Modelling mergers among polluting firms when environmental policy is endogenous

Economic Analysis and Policy 49 (2016) 1–6

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Modelling mergers among polluting firms when environmental policy is endogenous Mahelet G. Fikru Department of Economics, Missouri University of Science and Technology, 500 W 13th Street, Rolla MO 65409, USA

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Article history: Received 12 November 2014 Received in revised form 11 September 2015 Accepted 26 September 2015 Available online 30 September 2015 JEL classification: L Q34

abstract This article builds a theoretical model to study merger decisions among polluting firms. We adopt the idea of endogenous policies where governments adjust optimal policy after the occurrence of mergers. We find that the adjustment in policy provides additional incentives to merge. Given a specific model of merger process with endogenous policies, we find that the optimal merger is the one among highly polluting firms. Therefore, in the post-merger market the merged entity is dirtier compared to stand-alone firms. © 2015 Economic Society of Australia, Queensland. Published by Elsevier B.V. All rights reserved.

Keywords: End-of-the-pipe-type abatement Emission tax Pollution-intensity Cleaner technology

1. Introduction The literature on horizontal mergers has established that the primary motive for such deals is efficiency gain. Given two or more firms with different marginal cost of production, the acquisition of a high-cost firm by a low-cost firm would result in profitable mergers (Farrell and Shapiro, 1990; Levin, 1990; Barros, 1998; Collie, 2003; Qiu and Zhou, 2007). This is because, with no capacity constraints, the merged entity can shift production from the high-cost plant to the low-cost plant without changing total output. This article extends the discussion to firms producing a good with negative externality. We extend the horizontal merger model to polluting firms and address the following research question: What is the relationship between policies that regulate polluting firms and merger deals? Extending the merger theory to polluting firms is practical and has important policy implications for at least two reasons. First, evidences suggest that most of the merger deals take place among manufacturing firms, a majority of which contribute to pollution and greenhouse gas emissions. For instance, during 2009/2010 in Europe the value of mergers in pollutionintensive sectors identified by Hettige et al. (1995) accounted for about 80% of the value of deals and 81% of the volume of deals in the manufacturing sector (FactSet, 2010a). Another example is the USA in 2009 where among the top industries with the highest merger and acquisition (M&A) deal volume, M&As in polluting sectors accounted for over 55% of the total value of deals (FactSet, 2010b). This suggests that most of the M&As involve polluting firms, some with higher pollution than others. Therefore, one has to explicitly take into account pollution variables in the model of M&As. This study provides an introduction to integrating the ‘theory of M&A’ and the ‘theory of pollution’. Second, recent anecdotes suggest that manufacturing companies ought to be cautious of environmental liability when they purchase a competitor’s plant(s) (Gillston and Meyer, 2013). For example, there are many insurers that provide E-mail address: [email protected]. http://dx.doi.org/10.1016/j.eap.2015.09.002 0313-5926/© 2015 Economic Society of Australia, Queensland. Published by Elsevier B.V. All rights reserved.

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M.G. Fikru / Economic Analysis and Policy 49 (2016) 1–6

