Should public interest defense be
allowed in merger control?
Merel Joosten
Master’s Thesis to obtain the degree in Econometrics
University of Amsterdam
Faculty of Economics and Business Amsterdam School of Economics
Author: Merel Joosten
Student nr: 6137636
Email: mereljoosten@hotmail.com
Date: August 15, 2016
Supervisor: J. Tuinstra Second reader: M.P. Schinkel
Statement of Originality
This document is written by Student Merel Joosten who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Abstract
This thesis it has been investigates whether it is possible to allow public interest defense into merger control. A Bertrand model with heterogeneous goods is used. The results show that under certain conditions it is possible to allow public interest into merger control. However, the bandwidth for which this is possible is limited and restricted under certain characteristics of the model. For an extension of the model it is investigated if it is possible to compensate consumers for the loss they suffer due to the merger. The results show that it is possible to compensate the consumers for their utility loss.
Contents
1 Introduction 5
2 A Bertrand model with heterogeneous goods 9
2.1 pre-merger situation . . . 9 2.2 post-merger situation . . . 10
3 Can public interest defense be accommodated in merger control? 12
3.1 pre- and post-merger situation . . . 12 3.2 Results if more firms join the merger . . . 15 3.3 The efficiency of the production of sustainable goods . . . 18 4 Investments in sustainability in the pre-merger and post-merger
situa-tion 19
4.1 Investments in sustainability in the pre-merger situation . . . 20 4.2 Different structure of the cost function. . . 21
5 Influences on the utility of the consumers. 24
5.1 The influence of variable a . . . 25 5.2 The influence of variable b . . . 26 5.3 The influence of variable γ . . . 27
6 Change in welfare 29
7 Compensation of utility loss 32
7.1 Results . . . 34
1. Introduction
The scope of competition policy authorities changes over time. The competition au-thorities’ main concern is protecting the markets from anti-competitive behaviour. During assessments of mergers, acquisitions, collusion etc. usually only competition criteria are taken into account. This view is changing a little bit. Recently more and more arguments have evoked to accommodate public interest into the decisions of competition authorities. For example, in South Africa a merger between Coca Cola and SABMiller has been cleared with a number of conditions. These conditions are not only to protect consumers against anti-competitive behaviour, but a lot of the conditions impose public interest for the consumers. For instance, the current level of employment should be maintained for at least three years and the firm is prohibited to reduce the number of jobs by natural attrition (see ”South Africa imposes significant public interest conditions on Coca-Cola bottling merger” (GCR, May 2016)).
In the guidelines for horizontal mergers (2004) of the European Commission it is stated that: ”Corporate reorganisations in the form of mergers may be in line with the require-ments of dynamic competition and are capable of increasing the competitiveness of indus-try, thereby improving the conditions of growth and raising the standard of living in the Community” and ”, the Commission takes into account the factors mentioned in Article 2(1), including the development of technical and economic progress provided that it is to the consumers’ advantage and does not form an obstacle to competition” (Paragraph 76, European Commission, 2004). So if a merger is in the advantage to the consumers or when it raises the standard of living, it could be considered as one of the reasons to approve the merger by the EC (European Commission). This leaves some room for firms that want to merge to take public interests, such as health care, animal well being or sustainability, that raise such living standards, into their defense.
The main question in this thesis is: Should the public interest defense be allowed in merger decisions? This thesis uses a Bertrand model with heterogeneous goods, where merged firms can invest in the quality of the good after the merger (where this extra qual-ity represents e.g. sustainabilqual-ity). The basic model is an adapted version of a model that is introduced by Bowley (1924). I investigated whether it was possible to accommodate public interest defense into merger control. Under certain circumstances it is possible to
that is, a small interval of investments in sustainable goods.
A lot of research is done on mergers and their impact on the markets. Firms are only likely to merge if they will benefit from the merger. Mergers between firms in the same market have an anti-competitive effect on the market and could harm the consumers (Salant et al., 1983). A merger reduces the number of firms and therefor it will lead to less competition and higher prices, which is often sufficient to compensate for the output reduction of the merged firms (Perry and Potter, 1985). Such a merger is then profitable for firms but detrimental to consumers. Therefore, competition authorities research the effects intensively. However, after thorough investigation the merger may be approved, because synergies could arise in the market due to the merger. Farrel and Saphiro (2001) show that mergers can cause efficiencies and these efficiencies are often merger-specific. Merger control must be transparent in how the benefits will be weighted against the anti competitive effects. For merging parties it is very important to foresee the outcome of the merger assessment (McGowan et al. 1999) so the merging firms can decide whether the investments they make to propose a merger will be worth it.
Goppelsroeder et al.(2008) introduces the Werden-Froeb Index (WFI) to assist in eval-uating merger-specific efficiencies in horizontal mergers. In that paper an oligopoly model is used to assess to what degree marginal costs have to reduce in order to restore the pre-merger equilibrium prices and demand. Willig (2011) shows that in a lot of specific situations the competitive effects of the merger result in upwards pricing pressure (UPP). His research setting is a horizontal merger with firms that produce heterogeneous goods.
The next level in research about mergers and their impact is mergers between firms where one produce qualitative superior goods. Tuinstra and In ’t Veld (2014) conclude that a merger between cost efficient firms in Bertrand market may increase welfare. Tuinstra and In ’t Veld (2014) also mention that their analysis applies to mergers where products of the merging firms are qualitative superior. The next step will be to investigate differences in public interest. Blair et al (2014) conclude that quality mergers should be investigated case by case, since economic research shows that mergers can enhance quality. However, the results, especially in the health care industry, are not always consistent. Willig (2011) investigates an oligopoly with a standard good and a good with better quality. He con-cludes that after a merger, merged firms are most likely to raise the nominal prices of the product, resulting in the fact that the merger is apt to drive down the quality-adjusted
price. Consequently this increases demand and consumer welfare. Moreover, this way it is possible for the firm to generate additional net revenues.
The third level of mergers, is research in the field of sustainability and public interest accommodated in deciding whether or not to approve mergers. As the example that I started this introduction with shows that more and more competition authorities are dis-cussing to accommodate public interest defense into merger decisions. Some competition authorities already accommodate public interest into their decisions. Since it is a relatively recent topic, only a little research is done in this field of merger control.
In the field of public interest in cartel defense research has been conducted. Schinkel and T´oth (2016) investigate if it is possible to balance public interest defense into cartel defenses. They conclude that a public interest-cartel is not sustainable beyond a small number of consumers. These consumers combine a preference for private consumption with a low willingness to pay for the public good. These consumers select themselves. The authors argue that the information requirements for a competition agency to identify a genuine public interest-defense are prohibitively large by all standards.
