Harm to Society Caused by Cartel Formation
and the Indirect Umbrella Effect
Bart von Meijenfeldt
10470026
Bachelor thesis econometrics
and operational research
University of Amsterdam
Under supervision of
J. Tuinstra
Table of Contents
1. Introduction ... 1
2. Theoretical framework ... 3
3. Model ... 7
4. Solutions ... 9
5. Decomposition of cartel effects ... 10
5.1 Supplier profits ... 11
5.2 Retailer profits ... 11
5.3 Consumer damages ... 12
6. Results ... 12
6.1 Prices and quantities ... 13
6.2 Harm to society ... 14
6.3 Indirect merger paradox ... 16
6.4 Harm decomposition ... 17
6.5 Harm estimator ... 18
6.6 Fine enforcement considerations ... 22
7. Conclusions... 23
Appendix ... 24
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1. Introduction
Firms try to maximize profits. If more than one firm is active on a market, competition arises. This competition reduces profits to the firms. Therefore firms have the incentive to form a cartel. As a cartel they specify an amount of good produced or they fix the price of the good. This increases their profits if enough firms enter the cartel (Salant, Switzer & Reynolds, 1983). Though the firms in the cartel profit, it is well-known that society generally loses.
This is because firms which buy from the colluding firms suffer. First of all, their output reduces, so the profits on all those would-have-been-made-products are foregone. Secondly, they have to pay more for the products they bought from the cartel. This amount, the number of goods bought during the period of the cartel times the price increase caused by the cartel, is called the overcharge. The second effect gets somewhat offset, because generally, they in turn raise their prices to their buyers.
But now the same effects apply to the indirect buyers: reduced output, (indirect) overcharge and the damage that is passed on by changing their price. The price increase also hurts the consumers, because a price increase by a cartel generally increases prices to consumers too.
If there are suppliers to the cartel, they are also negatively affected because their output also gets reduced by the decreased demand of their good. Depending on the exact type of market settings, they sell their good for a higher or lower price and also buy from their supplier from a (generally) different price. So the suppliers also have the same effects as the buyers: reduced output, undercharge (the overcharge version for suppliers) and the new price from their inputs.
Though there are cartels which are profit-enhancing for society and also profitable for the members of the cartel (Tuinstra & In ‘t Veld, 2014), this is not the rule but the exception. Because of this, capitalist governments want to prevent firms from colluding and stop existing cartels, by imposing fines to firms whose colluding is discovered. In practice it is difficult to discover colluding firms, therefore it is important to know what kind of cartels create the biggest damage to society, so time and resources get spent on exposing cartels that are worst for society. Research in this field is also important??? to be able to calculate fair fines to wrongdoers after exposure and to know which parties to compensate and with what amount.
Already a lot of research has been done on this matter, one important work is the research of Basso & Ross (2010), they research the effect a cartel has in the supplier
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chain with heterogeneous goods. Their research is done in a three-layer production chain, where the number of firms in a market is held variable. The researchers find that the overcharge makes very large errors when measuring the harm due to cartels. They find that the level of competition in downstream markets changes the error made by the overcharge as estimation for total harm. They also find that the division of harm between the direct and indirect purchasers depends a lot on the degree of competition downstream. They argue that allowing both the direct purchaser and the indirect purchaser to retrieve their overcharge could lead to a better approximation of the actual harm.
Han, Schinkel & Tuinstra (2009) research the effects from cartels on homogeneous goods in a multiple layer production chain. Their research assesses damages to indirect and direct suppliers to the cartel, indirect and direct buyers from the cartel and the consumers. Both the number of layers in the production chain and the type of competition are held variable. They analyze the antitrust damages to both upstream markets (of the cartel) and downstream markets. They also find that in general the direct purchaser overcharge grossly underestimates the total antitrust harm.
An interesting effect of cartels which hasn't been researched in these two papers is the umbrella effect. This effect might happen when in a layer some, but not all, firms form a cartel. The effect is the change of price of the products of the remaining firms in that layer due to adaptation to this new situation. Profits increase for non-colluding firms, since worst-case scenario they could set the same quantity as the members of the cartel. The buyers of these non-colluding firms can both be harmed or benefit, depending whether the price respectively increased or decreased.
Kroon (2015) researches the umbrella effect in a heterogeneous goods market. It is assumed that an indirect supplier market supplies a homogeneous product to the direct supplier market, which then continues to refactor the product and sell this new, again homogeneous, product to the retailer market. The retailer market is a heterogeneous goods market and some of the firms in this layer form a cartel. He finds that the umbrella price effect is negative (the prices of the non-colluding firms decrease), if the products are weak substitutes. He also finds that the undercharges (the upstream version of the overcharges), are only a small fraction of the total direct damages to suppliers. Most of the damages are caused by the reduction in sales.
