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Economic integration and privatisation under diseconomies of scale
European Journal of Political Economy Vol. 21 (2005) 247 – 267 www.elsevier.com/locate/econbase
Economic integration and privatisation under diseconomies of scale Juan Carlos Ba´rcena-Ruiz, Marı´a Begon˜a Garzo´n * Departamento de Fundamentos del Ana´lisis Econo´mico, Universidad del Paı´s Vasco, Avenida Lehendakari Aguirre, 83 48015 Bilbao, Spain Received 14 February 2002; received in revised form 29 October 2003; accepted 23 February 2004 Available online 30 July 2004
Abstract In this paper we analyse whether it should be national governments that decide whether to privatise public firms (non-integration) or whether this decision should be delegated to a supranational authority (economic integration). We assume that two countries form a single market in which there is free trade and that each country has one public firm and n private firms. We show that, if the supra-national authority decides whether or not to privatise public firms, aggregated politically weighted welfare is no less than if the governments take this decision. We also show that aggregated politically weighted welfare is no less if the firms are owned by the governments rather than a supranational authority. D 2004 Elsevier B.V. All rights reserved. JEL classification: L33; Q28; F15 Keywords: International trade; Economic integration; Public firms; Privatisation
1. Introduction In the late 1980s there was a consensus in Western Europe in favour of a mixed economy including both public and private firms. Local and central governments created or purchase firms in a variety of sectors of the economy (including manufacturing and the service sector) for reasons that ranged from ideology to short-term strategic planning. As a result, EU governments own a significant percent-
* Corresponding author. Tel.: +34-94-601-38-15; fax: +34-94-601-37-99. E-mail addresses: [email protected] (J.C. Ba´rcena-Ruiz), [email protected] (M. Begon˜a Garzo´n). 0176-2680/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ejpoleco.2004.02.008
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age of the firms in the different sectors of industry in Europe.1 EU countries have subsequently privatised some of their public firms in recent years. In 1979 the United Kingdom privatised many of its public firms, and more privatisations, albeit on a smaller scale, followed in the rest of the then EC in the 1980s. In the 1990s the creation of the Single Market sparked further privatisation. However, in spite of this privatisation, no consensus was reached among EU governments regarding the number of firms in the different industries that should remain in public hands. Some governments favour going as far as possible with privatisation, while others prefer to continue with public ownership. At one extreme stands the UK, where most public firms have been privatised, and at the other stand Italy and Spain, where public ownership is still a major feature of many industries. The Treaty of Rome is neutral as regards public ownership of firms. This neutrality is the result of the EU’s having to accommodate within it the different levels of state ownership of firms and the different opinions of its member countries. The Treaty does not question the ownership of public firms, but it does indicate that all public sector intervention must be neutral in the sense that it must not affect competition within the Single Market. For instance, there is a ban on state aid that might distort competition between member countries. Parker (1998b, p. 23) argues that in spite of the neutral position maintained by the Treaty of Rome on public ownership, it has been recognised on some occasions that privatisation can be beneficial. For instance, in 1994 the European Commission indicated that the privatisation of public firms could, when governments deemed it compatible with their objectives, help to improve the competitive environment (European Commission, 1994, p. 11). In regard to this last question, it must be said that some countries are reluctant to privatise their state owned firms for fear that many will fall into foreign ownership.2 On the other hand, the individual governments are reluctant to transfer national sovereignty over public firms to Brussels (Parker, 1998b, p. 22). These arguments have led us to wonder from a theoretical viewpoint whether it is welfare-superior for each government to decide whether it privatises its public firms or for a supra-national body to be created that can decide whether to privatise public firms in different countries. For this latter case we also analyse whether ownership of these firms should be passed over to the supra-national authority. The literature that looks at the decision whether to privatise public firms usually considers only one country and one public firm (see for instance De Fraja and Delbono, 1989, 1990; White, 1996; Willner, 2001). This literature has been extended to privatisation decisions when there is international trade (see for instance Fjell and Pal, 1996; Pal and White, 1998), but the extensions continue to consider only one public firm, with firms
1
See, for instance, Parker (1998a) and McGowan (1993). Parker (1998b, p. 36) indicates that EU countries fear that the privatisation of their public firms will lead to a loss of national control over major industries, and that this has led some countries to limit the percentage of privatised firms that can be acquired by foreign investors. For instance in Belgium sales have usually taken place on the basis of a preselection of investors rather than through public share offers. In Spain, the privatisation processes staged in the 1980s involved the sale of minority share packages because the government did not wish to relinquish control of the firms involved. 2
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selling their products in a single country. The literature does not analyse whether it should be the government of each country or a supra-national authority that decides whether public firms in the different countries should be privatised. To consider this question, we consider two countries that form a single market in which there is free trade. Each country has one public firm and n private firms, which produce a homogeneous good with the same technology. If a public firm is owned by a government, its objective function is the politically weighted welfare or political benefit of that country, which includes the consumer and producer surpluses of the country. If the public firms are owned by a supra-national authority, the objective function is aggregate political benefit of the countries. We consider three possibilities: the first is that each public firm is owned by one government, which decides whether to privatise it or not (non-integration). In the second case there is a supra-national authority, which decides whether or not to privatise public firms, but these firms are owned by the governments (partial integration). In the third and final case there is a supra-national authority, which owns the public firms and decides whether these firms are privatised (full integration). For simplicity and in order to concentrate on whether or not the decision to privatise should be delegated to a supra-national authority, we do not here consider income other than