Mergers and (uncertain) Synergies in Oligopoly

Diploma Thesis, 2011

83 Pages, Grade: 2,0



1 Introduction
1.1 Literature Review

2 Industry Structure and it‘s Implications on Com- petition
2.1 The Static approach of Industry Structure
2.1.1 Monopoly
2.1.2 Cournot Competition
2.1.3 Bertrand Competition

3 Horizontal Mergers and the Effects on Quantities and Prices
3.1 The Effect of a Merger within Bertrand competition
3.1.1 Incentives for a Merger within Bertrand competition
3.1.2 Complementary Goods
3.1.3 Incentives to join a Merger
3.2 The Effect of a Merger within Cournot competition
3.2.1 Incentives for Mergers within Stackelberg games - Solv- ing the Merger Paradox
3.2.2 Incentives for Mergers - Solving the Merger Paradox
3.3 The Effect of a Merger within Cournot competition on Wel- fare

4 Horizontal Mergers and Synergies
4.1 Efficiency Gains
4.1.1 Economies of Scale
4.1.2 Economies of Scope
4.1.3 A critical view towards Synergies
4.2 Endogenous Mergers and Efficiency Gains

5 Horizontal Mergers and uncertain Synergies
5.1 Modeling Mergers and uncertain Synergies
5.1.1 The Bayesian Equilibrium
5.1.2 Merger with Uncertainty and the Impact of private Information
5.1.3 The Effects of Uncertainty within Bertrand competi- tion on Welfare

6 Conclusion
6.1 The Role of Uncertainty and the Consequences for Antitrust .
6.2 Concluding Remarks

1 Introduction

There are many opportunities for firms to cooperate and to coordinate their actions. Farell and Shapiro state that there is no necessity for mergers as cooperation and coordination can be achieved at an equivalent level via contracts: “..., modern economic theory observes that virtually anything that can be done with a merger can in principle be done instead with some kind of contract, perhaps a very complex (or restrictive) one.” (Farrell and Shapiro 2001, p. 691).

Nonetheless, recently many firms have announced intense interest in merger and acquisition activities[1]. There are clear advantages of mergers com- pared to e.g. strategic alliances although both provide the possibility to co- ordinate strategies. In contrast to alliances, a merger enables coordination of many diverse decisions that are not refined pre-merger. A merger may also leads to more market power and hence to better access to the financial market by obtaining an advantageous risk structure. Although a merger might need the approval of the competition authorities, it is the preferred coordination concept to maintain synergies. The prospect of sharing eco- nomic risks by obtaining a larger market share or being more diversified surely further motivates firms to coordinate their actions via mergers.

According to a survey[2] conducted by The Boston Consulting Group about firm‘s merger plans for 2010, 19 percent of the sample firms stated that they are planning at least one large-scale acquisition in 2010. The survey reveals the sectors where mergers are most likely, as for instance the chem- ical sector with 44 percent of companies and the insurance sector with 60 percent of companies.

Thus there is huge evidence that horizontal mergers and respectively acquisitions play an important role in our globalized market economy.

The industrial organization literature is justifiably shaped by many studies addressed to the impacts of horizontal merger formation. The globalized economy contains more possibilities to expand and to gather more profits and market power, but it is also susceptible to shocks as the recent global financial crisis has impressively shown. So there are chances but also risks and firms may capture the chances and additionally bear the risks much better through joint actions that involve coordination and synergies.

The core of my thesis is to discuss the strands of literature that deal with merger formation and to illustrate the theoretical improvements in mod- eling mergers that may replicate much better real-world scenarios. Ques- tions to be answered throughout my thesis are, who benefits from a merger and what are the consequences of it? Which firms are motivated to merge and how does uncertainty change the traditionally resolved consequences of mergers?

