 represents the loss of profit part of the full compensation definition. This harm is often referred to as the volume effect, the output effect or (in welfare terminology) the deadweight loss. In the guide this is explained as a lower demand due to higher prices since some customers will refrain from buying the product at the higher price. The size and shape of the deadweight loss depends mostly on the demand elasticity as can be seen in Figure1. Regardless of whether customers would have used the product for their own commercial practices at lower prices, thus actually have a loss of profit, or in the case of end-consumers where customers fail to enjoy utility, the guide states that: “Applicable legal rules may provide that some or all of such harm should be compensated for such failure to enjoy the usefulness of the product”. However, from this quote it seems like the guide is covering itself in using words as ’may’ and ’some’, instead of stating that legal rules must provide that all customers are compensated for this harm. In addition, the guide states that the total overcharge is the minimum harm that must be compensated, which raises even more doubts when it comes to the devotion of the EC trying to give customers full compensation.
The actual quantification guidance of the guide confirms the doubt of a heavier weight on quantifying the total overcharge instead of the deadweight loss. In the ’Meth-ods and Techniques’ section the estimation of a ’but-for’ price is explained. This is a hypothetical price, that is estimated through applying a regression analysis, that would have prevailed during the cartel period but without the cartel being active. See Figure
2 for the graphical explanation. The difference between the actual cartel price and the estimated but-for price (i.e. the overcharge) is necessary to calculate both the total
over-Figure 1: The area of total overcharge and deadweight loss underneath a demand curve
Source: European Commission(2013)
charge and deadweight loss.11 The overcharge calculation, which requires this but-for price estimation and the calculation of the overcharge is then relatively straightforward. The calculation of the deadweight loss is more complicated since both the demand elas-ticity and a hypothetical quantity that would have been bought at the estimated but-for price are needed. Therefore, one would expect that the explanation of the quantification of the deadweight loss is more thorough. However, the section on the quantification of the overcharge covers around nine pages, while the section on the quantification of the damage caused by the volume effect covers barely a single page. This meager description of the quantification of deadweight loss invigorates the doubt on the weight of the EC on fully compensating victims.
2.3 Critique
A subject with such a broad and current interest is likely to receive academic critique. Scholars have criticized the methods and legal situation of the EC on compensation for several years. Critical articles have been written about the topic before the implemen-tation of Directive 2014/104 and afterwards.
11Another potential method, used by Lavergne, R´equillart, and Simioni (2001) for example, is to
determine the price increase through market share indices such as HHI and PCM. However, this is less accurate than a but-for regression analysis since it merely uses a single index.
Figure 2: A graphical explanation of the but-for price estimation
Source: European Commission(2013)
Over 20 years ago,Landes(1983) andHjelmfelt and Strother(1991) already crit-icized the exclusion of deadweight loss in the damage calculation of antitrust cases.
Hjelmfelt and Strother (1991) were even unable to find a case where deadweight loss was included. Which is not that astonishing given that the discussion by then was not as active as now. Although the EU was founded after these articles were published, they were still discussed in academic literature early on and thus available to all mem-ber states of the EU. One would expect that the memmem-ber states would catch up on the outcry of scholars for the need of a different damage calculation method. However, as was stated in Section 2.2, the EC’s green paper that introduced this matter vaguely was published much later in 2005. More critique came in 2006 when Fisher (2006),
Leslie (2006) and R¨uggeberg and Schinkel (2006) brought up the problem of excluding deadweight loss after the green paper was published. R¨uggeberg and Schinkel (2006) states that: “The quantification of claims for price fixing evolved over time in the courts and is predominantly based on the so-called ’overcharge’” and “Based on actual sales, it ignores damages on sales that could have been made, if prices had been at competitive levels -that is, it underestimates the actual damages by the amount of the deadweight loss”. Leslie(2006) is a more elaborate article on the matter. This article explains how antitrust violations produce deadweight losses to society, how antitrust law does not
contain deadweight loss in the damage calculation and what the ramifications are for not including the deadweight loss.12 According toLeslie (2006), the main ramifications of excluding deadweight loss are that victims are not correctly compensated and vio-lators not correctly accused, which will lead to a negative effect on the deterrence of future violations. After 2006 it seems like the EC noticed the critique of the scholars and incorporated it in the white paper of 2008 and the quantification guide/directive proposal in 2013. Thus, the critique on the subject after 2013 is more peculiar. In 2014, but before Directive 2014/104 was published,Maier-Rigaud(2014) wrote that the proposed directive underestimates the relevance of the deadweight loss and that these damages will most likely not receive an equal treatment compared to the overcharge part of the total damage. A more recent article, that was written after the latest ’update’ from the EC, by Rosenboom et al. (2017) states that deadweight loss still is ignored. Along with the previously mentioned critique ofLaitenberger and Smuda (2015) about the legal issues for class-action lawsuits, it indicates that the EC failed to implement the critique and issues into a effective directive.
In addition, scholars were also concerned about the indirect effects of the exclusion of the deadweight loss in damage claims. Mainly about the effect on the deterrence of future violations. As stated in Maier-Rigaud (2014) the EC seems to forget that private enforcement is not merely about compensation, but also about deterring future violations. This is in someway a vicious circle of importance since the less deterrence there is, the more important compensation becomes and a larger focus on compensating victims will increase the deterring effect of violations. That being said, this effect works on two levels. The first is on victim-level since the less a victim can claim from being harmed, the less he will be likely to sue a company that he suspects being involved in antitrust matters (R¨uggeberg & Schinkel, 2006). The second is on the violator-level since firms involved in an antitrust matter will know beforehand what the damages will be based on if they are discovered and a lower potential damage claim will increase the likelihood of firms becoming involved in a cartel (Laitenberger & Smuda, 2015).