profits of public firms within their countries, that can affect the decision whether to privatise (in this regard, see Willner, 1999). Nor do we consider decisions made by politicians to achieve political objectives (Boycko et al., 1996, analyse this question), the existence of economies of scale (see Estrin and de Meza, 1995), differentiation in the goods produced by the firms (see Cremer et al., 1991), the fact that public firms are directed by managers (this question is analysed by Barros, 1995; Willner and Parker, 2000; White, 2001), mergers between private and public firms (see Ba´rcena-Ruiz and Garzo´n, 2003), the regulation of public firms (see Bo¨s, 1998) or partial privatisation (see Matsumura, 1998). Comparing the non-integration and partial integration cases, when the consumer and producer surpluses have the same weight in political benefit, we find that, if the number of private firms is small enough, no public firm is privatised in either case (since market competition would be greatly reduced). Aggregate political benefit of the two countries would therefore be the same in both cases. If the number of private firms is large enough, aggregate political benefit is greater if countries integrate partially: under nonintegration the governments decide whether to privatise for strategic reasons, but under partial integration the supra-national authority decides whether or not to privatise for reasons of efficiency. As a result, aggregate political benefit is greater in the latter case than in the former. Under partial and full integration the decision whether to privatise is delegated to a supra-national authority. However, in the former case, the public firms are owned by the governments, while in the latter they are owned by the supra-national authority. A comparison of these two cases shows that if the number of private firms is small (high) enough, neither public firm is (both are) privatised, so aggregate political benefit is the same in both cases. When there is an intermediate number of private firms, that political benefit is greater under partial integration than under full integration. The intuition is that, in the latter case, the public firms are more aggressive (produce more) than in the former
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case (since their objective functions are aggregate political benefit), and this reduces producers’ surpluses excessively even though it increases the surplus of consumers. When consumer surplus has a greater weight than producer surplus in political benefit, aggregate political benefit is no less under partial integration than under non-integration. Under partial integration political benefit is also no less than under full integration since, in this last case, public firms are excessively aggressive. We also compare the marginal cost of the public firm with the market price. De Fraja and Delbono (1989) show, considering one public firm and one country, that the marginal cost of the public firm equals the market price. Fjell and Pal (1996), by considering that there are both domestic and foreign private firms, show that the marginal cost of the public firm exceeds the market price. We show that under non-integration the marginal cost of the public firm exceeds (equals) the market price if consumer surplus has a greater (the same) weight than producer surplus in political benefit. Under full integration, the marginal cost of the public firm is lower than the market price if and only if the weight of the consumer surplus in political benefit is low enough. The paper is organised as follows. Section 2 presents the model. Section 3 shows the results obtained under non-integration when the political weights are equal. Section 4 shows the results obtained under integration when the political weights are equal. Section 5 compares the results obtained in the preceding sections. Section 6 studies the case in which political weights differ. Conclusions are drawn in Section 7.
2. The model We consider a single market comprising two countries, A and B. In each country there is one public firm, denoted by 0, and n private firms (n z 1). All firms produce a homogeneous good. For simplicity, we assume that there is free trade, there are no transportation costs and there is no possibility of discriminating between consumers from different countries. Therefore, consumers in both countries can buy the product from either a domestic or a foreign firm. The public firm of each country can be privatised, and this decision can be taken by the governments or by a supra-national authority. Therefore, three cases arise. In the first case, each public firm is owned by a government, which decides whether to privatise (nonintegration). In the second case, there is a supra-national authority, which decides whether or not to privatise public firms, but firms are owned by the governments (partial integration). In these two cases, we assume that, if a public firm is privatised, it is acquired by domestic investors, so that there are then n + 1 private firms in that country.3 In the third case, there is a supra-national authority, which owns the public firms and decides whether to privatise (full integration). The inverse demand function for the product in country k is: p = a 2yk (k = A, B), where p is the price for the good in the world market and yk is the amount of the good sold 3
We consider this assumption since, as pointed out in ,Footnote 2, EU countries fear that the privatisation of their public firms will lead to a loss of national control over major industries (see Parker, 1998b, pp. 36 – 37). It can be shown that the main results of the paper hold if we permit public firms to be acquired by foreign investors.
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in country k. The X world inverse demand Xnfunction for the product is: p = a yA yB, where n yA þ yB ¼ qA0 þ q þ q þ q . Let qki denote the amount of the good that Ai B0 i¼1 i¼1 Bi the firm i located in country k, firm ki, sells in the single market (k = A, B; i = 0, 1,. . ., n). The consumer surplus in country k, denoted by CSk, is: CSk=( yk)2, k = A, B. As is usually assumed in literature on mixed oligopoly (see, for example, De Fraja and Delbono, 1989, 1990), firms have the same technology, represented by the following cost function: C( qki)=( qki)2, k = A, B; i = 0,. . ., n.4 The profit function of firm ki is: pki ¼
a qA0
n X j¼1
qAj qB0
n X
! qBj qki q2ki ; i ¼ 0; . . . ; n; k ¼ A; B
ð1Þ
j¼1
We consider governments as seeking to maximize politically weighted welfare or political benefit. The objective function of government k includes Xn consumer surplus CSk and producer surplus in country k, PSk. The latter is PSk ¼ p . We use a linear i¼0 ki function for political benefit:5 Wk ¼ aCSk þ PSk ; 1Va < 2; k ¼ A; B:
ð2Þ
We propose a three stage game with the following timing. In the first stage, the decision is whether public firms should be privatised by governments or a supra-national authority. In the second stage, under non-integration, the two governments decide simultaneously whether to privatise their public firms; under economic integration, the supra-national authority decides whether to privatise the two public firms, only one of them or neither of them. In the third stage, each firm decides its output level. We solve the game by backward induction to obtain a subgame perfect Nash equilibrium.