My thesis is organized as follows, Section 2 briefly summarizes the differ- ences between competition à la Cournot and Bertrand. In Section 3 the impact of merger formation is discussed by examining the effects within price and quantity competition. To discover the incentives for mergers the profitability of merging in deterministic merger models lies in the center of interest in this section. The merger paradox will be introduced and also the attempts to overcome its puzzling result. Purely concentrative merger are found to be beneficial conditioned on the type of competition. Section 4 will focus on the most stated reason for mergers, efficiency gains and respectively synergies. A critical reflection of synergies will be pro- vided as the distinction of real synergies and pure cost gains have been entered the evaluation of profitable mergers in theory and in reality. Addi- tionally I present models that treat the decision to merge as endogenous, which seems to be a promising way to capture the nature of merge forma- tion more realistically. The link between cost rationalization and market concentration will be examined and also the divergent results will be dis- cussed. Mergers under uncertain synergies are illustrated in Section 5. The impact of uncertainty will be demonstrated in different approaches. Uncertainty about post-merger conditions can motivate firms to merge, for example uncertainty about future demand or cost efficiencies, especially when firms maintain informational advantages. In addition the effects of uncertainty on welfare are demonstrated in this section. The last section, Section 6 provides my final conclusion of the addressed questions.

1.1 Literature Review

The aim of merger literature is to model appropriately the process of merger formation, so that the the model‘s predictions reflect merger processes observed in reality. The competition authorities may be endowed with insights about mergers and the effects on welfare to avoid the rejection of welfare enhancing mergers (Type I error) and the approval of welfare reducing mergers (Type II error).

Salant et al. (1983) establish the merger paradox that has been frequently challenged in the last decades. The model‘s outcome reveals a rather pes- simistic view towards the profitability of mergers in Cournot games with homogeneous goods produced at a constant cost level. In contrast to the results of mergers in Cournot games where merging is almost never prof- itable, Deneckere and Davidson (1985) examine mergers where prices serve as the strategic variable.

Another model that analysis the incentives to merge of Cournot firms when merging is exogenous is illustrated by Perry and Porter (1985). They allow the merged firm to differ in its size compared to the unmerged firms, as the merging firms combine more capital the resulting merged entity will be larger. It is shown that for a cost function that is sufficiently convex, a merger of two firms will be beneficial. The impact of mergers on welfare is examined by Farrell and Shapiro (1990).

To solve the merger paradox a model where firms sequentially select their output levels is illustrated by Daughety (1990). Huck et al. (2001) also discuss the incentives for merger formation within a Stackelberg game and provide additional and contracting results compared to Daughety (1990). When horizontal mergers occur in a dynamic Cournot model, Dockner and Gaunersdorfer (2001) observe that mergers are always beneficial for the merging firms also without any cost efficiencies, which holds for any num- ber of the merging firms. In their model firms select their optimal quan- tities conditioned on the initial price level, also known as the Markovian strategy.

The approach by Kamine and Zang (1990) was the first model of endoge- nous merger formation. As the decision to merge is endogenously made by the firms, Kamien and Zang (1990) examine whether firms have incentives to merge until the industry is monopolized or partially monopolized. The latter approach is extended by Gaudet and Salant (1992) by introducing fix costs to the model of endogenous mergers.

Regarding the decision to merge as endogenous Horn and Persson (2001) conduct a cooperative two stage game, where firms can negotiate about the division of the profits obtained through a merger, the equilibrium owner- ship structure is found by the definition of the dominance relation.

The model conducted by Barros (1998) assumes firms to differ in their efficiency by producing homogeneous goods. He emphasizes the question what types of mergers are likely to occur between asymmetric firms and the impact that market concentration has upon the merger type. Neubecker and Stadler (2003) apply the cooperative merger game approach by Horn and Persson (2001) and examine the impact of market concentration and firm‘s asymmetry by referring to Barros (1998).

Rodrigues (2001) shows that the rationalization of fixed cost is desirable provided that the industry is not initially very concentrated or when com- petition is less intense. There are rather high incentives to merge when fixed cost savings are possible and the incentives are lower the more firms are initially in the industry. The merger is beneficial as the merged en- tity produces at the same output level as the unmerged firms, but obtains higher profits due to lower fixed costs. In contrast to the latter approach, Zhou (2008) examines the impact of uncertain production rationalization that might be obtained through a merger. He argues that this will be the driving force to merger formation as the fix cost saving argument cannot capture all features of merging observed and contradicts with general per- ceptions. Zhou (2008) finds the expected profit of the merged entity to be higher compared to the one‘s of the unmerged firms and thus firms are motivated to merge or to join a merger. Furthermore does the degree of uncertainty play a crucial role, greater uncertainty enhances the number of firms that wish to merge. Besides Deneckere and Davidson (1985), the Cournot model has served as the workhorse model so far.