There are even some competition authorities that accept a horizontal cartel-agreement if it promotes sustainable consumption or production. If consumers recognize the value of this sustainable consumption and production, it can even enlarge consumers’ surplus. This can be done when firms first invest in sustainability before choosing prices or output (Schinkel & Spiegel, 2016)
Could this public interest defense also hold during an assessment of a possible merger? To answer this question means that not only the effects in the market should be investi-gated, but also the effects for the consumers and whether they benefit from the merger. If the public interest argument should count in merger control, then the question arises how public interest should be integrated in this process. Reader (2016) conducts an empirical study of 75 domestic merger regimes. He identifies the six possible ways how countries in-tegrate public interest in merger control. He concludes that the public interest is treated in most countries as an ‘exception’ to a competition-based test or it is framed within sector-specific policy.
If public interest defense should be balanced in a merger decision, not only the assess-ment procedure must be transparent, it must also be shown that the average consumer really benefits from the merger. South Africa is a good example of a country that
in-corporated a test if the public interest argument should be given weight in the merger decision. (Thomson, 2015). Another example of a country that is investigating whether public interest should weigh in the decision to accept or deny a merger is the Netherlands. An example of this is that in 2016 The Autoriteit Consument en Mededinging (ACM) is investigating how public interest defense should be tested and integrated in health care mergers (ACM, 2016). Not all countries accept the public interest defense as an valid argument. However, after close investigation even countries that deny that public interest plays a role in their merger evaluation could possibly be prepared to admit that employ-ment and regional impact influence the evaluation process (Thomson, September 2015)
So efficiencies can be merger specific. However, assessment of mergers can be reviewed with sector-specific competition law and merger review. The ACM has a sector-specific competition law and public merger review for health care, public housing and education in the social sector. For the utilities sector water, electronic communications, post and media the ACM has sector-specific competition law as well. For this reason, when firms want to merge in these sectors, these sectors have their own specific merger assessment. Within some of these sectors there already exists some form of public interest accommodated in the assessment. As mentioned before in health care ACM is looking for new tests methods to accommodate public interest in the assessment. The second example of accommodating public interest into merger decisions is in the public housing sector. Mergers can only be approved if not too many social housing disappears from the market (Sauter, 2013).
Previous research of Bagnoli et al (2003) on competition and sustainability has been done. In their model firms compete for consumers, who are socially responsible. Their main conclusion is that in this setting, the public good is in most cases under provided. However, if the public good is linked to the sales of private good, the competitive envi-ronment can lead to excessive provision of the public good.
This thesis is structured as follows. In the next part I will give an introduction of the model. Then the results of the model will be showed. In the fourth part some charac-teristics of the model are tested. After that, it is investigated if there is a positive change in welfare. In part seven an alternative approach to the model is introduced and in the end a conclusion will be drawn whether public interest defence should be allowed in merger control.
2. A Bertrand model with heterogeneous goods
To investigate if public interest defense should be allowed into merger control, the pre-and post situation of the merger should be investigated. For this thesis firms compete on prices with each other, hence there is Bertrand competition.
2.1. pre-merger situation
In the model of the market, there are N differentiated goods being produced, so the products are heterogeneous. The representative consumer allocates its income M guided by its preferences. A utility function represents these preferences. The consumer maxi-mizes utility before the merger:
uc(q0, q1, .., qn) = q0+ a N X i=1 qi− 1 2b N X i=1 q2i −1 2γ N X i=1 X j6=i qiqj s.t. M = q0+ N X i=1 piqi
This utility function is twice differentiable. The marginal utility in this utility function is decreasing in each argument. Furthermore, a is a parameter and a > 0. The parameter γ represents the level of how much the products are differentiated. This means that if γ is close to zero then the goods are very differentiated. However, if γ is close to one, then the goods are almost perfect substitutes. So γ is bounded and γ ∈ (0, 1). Furthermore, qi are heterogeneous goods that have price pi. The consumer has an income of M . The
consumer can spend all its income on goods qi, where i∈ {0,1,...,N}. Good q0 represents
all the other goods consumers buy in life. If M is set large enough, consumers can con-sume enough other products from different markets. q0 has a normalised price of 1, so the
price vector looks like p = (1, p1, p2, ..., pn)0, where pi, i ∈ {1...N } is in proportion to p0 = 1.
Before the merger each good is produced by a separate firm. The firms in the market optimize their profit in a classic Bertrand competition manner. This means that firm maximizes its profit as follows:
πc= (pci − ci)Dic(p c 1, p
c −i)
Where Dc
i(pi, p−i) is the demand function for good qi in the pre-merger situation. This
demand function is derived from the utility function of the representative consumer of the pre-merger utility function. In this thesis a market where 2, 3, 4 and 7 firms are active are studied. The demand functions, that are derived from the utility function have the following form for firm 1 of a market where two firms are active:
Dc1(pci, pc−i) = 1 (b2− 1
4γ2)
(a(b − 0.5γ) + 0.5p2γ − bp1)
For markets where three, four or seven markets are active, the variables impact the de-mand function on the same manner. These dede-mand function are not demonstrated above, because of their complexity.
To find the equilibrium in the market, first, all firms in the market optimize their profit functions. Second, if the optimized prices and quantities are the best response to the opti-mized profits of the other firms in the market, then this results in a Bertrand-Nash equilib-rium. With the demand functions for the pre- -merger situation the indirect utility function can be calculated. The indirect utility function is Vc
i (N, ci, a, b, γ) = uci(q0∗c, q1∗c, ..., qN∗c)
Here qi∗ are the optimized values for qi and qci and pci are the quantities and prices of the
pre-merger situation. 2.2. post-merger situation
In the market the consumers value goods of a better quality, for instance products that are more sustainable. The level of these higher quality products are expressed by G and are integrated into the utility function. When firms want to merge, the products of the merged entity are higher valued by the consumers. This means that the utility function after the merger changes if firms merge, say for this model the first M firms, then M goods are valued higher. This increase is translated into the utility function with G. This transforms the utility function to the next form:
uM(q0, q1, .., qn) = q0+ (a + G) M X i=1 qi+ a N X i=M +1 qi− 1 2b N X i=1 qi2− 1 2γ N X i=1 X j6=i qiqj s.t. M = q0+ N X i=1 piqi
It is straightforward to see that this utility function satisfies the same conditions as utility function of the pre-merger situation.
After the merger the firms that have merged produce goods of better quality, since the goods are more sustainable then when the goods were in the pre-merger situation. Fur-thermore, the merged entity can compensate for the anti-competitive effect. This results also in extra production costs, to produce these more sustainable goods. The total profit of the merged firms, referred to as πm, if M firms merge are specified as follows:
πm = M X i=1 (pMi − ci) ∗ DiM(p M i , p M −i) − M X i=1 αG2. Again, here DM
i (pMi , pM−i) is the demand function of good i. However, this demand is
de-rived from the utility function, that the consumer has in the post-merger situation. For every good that is produced in a more sustainable manner extra costs of the following form: c(qi) = αG2, α = 0.5 are calculated.