3. Non-integration In this section we assume that each government decides whether to privatise its public firm. Given that there are two public firms that can be privatised, one in each country, there are four subgames that, by symmetry, can be reduced to three. These three subgames are the following: neither of the governments privatises (denoted by superscript NN), each government privatises (denoted by superscript PP), and one government does not privatise while the other government does; in this last case, we use the superscript NP to denote the country that does not privatise and the superscript PN to denote the other. Next we analyse each of the different subgames. 4 It can be shown that if the cost function is given by C( qki) = c( qki)2, the main results of the paper hold; i. e. the results of the paper are robust to changes in parameter c. 5 We assume that a < 2 to ensure that private firms produce a positive output level. We consider that a z 1 to ensure that the consumer surplus has a weight that is no less than the producer surplus in political benefit (see also Matsumura, 1998). If a < 1 our results can change and ‘‘non-realistic’’ equilibria can arise, since the ‘‘excessively low’’ weight of the consumer surplus distortions the objective function of public firms.
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3.1. Neither government privatises In the third stage of the game, the private firm ki chooses the output level, qki, that maximizes its profit function; the public firm 0 owned by government k chooses the output level, qk0, that maximizes its political benefit. Then: Lemma 1 . Under non-integration, when neither government privatises, the output level of firms, the consumer surplus, the profit of firms, the producer surplus and the political benefit in each country are, respectively: qNN 0 ¼
að3 nð1 aÞÞ að3 aÞ ; qNN ; ¼ i 15 þ 4n 3a 15 þ 4n 3a
CSNN ¼ pNN 0 ¼ PSNN ¼ W NN ¼
a2 ð3 þ 2nÞ2 ð15 þ 4n 3aÞ
; pNN ¼ i 2
2a2 ð3 aÞ2 ð15 þ 4n 3aÞ2
a2 ð3 n þ naÞð6 þ n 3a naÞ ð15 þ 4n 3aÞ2
;
;
a2 ð9ð2 aÞ n2 ð1 aÞ2 þ nð15 6a a2 ÞÞ ð15 þ 4n 3aÞ2 a2 ð18 þ nð15 þ 6a a2 Þ n2 ð1 6a þ a2 ÞÞ ð15 þ 4n 3aÞ2
;
; i ¼ 1; . . . ; n
ð3Þ
Using the output levels obtained in Lemma 1, we can compare the market price and the marginal cost of the public firm. We show the result in the following lemma. Lemma 2. Under non-integration, when neither government privatises, the marginal cost of the public firm equals the market price if and only if a = 1. The marginal cost of the public firm exceeds the market price if 1 < a < 2. This lemma shows that the marginal cost of the public firm equals the market price if the consumer and producer surpluses have the same weight in political benefit (a = 1). If a = 1, each public firm chooses the output level that maximises the political benefit of its government, taking into account that the consumer surplus has the same weight as the producer surplus in political benefit.6 6 Given the symmetry existing in this case, we obtain the same result as De Fraja and Delbono (1989) although we consider that there are two public firms instead of one. When the political weights differ, we find that the marginal cost of the public firm exceeds the market price. This result is also obtained by Fjell and Pal (1996) considering an industry with one public firm, m domestic private firms and n foreign private firms. In their model, for a given amount of total private firms’ output, the output level of the public firm is greater if some output comes from foreign firms, since foreign firms’ profit is not included in political benefit; therefore the producer (consumer) surplus has a lower (greater) weight in political benefit. As a result, they obtain that the public firm’s marginal cost equals the price only if n = 0. In our paper, when a increases, the output level of the public firms increases since the weight of the consumer surplus is greater; as a result, the marginal cost of the public firms exceeds the price.
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3.2. Only one government privatises Suppose that firm 0 in country A is sold to domestic investors. At the third stage, each of the 2n + 1 private firms chooses the profit-maximising output level, while qB0 maximises government B’s political benefit function. Then: Lemma 3. Under non-integration, when only one government privatises, the output level of firms, the consumer surplus, the profit of firms, the producer surplus and the political benefit in each country are, respectively: qNP 0 ¼
að6 2nð1 aÞ þ aÞ að6 aÞ PN ; qNP ; i ¼ qj ¼ 30 þ 10n 3a 30 þ 10n 3a
CSNP ¼ CSPN ¼ pNP 0 ¼
a2 ð6 þ 5nÞ2 ð30 þ 10n 3aÞ2
;
2a2 ð6 þ n 2a naÞð6 2n þ a þ 2naÞ ð30 þ 10n 3aÞ2
PN pNP i ¼ pj ¼
PSNP ¼
W PN ¼
ð30 þ 10n 3aÞ2
;
2a2 ð2ð18 3a a2 Þ þ nð30 a 4a2 Þ 2n2 ð1 aÞ2 Þ ð30 þ 10n 3aÞ2
PSPN ¼ W NP ¼
2a2 ð6 aÞ2
;
2a2 ð1 þ nÞð6 aÞ2 ð30 þ 10n 3aÞ2
;
;
a2 ð4ð18 þ 6a a2 Þ þ nð60 þ 58a 8a2 Þ n2 ð4 33a þ 4a2 ÞÞ ð30 þ 10n 3aÞ2 a2 ð2ð36 þ 6a þ a2 Þ þ 2nð36 þ 18a þ a2 Þ þ 25n2 aÞ ð30 þ 10n 3aÞ2
i ¼ 1; . . . ; n; j ¼ 0; . . . ; n:
;
; ð4Þ
If one public firm is privatised, it reduces its output level ( q0PN < q0NN), since its objective function is now its profit. But this reduction in output is not compensated by a sufficient variation in the output level of the other public firm ( q0PN + q0NP < 2 q0NN), since the objective function of the latter comprises only the political benefit of its country. As a result, the industry output level decreases after the privatisation of a public firm. In this PN case, p0NP>pNP i = pj if and only if a < ((6 + 2n)/(3 + 2n)); as market competition decreases following privatisation, the profit of the public firm increases more than the profit of the private firms if the parameter a is low enough, since the weight of the consumer surplus in social welfare is low enough.