Choné and Linnemer (2008) adapt the role of uncertainty on efficiency gains to a model where firms are engaged in price competition with differ- entiated goods and examine the effects that a merger has on welfare rather than on the profitability of mergers. In contrast, Amir et al. (2009) model Cournot competition with uncertain efficiency gains. Moreover, does the model depart from the assumption that all agents are perfectly informed. A further approach to capture uncertainty about the efficiency of a merged entity is conducted by Banal-Estanol (2007). The cost structure is either privately observed or public knowledge in a second model scenario. As Amir et al. (2009) introduce the probability parameter p, Banal-Estanol (2007) assumes that idiosyncratic uncertainty enters the Cournot model via the cost function.

2 Industry Structure and it‘s Implications on Competition

2.1 The Static approach of Industry Structure

In most of the industrial organization literature that is evaluating and ex- ploring the effects of mergers, as for example Salant et al. (1983), Farell and Shapiro (1990) or Kamien and Zang (1990), model merger formation in Cournot industries. The static Cournot model (Cournot, 1838)[1] with con- stant marginal costs across firms provides no evidence for the profitability of mergers. In equilibrium, prices and profits are lower than in the mo- nopolistic case, since the firms only maximize their own profits regarding the output of its rival as exogenously given. Since the industry structure is crucial for the implications of the profitability of mergers I will provide some insights about Cournot and Bertrand competition, whereas the case of monopoly is considered first.

2.1.1 Monopoly

In contrast to competitive firms, the monopolist does not take the market price as given. Consider that the inverse market demand is linear and given by p (Q) and the cost function by C (q). The monopolistic choice of quantity determines the market price as the monopolist faces the following maximization problem:

illustration not visible in this excerpt

and the first-order condition for a maximum is given when marginal rev- enue equals marginal cost, M R (q) = M C (q). Note, that for perfect com- petition the condition that marginal revenue equals marginal cost also has to hold but since marginal revenue equals the price which is exogenously given, the condition reduces to p = M C. The monopolist faces two ef- fects on its marginal revenue due to a change in output. First, an increase in output leads to higher revenues but at the same time the market price reduces. Hence, the reduced market price applies for the entire level of out- put of the monopolist. To give a different illustration of marginal revenue one can also use the elasticity of demand, where the elasticity of demand ε[2] reflects the change in demand in responds to a one percentage change in price. Marginal revenue can thus also be rewritten by,

illustration not visible in this excerpt

where the elasticity of demand in absolute values is given by[illustration not visible in this excerpt]. The latter equation yields,

illustration not visible in this excerpt

where the rate of change due to a price change determines the optimal supply level. Suppose that the elasticity of demand is perfectly elastic [illustration not visible in this excerpt] and the optimal price for a firm in perfect competition is again given by p = M C. Further consider the inelastic case, then the marginal revenue becomes negative and fails to be equal to marginal cost. Hence the point at which profit maximization is reasonable for a monopolist lies on the elastic part of the demand curve, when ε < − 1.

The Lerner index of monopoly power is inversely proportional to the elasticity of demand and formally given by,

illustration not visible in this excerpt

note that ε m is endogenously evaluated at qm. Intuitively, the smaller the elasticity of demand the larger will be the markup.

To determine the equilibrium values for a monopoly suppose a quite gen- eral inverse linear demand function of p (Q) = a − Q and costs of C (q) = cq. The maximization problem is then given by max π m = (a − q) q − cq with q a > c > 0. By solving the maximization problem the following equilibrium values for the monopolist are given by,

illustration not visible in this excerpt

where qm and pm denote the monopolistic quantity and the corresponding market price and π m the profit of the monopolist. Neither the price nor the level of output is socially desired. The monopoly case is the counterpart to perfect competition and in the discussion about merger it will also serve as a reference point.