The demand functions, that are derived from the utility function have the following form for firm 1 of a market where two firms are active:
D1M(pMi , pM−i) = 1 (b2− 1
4γ
2)((G + a) ∗ (b − 0.5γ) + 0.5γp2− b ∗ p1
For markets where three, four or seven markets are active, the variables impact the de-mand function on the same way. These dede-mand function are not demonstrated above, because of their complexity.
With the demand functions for post-merger situation the indirect utility functions can be calculated. The indirect utility is VM
i (N, M, ci, a, b, γ, G, α) = uMi (q0∗M, q1∗M, ..., qN∗M).
Here qi∗ are the optimized values for qi. and qMi and pMi are the quantities and prices of
the post-merger situation.
This model has one important property that should be checked beforehand. Would it be beneficial for the firms to invest in more sustainable products before the merger? If so, the situation changes, because not only the merged entity would be investing in the more sustainable products, all the firms in the pre-merger situation have an incentive to invest in more sustainable products as well, which gives a whole other market situation. I will get back at this issue in section 4.
3. Can public interest defense be accommodated in merger control?
For the results different types of markets are studied. Markets with initially 2,3,4 and 7 firms, where (pre-merger) each firm produces one heterogeneous good. Also the influence of the different number of firms that merge is studied.
3.1. pre- and post-merger situation
In a market where two firms merge, the effect on the indirect utility is negative for values of G close to zero. This is why for G close to zero the utility function of the post-merger situation will start below the utility function of the pre-merger situation. However, the indirect utility function of the post-merger is increasing in G. So if G is big enough then the value of the utility function of the post-merger situation exceeds the utility function of the pre-merger situation.
The profit function of the post-merger situation depends in two ways on the value of G. First, G has a positive effect on the profit function through the revenues, because demand in goods increases. Second, G has a negative influence on the profit function through the costs associated with producing the more sustainable goods. In this models these costs are 0.5G2. For small values of G the overall effect of G is positive on the profits. However, if G increases there is a turning point, where the influence of the cost function exceeds the extra value that is generated by the revenue through increased demand. From this point on the merger will not be profitable anymore.
I investigated whether there exists values of G such that the merger is still profitable and consumers utility is higher then before. I will call the set of values of G satisfying this the ’bandwidth’.
In a market where two firms merge, it turns out that there is a small bandwidth, where it is possible for firms to merge and in the post-merger situation invest in small values of G as illustrated in the graphs below. For the results that are shown below the following values for the parameters in the model are used: a = 1, b = 1, γ = 0.5 and ci = 0.
(a) overview (b) zoomed in
Figure 1: Market with two firms where the bandwidth for G is [0.14;1.55]. The right figure (b) is the zoomed in situation to show that indirect utility of post-merger is lower than indirect utility in pre-merger for G=0
(a) overview (b) zoomed in
Figure 2: Market with three firms where the bandwidth for G is [0.09;1.46]. The right figure (b) is the zoomed in situation to show that the indirect utility post-merger is lower than the indirect utility pre-merger for G=0
(a) overview (b) zoomed in
Figure 3: Market with four firms where the bandwidth for G is [0.06;1.35]. The right figure (b) is the zoomed in situation to show that the indirect utility post-merger is lower than the indirect utility pre-merger for G=0
(a) overview (b) zoomed in
Figure 4: Market with seven firms where the bandwidth for G is [0.03;1.18]. The right figure (b) is the zoomed in situation to show that the indirect utility post-merger is lower than the indirect utility pre-merger for G=0
Moreover, there is some space where the profit of the merged entity is greater than or equal to the profit in the pre-merger situation and where the utility function of the post-merger situation is greater than the utility function of the pre-post-merger situation. However, in markets where more firms are active the area where this is possible, becomes smaller, as illustrated above.The utility function of the post-merger situation increases faster above the utility function of the pre-merger if the number of firms active in the market(N ) increases. However, the profit of the merged entity decreases faster below the level of the profit in the pre-merger situation. The table below shows for which bandwidths of G it is still profitable for the merged entity to invest in the sustainable goods.
2 firms 3 firms 4 firms 7 firms
bandwidth G [0.15;1.55] [0.09;1.46] [0.06;1.35] [0.03;1.18]
The upper bound corresponds with the value of G such that the profit of the pre-merger situation equals the profit of the post-merger situation. The lower bound corresponds with the value of G such that the utility of the pre-merger situation equals the utility of the post-merger situation. The lower- and upper bound decrease if the number of firms, that compete in the market, increases.
3.2. Results if more firms join the merger
What is the effect on the market if more than two firms merge? As mentioned above, when two firms merge in the markets, the bandwidth, where it is possible to allow public interest defense in merger control exists. In the figures below there is a market where four firms compete. In the left panel of figure 5, two firms merge. In the right panel of figure 5, three firms in the market merge. Again a = 1, b = 1, γ = 0.5 and ci = 0.
(a) overview two merge (b) overview three merge
Figure 5: Market with four firms where in (a) two firms merge with the bandwidth for G:[0.06;1.35]. In (b) three firms merge with a bandwidth for G:[0.16;1.18]
As illustrated above, when in a market with 4 firms instead of 2 firms, 3 firms merge the bandwidth, where the merger is sustainable, decreases. However, there still remains a bandwidth for G where it is possible to accommodate public interest defense into merger control. The same occurs when in a market where seven firms are active, more and more firms will merge. Below it is illustrated what happens when a merger with two, three and four firms occur in the market with seven firms.
(a) overview two merge (b) overview three merge
(c) overview four merge
Figure 6: Market with seven firms where in (a) two firms merge with a the bandwidth for G:[0.03;1.18]. In (b) there is a merger with three firms. The bandwidth for G:[0.07;1.03].In (c) there is a merger with four firms. The bandwidth for G is [0.13;0.93]
Here the bandwidth, where public interest could be accommodated in merger control, decreases.
4 firms 7 firms 2 firms merge, bandwidth G is [0.06;1.35] [0.03;1.18] 3 firms merge and bandwidth G [0.16;1.18] [0.07;1.13] 4 firms merge and bandwidth G [0.33;1.09] [0.13;0.93]
If the number of firms increases the bandwidth becomes smaller. If more firms decide to merge the bandwidth, where it is possible to merge and accommodate public interest, decreases as well. The lower bound, where the pre-merger utility equals the post-merger utility, increases if more firms merge. Here there are two effects. Due to the merger the prices increase, which effect the utility negatively. The other effect is that in a merger where more firms merge there is more sustainability available for the same value of G. However, the first effect seems to be stronger, since the lower bound shifts to higher val-ues if more firms merge.
The upper bound, where the pre-merger profits equals the post-merger profits, de-creases if more firms merge. Producing sustainable goods is costly, this dede-creases the overall profits for the merged entity. If more firms join the merger, the increase due to the revenue is less strong then the extra costs for producing sustainable goods.