The aforementioned papers show that the total damages from a cartel and the allocation of damages to the harmed parties changes per market structure. Therefore it is important that relevant market structures are analyzed. The market structure analyzed in this paper is a market structure in which there are two different production chains and in
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one chain the suppliers form a cartel. What the damage to society caused by a cartel in this market structure is, is the focus of this paper. Especially what causes damage to increase and how accurate an overcharge-based estimator of the damages is. This information could guide governments on how to tackle the issue of cartels in society. The analysis is done in a mathematical model of the market structure, where firms are economic agents interested in maximizing their own profits.
This rest of paper is ordered in the following way. In section 2 is a more detailed explanation of the theories on cartel damages is given. In section 3 the model that is used is elaborated upon. In section 4 the solutions of the model are given. A brief decomposition of harm is given in section 5. In section 6 the results obtained are presented. The conclusion of the research is given in chapter 7. This papers ends with an appendix, to further elaborate some of the steps taken to solve the market equilibrium and which includes an additional figure.
2. Theoretical Framework
There are quite a few papers written about harm of cartels to society. Most papers only look at a few layers, but the paper of Han et al. (2009) holds the number of layers variable. Also it holds the number of firms active in a layer variable and also the layer where the cartel is active is held variable. The trade-off for this flexibility in analysis is the type of good, which is fixed as a homogeneous good. A clear overview is given of the decomposition of cartel effects. For every layer the effects are split into: the overcharge-effect, the pass-on effect (the amount of the price increase that the layer passes on to the next layer) and lastly the output effect, which is the loss of profits on would-have-been-made-products in the equilibrium, but now lost in the cartel situation. (They show that the direct purchaser overcharge, the overcharge of the direct buyers from the cartel is equal to the sum of all downstream overcharges minus the pass-on effects.) They also find that for linear demand the direct purchaser overcharged multiplied by three is exactly the upper bound of total downstream harm. Also they show that the damage to society in their model doesn't depend on the layer in which the cartel is formed.
Basso and Ross (2010) expand the theory by analyzing the damages in a three layer production chain, producing a heterogeneous good. The three layers are: the industry which forms the cartel, the downstream market and the consumers. The suppliers manufacture a good, sell it to the producers who continue to sell it on to the consumers. Discussion on damages in heterogeneous goods markets before the paper of Basso and
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Ross often assumed the direct buyer of the cartel is the final buyer. They show that both the downstream market which directly buys from the cartel and the consumers who indirectly buy from the cartel are damaged by the formation of the cartel. They allow for a conduct parameter which is used to analyze different models of competition. The researchers compare the overcharge as a measure for total harm to the downstream market and consumers to a more complex measure, the overcharge plus the lost surplus caused by the reduction of output to the downstream market.
They find that the complex measure's error is less than the simple measure's error. The complex measure's error increases if downstream markets get less competitive, if product substitutability is less or if less firms compete in the downstream market. The simple measure's error also increases for the three aforementioned causes, but furthermore increases if the marginal costs increases for the downstream firm or a higher price set by the cartel. They also show that the maximum fraction of harm that falls on direct buyers is never higher than two thirds. Both these measures are always still lower than the total harm. Therefore they analyze a third measure, the sum of both the direct and indirect overcharge, they find that this measure could both overestimate and underestimate the total harm, but is much closer to the total harm than the other measures.
One paper with an interesting and counterintuitive result is the paper written by Tuinstra & In ‘t Veld (2014). They show that cartels can be welfare-enhancing for society if the firms that collude have higher costs than the competing market. Their analysis is formed in a market where two industries compete with quantities as strategic variables. In these industries a variable number of firms is active. The products degree of substitutability is held variable. They find that if the cost in industry 1 are higher than the costs of industry 2, a cartel formed in the first industry increases social welfare in certain settings. This happens when the costs saved by having the more efficient industry overtake some of the production of the less efficient firms outweigh the reduction to consumer surplus. As implied in the previous sentence, the research also shows that consumer surplus always reduces due to the cartel.
The recent research of Kroon (2015), analyses the umbrella effect in a four layer production chain. The first layer consist of the indirect suppliers and the second layer consists of the direct suppliers to the retailer market. These suppliers produce homogeneous goods and Cournot competition applies. The firms in the third layer, dubbed the retailer market, buy the product from the direct suppliers and convert it into a heterogeneous product and sell it on to the fourth layer consisting of the consumers. Both Bertrand and Cournot competition is analyzed for these firms. In this market an
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incomplete cartel is formed, meaning not all firms in this retailer market join the cartel. The consumer utility is represented by the utility function introduced by Bowley (1924). These utility functions assume that people prefer to have heterogeneous goods and over consumption of a good reduces utility.
Damages to suppliers are decomposed into the following parts: undercharge, damage passed on to own supplier and the output effect. The profit of the colluding firms is decomposed into cartel overcharge, input cost effect, which is the price change of the input products bought caused by the cartel and lastly again the output effect. For the non-colluding retailers the same applies, but the cartel overcharge is replaced with the umbrella overcharge.