solutions to managing environmental risks that arise from acquiring ‘dirty’ plants (ACE Group Website, 2015). Furthermore, firms planning to make acquisition deals should evaluate the effect of environmental policy on those businesses they wish to acquire (Gehsmann and McCeney, 2009). Thus, merger theories that incorporate environmental policies and pollution parameters provide further insights on how merger incentives could be affected by pollution and resulting regulation affecting participating firms. In this article we use endogenous policies where governments adjust optimal policy after the occurrence of M&As. That is, optimal policies are sensitive to whether a merger has taken place or not; and pre-merger policies may differ from postmerger ones. Such endogeneity of policies has been discussed to some extent in theoretical environmental studies. For instance, Katsoulacos and Xepapadeas (1996) show that emission tax can be affected by a change in the number of firms in a sector. One possible cause for change in number of firms is consolidation through M&As. Barrett (1994b) argues that governments may lower emission tax for sectors with fewer firms to increase their competitiveness. Collie (2003) introduced endogenous trade policies to examine the effect of mergers on welfare. Similarly, Huck and Konard (2004) use endogenously determined trade policy to examine the profitability of mergers. With endogenous policies, we find that the adjustment in policy provides additional incentives to merge. Furthermore, our theoretical result suggests that, given a specific merger process, the highest incentive to merge is for firms with the highest pollution intensity in the industry. We also find that cleaner firms fair better when they remain independent than acquiring a dirtier firm. As a result in the post-merger market the merged entity (made up of highly polluting firms) is dirtier compared to stand-alone firms. The results obtained from this study have important policy implications. So far antitrust and industrial policies are determined independently from environmental factors and pollution issues. If highly-polluting firms have a significantly higher probability to merge as compared to less polluting firms in a given sector, then anti-trust agencies may find it useful to incorporate environmental criteria when accepting or rejecting merger proposals. In Section 2 we present a model of profit maximizing firms where asymmetries are introduced in terms of pollution intensity. In Section 3 we set up the endogenous policy model and study the incentive to merge. Section 4 endogenizes the merger decision to determine which of the firms, i.e., highly polluting or less polluting, actually engage in M&A at equilibrium. Section 5 concludes the discussion. 2. The model Following Lommerud and Sorgard (1997), Barros (1998), Fridolfsson and Stennek (2005a,b) and Kao and Menezes (2010) we introduce a Cournot triopoly industry where firms produce a homogeneous good. The economy is closed and all resources are fully employed. Demand for the good is linear and given by p = a − X where X = X1 + X2 + X3 , a represents the market size, Xi is the output level of firm i, i = 1, 2, 3, X is total output level and p is consumer price. All firms use an end-of-the-pipe-type abatement technology as in Lahiri and Symeonidis (2007) where initially production takes place producing gross pollution out of which the firm abates a certain amount whereas the rest is emitted. Each firm pays a per unit emission tax, t, for each unit of pollution it fails to abate. Firms incur cost of abating pollution, where the abatement cost function is assumed to be quadratic as in Barrett (1994a). Each firm’s abatement cost depends on its own abatement and no one else’s. g (Ai ) =

rA2i

(1)

2 Ai = θ (Xi ) − ei

(2)

θ (Xi ) = Zi Xi where Zi > 0

(3)

g (Ai ) is the abatement cost of firm i and fulfills g (Ai ) > 0 and g (Ai ) > 0. Ai is the abatement level of each firm, r is an efficiency parameter of the abatement technology and θ (Xi ) is gross pollution. Zi is pollution intensity and indicates how clean the production technology is. ei is emission level of each firm i. We assume Z1 > Z2 > Z3 where firms can be ranked according to their pollution intensity. Thus, firm 3 is the most clean firm whereas firm 1 is the most dirty firm in the given industry. The model involves two types of market distortions: oligopoly distortion where there is less competition and pollution distortion where there is disutility from emission. Environmental policies such as an emission tax are primarily designed to reduce the level of emission. On the other hand, the government would also like to reduce oligopoly distortion by providing a production subsidy. The objective of the production subsidy is to expand production without increasing consumer price. Governments pay production subsidies when consumers are not willing to pay a price that is high enough for a producer to recover costs. The production subsidy is assumed to be a specific subsidy, T , and the producer’s price is re-defined as the consumer price plus the subsidy, P = p + T , where P is the producer’s price and p is the consumer price (Keen and Lahiri, 1993). Similar to Salant et al. (1983) and Qiu and Zhou (2007) firms have identical marginal cost of production, c. The purpose of assuming identical and constant marginal cost is to control for merger incentives arising from more complex cost structures. Each firm i maximizes profit with respect to output and abatement level as follows ′

max πi = (P − c )Xi − Xi , Ai

rA2i 2

− tei .

′′

(4)

M.G. Fikru / Economic Analysis and Policy 49 (2016) 1–6

3

The first order profit maximizing conditions yield the following values (∗ indicates a value at equilibrium) 3 

a−c+T +t

− tZi

4 a + 3c − 3T + t

3 

(5)

Zi

i=1

p∗ =

(6)

4

πi∗ = (Xi∗ )2 + A∗i =

Zi

i =1

Xi∗ =

t r

t2

(7)

2r

.

(8)

As expected the subsidy increases production and reduces the market price. That is, dXi∗ /dT > 0 and dp∗ /dT < 0. Farrell and Shapiro (1990), Levin (1990), Fauli-Oller (2002) and Qiu and Zhou (2007) assume that asymmetry among firms is due to marginal cost of production. The asymmetries introduced in this study are in terms of pollution intensity (Zi ) and it is possible to express each firm’s effective marginal cost as c + tZi − T . Because marginal costs are assumed to be constant, a non-monopoly forming merger is followed by shutting down all plants except one where the merged entity operates (Qiu and Zhou, 2007). When a merger occurs among polluting firms, the resulting rationalization of production results in the shut down of a dirtier or cleaner plant. We assume that any two firms can decide to merge but merging to form a monopoly is prohibited as outlined by the US Merger Guidelines provided by the US Department of Justice and the Federal Trade Commission (1997). A non-monopoly forming merger changes the market structure from a triopoly to a duopoly. Suppose firm b (b for buyer) acquires firm s (s for seller), then the merged entity m (m for merged entity) uses either the cleaner or the dirtier technology. The merged entity and the outsider, o, (o for outsider) maximize respectively

πm = (Pm − c )Xm − πo = (Pm − c )Xo −

rA2j 2 rA2o 2

− tem where j = s or j = b − teo .