3.3. The efficiency of the production of sustainable goods
In the model the extra costs firms face for producing the sustainable goods are ci(G) =
αG2 per sustainable product the firms produce. For all the earlier results α = 0.5 has
been used. The cost function ci(G) with an α of 0.5 are quite efficient firms. So what
happens to the post-merger if the costs of sustainable goods become less efficient?
To answer this question it is important to take one thing into consideration: the profits should not decrease below the pre-merger profit, because then there is no incentive to merge at all. For the results a = 1, b = 1, ci = 0 and γ = 0.5 are used again.
(a) 2 firms (b) 3 firms
(c) 4 firms (d) 7 firms
Figure 7: What is the boundary value for α such that the merger still makes a profit
The results are all for the post-merger situation, where two firms merge. The area under the boundaries shows all the possible values α can have and at the same time where the merged entity still earns a higher profit than the firms earn in the pre-merger situation. The conclusion that can be drawn from the figures above, is that if the number of firms in the market increases, than α should be smaller. If more firms compete in the market, than the merged entity will be forced to produce more efficiently. If the merged entity is not capable to produce at such an efficient level, it should not merge at all.
4. Investments in sustainability in the pre-merger and post-merger situation As mentioned in the chapter about the model description it is important to conclude whether it pays to invest in more sustainable products in the pre-merger situation. If there is an incentive firms will invest even before firms can merge.
4.1. Investments in sustainability in the pre-merger situation
As it turns out it is for small values of G profitable for a firm to invest in more sustainable products. Even though there are extra costs associated with producing more sustainable products. In the picture below the extra costs associated with producing more sustainable products are: c(G) = αG2 with α = 0.5, the same costs that are used in the previous sections. This means that in the pre-merger situation it always pays if one firm in the market already produces sustainable goods for small values of G in the pre-merger situation.
(a) market with two firms (b) market with three firms
(c) market with four firms (d) market with seven firms
Figure 8: How much more profit does a firm make if it is the only firm in the market to invest in G, as a function of G.
In this setting the costs for producing sustainable goods are quite efficient. So what happens if the value for α is changes? Does there exist an α for which the firms do not have an incentive to invest in G in the pre-merger situation? So this means that the utility function of the pre-merger situation has the following form:
u(q0, q1, .., qn) = q0+ (a + G)q1+ a N X i=2 qi− 1 2b N X i=1 qi2− 1 2γ N X i=1 X j6=i qiqj s.t. M = q0+ N X i=1 piqi
and the profit function for firm 1 (the firm who is investing in G): π1c = Dc1(p1, p−1)(pc1− c1) − αG2
if the profit of firm 1 is always below the profit of the pre-merger situation of section 3.1 (call it πC where no firms invest in G) then it no longer pays to invest in G in a pre-merger
situation. As it turns out, to establish this result the value for α for values very close to G = 0 goes to infinity. In the figure of the previous section the boundary is shown for which value of G there holds πc
1 = πC and since for G = 0 there always holds π1c= πC this
means a part of πc
1 will always lie above πC for values of G close to zero unless α goes to
infinity. Hence here for values of G close to 0 it always pays to invest in G. 4.2. Different structure of the cost function.
It is unrealistic that costs close to infinity will still be profitable. That is why another pricing manner is for ci(G) = F + αG2 where F are sunk costs. To take realistic sunk costs
in this example (1/4)Dc
1pc1 is taken. In this way it can be calculated for which values of α
it no longer pays to invest in G in the pre-merger situation. Hence the profit function of π1 will become: π1 = D1c(p1, p−1)(p1− c1) − (1/4)Dc1p c 1− αG 2 (since F= (1/4)Dc1(p1, p−1)pc1)
(a) market with two firms (b) market with three firms
(c) market with four firms (d) market with seven firms
Figure 9: Here it is shown that a single firm is not going to invest in G for certain values of α. For a market with 2,3,4 and 7 firms active, this is respectively α=0.77, α=0.80, α=0.83 and α=0.85.
As it is demonstrated in the figures above for all values of G profits are equal or lower then πC. So for these values of α it does not pay for one firm anymore to invest in G.
For markets where two, three, four or seven firms compete the threshols value of alpha is respectively α=0.77, α=0.80, α=0.83 and α=0.85. If for these values of α the merger in section 3.1 still makes a higher profit than in the pre-merger situation, then there really exists a bandwidth of G where it is possible to accommodate public interest defense into merger control.
(a) market with two firms (b) market with three firms
(c) market with four firms (d) market with seven firms
Figure 10: As this figure shows there is still a small bandwidth for G where with the new cost the merged entity still makes a profit and therefore is sustainable. For a market with 2,3,4 and 7 firms these bandwidths are respectively [0.15;0.27],[0.09;0.39], [0.06;0.19] and [0.03;0.17]
The results above indicate that for a small bandwidth of G, it is not profitable for a single firm to invest in G in the pre-merger situation. The merged entity still makes a positive profit for small G. Hence it can be concluded that under a small bandwidth an specific settings it is possible to accommodate public interest in merger control. Further-more, it should be taken into account that it is just for very specific settings of the model. The bandwidth decreases if the number of firms in the market increases. However, only a market where two firms compete is an exception to this. This can be explained by the fact that this is the only market where a monopoly arises.
The merged entities earn more profit than the firms in the pre-merger situation earn for G = 0 with fixed costs of F = (1/4)D1c(pc1, pc−1)pc1. This means that even if α goes to infinity, then for values of G close to zero, the merged entity still earns more profit then
the firms earn in the pre-merger situation. For what values of the sunk cost F is it possible that the merged entity does not earn more profit then the firms earn in the pre-merger situation? In the table below thresholds of the sunk costs F are shown, if F exceeds these values in combination with an α = 0.5 the merged entity will no longer be profitable.
2 firms 3 firms 4 firms 7 firms threshold for F & α = 0.5 0.248 0.394 0.334 0.214
In combination with α = 0.5 there will be no incentive to merge anymore, since the merged entity will no longer be profitable. It is straightforward that when the number of firms increase the boundary for F decreases. When more firms are active, each firms earns a lower profit. The market where two firms compete is an exception, because here in the post-merger situation there is a monopoly in the market. This changes the characteristics of the market. The overall conclusion of this section is that under specific settings it is possible for the merged entity to be profitable, while it is not profitable for a single firm situation to invest in G in the pre-merger.
5. Influences on the utility of the consumers.
For all the previous results, the only variable that has been varied is variable G. All the previous results depend on the values of the variables: a, b and γ, since all the results are derived from the following utility function:
u(q0, q1, .., qn) = q0+ a N X i=1 qi− 1 2b N X i=1 qi2− 1 2γ N X i=1 X j=/i qiqj s.t. M = q0+ N X i=1 piqi
In the previous sections the values that were used to produce the results were: a = 1, b = 1 and γ = 0.5. What is the influence of these variables on the bandwidth of G? Is there still a positive bandwidth of G, where it is possible to accommodate public interest defense into the merger control?