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Lemma 4. Under non-integration, when only one government privatises, the marginal cost of the public firm is lower than the market price if and only if a < a*, where a*< ((6 + 4n)/(5 + 4n)), 1 < a*< 2. This lemma shows that the market price is greater than the marginal cost of the public firm if the parameter a is low enough (a < a*). This is due to the fact that when one public firm is privatised, that firm reduces its production, which is not compensated by a sufficient variation in the output level of the other public firm, so the output of industry decreases after privatisation. If a is high enough (a z a*), as the output level of the public firm increases with a, the reduction in the output level of the privatised firm is compensated by a sufficient variation in the output level of the other public firm. Therefore, in this last case the marginal cost of the public firm exceeds the price. 3.3. The two governments privatise In this case, each government privatises its public firm, which is acquired by domestic investors. Therefore, in each country there are n + 1 private firms. Each private firm chooses the output level that maximizes its profit function. Then: Lemma 5. Under non-integration, when the two governments privatise, the output level of firms, the consumer surplus, the profit of firms, the producer surplus and the political benefit in each country are, respectively: qPP i ¼
a a2 ð1 þ nÞ2 PP 2a2 ; CSPP ¼ ; pi ¼ ; 2 5 þ 2n ð5 þ 2nÞ ð5 þ 2nÞ2
PSPP ¼
2a2 ðn þ 1Þ ð5 þ 2nÞ2
; W PP ¼
a2 ðn þ 1Þð2 þ a þ naÞ ð5 þ 2nÞ2
; i ¼ 0; . . . ; n:
ð5Þ
Once we have solved the different subgames, we proceed to solve stage two. We analyse first the case in which the consumer and the producer surpluses have the same weight in political benefit (a = 1). Next, in Section 6, we shall study whether the results are robust to changes in parameter a. 3.4. The decision by the governments whether to privatise By using Lemmas 1, 3 and 5 we can compare the consumer and producer surpluses obtained in the different subgames when a = 1. This comparison is useful for studying the decision by governments whether to privatise. Lemma 6. Under non-integration, CSNN>CSNP = CSPN>CSPP and PSPP>PSNP>PSPN >PSNN. Given that each public firm chooses the output level that maximizes the political benefit of its government, it is more aggressive in the product market than private firms (i.e. its output level is greater). As a result, the highest industry output level is obtained when there
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are two public firms in the market and the lowest industry output level is obtained when all firms are private. Therefore, as the consumer surplus increases with industry output level, we obtain that CSNN>CSNP = CSPN>CSPP. The lowest (greatest) producer surplus is obtained when there are two (no) public firms in the market since the greatest (lowest) industry output level is obtained in that case. When only one government privatises, the producer surplus takes an intermediate value. As we saw in Lemma 3, q0NN>q0PN and 2q0NN>q0PN + q0NP. As a result, the level of industry output decreases after the privatisation of one public firm. Thus, producer surplus is lower when there are two public firms than when there is only one and, in this last case, producer surplus is lower than when all firms are private. When there is only one public firm in the market, producer surplus is greater in the country that owns that firm (PSNP>PSPN) since, as we saw in Lemma 3, when a = 1, the public firm makes a greater profit than the private PN firms (p0NP>pNP i = pj ). Next we solve the second stage of the game under non-integration. The following result is obtained. Proposition 1. Under non-integration, if n>na only one government privatises while if n V na neither government privatises, where na = 13.0316. 2
2
ð369þ102n10n Þ , which is Proof. From Lemmas 1, 3 and 5 we obtain that W NN W PN ¼ a8ð3þnÞ 2 ð27þ10nÞ2 positive if and only if n < na = 13.0316. Therefore, if one government does not privatise, the other government privatises (does not privatise) if n >na (n V na). On the other hand, a2 ð113þ54nþ4n2 Þ W NP W PP ¼ ð5þ2nÞ , which is positive for all n. Thus, if one government privatises 2 ð27þ10nÞ2 the other government does not privatise. 5
We consider first the decision taken by one government when the other government does not privatise. When parameter n is great enough (n >na), if one government does not privatise the other government privatises (W PN >W NN). In this case, the producer surplus has a greater weight than the consumer surplus in political benefit since the competition in the product market is high enough (and CSNN>CSPN while PSNN < PSPN). When n is low enough (n V na), if one government does not privatise nor does the other (W NN >W PN). In this case, consumer surplus has a greater weight than producer surplus in political benefit since the competition in the product market is low enough. The decision taken by one government when the other government privatises remains to be analysed. In this case, independently of n, when one government privatises, the other government does not (W NP>W PP). Lemma 6 shows that, when there is only one public firm in the market, the strategic behaviour of the public firm results in greater producer surplus in the country that owns that firm (PSNP>PSPN). This implies that, although PSNP is lower than PSPP, the difference between PSNP and PSPP is small. On the other hand, CSNP is greater than CSPP and the difference between CSNP and CSPP is great since the strategic behaviour of the public firm affects the consumer surplus of both countries equally. Thus, the difference between CSNP and CSPP is greater than the difference between PSPP and PSNP. As a result of the preceding arguments, we find that, when n is low enough (n V na), neither government privatises its public firm. When n is high enough (n>na), only one government privatises, and therefore there are two equilibria; in this case, the government