2.1.2 Cournot Competition

To explain the concepts of market interaction the static approach of Cournot competition is a widely used concept. As a simple form model it provides substantial knowledge about payoff interdependency in an imperfect com- petitive market structure. In the simplest form of the Cournot game all firms are identical and produce homogeneous goods. This means that each firm in the market faces the same profit maximization problem. In order to determine the equilibrium output level, the Cournot firm recognizes that each competitor has to make the same assumptions about its rivals. The firm could increase its profits by producing more but it is also aware of the fact, that if all firms do so, output, price and profits will converge to the perfect competitive outcome. Therefore is the increase in market share not desired by the firms and the Cournot equilibrium isstable. Hence firms are better off and profits are above the perfect-competition level of zero. The aggregate output level is lower in the Cournot case than in the fully com- petitive case, where firms act as price takers. In contrast, profit is higher than under quantity competition when a firm is the only producer in the market. When a firm acts as a monopolist there will be less aggregate out- put than under Cournot competition and the price turns out to be higher, which is due to the different maximization problem the monopolist faces. The static Cournot approach requires that the firms choose their individ- ual output level simultaneously, which can be seen as a strategic feature of this game. As the profits of the market participants depend on each other, the Cournot model can also be viewed in the light of game theory, where strategic behavior plays a crucial role. The Cournot equilibrium replicates the Nash equilibrium in quantities, both notations are commonly accepted and equivalently used. If one firm is exogenously forced to lower its production level, rivals will adjust by an increase in their production level, thus quantities are also known as strategic substitutes.

For the moment we consider firms that choose their quantities simultane- ously in order to maximize their profits. There is only one period of com- petition and hence no entry of other competitors is possible in this period. There are n firms in the industry and output chosen by firm i is denoted by qi. The output of all other firms except firm i is given by q − j, and ag- gregate quantity is thus given by [illustration not visible in this excerpt]. As consumers are able to substitute the equilibrium price depends on firm i ‘s supply and also on the production of all rivals. The equilibrium market price is determined by the inverse market demand that is a function of the quantities produced, and given for example by p (Q) = a − Q.

Instead of choosing its optimal quantity, firms may choose their optimal production capacities[3] which gives an alternative interpretation of the Cournot model. Firms can only supply conditioned on their chosen capacity limit, given by qi and the inverse demand reflects the market price given the equilibrium capacity choices of all firms in the market.

In order to maximize profit, firm i selects the quantity that leads to equality between the Lerner index [illustration not visible in this excerpt] andtheinverseofthedemandelasticity, formally given by,

illustration not visible in this excerpt

where c (qi) denotes the marginal cost of firm i.

Assuming a market with n identical firms, that produce homogeneous goods and face linear demand given above, the symmetric Cournot equilibrium values[4] will be given by,

illustration not visible in this excerpt

For the further purpose of analyzing the effects of mergers it will be convenient to measure market power and efficiency of the Cournot model, see for example Church and Ware (2000). As stated above, firm i select its optimal quantity according to the following relation,

illustration not visible in this excerpt

Where the elasticity of demand is reflected by ε in absolute values and the market share reflects how much of the aggregate output level is actually produced by a single firm and calculates as follows si = q i Q. The Lerner index is proportional to the inverse of the price elasticity of demand and the actual market share of firm i. When firm i becomes more efficient and thus obtains lower marginal costs, it also obtains a higher market share.

The previous equation (2.6) can be generalized in an appropriated way and the relation above can be rewritten as,

illustration not visible in this excerpt

The numerator on the right-hand side HHI[5] is known as the Herfindahl- Hirschman index and gives a picture of actual market concentration, and is zero for perfect competition and one in case of monopoly. If the HHI is in between zero and 1 one can evaluate the state of concentration in the market. On the left-hand side we have the Lerner-index for the whole market also known as the relative markup. The relative markup is the ratio between the profit margin and the price. A higher HHI results in a greater relative markup for keeping the elasticity of demand constant. There are a few observations regarding the above equation(2 . 7) that give general insights about the Cournot market structure and its features.

First, since the market share of a Cournot firm is less than one, the rela- tive markup will be lower than in a monopoly, further does the elasticity of demand limit the market power of a firm engaged in Cournot competi- tion. Secondly, the equilibrium prices will be above marginal cost and every market player does have market power, which becomes crucial when firms decide to merge. The third observation is quite important for the scope of this paper and states that more efficient firms will be larger since there is an endogenous relationship between the market share and marginal costs. It turns out that Cournot firms with a greater share on aggregate output have lower marginal costs compared to its competitors. Finally it can be said that the more intense competition becomes due to an increased num- ber of firms in the market the lower will be each firm‘s market power since the market share will drop. Intuitively, barriers to entry play a crucial role in the evolution of industry structure.