Connor and Lande (2006) found that in both the EU and US the fines imposed are
12Leslie (2006) also included a section what the incorporation issues of including deadweight loss are.
lower than the actual gain of the illegal actions by the violators and that this, in light of the optimal deterrence fee, is too low. For this conclusion they used a method that was first mentioned in Landes (1983). The idea behind this is that the optimal deterrence fee is equal to the ’net harm to others’ divided by the probability of being caught for breaching antitrust laws.13 Thus not only is it important to calculate the ’net harm to others’ for the compensation that victims deserve, it is also important for setting the optimal deterrence fine for violators.
2.4 Potential measures
One of the main questions concerning the full compensation of antitrust victims is how to determine what the full compensation is. In the EU, as mentioned before in Section2.2, a victim, after being compensated, should be in the same position that he would have been in if the violation had not taken place. Taking a deeper look into welfare theory shows that most measurements are based on two different styles of demand functions, namely Marshallian and Hicksian demand. Before discussing the various measurements it is practical to analyze these demand functions.
2.4.1 Marshallian vs. Hicksian
The Marshallian demand function is the most commonly known demand function. It originates fromMarshall(1890) in which Alfred Marshall wrote a leading textbook that guided many generations of economics students. In this textbook Marshall discusses many important principles of economics, but perhaps the most important are the de-mand function that afterwards is named a Marshallian dede-mand function and the general consumer surplus theory. A Marshallian demand function is a demand function in it simplest form. It describes the relationship between factors that influence demand, often price and income, on quantity demanded itself. Figure 3 shows a Marshallian demand curve, which is the line labeled with q(p, m). This line indicates what the observed demand q is given various prices p and income m. The Marshallian demand function is often referred to as the uncompensated demand function since it does not take into
13
The question what the optimal deterrence fee should be is not the subject of this thesis. Therefore, no discussion is included regarding the probability of being caught for antitrust violation
Figure 3: Marshallian & Hicksian demand curves
Source: Shin and Burke(2010) (’D’ added)
account wealth effects. It assumes that consumers will spend their fixed income such that they maximize utility. To illustrate, the Marshallian demand function is derived by solving the following problem of maximization for consumers with n goods available:
max q u(q) subject to n X i=1 piqi= p ∗ q ≤ m (1)
Thus, along the line, utility changes for consumers. Consider, as the graph shows, an increase in the price of a certain good. Keeping quantity equal for all other goods, a consumer can now buy less goods than before and is therefore left with a lower utility. Even if he doesn’t change his consumption of all other goods, his choice will be less optimal than before.
It is important to note that a consumer does not necessarily decrease the quantity demanded of the price-increased good. This is because of two different effects. Con-sumers are expected to switch their consumption of the price-increased good towards the consumption of other goods since these have become relatively cheaper. This effect is called the substitution effect. There could also be an offsetting effect, which is called the income effect. When the price of a good increases, it reduces the purchasing power
of consumers. Consumers might consume more of a good if this is an inferior good. If this positive income effect dominates the negative substitution effect of a good then total quantity consumed by a consumer might increase with a price increase. This is called a Giffen good, named after the British statistician Robert Giffen. In the remainder of this thesis it is assumed that goods are normal for the sake of the argument.
The concept of the Hicksian demand function originates from critique on the de-velopment of welfare theory by Hicks (1939). According to Hicks not enough research had been done on this topic and therefore he stated: “I propose to set out briefly and simply the main lines of the new welfare economics”. After this statement Hicks pub-lished a series of articles in which he builds on the, by then, current welfare theory, that eventually led to the specification of the Hicksian demand function. In essence, this demand function takes into account the income effect. In other words, it describes for a certain level of utility the most cost-effective consumption bundle. To illustrate, in Figure3 the Hicksian demand curves are the lines with the label h(p, u). The Hick-sian curve that crosses through point E0 represents the most cost-efficient consumption
bundle h to obtain the utility u0 that a consumer would have received in the situation
without a price increase. Logically, the Hicksian demand curve that crosses through point E1 represents the same, but then for the utility in the situation where there was a
price increase. Where with the Marshallian demand function the utility did not remain equal along the curve, this is the case with income for the Hicksian demand function. With an increase in price, consumer shall need a higher income level to obtain the same level of utility.14
2.4.2 EV/CS/CV
Both the Marshallian and Hicksian demand functions offer methods for compensating a person for welfare loss. The goal is to find a method that has the best fit with the EC’s legal requirement, namely that a victim will be in the same position that he would have been in if the violation had not taken place. The most basic method for calculating welfare loss is the calculation of consumer surplus (CS), which requires the Marshallian
14
This is again not true when looking at inferior goods. From a graph it is easily observed if this is the case since then the Marshallian demand curve will be steeper than the Hicksian demand curve.
demand curve. In Figure3the CS loss due to a price increase is the area BCE0E1. The
CS is defined in Marshall 1930 as: “The excess of the price which he would be willing to pay rather than go without the thing, over that which he actually does pay, is the economic measure of this surplus satisfaction. It may be called consumer’s surplus”. In other words, compensating a victim with the CS is returning the monetary valuation that he would otherwise have been willing to spend on the product. As previously mentioned, only the Hicksian demand curve holds utility constant, therefore compensating a victim with the CS does not place him in the exact same position as if the violation had not taken place. Thus, the CS method is not an exact measure of welfare change (Varian,
1992). Nonetheless, it is an improvement compared to only compensating the total overcharge, which in Figure3 is the overcharge(τ) multiplied by q1.