5.1. The influence of variable a
To examine the influence of these variables varying values are used to see how the values of the utility functions and the profit functions changes. Firstly, different values of the variable a are examined. In the figures below it is illustrated how the behaviour of the utility functions and the profit functions change if G increases. It is illustrated for markets where 3 are active.
(a) profit function (b) utility function
Figure 11: Here the influence of variable a is shown. The dotted line illustrates the post-merger situation and the line the pre-merger situation
The dotted line illustrates the post-merger situation and the lines the pre-merger sit-uation. If a increases the utility functions increase linear. This is a straightforward result, because the utility functions are linearly dependent on a. The same holds for the profit. However, the increase in G, when the profit of the post-merger situation equals the pre-merger situation is higher than the increase in G, when the utility function of the post-merger situation equals the pre-merger situation. Hence the bandwidth for G where it is profitable for firms to merge and where consumers have a higher utility increase if a increases. In the table below the bandwidth for G is shown for a = 1, a = 4, a = 12 and a = 20:
a = 1 a = 4 a = 12 a = 20 2 firms [0.15;1.55] [0.57;6.21] [1.71;18.63] [2.86;31.05] 3 firms [0.09;1.46] [0.38;5.84] [1.13;17.52] [1.88;29.19] 4 firms and 2 merge [0.06;1.35] [0.27;5.51] [0.80;12.38] [1.33;27.53] 4 firms and 3 merge [0.16;1.18] [0.65;4.74] [1.95;14.22] [3.26;23.70] 7 firms and 2 merge [0.03;1.18] [0.13;1.69] [0.38;5.45] [0.63;9.26] 7 firms and 3 merge [0.07;1.13] [0.29;4.12] [0.86;12.38] [1.43;20.62] 7 firms and 4 merge [0.13;0.93] [0.50;3.72] [1.50;11.15] [2.50;18.58]
The table shows that a has a positive effect on the bandwidth where it is possible to accommodate public interest defense into merger control. The results in the table show that a has a positive effect on the bandwidth of G. If a increases, the bandwidth of G increases as well. The lower bound, where the utility of the pre-merger situation equals the post-merger situation, increases if a increases. This is bad for the merged entity. When the lower bound increases the merged entity has to invest more in G, because only then the merger will be profitable
5.2. The influence of variable b
To examine the influence of the variable b on the utility and profits, different values of b are used. In the figure it is shown what happens to these functions if G increases in a market where three firms compete. Again the dotted line illustrates the post-merger
(a) profit function (b) utility function
Figure 12: Here the influence of variable b is shown. The dotted line illustrates the post-merger situation and the line the pre-merger situation
situation and the lines the pre-merger situation. If b increases the utility functions and profit functions decrease for the pre- and post-merger situations. Furthermore, for the post-merger situation both functions decrease. However, if b increases the speed with which the functions decrease becomes faster. Moreover, the bandwidth for G where it is possible to accommodate public interest defense into merger control decreases if b increases. If all other variables are held constant (a=1, γ = 0.5), then for b = 1, b = 4, b = 12 and b = 20 the bandwidth can be found in the table below:
.
b = 1 b = 4 b = 12 b = 20
2 firms [0.15;1.55] [0.03;0.42] [0.01;0.19] [0.006;0.14] 3 firms [0.09;1.46] [0.03;0.41] [0.01;0.19] [0.006;0.14] 4 firms and 2 merge [0.06;1.35] [0.03;0.40] [0.01;0.19] [0.01;0.14] 4 firms and 3 merge [0.16;1.18] [0.06;0.43] [0.02;0.21] [0.01;0.16] 7 firms and 2 merge [0.03;1.18] [0.04;0.38] [0.01;0.19] [0.01;0.14] 7 firms and 3 merge [0.07;1.13] [0.05;0.39] [0.01;0.20] [0.01;0.15] 7 firms and 4 merge [0.13;0.93] [0.07;0.40] [0.02;0.21] [0.02;0.16]
The table shows the negative effect that variable b has on the bandwidth of G. An increase in b leads to a decrease of the bandwidth of G. If enough firms are active in the market, the bandwidth will even become almost zero. The lower bound decreases as b increases. The upper bound decreases if b increases.
5.3. The influence of variable γ
To examine the influence of the variable γ on the utility and profit, different values of γ are used. In the figure it is shown what happens to these functions if G increases in a market where three firms compete.
(a) profit function (b) utility function
Figure 13: Here the influence of variable gamma is shown. The dotted line illustrates the post-merger situation and the line the pre-merger situation
Again the dotted line illustrates the post-merger situation and the lines the pre-merger situation. If γ increases the utility functions and profit functions decrease int the pre- and post-merger situations. However, for the post-merger situation both functions decrease. However if γ increases the speed with which the functions decrease becomes faster. Hence the bandwidth for G where it is possible to accommodate public interest defense into merger control decreases if γ increases. If all other variables are held constant (a=1, b=1), then for γ = 0.01, γ = 0.40, γ = 0.80 and γ = 0.99 the bandwidth can be found in the table below:
γ = 0.01 γ = 0.2 γ = 0.8 γ = 0.99
2 firms [0.003;2.20] [0.05;1.89] [0.25;1.33] [0.33;1.23] 3 firms [0.003;2.20] [0.05;1.82] [0.12;1.24] [0.13;1.15] 4 firms and 2 merge [0.003;2.20] [0.04;1.76] [0.07;1.17] [0.07;1.10] 4 firms and 3 merge [0.01;2.25] [0.01;2.25] [0.09;1.65] [0.19;0.91] 7 firms and 2 merge [0.002;1.34] [0.03;0.99] [0.02;0.56] [0.02;0.51] 7 firms and 3 merge [0.005;2.23] [0.06;1.50] [0.06;0.81] [0.05;0.75] 7 firms and 4 merge [0.07;2.24] [0.09;1.42] [0.11;0.70] [0.09;0.62]
The influence of γ is negative on the bandwidth of G as is shown in the table above. If the value of γ increases, the bandwidth of G decreases. If more firms merge the bandwidth of G increases. If γ increases the lower bound increases also. The upper bound decreases if
γ increases. Hence γ has a negative effect on the profit of the merged entity, because of the price increase in the post-merger situation.
For a demonstration of the influence of the variables, a market where three firms compete and two firms merge is illustrated. However, the results for the market where three firms compete, also hold for the general case as demonstrated in the tables. Hence, in general if a increases all the four functions increase, resulting in an expansion of the bandwidth of G, where it is possible to accommodate public interest defense in merger control. For b and γ there holds the exact opposite. If both values increase all the four functions decrease, resulting in a decrease of the bandwidth of G. Therefor, the possible bandwidth, where it is possible to accommodate public interest into merger defense control, shrinks.