The effects of exogenous changes on the Cournot equilibrium are demon- strated next. Note that the Cournot equilibriumis stable and unique[6] through- out the comparative static analysis. There are two non-identical firms in the market that compete in quantities and face linear demand. A decrease in firm 2´s marginal costs (c 2 < c 1) will change its best-response function. Graphically the best-response function of firm 2 shifts outward. The output of firm 2 is directly effected and it is profitable for firm 2 to exceed output. It can be shown that firm 2‘s output increases with firm 1‘s marginal costs and decreases with its own marginal costs. Since firm 2 provides more output, firm 1 will reduce its supply and therefore firm 2 faces a higher residual demand and is encouraged to produce even more. This can be seen as an indirect effect of the lower marginal costs of firm 2. Due to the re- duction in marginal costs of firm 2 the aggregate output level is increased whereas output of firm 1 is lower and the output of firm 2 is greater than before. Hence that the profit of either firm changes in the same direction as the supply is effected by the decrease in marginal cost of firm 2. The equilibrium values for the asymmetric Cournot duopoly game for i, j ϵ [1 , 2] are given by,

illustration not visible in this excerpt

Consider next an exogenous change of the number of firms competing in the market. Reducing the amount of competitors results in less intense competition and therefore each firm‘s profit increases. Hence that individ- ual supply and so the aggregate output level decreases and that the price rises above its previous level. The reverse effect occurs when the number of firms is exogenously increased. Suppose again n identical firms, when all firms provide the same level of output and have the same market share in the symmetric equilibrium of [illustration not visible in this excerpt] then equation (2.6) can be restated as,

illustration not visible in this excerpt

and provides insights about how market power is evaluated. Individual market power increases as soon as there are less competing firms in the market. The relative markup for the whole industry increases. Vice versa, when n becomes relatively large then the price converges towards marginal cost. In the extreme price will be equal to marginal cost as the number of competitors goes to infinity. Note that the Cournot equilibrium is not so- cially optimal because overall production is not maximized and the result- ing market price is in between perfect competition and monopolistic competition. As the number of firms becomes large [illustration not visible in this excerpt] the Cournot equilibrium will be almost competitive and each Cournot firm has only a small market share and nearly acts like a price taker.

The Cournot model where firms choose the output level simultaneously can be extended to a strategic game where firms sequentially determine output. In the so called Stackelberg game, the leading firm has the first- mover advantage and selects the output level first. The follower firm selects its output level conditioned on the output obtained by the leader in order to make its optimal choice, but the output level will fall short of the leading firm‘s output level.

2.1.3 Bertrand Competition

Rather than quantities, many economists argue that it is more realistic that firms compete in prices, and therefore studied mergers in Bertrand competition[7]. Before turning to the effects of horizontal mergers in Bertrand oligopoly, I want to give more insights of the pre-merger situation of firms that compete in prices.

Consider an industry that consists of n firms that produce substitutable goods, that are eventually imperfect substitutable at constant marginal costs. The maximization problem of a Bertrand firm is to find the opti- mal price given the prices of its rivals in the market, which is done by setting marginal revenue equal to marginal costs. All firms set their prices simultaneously and non-cooperatively while firm i faces linear demand of qi = Di (pi,p 2 ,...,pn). The demand for the goods provided in the market are inter-related, and depend on firm i ‘s own product price, denoted by pi as well as on the prices of the goods produced by all other competitors. Firm i thus has to be aware of its residual demand and how it is affected by a price change. Note that consumers are able to substitute and to purchase the least expensive good available. When firm i increases price the con- sumers will buy less and firm i suffers losses. By how much the demand will go down depends on the elasticity of demand and on the degree of sub- stitutability. For perfect substitutable goods, the demanded output of firm i converges to zero as long as there are enough substitutable goods that can be purchased instead of firm i ‘s good. Furthermore does the elastic- ity of demand depend on all other prices and if there are many competing firms that provide goods that are close respectively perfect substitutes the elasticity of demand for qi will be high and induces a high willingness to substitute. The reduced demand firm i is to serve is determined by the own-price elasticity. Profits are maximized when the optimal price implies that the inverse of the own-price elasticity of residual demand for firm i ‘s output equals the Lerner index, which is formally given by,