It is shown that if the supplier markets have linear cost functions, the cartel in the retailer market does not affect the prices set by the suppliers. Kroon also finds that for both Bertrand and Cournot competition in the retailer market equilibrium prices are higher for linear costs compared to quadratic costs. He shows that the umbrella price effect can both be positive and negative, the negative effect occurs when products are weak substitutes. He also finds that upstream damages compared to downstream damages are most significant if both the suppliers and the retailers have quadratic cost functions, instead of linear cost functions. Furthermore he shows that the damages caused to suppliers are mainly caused by the reduction of output, the undercharges are only a small part of the total damages. He argues that it is doubtful that colluding firms prefer to stay in the cartel, since non-colluding firms profit more than the colluding firms. He provides data showing that most of the time for a certain type of product differentiation only one cartel size is stable (this size depends on the type of competition and the type of costs).
In ‘t Veld (2010) researches the distribution and size of the cartel damages when there is substitutability from input for the direct buyers. He uses a three layer production chain. In the first layer there are two different input markets. Both markets produce a homogeneous good, but the goods from the different markets are heterogeneous from each other. The second layer is the downstream market which buys from the input markets and produces a product to sell on to the consumers. The input market where a cartel is formed is called the primary input market. The other input market is called the secondary input market. The analysis shows the different cartel damage effects depending on whether the competition in a market is Cournot competition or Bertrand competition. Also In ‘t Veld researches the effect of different production functions in the downstream market. He omits the analyses of unprofitable cartels, since firms have no incentive to take part in such a cartel. He decomposes damages in the overcharge effect, pass-on effect, output
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effects and in the substitution effect. The first three effects are well-known, the substitution effect is not generally relevant in the market structures which are analyzed. The substitution effect is the effects caused by downstream firms changing the distribution of their input quantities.
In ‘t Veld’s findings show that downstream firms are always harmed by the cartel formation in the input market. He also shows that when profit margins are thin, most harm is passed on to consumers. Even when profits margins aren't thin, damage is always passed on to the consumers according to his findings. Consumers are thus always harmed by the higher price caused due to the pass-on effect. He finds that total harm decreases if substitutability between the inputs increases, which is to be expected. A important finding of him is that the overcharge error of estimating the total downstream harm can increase even more in his market structure compared to the one Basso and Ross(2010) use. The secondary input market in the research of In ‘t Veld can both benefit or be harmed by the cartel formation according to his findings. He argues that therefore it is fair that these firms can sue the cartel. Also in his settings he finds that it is possible that the cartel increases profits to society, this is caused mainly by the, in those cases, increased profits by the secondary input market. He argues that the cartel can only be profit-enhancing to society in Cournot competition, since profits in Bertrand competition of the secondary input market are small. Similarly as in Tuinstra & In ‘t Veld (2014), he shows that in these cases cost efficiency occurred by a shift to the non-colluding market.
Though more papers are written on cartel damages, these paper show both important results which are made in the theory of cartel damages and the diversity of cartel damages depending on the market structures that are used. To add to the current literature on cartel damages, two different production chains which both produce a homogeneous good are analyzed. Though the good of a production chain is homogeneous the products of the different production chains are heterogeneous from each other. In one of the two production chains the suppliers form a cartel. It is expected that a similar effect to the umbrella effect takes place. The damages to society due to cartel formation in one of the supplier markets is the main focus of this paper. Especially the correctness of an overcharge based fine as compensation for total damages is researched. To analyze this, a mathematical model is set up, in which it is assumed that all the firms are economic agents only interested in maximizing their own profits.
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3. Model
The model that is used, is used to analyze the effects of cartel formation, accounting for the effect I dubbed the indirect umbrella effect. This term is similar to the umbrella effect, but there is a small difference. The umbrella effect means the change in price of the non-colluding firms due to a cartel formed by firms competing for the same customers. Since in the market structure researched in this paper, the non-colluding firms do not compete for the same customers as the colluding firms, using this term would not be proper. Therefore the corresponding price effect occurring in this paper is described as the indirect umbrella effect, with the only difference with the normal umbrella effect being that the non-colluding firms don’t directly compete for the same customers. The way they do compete with each other is through their corresponding retailer market, since the retailer markets compete for the same customers.