’Exact’ welfare measurements can be derived from the Hicksian demand functions. The two best known measurements are the Equivalent Variation (EV) and the Compen-sating Variation (CV). Currie, Murphy, and Schmitz (1971) defines the EV and CV as follows:15
1. Equivalent Variation is the amount of compensation, paid or received, that will leave the consumer in his subsequent welfare position in the absence of the price change.
2. Compensating Variation is the amount of compensation, paid or received, that will leave the consumer in his initial welfare position following the change in price.
The mathematical definitions are:
EV = E(p1, u1) − E(p0, u1) (2)
CV = E(p1, u0) − E(p0, u0) (3)
where u1and u0 are the new and initial levels of utility, p1 and p0are the new and initial
levels of price and E(p, u) is the expenditure function that gives the minimum expenses needed to obtain a certain utility for a given price. To clarify, the expenditure function
15
There are two other measures (Equivalent Surplus & Compensating Surplus) described in this article that occur when consumers have buying constraints. However for the sake of the argument we do not impose buying constraints on consumers. Therefore, they are irrelevant.
is defined by the following problem of minimization for consumers:
E(p, u∗) ≡ min
q p ∗ q subject to u(q) ≥ u ∗
(4)
Where u∗ represents a specific utility level.
In Figure 3 the EV with a price increase is the area BCDE1 and the CV with
a price increase is the area ABCE0. Since in antitrust matters the price will increase
and victims arrive at a lower welfare position, it should be the case that consumers are compensated towards their initial higher welfare position. Clearly, the CV has the best fit with this intuition of welfare compensation and the EC’s legal requirement. This is confirmed by scholars over the last years who argue that the CV is a better measure of a consumer welfare loss compared to EV or CS (Creedy,2006;Lavergne et al.,2001;
Shin & Burke, 2010). Willig (1976) also admits this, however he also states that the differences between CS and CV are typically so small that they can be disregarded. Though this may be the case for a single consumer. Logically, this is no argument when someone is victimized and has the right to be fully compensated. In addition, when a claim is bundled, the individual difference may be small but the difference in the total damage can be of a significant amount.
There is another measurement mentioned in a recent article byRosenboom et al.
(2017), namely the Slutsky Compensating Variation. This measurement is based on the idea that consumers should be able to buy the initial bundle of goods even with an increase in the price of these goods. In Figure 3 this would mean that the area of the Slutsky Compensating Variation would be the overcharge (τ) multiplied by q0. This
measurement is bigger than the CV, which implies overcompensation and thus violates the requirement from EC Directive 2014/104 that no overcompensation is allowed.16 This makes the Slutksy Compensating Variation a less preferable measurement. There-fore, when the Hicksian demand curves are known, the CV is the best measure for consumer compensation.
16
According toFisher(2006), overcompensation could cause consumers to encourage injury and thus creates a moral hazard problem of consumers avoiding risks which they expect to turn out badly. Although, this would be less likely in an antitrust situation since consumers should be unaware of the presence of the violation. Overcompensation may however increase the amount of (fair) claims due to the potential welfare gain.
2.5 Incorporation issues
One would expect the EC to pick up on the literature regarding the correct measurement of welfare loss for consumers. Even scholars noted the irony of the inability to include the deadweight loss in damages.17 However, the total overcharge is still the most commonly used method (Rosenboom et al., 2017). A fairer compensation measurement would be to use either the CS or CV. Apparently it is not that straightforward to implement either one of these measures. The legal and quantification issues of the implementation of a fairer measurement for consumers are explained in this section.
2.5.1 Legal issues
There are several legal problems that deter the implementation of a fairer measurement for consumers. Mostly, these issues relate to court-specific problems. An important legal constraint is the statutory limitation period (R¨uggeberg & Schinkel, 2006). With a shorter period to come up with damage estimations, it is harder to prove a more complex estimation method. The representatives of the victim might prefer to ’play it safe’ and use the total overcharge measurement. Still, as the saying goes: without struggle, there is no progress. Thus, with less attempts made to quantify the CV, the less likely it is that the CV will become the new standard in antitrust cases. Another problem arises when it comes to the judges. Often judges are not trained in understanding the difficult modelling of damages (Fisher, 2006). A sophisticated approach, such as the CV, might be too complex for them. Therefore, they may not be capable of observing quantification malpractice.