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that does not privatise has greater political benefit than the other government, but both governments are better off than if neither public firm is privatised. It must be noted that, in this case, firms are never both privatised.7
4. Economic integration In this section we assume that there is a supra-national authority. We consider two types of economic integration: partial and full. 4.1. Partial integration Under partial integration a supra-national authority decides whether public firms are privatised, but the firms are owned by governments. In this case, when a = 1, the following result is obtained. Proposition 2. Under partial integration, if nc < n the supra-national authority privatises both public firms; if nb < n V nc the supra-national authority privatises only one; and if n V nb neither firm is privatised, where nb = 1.5917 and nc = 1.8364.8 2
2
ð153þ42nþ34n Þ Proof. From Lemmas 1, 3 and 5 we obtain that W NP þ W PN 2W NN ¼ a4ð3þnÞ , 2 ð27þ10nÞ2 2
2
4a ð19þ3nþ4n Þ , which is positive if and only if n>nb = 1.5917; 2W PP W NP þ W PN ¼ ð5þ2nÞ 2 ð27þ10nÞ2 2
2
a ð9þ2nþ2n Þ , which is which is positive if and only if n>nc = 1.8364; 2W PP 2W NN ¼ 4ð3þnÞ 2 ð5þ2nÞ2 positive if and only if n>nd = 1.6794. 5
The intuition underlying this result is the following. When the number of private firms is low enough (n V nb), as the competition in the product market is also low enough, the privatisation of either of the public firms causes a reduction in the consumer surplus that is greater than the increase in the producer surplus. Thus, in this case neither public firm is privatised by the supra-national authority. When n is great enough (n>nc), the competition in the product market is also great enough, and thus both public firms are privatised, since the reduction in the consumer surplus is compensated by an increase in the producer surplus. As a result, in this case the supra-national authority privatises both public firms. When the number of private firms takes an intermediate value (nb < n V nc) the supranational authority privatises only one public firm. Under partial integration, although it is the supra-national authority that decides whether to privatise public firms, these firms are owned by governments; thus, each public firm maximizes the political benefit of its government. This means, as we have seen in Lemma 3, that, if one public firm is 7 The result obtained here is different from that obtained by De Fraja and Delbono (1989). They consider only one country and one public firm, so they cannot obtain the result in which only one public firm is privatised since this result is driven by strategic reasons. 8 To obtain this proposition, we assume that firms have the following cost function: C( qki) = c( qki)2, where c = 1. In this case, the supranational authority privatises only one public firm if nb = 1.5917 < n V nc = 1.8364; in this zone, n is not an integer. However, there exist values of parameter c such that in the zone in which the supranational authority privatises only one public firm, n is an integer. For example, if c = 3/7, then nb = 1.0270 < n V nc = 2.099.
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privatised, the reduction in its output level is not compensated by a sufficient increase in the output level of the other public firm (since its objective function comprises only the political benefit of its country).9 In this interval, although the consumer surplus decreases after the privatisation of one public firm, this reduction is compensated by an increase in the producer surplus (since, as we have seen in Lemma 3, the profit of the public firm rises). This means that, when the number of private firms takes an intermediate value, only one public firm is privatised by the supra-national authority. It has to be noted that, as the two countries are identical, either of the two public firms could be privatised. 4.2. Full integration Under full integration there is a supra-national authority which owns the public firms and decides whether they are privatised. If neither public firm is privatised, the two public firms choose the output level that maximises the aggregate political benefit of the two governments. In this case, if a = 1, we obtain the following result. Lemma 7. Under full integration, when neither government privatises, the output level of the firms, the consumer surplus, the profit of the firms, the producer surplus and political benefit in each country are, respectively: qNN 0 ¼
að3 2nð1 aÞÞ að2 aÞ ; qNN ; ¼ i 18 þ 4n 6a 9 þ 2n 3a
CSNN ¼ pNN 0 ¼
a2 ð3 þ 2nÞ2 4ð9 þ 2n 3aÞ
; pNN ¼ i 2
2a2 ð2 aÞ2 ð9 þ 2n 3aÞ2
;
a2 ð27 18a 4nðn þ 3Þð1 aÞ2 Þ
PSNN ¼ W NN ¼
4ð9 þ 2n 3aÞ2 a2 ð27 18a þ 4nð5 2a a2 Þ 4n2 ð1 aÞ2 Þ 4ð9 þ 2n 3aÞ2
;
a2 ð9ð3 aÞ þ 4nð5 þ a a2 Þ 4n2 ð1 3a þ a2 ÞÞ 2ð9 þ 2n 3aÞ2
; i ¼ 1; . . . ; n:
ð6Þ
If both public firms are privatised, we obtain the same result as in Lemma 5, since all firms are private. Finally, if there is only one public firm, it chooses the output level that maximises the aggregate political benefit of the two countries. In this case, we obtain the following result.10 9 NN In fact, under partial integration, qNP if and only if n < 1.5. If the objective function of the public 0 >q0 firm is the aggregate political benefit of the two countries, when one public firm is privatised the other public firm increases its output level (as much as possible) to compensate for the reduction in the output level of the privatised firm. 10 When a = 1, we consider the same model as De Fraja and Delbono (1989), since they assume only one country and one public firm.