Since in the homogeneous market structure of Han et al. (2010) companies generally don’t pass on the total overcharge, it is likely that the indirect umbrella effect reduces per additional layer in the production chain. Therefore in this paper three layers per production chains are chosen, the minimal amount of layers necessary to analyze this effect. These production layers consist of a supplier market, a retailer market and the consumers. The supplier market sells a product to the retailer market in their production chain, the retailer market then sells it on to the consumers. All firms in the production chain compete on quantity. In this model the supplier market has no costs and the retailer markets only cost is the price the supplier market sets for their product times the amount of product bought. Though abstracting the costs is not optimal, in this paper this choice is made to reduce the complexity furthermore I suspect that the costs do no significantly
influence the results. Besides this paper is only a start in exploring this market structure. For the retailer market the inverse demand functions introduced by Singh
and Vives (1984) are used and the number of different production layers is fixed at two. The inverse consumer demand functions are the following:
P1(Q1,Q2) = 1 – Q1 – Q2 and P2(Q1,Q2) = 1 – Q1 – Q2,
Where Pi and Qi are respectively the price and consumption of commodity i = 1,2 in the retailer market and the degree of substitutability is measured by . = 1 implies perfect substitutability, and = 0 means the products are completely heterogeneous.
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Figure 1: Market structure
The number of firms in the supplier market are m1 and m2 and in the retailer market
there are n1 and n2 firms active. Firms in both the supplier market and in the retailer market
compete on quantity and are assumed to be profit-maximizers. The input prices set by the supplier markets are w1 and w2, the prices set by the retailer market are P1 and P2. The
amount of product sold by a company in the supplier market is z1*, z2*respectively for
pro-ducers of product 1 and 2 in the equilibrium. In a similar way q1* and q2* stand for the
amount of product sold by the companies in the retailer markets in the equilibrium.
It is assumed that a cartel is formed in the supplier market of product 1. The damages created by this cartel are calculated by comparing the cartel situation to the situ-ation that would have existed if there was no cartel, the but-for state. The but-for state is solved by backwards induction. First the prices and quantities of the retailer market de-pending on the input prices are provided, and then the equilibrium quantities and prices for the supplier market are solved. By changing the number of firms active in the supplier market of product 1 to one in the solutions of the but-for world, the cartel situation is solved.
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To prevent confusion over the meaning of the term “market implementation” in this paper, the interpretation is explained here. The market implementation simply means the exact number of firms in each market and the degree of product differentiation.
4. Solutions
As was indicated in the previous section, the market structure is solved by back-wards induction. Already a similar market structure is solved by Tuinstra & In ‘t Veld (2014), which is the market structure that is used in this paper without the supplier market. After replacing the costs of the retailer market with the input prices set by the supplier market and the variables in the inverse demand functions with the constants used in this paper, the solutions of the retailer markets can be found in a similar way as Tuinstra and In ‘t Veld found them. The solutions are as follows.
Lemma 1 Let ( ) , then the equilibrium quantities set by the firms in
the retailer market of product 1 and 2 respectively are:
= ( ) (
) and
( )( ) ( ( ) ).
with ( ) , ( )( )
The equilibrium prices are given by and . The total profits for the retailer market of product 1 and 2 respectively are ( ) and ( ) .
They also show that the consumer surplus is as follows.
CS ( ( ) ( ) ) Which is the same as:
CS (( ) ( ) )
Using the solution of the retailer markets, the supplier market equilibrium is as follows. An explanation of how these equations are exactly obtained is given in the appendix.
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Lemma 2 Let ( ) , then the Cournot-Nash equilibrium is given by all
firms in the supplier market of product 1 producing and the firms in the supplier market of product 2 producing , where
( ) ( )( (( )( ) )( )( ) (( )(( ) )) (( )( )( )( ) )( ) and ( ) (( )( ) ) ( ( )( ) (( )( )( )( ) ) ( )(( )( )( )( ) )( ) ).
Total production is given by and , the input price of product 1 is given by (( ( )( ) ) ) (( )( ) ) and of product 2 by
(( )( ) ( ) ) (
)
(( )( ) ) . The total profits of the supplier
market of product 1 and 2 respectively are and .
In the case of collusion the firms in the supplier market of product 1, maximize their total profit. Since they have no costs, the profits are maximized by setting the total produc-tion equal to that of a monopolist, so in the formulas used it corresponds with setting m1
equal to one. The exact distribution of production per firm in the cartel does not cause changes for any other agent outside of the cartel, so is not specified. Only the total produc-tion of the cartel matters. For all the calculaproduc-tions and graphs in the results secproduc-tion, the necessary condition for the equilibriums is checked and is indeed satisfied.
5. Decomposition of cartel effects
As is shown in several papers, a cartel affects all agents in the market. In many analyses, one vertical production chain is assumed and the damages to all other agents caused by the formation of a complete cartel are analyzed. But in incomplete cartels, the non-colluding firms profit as is shown in Kroon (2015). Since the cartel in this paper can be seen as an incomplete cartel, with the non-colluding firms the supplier market of product 2, similar results are to be expected. Section 6.2 shows which parties profit and which are harmed. This section shows that the suspicion is founded, the non-colluding firm do indeed
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also profit. Even the firms in the retailer market of product 2 profit due to the cartel. The harmed parties are the direct and indirect buyers of the cartel, respectively the firms in the retailer market of product 1 and the consumers. In this section a simple decomposition of the effects is given for all agents in the market. This decomposition is similar to the one used by Han et al. (2009).