illustration not visible in this excerpt

The Lerner index gives the relative profit margin of firm i and as the elas- ticity of demand reflects the degree of substitution possibilities it can be said, that prices converge to marginal costs the more consumers are able to substitute one good for another. Every firm in the industry is aware of the fact that any competitor is possibly loosing consumers as goods are substitutable and thus is the individual price level pi affected by the rivals strategies. There is a positive relation between marginal cost and product price, and when marginal cost are increased the price will also be higher in order to have the Lerner index to be equal to the inverse elasticity. A firm that observes higher prices for the goods of its rivals will find it opti- mal to raise its own price and to adjust its output to a higher level, which refers to the fact that prices are strategic complements. In order to adjust the output level, firms need to have flexible production capacities. And the firm will be able to serve a higher residual demand for a higher price as rival‘s product price is increased. The inverse effect occurs when a firm is able to lower the price for its product due to a newly developed technology, this decrease will cause the industry prices to adjust to a lower price level in equilibrium, which will been shown in further details next.

Consider first the case where consumers are indifferent of either buying from firm 1 or firm 2 thus the products are perfect substitutes and raise consumer‘s utility equally. The competing firms are identical with marginal cost of c and the firms are able to serve the entire demand, to be precise they are not capacity constrained[8] and in the short-run nature of the this model the possibility of market entry is excluded. The price level determines how much consumers will demand from the one or the other firm. When the goods are perfectly substitutable and the price happens to be equal across firms then either firm supplies half of the market demand by assumption. When prices differ across firms, consumers will only buy from the low-price firm and the demand that firm 1 is going to serve in any case is given by,

illustration not visible in this excerpt

while this schedule respectively provides the demand firm 2 faces. The Bertrand equilibrium[9] also known as the Nash equilibrium in prices, is given by,

illustration not visible in this excerpt

The main result of the Bertrand equilibrium is that two firms are enough for competition. The so-called Bertrand paradox yield that both firms charge a price equal to marginal cost and that the market is perfectly competitive with zero profit. The Bertrand paradox can be solved when firms produce differentiated products.

Next, suppose there are two Bertrand firms that are non-identical with firm 2 being the more efficient firm, c 1 > c 2. Both firms produce goods that are perfectly substitutable. According to Tirole (1989) there are two possible scenarios. First, consider the case where marginal cost of firm 1 is below firm 2‘s price that it would charge provided it can act like a monopolist, c 1 ≤ pm (c 2). Firm 2 can marginally undercut its rival by τ and charges pB 2 = c 1 − τ, while firm 1 charges pB 1 = c 1. Since the low cost firm will serve the entire market, firm 2 provides a quantity of, [illustration not visible in this excerpt] 1, which results in equilibrium profits of the two firms is given by,

illustration not visible in this excerpt

Secondly, consider the marginal cost of firm 1 to be higher than the monopoly price firm 2, that it would charge being the only supplier, c 1 > pm (c 2). Here firm 2 does not need to undercut firm 1. Firm 2 can charge the monopoly price since it is nevertheless the low cost firm and captures the uncontested monopoly profit. The Bertrand equilibrium profits in this case will be,

illustration not visible in this excerpt

Now reconsider an industry that provides imperfect substitutes[10] and let there be two competing firms in the market that obtain constant marginal cost of production. The profit function of firm 1 reads as follows,

illustration not visible in this excerpt

with demand not only depending on firm 1‘s price but also on firm 2‘s price. Since the two goods are imperfectly substitutable firm 1 may still serve some demand although it‘s price is higher. The optimal price firm 1 sets is depending on firm 2‘s price. Given that firm 2 charges p 2 firm 1 must find out in which way its own profit is affected by a change of its own price. The effects on profit that have to be taken into account by firm 1 when its price is increased by dp 1 become obvious in the following,