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Lemma 8. Under full integration, when only one government privatises, the output level of firms, the consumer surplus in each country, the profit of firms, the aggregate producer surplus and the aggregate political benefit are, respectively: qNP 0 ¼
að2 þ a 2nð1 aÞÞ að3 aÞ PN ; qNP ; i ¼ qj ¼ 14 þ 4n 3a 14 þ 4n 3a
CSNP ¼ CSPN ¼ pNP 0 ¼
a2 ð5 þ 4nÞ2 4ð14 þ 4n 3aÞ2
;
a2 ð2 2n þ a þ 2naÞð7 þ 2n 4a 2naÞ
PN pNP i ¼ pj ¼
ð24 þ 4n 3aÞ2 2a2 ð3 aÞ2 ð14 þ 4n 3aÞ2
PSNP þ PSPN ¼ W NP þ W PN ¼
;
; i ¼ 1; . . . ; n; j ¼ 0; . . . ; n;
a2 ð32 13a 2a2 þ nð26 4a 6a2 Þ 4n2 ð1 a2 Þ ð14 þ 4n 3aÞ2
;
a2 ð64 a 4a2 þ 4nð13 þ 8a 3a2 Þ 8n2 ð1 4a þ a2 ÞÞ 2ð14 þ 4n 3aÞ2
:
ð7Þ
We analyse first the case in which the consumer and the producer surpluses have the same weight in political benefit (a = 1). In Section 6 we shall study whether the results are robust to changes in parameter a. Proposition 3. Under full integration, if n>nd the supra-national authority privatises both public firms while if n V nd neither of them is privatised, where nd = 1.6794. 2
2
a ð27þ2nþ4n Þ , Proof. From Lemmas 5, 7 and 8 we obtain that W NP þ W PN 2W NN ¼ 4ð3þnÞ 2 ð11þ4nÞ2 2
2
ð23þ12nþ8n Þ which is positive if and only if n>n/ = 2.3600; 2W PP W NP þ W PN ¼ a2ð5þ2nÞ , 2 ð11þ4nÞ2 2
2
a ð9þ2nþ2n Þ which is positive if and only if n>nh = 1.1040; 2W PP 2W NN ¼ 4ð3þnÞ , which is 2 ð5þ2nÞ2 positive if and only if n>nd = 1.6794. 5
The difference between partial and full integration is that in the latter case public firms choose the output level that maximises the aggregate political benefit of the two countries, while in the former case each public firm chooses the output level that maximizes the political benefit of its government. Thus, when only one public firm is privatised, under full integration the other public firm increases its output level (as much as possible) to compensate for the reduction in the output level of the privatised firm;11 under partial integration the other public firm behaves strategically and, thus, its output level is lower than under full integration. If the supra-national authority privatises only one public firm, the privatised firm reduces its output level, while the other public firm increases its output level. However, 11
NN It can be shown that, under full integration, qNP 0 >q0 for all n.
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although the objective function of the public firm is the aggregate political benefit, this last firm cannot increase its output level enough to compensate for the reduction in the output of the industry, since its production costs are quadratic. Moreover, given that the production costs are quadratic, it is cheaper to produce a given output level using two public firms than using one. Therefore, the supra-national authority never privatises only one public firm. As a result of the preceding arguments, when the parameter n is low enough (n V nd), neither public firm is privatised. However, if n>nd, the supra-national authority privatises both firms since competition in the product market is great enough.
5. Comparison between the three types of integration when political weights are equal In this section we solve the first stage of the game. Comparing the aggregate political benefit in the three types of integration, we obtain the following results. Proposition 4. When political weights are equal, the aggregate political benefit under partial integration is no less than under non-integration. This proposition states that non-integration is (weakly) dominated by partial integration. By comparing Propositions 1 and 2, we find that, if n V nb, the aggregate political benefit is the same under partial integration as under non-integration, since in both cases neither public firm is privatised. When n>nb, under non-integration, the governments decide, for strategic reasons, whether their public firms are privatised or not. However, under partial integration there is a supra-national authority that decides, for reasons of efficiency, whether the public firms are privatised. As a result, if n >nb, aggregate political benefit is greater under partial integration than under non-integration, and the political benefit of each government could increase if the decision regarding privatisation were delegated to a supra-national authority. If nb < n V nc, under partial integration only one public firm is privatised, while under non-integration neither of them is privatised, and aggregate political benefit is greater in the first case. In this interval, under non-integration, given that the country that privatises obtains a lower political benefit than the other country (W NN >W PN ), neither of the two governments wants to privatise. Under partial integration, given that n takes an intermediate value, the supra-national authority privatises only one public firm. As in this interval W NP >W NN > W PN, the country that privatises would prefer not to delegate the decision whether to privatise to a supra-national authority (this country would prefer not to privatise). But, as W NP + W PN > 2W NN, the country that privatises could be compensated by the other country by way of a monetary transference, and both countries would obtain greater political benefit under partial integration than under non-integration. If nc < n V na, under partial integration both public firms are privatised, while under nonintegration neither of them is privatised, and the aggregate political benefit is greater in the first case. In this interval, as W NN < W PP, the two governments obtain a greater political profit by delegating the decision whether to privatise to a supra-national authority. Finally, when n>na, under partial integration both public firms are privatised while under non-integration only one is, and aggregate political benefit is greater in the first
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case. In this interval W NP > W PP and, thus, the government that owns the public firm would not want to privatise it. But, as W NP + W PN < 2W PP, this government could be compensated by the other government by way of a monetary transference, and both countries would obtain a greater political benefit under partial integration than under non-integration. Now that we have compared non-integration and partial integration, let us compare partial and full integration. Proposition 5. When political weights are equal, aggregate political benefit under partial integration is no less than under full integration.12 This proposition states that full integration is (weakly) dominated by partial integration. By comparing Propositions 2 and 3, we find that, if n V nb, aggregate political benefit is the same in both cases, since in neither case is either public firm privatised. Given that consumer surplus has the same weight as producer surplus in political benefit and that there are no asymmetries in the model,13 the output levels of both the public firms and the private firms (and, thus, the consumer and producer surpluses) are the same under partial and full integration. If n>nc, both public firms are privatised in both cases and, thus, the aggregate political benefit is also the same. It only remains to compare the two types of integration in the interval nb < n V nc. In this interval, as Proposition 2 shows, under partial integration only one public firm is privatised since the aggregate political benefit is greater than if the two public firms are privatised or if neither of them is privatised. In this interval, under full integration, the supra-national authority privatises both public firms (if nd < n V nc) or neither of them (if nb < n V nd). And it must be noted that when there are two public firms in the market, aggregate political benefit is the same in the two types of economic integration; if all firms are private, the same aggregate political benefit is also obtained in both cases. Therefore, in this interval, partial integration generates a greater aggregate political benefit than full integration.14 In the interval nb < n V nd, under full integration neither public firm is privatised while under partial integration only one public firm is privatised. If neither public 12 If we allow partial privatisation of public firms (see Matsumura, 1998; Ba´rcena-Ruiz and Garzo´n, 2003), the supra-national authority would choose the percentage of the shares of the public firms that is held by governments (under partial integration) or by the supranational authority (under full integration). In both cases, the supra-national authority chooses partially to privatise public firms (and, thus, we have semi-public firms). There is a greater aggregate political benefit under full integration than under partial integration since, in the first case, the supra-national authority can choose the level of ‘‘aggressiveness’’ of the public firms by choosing the percentage of the shares of the public firms that it wants to hold (the lower this percentage is, the lower the output level of the semi-public firms). 13 When consumer surplus has a different weight than producer surplus in political benefit, aggregate political benefit is different under partial and full integration. 14 An alternative explanation for this result is the following. In the interval nb < n V nc, if there are two public firms in the market, as under full integration these firms maximise aggregate political benefit, the competition in the product market is excessively high. In this interval, if the two public firms are privatised, under full integration the competition in the product market is excessively low. Under partial integration, in this interval, as the supranational authority privatises only one public firm and the other public firm maximises the political benefit of its government, the competition in the product market takes an intermediate level. Therefore, in this interval, a greater aggregate political benefit is obtained under partial integration than under full integration.