2.5.2 Quantification issues
One of the main reasons why courts have refrained from correctly compensating victims is the difficulty of quantification (Maier-Rigaud,2014). R¨uggeberg and Schinkel(2006) augments this by stating that the quantification and the modelling of the proper method is difficult. It is important to know at which stage in the quantification progress the
17Hovenkamp (1989): “Ironically, even though the traditional deadweight loss triangle is the oldest
recognized and least controversial of monopoly’s social costs, the existing rules of antitrust standing rarely permit the deadweight loss to become the basis of a damages action”
issues arise. As can be seen from Figure 3 there are several aspects that need to be derived in order to obtain the CV.18 First, the overcharge needs to be known. Without the overcharge it would be impossible to calculate the total overcharge, which is the lowest (discussed) compensation. For this the but-for price must be determined.19 The estimation of a but-for price is not a straightforward calculation (Lopatka & Page,2003). The difficulty here is the determination of a counterfactual situation (Fisher,2006;Han, Schinkel, & Tuinstra, 2009; Leslie, 2006). To determine a correct counterfactual situa-tion informasitua-tion is needed about the demand of consumers and market structure, which is often determined by many variables of which data is often not available (Laitenberger & Smuda,2015;McKenzie & Ulph,1986;Rosenboom et al., 2017). However, since the total overcharge is the most commonly used method by the EC it seems that in practice this is possible. The problem of a counterfactual situation also creates a problem in the second aspect needed to quantify the CV, namely the counterfactual quantity. In order to determine this counterfactual quantity, the Marshallian demand curve must be estimated, which is also a difficult estimation (Leslie, 2006). With the (supposed) knowledge of a but-for price, the demand curve should estimate what the but-for quan-tity is.20 The last step, but perhaps the toughest, is the determination of the Hicksian demand function. To determine the CV the utility of a consumer at the counterfactual situation needs to be known. However, it is very difficult, if not impossible, to determine a utility function (Hausman,1981;Rosenboom et al.,2017). As a result,Rosenboom et al. (2017) states that the CV does not seem feasible as an application to fully compen-sate consumers involved in antitrust cases. This implies that consumers either receive overcompensation or undercompensation. However, there are methods that allow the determination of the CV with only knowledge of a demand function.21 These methods
are described in the next section.
18
In this section it is assumed that the actual price and quantity are known
19For a more detailed explanation of the but-for price see section2.2 20
Using the but-for price estimation and the demand curve estimation it is already possible to deter-mine the CS measurement.
21
Note that this will not be the actual CV but an estimated CV that includes estimation errors. Nonetheless, as Leslie (2006) puts it: “reasonable estimates are possible. And that is all that the standard for antitrust damages requires”
3
Methodology
As mentioned in section2.5.2there are various methods that allow the determination of the CV with only the knowledge of a (market) demand function. This section will elab-orate further on this topic. Section3.1discusses these potential methods and shows the mathematical steps. In section 3.2 some cautionary notes and conditions are described when starting with a (aggregate) demand function to calculate welfare changes. Section
3.3concludes this chapter by describing the process of demand estimation and showing a numerical example of a price increase on welfare losses using two potential methods.
3.1 Potential Methods
The first step towards a method that could obtain the CV with only knowing the demand function was presented inHausman(1981). This paper was a response onWillig(1976), where it is argued that, due to the approximation of either the CV or EV, the CS is an acceptable measurement of welfare loss. Hausman (1981) dissents from this argument by stating that no approximation is required in the calculation of exact welfare losses.
Hausman (1981) reasons that from an estimation of a Marshallian demand function it is possible to obtain a measure of ’exact’ welfare changes and the corresponding estimation errors. From a Marshallian demand function, by using Roy’s Identity and solving a differential equation, the indirect utility and, consequently, the expenditure function can be derived. From this expenditure function and equation (5), the value of the CV can be derived. However, since it is highly likely that an academic pioneer endures critique, it was inevitable that Hausman(1981) did too.
An important limitation of the method created byHausman(1981) is that solving the differential equation becomes (nearly) impossible to solve when it involves multiple price changes (Breslaw & Smith, 1995; Creedy, 2006; Lavergne et al., 2001; Shin & Burke,2010). Moreover, even if there was a single price change, with a complex demand function it could still be a difficult task to integrate back to the expenditure function
(Breslaw & Smith, 1995; Lavergne et al., 2001; Shin & Burke, 2010).22 In addition,
McKenzie and Ulph (1986) states that there are demand functions that give a better representation of consumer demand but do not have a corresponding closed form of an expenditure or a utility function, which could create uncertainty when numerically evaluating underlying forms of the demand function. Therefore, not long afterHausman
(1981) was published, other (numerical) methods were published. These methods do not need to solve a differential equation and could solve more complicated demand functions and systems with multiple price changes (Shin & Burke,2010).
Vartia (1983) was the first to provide such a method. Through the use of an algorithm, Vartia shows that with the concepts of revealed preference and integrability theory it is possible to obtain an approximation of the Hicksian demand function from a Marshallian demand function. As the author puts it: “Our Main Algorithm generates sequences of quantity vectors that approximate the indifference surface more accurately and converge quickly towards it”. While Vartia states that the convergence is quick, others find that this is a drawback of the method and that a faster convergence is possible. 23
Breslaw and Smith(1995) proposed a more simple and efficient method that dealt with this drawback. This method builds on the approach used by McKenzie (1976) and uses a Taylor series expansion of the expenditure function about initial prices.24 According to them their method has two advantages compared to the method byVartia
(1983). The first one is that the algorithm in this method converges faster. By using a second-order approximation the algorithm converges quadratically, while Vartia’s algo-rithm converges linearly and therefore it has a faster rate of convergence.25 The second
22According toIrvine and Sims (1998), economists sometimes choose for demand functions such as
the linear expenditure function (LES) or the almost ideal demand system (AIDS), which make the integration relatively easier. However, these demand functions might sometimes requires researcher to impose constraints on the parameters in the function. These restrictions might not correctly reflect the observed data.