(9) (10)

The subscript j indicates the firm whose technology is used by firm m post-merger. Pm is the producer’s price in a duopoly market. The first order conditions yield p∗m = (a + 2c − 2T + tZo + tZj )/3 where p∗m > p∗ and Xm∗ = (a − c + T − 2tZj + tZo )/3, X0∗ = (a − c + T − 2tZ0 + tZj )/3. As in Salant et al. (1983) we find that the merged entity produces less than the sum of the independent firms, Xb∗ + Xs∗ > Xm∗ . Profit of the merged entity at equilibrium is πm∗ = (Xm∗ )2 + t 2 /2r. From πm∗ one can see that using the cleaner of the two plants, b or s, yields a higher profit for the merged entity, keeping other things constant. That is, profit will be higher for the merged entity if Zj is kept as low as possible. Because of this, it is in the best interest of the merged entity to continue production in the cleaner plant and shut down the relatively dirtier plant. Firms merge only if the merged entity’s profit is greater than the sum of the independent profits. Hence, the profitability of a merger is defined as

∆ = πm∗ − πb∗ − πs∗ .

(11)

Similarly, Salant et al. (1983) argued that ∆ represents the increase in joint profit when firms collude. Policy instruments such as an emission tax and production subsidy are not arbitrarily set, rather they are optimally chosen by maximizing a social welfare function. Welfare in the country is defined as the sum of consumer surplus, profits, revenue collected from emission tax less disutility from emission and subsidy. W =

1 2

X2 +

n  i=1

πi − TX + (t − ψ)

n 

ei

(12)

i =1

where n = 3 in a triopoly market and n = 2 in a duopoly market after a merger takes place. The marginal disutility of emission, ψ , is assumed to be constant and positive. 3. Incentives to merge with endogenous policy When policies are endogenous, they adjust when the market structure changes due to a merger (Katsoulacos and Xepapadeas, 1996; Barrett, 1994b). That is, pre-merger optimal policies are different from post-merger ones. Firms contemplating a merger take into account this induced change in optimal policies.

4

M.G. Fikru / Economic Analysis and Policy 49 (2016) 1–6 Table 1 Post-merger possibilities when relatively cleaner plants are used for production. Merging firms

Plant used post-merger

Shut-down plant

Post-merger policy ∗ tm

Tm∗

1 and 2

2

1

ψ[1 + 4r (Z2 − Z3 )2 ]

a−c 2

+

ψ(Z2 +Z3 ) r (Z2 −Z3 )2

2 and 3

3

2

ψ[1 + 4r (Z1 − Z3 )2 ]

a−c 2

+

ψ(Z3 +Z1 ) r (Z3 −Z1 )2

1

ψ[1 + (Z2 − Z3 ) ]

a−c 2

+

ψ(Z3 +Z2 ) r (Z3 −Z2 )2

1 and 3

3

r 4

2

4 4 4

[ [ [

2 2 2

− 1] − 1] − 1]

In the pre-merger market, the following optimal policies are obtained by maximizing welfare with respect to t and T respectively:

 t =ψ ∗

T∗ =

1+

a−c 3

2r

3 

9

ψ +



 Zi2

− Z1 Z2 − Z2 Z3 − Z3 Z1

(13)

i =1 3  i =1





Zi  2r

9

3 

Zi2

− Z1 Z2 − Z2 Z3 − Z3 Z1

i =1

  



 3

  − 1 . 

(14)