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firm is privatised, the same aggregate political benefit is obtained under full and partial integration. In this last type of integration, when only one government privatises, the aggregate political benefit is greater than if neither government privatises (W NP + W PN >2W NN ). However, when only one government privatises, this government obtains a lower political benefit than if neither government privatises (W PN < W NN). But, as W NP + W PN >2W NN, the government that privatises could be compensated by the other government by way of a monetary transference, and both countries would obtain a greater political benefit under partial integration than under full integration. In the interval nd < n V nc, under full integration both public firms are privatised while under partial integration only one public firm is privatised. It must be noted that if both public firms are privatised the same aggregate political benefit is obtained under full and partial integration. In this last type of integration, if there is one public firm in the market the aggregate political benefit is greater than if all firms are private (W NP + W PN>2W PP). However, if there is only one public firm in the market, the government that does not own the public firm obtains a lower political benefit than if all firms are private (W PN < W PP). But, as W NP + W PN>2W PP, both countries would obtain a greater political benefit under partial integration than under full integration if the government that does not own the public firm is compensated by the other government by way of a monetary transference. By using Propositions 4 and 5, we can solve the first stage of the model when the consumer surplus has the same weight as the producer surplus in political profit. We obtain the following result. Proposition 6. When political weights are equal, the decision whether to privatise the public firms is delegated to a supra-national authority, but the ownership of the public firms is held by governments. Next we consider that the weights attached to the arguments of political benefit are different, in order to analyse whether the results obtained in the preceding sections are robust to changes in the parameter a.
6. Non-integration, partial integration and full integration when political weights differ When political weights differ, under non-integration neither government privatises its public firm if n V nNI1 (zones I and IV in Fig. 1). Only one government privatises if nNI1 < n V nNI2 (zone II in Fig. 1). Finally, both governments privatise if n>max{nNI1, nNI2} (zone III in Fig. 1). The values of nNI1 and nNI2 are collected in Appendix A. When a = 1 (see Proposition 1), given that consumer surplus has the same weight as producer surplus in political benefit, competition in the product market is never high enough for both public firms to be privatised. However, when a>1, both governments privatise if n is high enough, for a given value of a (zone III in Fig. 1). In this case, the weight of producer surplus in political benefit is sufficiently greater than that of consumer surplus and the competition in the product market is high enough for both public firms to be privatised. In zone II, only one government privatises. In zones I and IV of Fig. 1 neither government privatises its public firm since competition in the product market is low enough for all a.
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Fig. 1. Non-integration when political weights differ.
Under partial integration neither public firm is privatised if n V nPI1; the supra-national authority privatises only one if nPI1 < n V nPI3; finally, the supra-national authority privatises both of them if n>nPI3. The values of nPIi (i = 1, 3) are collected in Appendix A. The intuition underlying this result is the same as in Proposition 2. For a given value of a, when the number of private firms increases competition in the product market also increases; thus, if n is low enough neither public firm is privatised, if n takes an intermediate value only one is privatised and if n is large enough both are privatised. Under full integration neither of the public firms is privatised if n V nFI2, whereas the supra-national authority privatises both of them if n>nFI2. The value of nFI2 is shown in Appendix A. The intuition underlying this result is the same as in Proposition 3. Given that the production costs are quadratic, it is cheaper to produce a given output level using two public firms than using one. Therefore, the supra-national authority never privatises only one public firm: it privatises either both or neither. After analysing the three types of integration when political weights differ, we compare them in order to study whether the results obtained in Section 5 are robust to changes in parameter a. We obtain the following result. Proposition 7. When political weights differ, aggregate political benefit under partial integration is no less than under full integration and non-integration. We saw in Section 5 that when a = 1, aggregate political benefit is greater or equal under partial integration than under non-integration. This result is also obtained when a>1, since
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under partial integration there is a supra-national authority, which decides, for reasons of efficiency, whether public firms are privatised. Under non-integration, the government of each country decides, for strategic reasons, whether its public firm is privatised or not. When a = 1, aggregate political benefit is no less under partial integration than under full integration. This result is also obtained when a>1. When a and n are such that the supranational authority privatises both public firms, aggregate political benefit is the same under partial and full integration, since private firms produce the same output level in both cases. When a and n are such that the supra-national authority does not privatise either public firm, aggregate political benefit is greater under partial integration. When a>1, the output level of the public firms is greater under full integration, since public firms are much more aggressive in this case (when a = 1 aggregate political benefit is the same due to the symmetry of the model). When a and n are such that different equilibria are obtained in the two cases, aggregate political benefit is greater under partial integration, since, given that the objective function of public firms is aggregate political benefit, these firms are very aggressive in the product market and, thus, competition in the product market is very high.