6. Change in welfare
Another way to approach the post-merger situation is to look at the welfare change due to the merger. The results of the previous section all show that only for very small values of G consumers suffer utility losses. However, if the increase in profits is higher than the loss of utility the overall welfare in the market can still be positive. Therefor, the change in welfare between the pre- and post-merger is positive for small values of G. First, it is investigated what happens if only two firms merge in the market. If more firms are active in the market the change in welfare decreases faster below zero. As is shown in the figure below:
If the results of this figure show that there is a bandwidth were the change of welfare is positive for values of G. These bandwidths are illustrated in the figures below:
(a) welfare 2 firms (b) welfare 3 firms
(c) welfare 4 firms (d) welfare 7 firms
Figure 15: How the value of G influences the welfare of the market
2 firms 3 firms 4 firms 7 firms bandwidth G [0;2.23] [0;2.08] [0;1.78] [0;1.64]
It can be concluded that this bandwidth becomes smaller when more firms in the market are active. If the number of firms increase in the market the bandwidth, where the change in welfare is positive, decreases.
What happens to the change in bandwidth when more then two firms merge? The answer is illustrated in the figures below. These figures show that if more firms merge in the market the welfare decreases faster to zero. For values of G close to zero the change in welfare is higher for mergers where more firms join the merger in the same market. This
result is again, quite straightforward. Profits of the post-merger situation are higher for small values of G.
(a) market with 4 firms (b) market with seven firms
Figure 16: How the value of G and number of firms that merge influence the welfare of the market
4 firms 7 firms 2 firms merge, bandwidth G is [0;1.78] [0;1.64] 3 firms merge and bandwidth G [0;1.48] [0;1.10] 4 firms merge and bandwidth G [0;1.23] [0;0.94]
For the other variables that influence the welfare (a, b and γ), their influence is the same as the influences these variables have on the utility function in the previous section. The table shows for what values of G and values of the variables, leaving the other variables constant, the change in welfare in the post-merger situation is positive.
a = 1 a = 4 a = 12 a = 20 2 firms [0;2.22] [0;8.90] [0;26.70] [0;44.50] 3 firms [0;2.08] [0;8.31] [0;24.93] [0;41.54] 4 firms [0;1.78] [0;7.78] [0;23.35] [0;38.91] 7 firms [0;1.64] [0;2.08] [0;4.88] [0;8.26] b = 1 b = 4 b = 12 b = 20 2 firms [0;2.22] [0;0.45] [0;0.20] [0;0.14] 3 firms [0;2.08] [0;0.43] [0;0.19] [0;0.14] 4 firms [0;1.78] [0;0.41] [0;0.19] [0;0.12] 7 firms [0;1.64] [0;39] [0;0.19] [0;0.11] γ = 0.01 γ = 0.20 γ = 0.80 γ = 0.99 2 firms [0;4.16] [0;3.09] [0;1.76] [0;1.56] 3 firms [0;4.14] [0;2.92] [0;1.72] [0;1.65] 4 firms [0;4.12] [0;2.78] [0;1.74] [0;1.65] 7 firms [0;1.67] [0;1.10] [0;0.58] [0;0.56]
The variable a has a positive effect on the bandwidth G if a increases, the bandwidth increases in all possible market settings. It can be concluded that a influences the change in welfare positively. The variable b decreases the bandwidth of G, for which values the change in welfare is positive. The variable b has a negative on the bandwidth of G, where the change in welfare is positive. The variable γ has the same effect as variable b. Only the effect of b on the change of welfare is more severe then the effect of γ. These results match the results of section 5. The influence that a, b, and γ have on the change of welfare, is mathematical the same as the influence they have on the profits of the merged entity, because the profit that the merged entity earns has the biggest influence on the change in welfare. This influence is stronger than the influence of the consumer surplus on the change of welfare.
7. Compensation of utility loss
There is another way to approach the changes that occur in this model due to the merger. Two firms merge and the sustainable products of this merged entity gain their own extra value of appreciation, G1 and G2. It has been shown that if two firms merge in
this setting for small values of G1and G2consumers’ utility decrease. The question here is,
is it possible for certain values of G1 and G2 to compensate for the loss in utility, while the
merged entity still makes a profit? This question is in line with the paper ’Quantifying the scope for efficiency defense in merger control: The Werden-Froeb-index’(Goppelsroeder et al, 2008), where it is examined how to assist in evaluating merger-specific efficiencies in horizontal mergers. In this paper an oligopoly model is used to assess in what degree marginal costs have to reduce in order to restore the pre-merger equilibrium prices and demand.
For this thesis the structure of the model of the pre-merger situation stays exactly the same. The model of the post-merger situation changes a bit. In the model only two firms merge and hence there is a little improvement on the original utility function:
u(q0, q1, .., qn) = q0+ (a + G1)q1+ (a + G2)q2+ a N X i=3 qi− 1 2b N X i=1 q2i − 1 2γ N X i=1 X j6=i qiqj s.t. M = q0+ N X i=1 piqi
From the utility function the demand function D1(p1, p−1) is derived. For a market where
two firms are active this demand function has the following form: D1(p1, p−1) = (b2−11
4γ2)
((γ ∗ (12G2+12a +12c2))/2 − b ∗ (21G1+12a +12c1) + (G + a) ∗ (b −12γ))
The demand functions of the markets where more firms compete depend on the variables a, b and γ on a similar way. and the profit of the merged entity (πm) in this section looks
like:
πm = (p1− c1)D1(p1, p−1) − αG21+ (p2− c2)D2(p2, p−2) − αG22
Here α = 0.5. All the other assumptions on the model remain the same as before. Again, the same markets are examined, hence a market where two, three, four or seven firms compete. In this section only two firms in the market will merge. The indirect utility function here results from plugging in the optimized values in the original utility function, resulting in Vi(N, M, a, b, γ, G1, G2, α) = ui(q0∗, q1∗, .., qN∗)
7.1. Results
There is an area where it is possible to compensate the utility loss, that the consumers suffer due to merger. This area lies on or outside of the red and blue lines. For the area of G1 and G2 where there is only a red line it is the area above the red line. The area above
the green line shows the area where it has positive values for G1 and G2. If the number of
firms increase in the market, the area where it is possible to compensate the utility loss increases.
The area where it is possible to compensate the utility loss and where it is possible for the firms to still earn positive amount of profit, lies on or between the yellow and purple lines. For the area of G1 and G2 , where there is only a purple line it is the area under
the purple line. For only the positive values of G1 and G2 it is the area above the green
line. If the number of firms in the market increase, the area for positive amount of profit and values of G1 and G2 decreases.
Combining both results together and then the area is found, where it is possible to compensate the utility loss suffered by the consumers and still make a profit for the merging firms that is above the profit of the pre-merger situation for positive values of G1 and G2.
If the number of firms increase in the market, this area decreases.