The optimal emission tax pre-merger is positive and primarily used to reduce emission. If Z1 = Z2 = Z3 , then the optimal emission tax is equal to the Pigovian tax, t ∗ = ψ . Thus, it is firm heterogeneity in terms of pollution intensity that causes deviation of emission tax from the Pigovian tax (Conrad, 1996; Fikru and Lahiri, 2013). For all positive output we find T ∗ > 0 which confirms that the government subsidizes consumption in order to reduce oligopoly distortion of ‘‘too little’’ consumption. Suppose firm b acquires firm s, then the government re-optimizes welfare where the new policies post-merger are calculated as:   r ∗ tm where j = s or j = b (15) = ψ 1 + (Zj − Zo )2 4   ψ(Zj + Zo ) r (Zj − Zo )2 a−c + −1 . (16) Tm∗ = 2 4 2 ∗ The optimal emission tax post-merger, tm , is positive whereas Tm∗ > 0 indicating a subsidy as before. Depending on which firms merge we have a total of three possible cases for the optimal policies. We rule out cases where the dirtier plant is used for production post-merger because as noted above this will reduce post-merger profits, keeping other factors constant. Table 1 presents the three cases. ∗ Irrespective of which firms merged, when the cleaner technology is used post-merger, we find that t ∗ > tm as long as there is sufficient gap between the pollution intensities of the three firms. For example if firm 2 buys firm 1 and uses the ∗ cleaner technology which belongs to firm 2, then t ∗ > tm as long as Z1 ≥ 1.12Z2 and Z2 ≥ 1.12Z3 hold. One possible ∗ explanation why t ∗ > tm holds may be because gross pollution is lower in the post-merger market compared to premerger levels, irrespective of which plant closes. Due to the resulting reduction in gross environmental impact, there is no need to penalize producers at a higher level. Furthermore, emission tax is uniform for all producers irrespective of their heterogeneity. ∗ Because t ∗ > tm firms in the duopoly market, including the merged entity, enjoy a lower emission tax incentive as compared to independent firms in a triopoly market. This endogenous reduction in emission penalty provides additional incentives for firms to merge. Comparing the optimal subsidies pre- and post-merger, we find Tm∗ > T ∗ for a large a. This is not a surprising result because the oligopoly distortion is higher post-merger. The higher subsidy the merged entity gets post-merger also may serve as an additional incentive to merge. We evaluate πm∗ using post-merger optimal policies and evaluate πs∗ and πb∗ using pre-merger optimal policies. Then we express ∆ as a quadratic function of the market size, a, and find conditions that make ∆ > 0.

∆(a) =



∗ ∗ Zj + t m Zo a − c + Tm∗ − 2tm

3

 −

∗

∗

∗

2

 −

a − c + T ∗ + t ∗ Z1 + t ∗ Z2 + t ∗ Z3 4

∗

a − c + T + t Z1 + t Z2 + t Z3 4

− t ∗ Zs

2 +

(tm∗ )2 2r

−

(t ∗ )2 r

− t ∗ Zb

2

(17)

where Tm∗ and T ∗ are functions of a where dTm∗ /da = 1/2 and dT ∗ /da = 1/3. Using chain rule, we find the following first and second order conditions: d∆(a) da

=

3Xm∗ − 2X1∗ − 2X2∗ 3

(18)

M.G. Fikru / Economic Analysis and Policy 49 (2016) 1–6

d2 ∆(a) da2

=

1 18

5

.

Because the second order condition is positive the ∆(a) function has a global minimum. This implies that ∆(a) > 0 as long as a > Max(0, aˆ ) where aˆ is the highest quadratic root of ∆(a). This condition shows that the proposed merger is profitable as long as the market size (a) is sufficiently large. One evident source of incentive to merge is the endogenous policy. Emission tax declines and subsidy increases after the merger takes place. Even though higher subsidy post-merger has a role in making the proposed merger a profitable one, we ∗ still get t ∗ > tm and ∆ > 0 even with T = 0. One implication of our result is that polluting firms may merge in anticipation of change in environmental policies. Gehsmann and McCeney (2009) argue that despite the difficulty in trying to fully anticipate changes in environmental regulation, firms should incorporate possible changes in regulation in their business deals including M&A decisions. For example, one reason for the recent lack of recovery of M&A activities in the oil and gas sector in the USA could be the impact of the new US energy regulation and the proposed cap-and-trade which makes valuation difficult (Energy M&A Forum, 2009). 4. The post-merger market with endogenous policy In this section we endogenize the merger decision to find which of the three firms have the highest incentive to merge. In other words, we study which of the three possibilities presented in Table 1 materializes. In this way, we study the resulting post-merger market and determine whether merged entities are highly polluting compared to outsiders. For example, if firm 2 acquires firm 1, and shuts down plant 1 the resulting merged entity is dirtier compared to the outsider, firm 3. If firm 3 and 2 merge and operate on firm 3, the merged entity is cleaner compared to the outsider, firm 1. If firm 3 and 1 merge to operate on firm 3, the merged entity is cleaner than the stand-alone firm 2. Previous studies have examined endogenously created mergers under different assumptions and processes. For example in Kamien and Zang (1990) each owner in a Cournot oligopoly market simultaneously announces a bid and ask price; each firm also takes into account that if it stays out of the merger deal, the others may merge. Gaudet and Salant (1992) generalize the Kamien–Zang model by including price competition. Horn and Persson (2001) treat the merger process as a cooperative game where the payoff for participants is assumed to be independent from action of outsiders. In Rodrigues (2001) a two stage game model is used to model endogenous mergers. In the first stage firms decide to merge or not by announcing sequentially whether they are available for merger or not; in the second stage remaining firms compete in the output market. We model the merger process as a simultaneous one-shot game. Firms play a two stage game and only one merger takes place. Forming a monopoly through a merger deal is prohibited. In the first stage, all three firms offer a bid to acquire other firms and set an ask price to offer their company for sale. As in Qiu and Zhou (2007) when two firm merge, only firms with a higher profit offer bids to buy out less performing firms. In our case, since π3 > π2 > π1 firm 1 is a potential seller, firm 2 can sell to firm 3 or buy out firm 1, and firms 3 is a potential buyer. Furthermore, as indicated before keeping Zj as low as possible will increase the merged entity’s profit post-merger. Hence, merged entities always seek to keep the cleaner technology. Firms who get offers can choose to either accept or reject the offer. If the offer is accepted the merger is formed, otherwise firms exist independently and no merger is formed. Eligible firms also simultaneously post a reservation price to sell their ownership to other firms. Reservation prices are set equal to profit the firm would earn as an independent entity in the pre-merger market. Sellers compare prices and accept the highest bid if and only if the offer is greater than their reservation price. Acquiring firms ensure that their bids are not too high so as to make their net profits post-merger negative. In the second stage the merged entity produces à la Cournot. We solve the model using backward induction. The maximum offer that a buyer b can give to a seller s can be expressed as Ob,s = πm∗ − πb∗