5.1 Supplier profits
The cartel reduces its output, causing its price to increase. The reduction in profit on would-have-been-made products is overcompensated by the extra profits on the products sold. The non-colluding supplier market responds to this cartel by increasing their output, but the total production of both products reduces. This causes the change in profit for both of the supplier markets to be as indicated below.
( ) ( ) i = 1,2
With OCD,i the direct overcharge and the output effect in layer one for product i,
the change in profits caused by the change in output. Independently of the layer a firm is in, this effect will be negative if the firm is in the production chain of product 1, and positive for the firms in the production chain of product 2.
5.2 Retailer profits
The firms in the retailer markets pay higher input prices, but in turn their prices to their consumers increase. In a similar way the output effect affects them, making the total change in profit the following.
( ) ( ) ( ) ( ) ( ) ( ) i = 1,2
With the indirect overcharge, the number of products sold times the price increases
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5.3 Consumer damages
The damages to the consumers depend solely on the change in production of the two products. Tuinstra & In ‘t Veld (2014), show that consumer damages are as follows.
(( ) ( ) ( ) ( ) ( )
6. Results
With the solutions of section 4 and the harm decomposition of section 5 different aspects of cartel formation in this market are analyzed. Beginning with the change in price and quantity, followed by the harm to society. After that it is shown which parties suffer and gain and also the correctness and fairness of the estimator of total harm proposed by Bas-so and Ross (2010), is analyzed. The chapter concludes with an elaboration of aspects the government should account for when using an overcharge-based estimator for the total harm. Because of the complexity of the formulas, all analysis following is done numerically.
To analyze the effects of changes in the market characteristics on the harm to soci-ety, different markets are analyzed and in those markets the difference of a market charac-teristic is analyzed. The market structures differ in the size of the supplier markets, the size of the retailer market and the degree of product differentiation. Below is a table showing the number of firms in a different type of market implementation active, with the abbrevia-tions used to refer to the markets. When for example the number of firms in the cartel is analyzed, the amount of firms in the cartel does differ from the number specified in the ta-ble. The different degrees of product differentiation analyzed are generally 0.3, 0.6 and 0.8, corresponding with high, medium and low product differentiation.
Table 1: Market characteristics
Abbreviations
ss small supplier market small retailer market 5 5 2 2
sb big retailer market 5 5 6 6
bs big supplier market small retailer market 12 12 2 2
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6.1 Prices and quantities
It is well-known that cartel formation increases the price of the product they are producing, but sometimes the price of a competing product decreases for weak substitutes as is shown in Kroon (2015). He dubbed this a negative umbrella effect. Since the price of product 2 always increases in the market structures that are researched, it seems that the indirect umbrella effect is always positive. Furthermore the graphs show that the price in-crease of product 1 dein-creases and of product 2 inin-creases if the degree of product differen-tiation decreases. This is because the consumers are less willing to buy the artificially ex-pensive product of the cartel if there is a good substitute. The same effects occur for the input prices. After comparison of the input prices to the prices of the product sold it be-comes clear that due to the cartel the retailer market of product 1 makes less profit per product sold and the retailer market of product 2 earns more profit per product sold.
Figure 2: Price increases due to cartel formation compared to degree of product differentiation.
Top left depicts ss, top right sb, bottom left bs and bottom right bb. The dashed/dotted line stands for the increase in price of product 1, the dotted line of product 2, the straight line for the input price of product 1 and the dashed line for the input price of product 2.
Figure 3 shows another not very surprising result, due to cartel formation the quanti-ty of product 1 sold declines and of product 2 increases. The firms in the cartel increase their profits by reducing the output from the equilibrium, and the firms in the supplier mar-ket in product 2 increase their production to profit most from the decrease in production of market 1. Since the decrease in production by the colluding firms outweighs the increase in production of the non-colluding firms, total production declines. The graphs also convey that the effect of an increase in theta on the quantity of product 1 sold is not clear. It in-creases for low levels of but dein-creases at the end, circa 0.75. As can be seen in the figure, the extra amount of product 2 sold is higher for more similar products. The sum of
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these two changes in output, create the change of total output of the sum of the two prod-ucts. It is important to note that the decrease in total output is smallest for homogeneous products.
Figure 3: Quantity changes due to cartel formation compared to degree of product differentiation.
Top left depicts ss, top right sb, bottom left bs and bottom right bb. The straight line stands for the change in total output of product 1and the dashed line for the change in total output of product 2. The dotted line for the change in total output of the sum of product 1 and 2.
6.2 Harm to society
Different definition have been used in papers of (total) harm/cost to society. In this paper total harm/cost to society signifies the total decrease in welfare to society, including the profits made by the firms in the cartel.