(a) 2 firms in market (b) 3 firms active in market
Figure 17: In the area for positive values of G1 and G2 between the profit boundaries and outside the
utility boundaries it is possible to (over) compensate the loss suffered by the consumers in the market
Here the results for the markets where two or three firms are active. There is an area where for positive values of G1 and G2 it is possible to compensate the change of the
market where four and seven firms markets are active results are shown below: There is an
(a) 2 firms in market (b) 3 firms active in market
Figure 18: In the area for positive values of G1 and G2 between the profit boundaries and outside the
utility boundaries it is possible to (over) compensate the loss suffered by the consumers in the market
area where for positive values of G1 and G2 it is possible to compensate the change of the
utility functions and where it is still profitable for the firms to merge. In the results above it is demonstrated that when the number of firms increase, the area, where it is possible to compensate the loss in utility and at the same time where it is possible for the merged entity to earn a higher profit then in the pre-merger situation for positive values of G1 and
G2, decreases. This can be explained, because when more firms are active in the market,
the firms’ earnings relatively decreases. Hence the merged entity earns relatively less in a market where more firms compete. Therefor, when the merged entity is still profitable in a market where more firms compete, the values of G1 and G2 have a lower limit.
8. Conclusion
In this thesis it is examined if it is possible from an economic point of view to allow public interest defense into the merger control. To answer this question a Bertrand com-petition model is used. It seems that it is possible to allow public interest defense into merger control under specific settings of the model. It is shown in the first sections that it is possible to allow it, if the products are valued a little over the goods of the pre-merger situation (this is when in the experiment the value of G is small). It shows that if in a market more firms join the merger then with every extra firm that joins the bandwidth, where it is possible to allow public interest into the merger control, decreases.
For the cost structure findings show that even if the extra costs of the production of these more sustainable goods explode for values of G close to zero, the merger could still be beneficial. The change in the total welfare in the market is also examined. Here the conclusion can be drawn that for small bandwidth of G the change in Welfare is positive. Hence for the total welfare it could also be beneficial to allow public interest into merger control.
The footnote to this conclusion however, is that in this model in the pre-merger situ-ation there is also an incentive for a firm to invest in the sustainable goods. If the costs of production rise, then at a certain value for the extra cost for producing a sustainable good it will not be beneficial anymore to produce the more sustainable good in the pre-merger situation. For a small bandwidth of G it could still be beneficial for the pre-merger under these specific settings. Therefor, the merger can be sustainable under these specific settings. In this thesis this is proved by a cost structure, where there are sunk costs. For further research it could be interesting to research different types of cost structures for the extra costs of producing the sustainable goods.
Another approach to solve this question is to look if consumers in the market can be compensated for the loss they suffer due to the merger. In this type of model the sus-tainable goods were valued extra by G1 for good 1 and G2 for good 2. Here is an area
found for combination of G1 and G2 to compensate the loss the consumers suffer from the
merger.
So the overall conclusion that could be drawn from this thesis is that under specific conditions there is a small bandwidth to allow public interest defense into the merger control.
Literature
ACM (2016), ”Position paper Autoriteit Consument en Markt Rondetafelgesprek fusietoets zorginstellingen” , (ACM,2016)
Bowley, A. L. (1924). The mathematical groundwork of economics: an introductory trea-tise.
Bagnoli, M., & Watts, S. G. (2003). Selling to socially responsible consumers: Com-petition and the private provision of public goods. Journal of Economics & Management Strategy, 12(3), 419-445.
Blair, Roger D., and D. Daniel Sokol. ”Quality Enhancing Merger Efficiencies.” Iowa Law Review, Forthcoming (2014).
Carletti, E., Hartmann, P., & Ongena, S. (2015). The economic impact of merger control legislation. International review of law and economics, 42, 88-104.
European Commission (2004), Guidelines for horizontal mergers, http://eur-lex.europa.eu/legal-content/EN/TXT/PDF/?uri=CELEX:52004XC0205(02)&from=EN
GCR (2016), ” South Africa imposes significant public interest conditions on Coca-Cola bottling merger”, 11 May 2016
Farrell, J., & Shapiro, C. (2001). Scale economies and synergies in horizontal merger analysis. Antitrust Law Journal, 68(3), 685-710.
Goppelsroeder, M., Schinkel, M. P., & Tuinstra, J. (2008). Quantifying the scope for efficiency defense in merger control:The WerdenFroebindex.. The Journal of Industrial Economics, 56(4), 778-808.
In’t Veld, Daan Laurens, and Jan Tuinstra. ”Market-Induced Rationalization and Welfare Enhancing Cartels.” (2014).
Perry, M. K., & Porter, R. H. (1985). Oligopoly and the incentive for horizontal merger. The American Economic Review, 75(1), 219-227.
Reader, D. (2016). Accommodating Public Interest Considerations in Domestic Merger Control: Empirical Insights.
Salant, S. W., Switzer, S., & Reynolds, R. J. (1983). Losses from horizontal merger: the effects of an exogenous change in industry structure on Cournot-Nash equilibrium. The Quarterly Journal of Economics, 185-199.
Sauter, W. (2013). Sectorspecifiek mededingingsrecht en fusietoetsing. RegelMaat, 28(2), 77-94.
Schinkel, M. P., & Spiegel, Y. (2015). Can Collusion Promote Sustainable Consump-tion and ProducConsump-tion?. Amsterdam Law School Research Paper, (2015-49).
Schinkel, M. P., & T´oth, L. (2016). Balancing the Public Interest-Defense in Cartel Offenses. Amsterdam Law School Research Paper, (2016-05).
Schinkel, M.P., Tuinstra, J., & R¨uggeberg, J.. ”Illinois Walls: how barring indirect pur-chaser suits facilitates collusion.” The RAND Journal of Economics 39.3 (2008): 683-698.