23Though not dealing with this drawback, McKenzie and Ulph(1986) adjusts the model of Vartia
(1983) with a different calculation path. The reason for this is, according to the authors: “Vartia’s method has the advantage that it is algebraically more compact. On the other hand, our method en-ables a better understanding of the structural relationships between consumer demands and preferences and thus affords greater ease in its economic interpretation”. For full explanation and mathematical derivations of this adjusted model, seeMcKenzie and Ulph(1986)
24
These initial prices can vary when either the CV or the EV is being calculated.
advantage is that the confidence intervals are more easily calculated in this method. Since a change in welfare depends on the estimated parameters of a demand function, the confidence intervals depend on the accuracy of the estimation of these parameters. According to Breslaw and Smith (1995), the estimation of these confidence intervals is easier with an approximation based on a Taylor series expansion than a trapezoidal approximation, which is used inVartia(1983). Thus, the method byBreslaw and Smith
(1995) is preferred for the estimation of welfare changes compared to the method by
Vartia(1983).
Since the method ofBreslaw and Smith(1995) involves an approximation of wel-fare measurements and errors, where the method by Hausman (1981) could calculate the exact change in welfare and the estimation errors, it would be most interesting to see how far apart the two methods would be when estimating the CV. In order to answer this problem, first the two methods are explained mathematically along with points of attention. Then, with a hypothetical price change and demand estimation, the two methods are compared.
3.1.1 Hausman
Before the method in Hausman (1981) is explained, it is useful to explain the duality properties that connect the expenditure, utility and the demand functions. Firstly, an important property is Shephard’s Lemma, which states that the partial derivative of the expenditure function (equation (4)) with respect to price i is the Hicksian demand function of good i:
hi(p, u∗) =
∂E(p, u∗) ∂pi
. (5)
Secondly, an important function is the indirect utility function. This is a function that connects the utility function and the expenditure function (equations (1) and (4)). It is a solution to the following optimization problem:
v(p, m) ≡ max[u(q) : p · q ≤ m]. (6)
different levels of income and prices given that total expenses are less or equal than income. The indirect utility function has an important property called Roy’s Identity:
qi(p, m) = −
∂v(p, m)/∂pi
∂v(p, m)/∂m, (7)
which shows that a Marshallian demand function can be derived from the indirect utility function by taking the partial derivatives with respect to price and income.
With these functions and properties it is possible to derive the Hicksian demand function by starting with a Marshallian demand function. The idea ofHausman(1981) is to first integrate the Marshallian demand function after applying Roy’s Identity to derive the indirect utility function. By inverting the indirect utility function, the ex-penditure function can be derived and consequently, through Shephard’s Lemma, the corresponding Hicksian demand function. For clarification, an example which is also used in the article by Hausman, is shown below.
First, for a single good case, the following linear Marshallian demand function is considered:
q(p, m) = α + βp + γm, (8)
where α is a constant and β and γ are the coefficients of price and income, respectively. For a comparison of welfare situations it is essential to stay on the given indif-ference curve (Hausman,1981). Also from equation (6) the following must hold for an initial level of utility u0:
v(p(t), m(t)) = u0, (9)
where t is a time index. Therefore, in the case of a price change, it should hold that:
∂v ∂p(t) ∂p(t) ∂t + ∂v ∂m(t) ∂m(t) ∂t = 0 (10)
This shows that in the case of a price increase (decrease), which has a negative (positive) effect on the indirect utility function, there should be an opposite effect of income on indirect utility to maintain utility on the same level. Rearranging this equation and
substituting Roy’s Identity from equation (7) results in:
dm
dp = α + βp + γm (11)
Solving this ordinary differential equation with c as the constant of integration gives:
m = c · eγp− 1 γ βp +β γ + α (12)
Please note that the full mathematical steps starting from equation (11) towards equa-tion (12) are shown in Appendix A. AsHausman(1981) points out that the constant of integration c depends on the initial level of utility u0, c = u0 can be chosen as the
car-dinal utility index. Then, by interchanging the utility and income variable in equation (12), the indirect utility function is obtained:
v(p, m) = e−γp· m + 1 γ βp +β γ + α (13)
Then by again interchanging the utility level and the income level results in the following expenditure function: E(p, u) = u · eγp−1 γ βp +β γ + α 26 (14)
The initial level of income is given as m0 and since m0 = E (p0, u0), equation (3) can
now be rewritten to:
CV = E(p1, u0) − E(p0, u0)
= E(p1, u0) − m0, (15)
In the remainder, the level of income is assumed to be constant at the initial level m0.
Through combining equations (14) and (15) the following formula for the CV is derived:
26
Notice the similarity with equation (12). An important difference is that equation (12) is not an expenditure function since it does not involve a measure of utility (yet) but only a constant of integration.
CV = u0· eγp1 − 1 γ βp1+ β γ + α − m0 (16)
In addition, knowing that the CS is the area underneath the Marshallian demand curve and in between a certain change in price, a measure for the CS can also be derived:
CS = Z p1 p0 q(p, m) dp = Z p1 p0 (α + βp + γm) dp = αp +β 2 · p 2+ γmp p1 p0 (17)
Thus, it is possible to go from an observed demand function towards a Hicksian demand function without knowing a direct utility function, as can be seen from the example.27 There is another potential method for this problem, which was mentioned previously, namely the method from Breslaw and Smith (1995). This method is de-scribed in the next subsection.