A obvious suspect of increasing the harm to society is the size of the cartel. As is shown in figure 4, the damages caused by the cartel do indeed increase if the size of the cartel increases. All the graphs show that this increase is highest for low values of the car-tel size, indicating that the increase in damage per extra firm reduces for bigger carcar-tels. Also a higher degree of product differentiation indicates a higher amount of damages to society caused by an increase in the size of the cartel.
Result 6.1 An increase in the size of the cartel, causes more harm to society. This
in-crease in harm to society for increasing the size of the cartel is bigger if the product differ-entiation is high (small ) or the initial size of the cartel is small.
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Figure 4: Harm to society compared to cartel size.
Top left ss, top right sb, bottom left bs, bottom right bb. The straight line depicts = 0.3, the dot/dashed line = 0.6 and the dashed line = 0.8.
Another interesting variable whose effect on harm to society might be more difficult to predict is the degree of product differentiation. The graphs in figure 5 are very clear on this though. They show that the damages to society are highest if product substitutability is low. Figure 4 shows that the difference between the minimal amount of firms necessary to form a cartel compared to a very big cartel (30 firms) is smaller than 0.06. The degree of product differentiation can change the damages to society more than twice as much, as is shown in figure 5. Indicating that for governments it might be most interesting to spend re-sources trying to discover collusion in supplier markets whose product heterogeneity is high compared to the other supplier market. The explanation for the for the high damages caused by cartel formation without a strong substitute can be found in figure 3, the reduc-tion of total producreduc-tion of both goods is highest for small .
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Figure 5: Harm to society compared to degree of product differentiation.
In the left figure are the SS (straight) and the SB (dashed), in the right figure the BS (straight) and the BB dashed).
Figure 6 plots the harm to society compared to the retailer market size for a small supplier market and a bigger one. The size of both retailer markets are the same, and on the x-as the number of firms of both markets is given. It shows that for a small size of the retailer market, damages caused by the cartel are highest. But compared to the product differentiation or the size of the retailer market this effect is small.
Result 6.2 Both an increase in product differentiation as a decrease in size of the retailer
market increases harm to society. But the effect of product differentiation is much bigger than the effect of the size of the retailer market.
Figure 6: Harm to society compared to retailer market size.
In the picture on the left is a small supplier market (5 firms per product), in the picture on the right a big supplier market (12 firms per product). The straight line depicts = 0.3, the dot/dashed line = 0.6 and the dashed line = 0.8.
6.3 Indirect merger paradox
A cartel can only be profitable if at least 80% of the firms form according to Salant, Switzer & Reynolds (1983). They named this the merger paradox. In my model all firms in the market join the cartel, but there is another indirectly competing supplier market which does not collude. If the size of the non-colluding market is big, or the amount of product differen-tiation is low, the market power of the colluding firms is low. This results in not being able to abuse the system by profiting from forming a cartel as can be seen in figure 7. I named this paradox the indirect merger paradox, since it is comparable to the merger paradox, the only difference is that the non-colluding firms now compete indirectly for the same cus-tomers.
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the bottom left graph of picture 7, three colluding firms can make a profit if the other mar-ket exist of nineteen firms or less (13.6%) instead of the 80% threshold of the merger pardox. The size of the retailer market appears to be important too, for homogeneous products it appears to be more difficult to profit from cartel formation if the retailer market is bigger.
Figure 7: Profit cartel market compared to number of supplier market size product 2.
In the pictures on the left is a small retailer market (2 firms per product), in the picture on the right a big retailer market (6 firms per product). The number of firms in the supplier market of product 1 is 2 on the left, and 3 firms on the right. The straight line depicts = 0.4, the dashed line = 0.7 and the dotted line = 1.
6.4 Harm decomposition
Which parties benefit and which parties are harmed by cartel formation is arguably the most important part of cartel analysis. Analysis in these parts prevents wrongfully compen-sating parties which are not harmed and making sure it is clear which parties should be compensated.
The graphs in figure 8 clearly indicate that only two parties are harmed, the con-sumers and the retailer market of product 1. The former is harmed most, but the latter’s harm can get very close to the consumer’s harm. It is also very important to note that the cartel’s extra profits become very small for high values of . This means that supplier mar-kets have a higher incentive to collude for a higher degree of product differentiation with other supplier markets. This is unfortunate since cartel formation costs to society are high-est for small values of (result 6.2).
Result 6.3 Firms in the supplier market profit most from formation a cartel if the product
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Another noteworthy result from figure 8 is that both the non-colluding supplier mar-ket and the corresponding retailer marmar-ket could profit more from the cartel than the cartel itself. The supplier market does always profit less than the retailer market.
Result 6.4 Due to a cartel, besides the firms active in the cartel, all the firms active in
pro-ducing product 2 gain, but the firms in the retailer market most. Both the consumers and the retailer market buying of the colluding firms lose.