Thomsen, S, OECD FDI Regulatory Restrictiveness Index: A tool for benchmarking countries, measuring reform and assessing its impact (Overview presentation, OECD 2014) ¡http://www.slideshare.net/OECD-DAF/oecd-fdi-regulatory-restrictiveness- index?ref= http://www.oecd.org/investment/fdiindex.htm¿ 20 September 2015
Appendix A.1
In a model where oligopolies compete on quantities, it is important to know what the utility function of the average consumer is. In this thesis the utility function in the pre-merger situation is:
u(q0, q1, q2, G) = q0+ a ∗ (q1+ q2) −21b ∗ (q21+ q22) − 12γ(q1∗ q2)
in the post-merger situation it is:
um(q0, q1, q2, G) = q0+ (a + G) ∗ (q1+ q2) − 12b ∗ (q21+ q22) −12γ(q1∗ q2)
The budget constriction is: M = q0+ p1∗ q1+ p2∗ q2
Optimizing the utility function in the pre merger situation under the budget constrain as restriction gives a Lagrange of:
L = u(q0, q1, q2, G) + λ(Mi− (q0+ p1∗ q1+ p2∗ q2))
L = q0+ a ∗ (q1+ q2) + a −12b ∗ (q12+ q22+ G) −21γ(q1∗ q2+) + λ(Mi− (q0+ p1∗ q1+ p2∗ q2))
Optimizing the utility function in the post- merger situation under the budget constrain as restriction gives a Lagrange of:
Lm = u(q0, q1, q2, G) + λ(Mi− (q0+ p1∗ q1+ p2∗ q2))
Lm = q0+(a+G)∗(q1+q2)+a−12b∗(q21+q22+G)−12γ(q1∗q2+)+λ(Mi−(q0+p1∗q1+p2∗q2))
F.O.C. pre-merger
Taking the first order conditions to xi and G: δL δq0 = 1 − λ = 0 δL δq1 = a − bq1− 1 2γq2− λp1 = 0 δL δq2 = a − bq2− 1 2γq1− λp2 = 0 M i − (q0+ p1∗ q1+ p2q2+ pG∗ gi) = 0
Out of the first F.O.C. I can conclude that λ = 1
F.O.C. post-merger
Taking the first order conditions to xi and G: δL δq0 = 1 − λ = 0 δL δq1 = (a + G) − bq1− 1 2γq2− λp1 = 0
δL
δq2 = (a + G) − bq2−
1
2γq1− λp2 = 0
M i − (q0+ p1∗ q1+ p2q2+ pG∗ gi) = 0
Out of the first F.O.C. I can conclude that λ = 1
pre-merger situation
From the budget constrain follows: q0 = M − p1 ∗ q1 − p2 ∗ q2. The demand for the
commodities of q1, q2 and gi are independent of M, if M is large enough
I can rewrite: q1 =
(a+G)−12γq2−p1
b
So there also holds: q2 =
(a+G)−1 2γq1−p2
b
Plugging these equations in each other results in: q1 =
a−12γ(a− 12γq1−p2) b −p1 b q1 = ab−12γ(a−12γq1−p2)−p1b b2 q1 = a(b−12γ)+12γp2−bp1 b2−1 4γ2
In a similar way there can be calculated that: q2 =
a(b−12γ)+12γp1−bp2)
b2−1 4γ2
Since consumer i is a representative consumer for all the consumers the total demand for good 1 and 2 is:
D1(p1, p2, G) = PN i=1q1 = N ∗ q1∗ = N ∗a(b− 1 2γ)+ 1 2γp2−bp1 b2−1 4γ2 D2(p1, p2, G) = PN i=1q2 = N ∗ q2 = N ∗a(b− 1 2γ)+ 1 2γp1−bp2 b2−1 4γ 2
A firm that produces heterogeneous goods tries to maximize: π = (p − c)D(p)
So for firm 1 and 2 maximize their profits as follows: π1 = (p1− c)D1(p1, p2, pg, gN, g−i)
π2 = (p2− c)D2(p1, p2, pg, gN, g−i)
For firm one to maximize profit dpdπ
1 = D1(pi) + (p1− c)
dD1(pi)
dp1 = 0
Let’s assume that the marginal costs c1 are constant and do not depend on p1 dπ dp1 = N ∗ a(b−12γ)+12γp2−bp1 b2−1 4γ 2 − (p1− c1) ∗ N b b2−1 4γ 2 = 0
Solving this for p1 gives: p1 = 12 ∗
a(b−12γ)+12γp2−c1b
b Since the firms are similar and firm 2
p2 = 12 ∗ a(b−12γ)+12γp1−c2b b plugging this i p1: p1 = 12 ∗ a(b−12γ)+12γ12∗a(b− 12γ)+ 12γp1−c2b b −c1b b So pC1 = a(b−g)(2b+ 1 2γ)−c2b 1 2γ−2b 2c 1) 4b2−1 4γ2 And pC 2 = a(b−g)(2b+12γ)−c2b12γ−2b2c1) 4b2−1 4γ2
So profit for firm 1 becomes: π1C = (p1− c)D1 = (4b(a(8b
2−2bγ−γ2)−8(b2+γ2)c
1+2bγc2)2)
((4b2−γ2)(−16b2+γ2)2)
utility function pre-merger
Plugging these values and prices into the utility function gives the indirect utility function: ViC = −(g4+b2(64−20g1 2))2(8b 2g(2bc 2g − c1(8b2+ g2) + (8b2− 2bg − g2)a)(2bc1g − c2(8b2+ g2) + (8b2− 2bg − g2)a) − 4b(2bc2g−c1(8b2+g2)+(8b2−2bg−g2)a)(a(8b2−2bg−g2)+2bg(c2)+8b2(c1)) ((16b2−g2)(g4+b2(64−20g2)) − 4b(2bc1g−c2(8b2+g2)+(8b2−2bg−g2)a)(a(8b2−2bg−g2)+2bg(c1)+8b2c2)) ((16b2−g2)(g4+b2(64−20g2)) − 1 (−g4+4b2(−16+5g2))4ba(2a(8b 2− 2bg − g2) − 8b2(c 1+ c2) + 2bg(c1+ c2) − g2(c1+ c2)) + (1/(8b2− 2g2))(a2(−2b + g) + a(2b − g)(c 1+ c2) + g(c1)(c2) − b(c21+ c22)) − 1 (g4+b2(64−20g2))2)8b 3((2bc 2g − c1(8b2 + g2) + (8b2 − 2bg − g2)a)2 + (2bc1g − c2(8b2 + g2) + (8b2− 2bg − g2)a)2) + M Where g=γ post-merger situation
If firm 1 and 2 merge the merged firm becomes a monopoly that maximizes the profit: πM = (p
1− c1)D(p1, p2, G) + (p2− c2)D(p1, p2, G) After the merger the firms becomes a
monopoly.
For the situation of the monopoly the firm maximizes: πM = (p1− c1)D1(p1, p2, G) + (p2− c2)D2(p1, p2, G) dπM dp1 = D(p1, p2, G) + (p1− c1) dD1 dp1 + (p2− c2) dD2 dp1 = 0 dπM dp1 = N ∗ (a+G)(b−12γ)+12γp1−bp2 b2−1 4γ2 − (p1− c1) ∗ N ∗(b−1 b 2γ)(b+γ) + N ∗ (p2− c2) 1 2γ (b−12γ)(b+γ) = 0 So p1 = (a+G)(b−12γ)+γp2+c1b−c212γ 2b And p2 = (a+G)(b−12γ)+γp2+c2b−c112γ 2b
Plugging this back into each other results in:p1 =
(a+G)(b−12γ)+γ(a+G)(b− 12γ)+γp1+c2b−c112γ 2b +c2b−c1
1 2γ
2b
This results in: pM
This leads to: pM2 = 12(a + G + c2)
and the profit is
πM = 8b2−2γ1 2(a + G − c1)((2b − γ)(A + G) − 2bc1+ c2γ) +
1
8b2−2γ2(a + G − c2)((2b − γ)(A +
G) − 2bc2+ c1γ)
utility function post-merger
Plugging these values and prices into the utility function gives: uMi = Mi+ 2b2−2γ1 2((a + G)
2(2b − γ) − (a + G)(2b − γ)(c