illustration not visible in this excerpt

where [illustration not visible in this excerpt] represents the raise in profits brought about by the con- sumers who still buy from firm 1. Consumers have to pay the new price that lies [illustration not visible in this excerpt] above the previous price charged per unit. The slope of the [illustration not visible in this excerpt] demand curve [illustration not visible in this excerpt] gives the rate of change in demand provided prices [illustration not visible in this excerpt] change. As [illustration not visible in this excerpt] 1 gives the total decrease in quantity resulting from the [illustration not visible in this excerpt] increase of the price by [illustration not visible in this excerpt] 1, the term [illustration not visible in this excerpt] tells firm 1 the loss in total profit. Dividing equation(2.12) by [illustration not visible in this excerpt]and setting it equal to zero gives the optimal price for firm 1,

illustration not visible in this excerpt

Note that this gives the best-response of firm 1 towards any price charged by firm 2. The Bertrand equilibrium with equilibrium prices denoted by pB 1 and pB 2 can be characterized by the following two equations,

illustration not visible in this excerpt

As both firms sell a positive output, prices that satisfy the above equality exceed marginal cots. In markets for imperfect substitutes firms are able to exercise market power although there is price competition. Accordingly to the above Cournot approach, market power can be measured by the Lerner index. Rearranging the best-response functions gives,

illustration not visible in this excerpt

with ε i as firm‘s own-price elasticity of demand. The elasticity of demand reflects the consumer‘s willingness to substitute, and if products are differ- entiated the willingness to substitute depends on the degree of differenti- ation. If the goods are close substitutes consumers are more likely to shift

demand towards the low-price firm, and for perfect substitutes the highprice firm remains with zero profits as it has been shown above. The result of the standard Bertrand equilibrium that prices are equal marginal costs holds independent of the number of firms in the market and is socially desirable. But as soon as goods become imperfect substitutes the Bertrand paradox is not obtained anymore.

3 Horizontal Mergers and the Effects on Quantities and Prices

It is common knowledge that mergers to monopoly are always profitable for the firms since the combined profits are maximized, see e.g. Salant et al. (1983). The industry structure and firm‘s objectives are crucial for the analysis of mergers. If there are no synergies resulting from the merger then the Cournot equilibrium exhibits higher prices as a result of less com- petition and a reduced aggregate output level after the merger. In Bertrand competition with firms producing differentiated products, a merger bene- fits either the merged entity and the remaining independent firms in the market, hence that there is an incentive to converge towards monopoly. As prices will rise after a merger the profits increase likewise. Note, that goods need to be differentiated by assumption otherwise the Bertrand paradox holds and prices equal marginal cost and no profits are to gain.

3.1 The Effect of a Merger within Bertrand competition

To examine the impact of merger formation on the equilibrium values, one has to be aware of several implications. The newly merged entity faces a different maximization problem than the separated firms have faced before the merger occurred. Additionally does the merger induce the non-merged firms to react, respectively to adjust to the new situation.


[1] See Financial Times Deutschland 09.11.2010: ”Mergers & Acquisitions - Von der Fusionitis anstecken lassen”.

[2] The Boston Consulting Group (2009).

[1] The historical Cournot model considers two firms that react optimally to its rivals in a dynamic model.

[2] Note that the elasticity of demand is almost always negative except for Giffen goods.

[3] See Kreps and Scheinkman (1983).

[4] Cournot equilibrium values are subscripted with C

[5] illustration not visible in this excerpt

[6] When identical firms charge identical prices and provide the same output the equilibrium is unique, see Tirole (1988).

[7] See Deneckere and Davidson (1985) among others.

[8] For further insights on capacity-constrained competition, see Kreps and Scheinkman (1983) among others.

[9] Bertrand equilibrium values are subscripted with B.

[10] According to Church and Ware (2000).

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Mergers and (uncertain) Synergies in Oligopoly
Humboldt-University of Berlin  (Wirtschaftstheorie II)
VWL - Mikroökonomie, Industrial Organization
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uncertain synergies, efficiency gains, mergers & acquisition, Industrial Organization, Bertrand competition, Cournot competition, horizontal mergers
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Kathrin Tiecke (Author), 2011, Mergers and (uncertain) Synergies in Oligopoly, Munich, GRIN Verlag,


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