Figure 8: Harm decomposition compared to degree of product differentiation.
Top-left ss, top-right sb, bottom-left bs and bottom-right bb. The positive blue straight line stands for the change in cartel prof-its, the negative green straight line for the change in consumer surplus, the dashed line for the change in supplier profits of product 2 , the dashed/dotted line for the change in profits for the retailer market of product 1 and the dotted line for the change in profits for the retailer market of product 2.
6.5 Harm estimator
Knowing that both the direct and indirect buyers from the cartel are the harmed parties, the next part of this research is about finding out how easy and therefore practical estimators compare to the harm to society. Historically the American government used to base the fine for the wrongdoers on the basis of overcharge. Basso and Ross (2010) show, as many other papers also show in different market settings, that the direct overcharge gen-erally makes a big underestimation of the harm. Basso and Ross argue that allowing both the buyers from the cartel to retrieve the direct overcharge as the indirect buyers to re-trieve the indirect overcharge, would be generally be closer to the total damages. Their analysis is done with one production chain.
To analyze the correctness of the estimator with two production chains, the follow-ing graphs show damages divided by the measure of compensation. A number higher than one means the compensation is lower than the actual damage, a number lower than one
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means the compensation is higher than the actual damage.
Figure 9 shows that the sum of these overcharges compared to the total damages is not affected much by the degree of product heterogeneity. Also in these four markets, this estimator is close to the amount of actual harm. Unfortunately, this way of retrieving damages does not seem completely fair to the retrieving parties. Consumers are always undercompensated, since the overcharge is only part of decrease in utility the other part being the reduction in consumption. The graphs also show this effect. Furthermore the graphs tell that the consumer’s compensation is fairest for homogeneous products. It is then logical to conclude that the retailer market often is overcompensated and the graphs do indeed indicate this, but for more homogeneous products the firms in the retailer market can also be undercompensated.
As is shown in section 5.2 the loss of the retailer market is as follows.
In the cases that the retailer market is overcompensated that must mean that the indirect overcharge is bigger than the output effect of the retailer market of product 1.
In the cases that the retailer market is undercompensated the opposite is true, the output effects outweighs the indirect overcharge.
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Figure 9: Error overcharge estimators compared to degree of product differentiation.
Top-left ss, top-right sb, bottom-left bs and bottom-right bb. The dotted line depicts the correctness of the sum of both
over-charges to total harm to society. The straight line depicts the correctness of the direct overcharge estimator to the damages to the retailer market. The dashed line depicts the correctness of the indirect overcharge as the estimator to the damages of the consumers.
The story figure 10 tells is important for the correctness of the estimator. For small retailer markets, the estimator underestimates the total damages, but as the firms in the retailer market increase, the estimator becomes more in the favor of the retrieving parties. This underestimation of the damages to the retailer market only appears to occur for a small retailer market, declining greatly after the first firms join the market. The consumer’s correctness of compensation is less affected by the size of the retailer market. It increases slightly for a bigger retailer market.
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Figure 10: Error overcharge estimators compared to size retailer market.
The graphs on the top depict the correctness of both overcharges as an estimator for the total damages, the middle graphs
the correctness of the direct overcharge as an estimator for the retailer market damages, the graphs on the bottom the cor-rectness of the indirect overcharge as an estimator for the consumer damages. The graphs on the left depict a small supplier market (m1=m2=12) and the graphs on the right a big supplier market (m1=m2=12). The straight line, dotted/dashed line and
dashed line respectively stand for = 0.3, = 0.6 and = 0.8.
As can be seen in figure 11, the number of firms in the cartel influences the correctness of the estimator. Both the retailer market and the consumers will be rewarded relatively less. Whether this improves or worsens the correctness of the estimator is ambiguous. This results appears to hold regardless for the number of firms in the non-colluding supplier market, since in figure A.1 at the end of the appendix the same results is found for a bigger non-colluding supplier market.
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Figure 11: Error direct overcharge estimators compared to cartel size.
The graphs on the top depict the correctness of both overcharges as an estimator for the total damages, the middle graphs the correctness of the direct overcharge as an estimator for the retailer market damages, the graphs on the bottom the cor-rectness of the indirect overcharge as an estimator for the consumer damages. The figures on the left indicate a small retailer market (2 firms), and on the right a big retailer market (6 firms) the number of firms in the non-colluding supplier market is held at 5. The straight line, dot/dashed line and dashed line respectively depict = 0.3, = 0.6 and = 0.8.
6.6 Fine enforcement considerations
It appears that this estimator on average in practice could be close to the total damages, and the correctness does not fluctuate considerable in the analyzed markets. The bigger issue which comes with enforcing both overcharges as compensation for the total damag-es is the distribution between the harmed partidamag-es. The consumers are always undercom-pensated and the retailer market generally overcomundercom-pensated. Besides the fluctuation of the correctness of these two estimators appears to be sizeable, as can be concluded from figures 9-11.