(19)

where Ob,s is the maximum possible offer that a buyer would give to its target. Acquiring firms are willing to offer as much as but not greater than the difference between the profit earned as a merged entity and what they would earn as independent firms. We evaluate all profits using optimal policies in the respective markets. That is, we use t ∗ and T ∗ to evaluate independent ∗ profits (π ∗ ) and post-merger policies, tm and Tm∗ , to evaluate profit of the merged entity (πm∗ ). We first compare O3,1 and O2,1 to determine whose offer firm 1 would accept. We express the difference in the two offers as a function of the market size, a as follows: k(a) = O2,1 − O3,1 = πm∗ ,2,1 − π2∗ − πm∗ ,3,1 + π3∗ k′ (a) = (Z2 − Z3 )



2 ∗ ∗ t − tm 3

(20)



k′′ (a) = 0 where πm∗ ,2,1 and πm∗ ,3,1 represent post-merger profit when firms 1 and 2 and firms 3 and 1 merge. k′ (a) > 0 as long as 36 r > . This condition ensures that abatement costs are not too low. 2 2 16Z1 (Z1 −Z2 )−11(Z2 −Z3 )−2Z3 (8Z1 −19Z2 )

6

M.G. Fikru / Economic Analysis and Policy 49 (2016) 1–6

Since the k(a) function has a positive slope for some reasonable conditions, we know that having a large enough a is sufficient to make k(a) > 0 and thus O2,1 > O3,1 . This means that firm 1 would accept firm 2’s but reject firm 3’s offer. Firm 1 is better-off by accepting 2’s offer than earning independent profit because O2,1 > π1∗ . As long as firm 2’s actual offer is slightly higher than O3,1 firm 1 will accept it because O3,1 > π1∗ . Firm 2 is better-off merging with firm 1 as compared to earning independent profit because πm∗ ,2,1 − actual offer > π2∗ , where O3,1 < actual offer < O2,1 . It is not in the best interest of firm 3 to offer a bid to buy firm 2. This is because, firm 3 can earn a higher profit being an outsider than offering to merge with firm 2. That is, π3∗,o > πm∗ ,3,2 − O3,2 . This may be because the optimal post-merger tax when firm 3 and 2 merge is not as low as the optimal post-merger tax when firm 2 buys 1. This implies the tax incentive, among other things, is not strong enough to attract firm 3 to buy 2. Thus, we find that if the merged entity’s choice is to use the cleanest of the two participating plant, the optimal merger is the one between firm 1 and firm 2. As a result, in the post-merger market, the merged entity is dirtier compared to the independent firm in the industry. 5. Conclusion This article extends the theory of horizontal mergers by examining merger incentives among polluting firms when policies are endogenous. Endogenous policies imply that governments change optimal policy when a merger takes place. We find that the change in optimal policy is favorable for firms contemplating M&As. This result implies that even though the primary target of environmental policies is to reduce pollution, they may have an additional effect on the market structure by influencing firm’s decision to engage in M&As. 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