3.1.2 Breslaw & Smith
The Breslaw and Smith (1995) algorithm starts with a Taylor series expansion of the expenditure function on the right-hand side of equation (3) about (p0, u0), which results
in: CV = E(p0, u0) + ∂E(p0, u0) ∂p ∆ + 1 2 ∂2E(p0, u0) ∂p2 ∆ 2+ ... + R − m0 = ∂E(p0, u0) ∂p ∆ + 1 2 ∂2E(p0, u0) ∂p2 ∆ 2+ ... + R = h(p0, u0)∆ + 1 2 ∂h(p0, u0) ∂p ∆ 2+ ... + R (18)
Where ∆ is the change in price (p1-p0) and R is the remainder term. The last step of
equation (18) uses Shephard’s Lemma (see equation (5).
Knowing that, at the initial equilibrium, the Marshallian demand curve intersects
27
It is important to note that, asHausman(1981) puts it: “This procedure yields a local solution to the differential equation over some domain in price space. It is not always the case that there exists a global solution”
with the Hicksian demand curve with equal utility and quantity and that consumers spend their full budget in the most cost-efficient way to arrive at this utility, the following must hold:
h(p, u0) = q(p, E(p, u0))
= q(p, m) (19)
By differentiating equation (19) the Slutsky equation is obtained, which describes the relationship between changes:
S(p, m) = ∂h(p, u0) ∂p = ∂q(p, m) ∂p + h(p, u0) ∂q(p, m) ∂m (20)
where m = E(p, u0). This Slutsky equation shows the effects mentioned in section2.4.1
of a change in price on quantity demanded. The first and second terms on the right-hand side of equation (19) represent the substitution effect and income effect, respectively. Note that the parameters present in the Slutsky equation can all be obtained through an estimation of the Marshallian demand function (Shin & Burke, 2010). Lastly, by substituting equations (18) and (19) into equation (17), which gives the approximated CV:
CV = q(p0, m0)∆ +
1
2S(p0, m0)∆
2+ ... + R (21)
Note that the total size of the remainder term R depends on the expansion order and the size of ∆. A higher order of expansion means that equation (19) is repeatedly differentiated. However, with a high value of ∆, which may well be the case28, using only a second-order approximation may give inaccurate results of the approximation of the CV. Therefore, (Breslaw & Smith, 1995) introduced a sophisticated solution to remove this inaccuracy, by splitting up the price difference in many small steps. Then, for all these small steps, equation (20) is repeatedly calculated, where for each next price
28Connor and Bolotova (2006) conducted a meta-analysis on literature that estimated the average
cartel overcharge. With a sample of over 800 cartel cases over the last 250 years they found that the cartel overcharges have a mean value of 29%
step the income included in the Marshallian demand curve is augmented by the sum of CV over all previous steps. This is possible since the Hicksian and Marshallian demand curves intersect at each step. Accordingly, for each step n with a price change from pn
to pn+1,
h(pn+1, u0) = q(pn+1, e(pn+1, u0))
= q(pn+1, e(pn, u0) + CVn)
= q(pn+1, mn+ CVn)
= q(pn+1, mn+1) (22)
This algorithm was programmed into MATLAB (see Appendix B for the code), which can easily derive the CV for an estimated Marshallian demand function and a known overcharge.29 However, before a numerical example of this is shown, several points of attention regarding the integrability problem and the usage of an aggregate demand function in both methods are discussed since this is of importance for drawing conclu-sions.
3.2 Use with caution
3.2.1 Integrability conditions
A Marshallian demand function is obtained through maximizing an individual’s utility function. However, in both methods described in the previous sections the starting point is directly the demand function. Therefore, first it must be checked whether the demand function is consistent with consumer utility maximization (Creedy, 2006;
Hausman, 1981; Mas-Collell, Whinston, & Green, 1995). This situation is known as the integrability problem. Mas-Collell et al. (1995) state that the demand function is consistent with consumer utility maximization if the demand function is a continuous function, homogeneous of degree zero, satisfies Walras’ Law and the Weak Axiom of Revealed Preferences (WA). Additionally, they include that these hold if and only if the
29
The algorithm can also calculate the variance of the estimated CV. For an explanation of the mathematical steps for this calculation see section 3 ofBreslaw and Smith(1995).
demand function has a substitution matrix that is symmetric and negative semi-definite for all bundles of price and income.
FollowingCreedy(2006), for the substitution matrix to be symmetric and negative semi-definite it require that the substitution terms si,j = ∂hi/∂pj = ∂2E(p, u)/∂pj are
also negative and that all substitution terms are equal, si,j = sj,i. By using a slightly
different form of the Slutsky equation described previously these conditions can be easily checked: si,j = ∂qi ∂pj + ∂qi ∂mqj (23)
This is the case where multiple goods are involved. In a single good case this integra-bility condition merely requires that the Hicksian demand curve of that single good is downwards sloping, which would be the case in the demand function of the example (see equation (8)). Thus, this demand function satisfies the integrability conditions if:
∂q ∂p+
∂q
∂mq < 0 (24)
This means that q < −β/γ and if now the known demand function q is substituted the following requirement is obtained:
m < −1 γ β γ + α + βp (25)
This simplification is important since it shows that without an income effect, γ = 0, in all cases the integrability condition is very simply satisfied and then the CS, EV and CV are all equal (Creedy,2006).