From figure 8 it can be concluded that the fraction of total damages to consumers and firms in the retailer market of product 1 varies, again depending on the number of firms and the product differentiation. This implies that distributing a fixed fraction of the two overcharges to the consumers and the rest to the retailer market would not be fair, even if this fraction would be the average damage. Depending on the specifics of the market, one party will generally be favored at the expense of the other party.
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Governments could consider retrieving both overcharges of the colluding market and depending on the market implementation decide how to distribute the retrieved amount. Even though the correctness of the estimator in total fluctuates little, governments could multiply the overcharges with a factor appropriate for the specifics. This would mean that, depending on the way in which the overcharges are estimated, possible extra analy-sis needs to be done. Though for governments placing much importance on the fairness of fines, doing this extra analysis should at the very least be seriously considered. If govern-ments care mainly about deterring firms from colluding, this is less important.
7 Conclusions
The purpose of this paper is to analyze the effect of cartel formation in the supplier chain, accounting for a (possibly) heterogeneous production chain next to it. The im-portance of this is clear, first of all, to know in what kind of markets it is best to try to dis-cover colluding supplier markets. Secondly to figure out which parties need to be compen-sated after a cartel is discovered and by what amount.
It is concluded that he extra profits of colluding firms in the supplier market are highest if there are no strong substitutes to the product they produce. Therefore firms have the highest incentive to collude and therefore most likely to for a cartel in the case of low product differentiation.
This is very unfortunate since total harm to society is also highest in this case. Two other factors that influence the harm to society caused by cartel formation are the number of firms in the colluding market and in the retailer market. Factors that increase harm to society ordered from most important to least important factor are: no strong substitute to the produced product, a big supplier market and a small retailer market. Since a bigger supplier market makes it more difficult to form a cartel it could be argued that that factor is not relevant. Either way governments should focus especially on markets that have no strong substitutes and with lesser importance, markets that have small retailer markets. It is clear that other production chains are not negatively affected by collusion in the supplier market of a different production chain, on the contrary they even profit. Therefore they do not require compensation. The only parties requiring compensation are the direct and indirect buyers of the cartel. The indirect buyers are in this market structure even harmed more than the direct buyers. Therefore it is very important that standing to indirect buyers is granted.
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better approximation for the total harm than only the direct overcharge. But they did warn that if these damages are distributed by allowing each party to retrieve their own damage, the allocation might not be fair. The research in this paper showed the same result, the consumers are always undercompensated, while most of the time the direct buyers are overcompensated. The estimator did appear to be close to the sum of the damages to the-se two parties.
For governments who do not highly value a fair distribution of damage recovery, but whose only concern is that the wrongdoers recover the damages, this way of retrieving damages seems appropriate. For governments who want to make sure the distribution does take in account which party suffered which fraction of the damages, more than just the overcharge must be found. In this paper it is concluded that no fixed percentage of the total retrieved damages would give a fair distribution, since depending on the exact amount of firms in each market and the degree of product differentiation, the distribution of damages differs. Each cartel that is discovered should be analyzed to find the true distribu-tion of the damages. Besides that is should also be considered to analyze the amount of damages per situation, even though this estimator appears to be on average very close. The exact market implementation does change the correctness of the estimator.
Appendix
The equations Tuinstra & In ‘t Veld (2014) are as follows.
= ( )
( )( ) ( )
( )( ) ( ( ) ).
With this set of equations the inverse demand functions of the input prices are found and represented in the following way:
( ) (( )( ) ) (( )( ) ) (( )( ) ) ( ) (( )( ) )
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Firm i in the supplier market of product 1 set its quantity z1i in order to maximize
(∑ ∑ ) and firm j in the supplier market of product 2 set its quantity z2j in order to maximize (∑ ∑ ) . The m1 + m2 first-order conditions
are given by:
(( ( )( ) ) )(∑ ) (( )( ) )∑ )
(( )( ) )∑ ( )
(( )( ) )(∑ ) ,
The solution is given by , for and for . The prices and profits following are given in section 4.
Figure A.1 Error direct overcharge estimators compared to cartel size.
The graphs on the top depict the correctness of both overcharges as an estimator for the total damages, the middle graphs the correctness of the direct overcharge as an estimator for the retailer market damages, the graphs on the bottom the correctness of the indirect overcharge as an estimator for the consumer damages. The figures on the left indicate a small retailer market (2 firms), and on the right a big retailer market (6 firms) the number of firms in the non-colluding supplier market is held at 12. The straight line, dot/dashed line and dashed line respectively depict = 0.3, = 0.6 and = 0.8.
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References
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In ‘t Veld, D. (2010). Cartel harm with input substitutability: theory and an application. University of Amsterdam.
Kroon (2015). Suppliers damages and the umbrella effect of price cartels. University of Amsterdam.
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