3.2.2 Aggregated demand conditions
The application of individual welfare loss measurements such as the CV or EV is not as straightforward when an aggregated demand function is used. In the analysis of antitrust cases it will be most likely that an aggregated demand function is used instead of a bundle of individual demand functions. The reason for this is that their will not be sufficient data available for the individual demand functions (Hausman, 1981; Mas-Collell et al., 1995). However, there are several conditions that should hold in order
for the aggregated demand to be of use in a welfare change analysis. These conditions are described in Mas-Collell et al.(1995). They are based on three questions that the authors ask themselves:30
1. “When can aggregate demand be expressed as a function of prices and aggregate wealth?”
2. “When does aggregate demand satisfy the weak axiom?”
3. “When does aggregate demand have welfare significance?”
The first question focuses on whether an aggregated demand function is correctly modelled by using only aggregated variables. As mentioned before, these variables might be the only data available to an econometrician and therefore this question is of significant importance. Since it is expected that prices will be equal for every individual, this question mostly focuses on wealth/income effects. This results in the following aggregated demand derivation for I consumers:
q(p, m1, . . . , mI) = I
X
i=1
qi(p, mi) (26)
According toMas-Collell et al.(1995), with this aggregated demand derivation, using a total (or average) form of income requires that all individuals have the same coefficient on income in indirect utility functions of the Gorman Form, which is the following for an individual i:31
vi(p, mi) = αi(p) + β(p)mi. (27)
In the example given in section 3.1.1 this would mean that e−γp, and therefore γ, is equal for all individuals. This is a severe restriction that needs to hold. However, there is a different way in which aggregate demand can always be written as a function of prices and aggregate income. In this case there is a change in the distribution of income. Where it was first the case that income could be distributed in any way across
30
Please note that the conditions that answer the questions somewhat overlap, though the questions are conceptually different. Furthermore, for all proofs and propositions of these conditions see Mas-Collell et al.(1995)
individuals, individual income should now be a function of prices and aggregate income.
Mas-Collell et al. (1995) call this the wealth distribution rule, for which we can rewrite equation (23) to:
q(p, m) =X
i
qi(p, mi(p, m)) (28)
This equation shows that aggregate demand can now be a function of only prices and aggregate income.
The second question originates from the concern ofMas-Collell et al.(1995) if an aggregate demand function correctly reflects the positive properties of the individual demand functions. As was mentioned in the previous section, the following properties of demand must hold: Continuity, homogeneity of degree zero, Walras’ Law and the WA. From equation (23) it is clear that continuity, homogeneity of degree zero and that Walras’ Law carry over to the aggregate demand function (Mas-Collell et al., 1995). However, it is yet unclear for which conditions the aggregate demand function also satisfies the WA. According to Mas-Collell et al. (1995), there are situations in which the aggregate demand function might not satisfy the WA. Additionally, they state that an aggregate demand function must also satisfy the WA in order to compensate every individual for price or income changes. Logically, this condition is also of significant importance for the compensation of individuals in antitrust cases. Still, it needs to be clear when the WA is satisfied in an aggregate demand function. Previously it is concluded that, in order to use aggregate income, income should be distributed according to the wealth distribution rule. For the sake of concreteness, Mas-Collell et al.(1995) use a more simplistic example of the wealth distribution rule. Here the distribution of income is fixed and independent of prices. Every individual receives a share αi≥ 0 such
that mi(p, m) = αim and where Piαi = 1. From this we can rewrite equation (28 to:
q(p, m) =X
i
qi(p, αim) (29)
By using this example of an aggregate demand function the authors find that the WA is satisfied for the following properties:
2. (1/αi) · qi(p, αim) is equal across all individuals (proportional consumption)
For both of these properties it holds that dp · S(p, m)dp < 0 when dp 6= 0 is not proportional to p and where S(p, m) is a Slutsky function of prices and income. Similar to the solution to the integrability problem, this equation implies that the Slutsky function should be negative in order for the WA to be satisfied.
Especially the property of equal income effects is interesting. Consider the situ-ation where every individual has a Gorman indirect utility function (see equsitu-ation (27) where the income coefficient β(p) is equal across all individuals. In this situation there are equal wealth coefficients and thus the WA is satisfied. However, from the problem of the first question, it is known that this Gorman indirect utility function with equal wealth effects is required when there is no wealth distribution effect in the aggregate demand function. Therefore, with a fixed distribution of income it is a less demanding property for the aggregate demand to satisfy the WA than with an invariant distribution of income. Mas-Collell et al. (1995) explain this in the following way: “if the second property holds, then the first also holds, but aggregate demand (for a fixed distribution of wealth) may satisfy the weak axiom even though aggregate demand may not be in-variant to redistribution of wealth (e.g. individual preferences may be homothetic but not identical)”.
The third question focuses on when the aggregate demand function can be used to measure changes in social welfare when a fictional consumer is used as a representative for the aggregate demand function. First of all it is important to clarify why this is important in an antitrust case. From section2.1it is clear that class-action lawsuits are becoming gradually more important. In these claims it will be practically unfeasible and if for every individual with different preferences the CV should be calculated (Leslie,
2006). Therefore a representative consumer is needed and its preferences can then be used to measure welfare changes of society. Yet, it is not always the case that for an aggregate demand function there exists such a representative consumer. According to
Mas-Collell et al. (1995) there are two different senses of a representative consumer: A positive representative consumer and a normative representative consumer. A posi-tive representaposi-tive consumer would, when being faced with the same budget as society,
maximize utility such that it generates the aggregate demand function. There exists a positive representative consumer if the aggregate demand curve satisfies the proper-ties of demand mentioned in the previous paragraph. Or, in mathematical terms, if S(p, m) < 0. In order to treat the aggregate demand function as an individual demand function when measuring welfare changes it is required that there is a positive repre-sentative consumer. However, this is not the only requirement since it also necessary to assign welfare significance to the ’represented’ aggregated demand function. This is where the normative representative consumer comes in. An easy explanation of the nor-mative representative consumer is that it is actually a positive representative consumer that is also maximizing its utility according to the social welfare function.32 The social welfare function is a function that consists of a bundle of individual utilities. Thus, the conditions when an aggregate demand function is generated by a normative representa-tive consumer are essential. First of all,Mas-Collell et al.(1995) conclude that when all individuals have a Gorman indirect utility function (where β(p) is equal across all indi-viduals) and where the social welfare function maximizes the sum of individual utilities (utilarian), then the aggregate demand function can always be generated by a normative representative consumer. Furthermore,Mas-Collell et al.(1995) conclude that if the fol-lowing matrix is positive semidefinite there exists a normative representative consumer:
X
i
Si(¯p, ¯mi) − S(¯p, ¯m), (30)
where ¯p and ¯m are fixed values of price and income, respectively. Note that it is not always the case that if a positive representative consumer exists that there will also be a normative representative consumer. If S(¯p, ¯m) is negative but not as negative as P
iSi(¯p, ¯mi) then there exists a positive representative consumer, but not a normative
representative consumer for any social welfare function.
Now that there are conditions and answers for all three questions asked in Mas-Collell et al.(1995), it is clear that the use of an aggregated demand function to measure welfare changes is not that straightforward. It depends on several factors including, for example, the distribution of wealth. With all methods and conditions described, a
hypothetical antitrust situation can show if it is feasible to calculate the real damage done to consumers and, if so, which method is the best suitable for this application.
3.3 A ’Real’ Case
Suppose that in a hypothetical market there has been an antitrust violation. The price of a good has increased (illegaly) and the goal would be to estimate the CV. As we have seen in the previous section, this could be done with either the method of Hausman
(1981) or Breslaw and Smith (1995). However, preliminary steps need to be taken in order to arrive at the correct measure of the CV.
3.3.1 Demand function estimation
For a valid analysis of the full damage to consumers, the but-for price estimation and demand estimation need to be properly executed. In the remainder of this section the focus is on the demand function estimation since this is of particular importance for correctly estimating the deadweight loss (DWL).33
Perhaps one of the most important parts of estimating a demand function is to first start understanding consumer behaviour, the respective industry and its institutions
Davis and Garces (2009). Only then can one correctly specify a demand model and decide which variables influence demand. There are several aspects that need to be taken into account when specifying a demand model.
One of the reasons why it is important to first start understanding consumer behaviour and the industry correctly is to make a decision whether to estimate demand with a continuous choice model or discrete choice model. A continuous choice model is the more common known demand function that determines how much of a good will be bought. The discrete choice model determines when a consumer will buy a certain good and when he/she will not.34 In an antitrust analysis it will be most likely that continuous choice models are estimated since the counterfactual quantity is needed for the estimation of either the CS or CV. Estimations of a discrete choice model will only
33
Logically, the but-for price estimation is also important for estimating the DWL, but since this less trivial for estimating DWL and more common in antitrust analysis, this is left out. The but-for price estimation is assumed to be properly executed such that a given but-for price is correct.
34
show the effects on the likelihood of a consumer buying a product or not.
Another important reason is to correctly decide if the market in question consists of homogeneous or differentiated goods. This is of severe importance since it greatly influences the demand estimation. In the case of homogeneous goods the estimation will be more simplistic than with differentiated goods. With homogeneous goods the estimation is of a single demand function instead of a system of demand functions with differentiated goods. For example, with rice, which is often seen as a relatively homogeneous good, the demand function could take the following form:
q = α + βp + γy + , (31)
where α, β and γ are the parameters that are estimated and is the error term. In the heterogeneous market of hotel accommodation consumers are offered different rooms to choose from. Each with their own demand function that consists of their own respective price and prices of other options. The system of demand functions for N products that follows could take the following form:
q1= α1+ β11p1+ β12p2+ · · · + β1NpN + γ1y + 1 q2= α2+ β21p1+ β22p2+ · · · + β2NpN + γ2y2 .. . qN = αN + βN 1p1+ βN 2p2+ · · · + βN NpN + γNyN (32)
Clearly, since this involves more parameters and variables, this would be more of a challenge to estimate correctly.
Then there is the issue of the functional form of a demand function that must be clear. The choice of the functional form will have an effect on the results of the estimation. A practitioner could for example choose to specify the demand function as a linear demand function (as in equations (31) and (32)) or a log-linear demand function. There are many other forms available, but the main point is that for each of these various forms the estimation results will be different. While different demand estimation results do not affect the total overcharge estimation, it does affect the estimation of either