7. Conclusions The literature on mixed oligopoly does not analyse whether governments want to delegate the decision whether to privatise public firms to a supra-national authority. To analyse this idea, we consider three possible cases: non-integration, partial integration and full integration. By comparing these three cases, when political weights are equal, we find that aggregate political benefit is no less under partial integration than under full integration or non-integration. In a comparison between non-integration and partial integration, we find that, if the number of private firms is low enough, no public firm is privatised in either case and aggregate political benefit of the two governments is therefore the same in both cases. If the number of private firms is high enough, aggregate political benefit is greater if countries integrate partially. This is due to the fact that, under nonintegration, governments decide whether to privatise for strategic reasons, but under partial integration the supra-national authority decides whether or not to privatise for reasons of efficiency. As a result, aggregate political benefit is greater in the latter case than in the former. A comparison of partial and full integration cases shows that, if the number of private firms is low (high) enough, neither public firm is (both are) privatised, so aggregate political benefit obtained is the same in both cases. When there is an intermediate number of private firms, we find that aggregate political benefit is greater under partial integration than under full integration, even though in the former case each public firm chooses the level of production that maximises the political benefit of its government, while in the latter it chooses the level of production that maximises aggregate political benefit. When consumer surplus has a greater weight than producer surplus in political benefit, we find that aggregate political benefit is no less under partial integration than under nonintegration. Under partial integration, aggregate political benefit is also no less than under full integration, since, in this last case, public firms are excessively aggressive.
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We have not considered asymmetries. For example, we could assume that there is a different number of private firms in each country, that the production function of firms is linear or that the weight that consumer surplus has in political benefit differs from between countries. This could modify the results obtained in the paper, but this issue is left for further research.
Acknowledgements We thank F. van Winden and three referees for helpful comments. Financial support from Fundacio´n Empresa Pu´blica, BEC (2000/0301) and UPV (Subvencio´n a grupos, 2001) is gratefully acknowledged.
Appendix A A.1 . Non integration Using Lemmas 1, 3 and 5 we obtain that, under non-integration, W NN >W PN if and only if n < nNI1, and W NP >W PP if and only if n < nNI2; nNI2>nNI1 if and only if a < 1.7142. The values of nNI1 and nNI2 are shown in Fig. 1, in which we identify four zones. Zone I groups the values of n such as n V min{nNI1, nNI2}. Zone II groups the values of n such as nNI1 < n V nNI2. Zone III groups the values of n such as n>max{nNI1, nNI2}. Finally, zone IV groups the values of n such as nNI2 < n V nNI1. In zones I and IV neither government privatises its public firm. In zone IV there are two equilibria: in one of them both governments privatise and in the other neither government privatises. It can be shown that the second equilibrium Pareto dominates the first. In zone II only one government privatises. Finally, in zone III both governments privatise. Under non-integration, W NN = W PN for those values of a and n such that: 540 108n þ 252n2 þ 100n3 þ 144a þ 273na 332n2 a 100n3 a þ 72a2 þ 48na2 þ 60n2 a2 18a3 9na3 ¼ 0: The value of the parameter n that solves the preceding equation is: 1=3 1 1 2 126 166a þ 30a þ A nNI1 ¼ 150ða 1Þ B þ 675ða 1ÞC ! þ ðB þ 675ða 1ÞCÞ1=3 ; where A = 23976 70407a + 51991a2 5685a3 + 225a4, B = 12643776 31118823a + 27981558a2 13322701a3 + 4210065a4 391500a5 3375a6, C = (320620032 81 9 38 82 2 4a + 73 9 63 85 1 3a2 31 9 70 23 7 1a3 + 1 42 0 06 14 2a4 9 25 11 84 7a5 + 34307145a6 5294493a7 + 224208a8 + 7695a9)1/2.
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It can be shown that W NN >W PN if and only if n < nNI1. Under non-integration, W PN = W PP for those values of a and n such that: 60 þ 12n þ 40n2 þ 16n3 þ 62a þ 51na 36n2 a 16n3 a 9a2 9na2 ¼ 0: The value of the parameter n that solves the preceding equation is: 0 !1=3 1 1 1=3 @20 18a 22 D pffiffiffi nNI2 ¼ 24ða 1Þ E þ 3 3ða 1ÞF ! p ffiffi ffi 1=3 ; þ 22=3 ðE þ 3 3ða 1ÞFÞ
where D = 64 + 297a 261a2 + 27a3, E = 7400 14202a + 5535a2 + 1512a3 243a4, F=(1989312 3265504a 1000260a2 + 4611168a3 2992653a4 + 730458a5 76545a6 + 2916a7)1/2. It can be shown that W NP > W PP if and only if n < nNI2, where nNI2 > nNI1 if and only if a < 1.7142. A.2 . Partial integration Using Lemmas 1, 3 and 5 we obtain that, under partial integration, 2W NN >W NP + W if and only if n < nPI1, 2W NN > 2W PP if and only if n < nPI2 and W NP + W PN > PP 2W if and only if n < nPI3, where nPI1 < nPI2 < nPI3. Under partial integration, 2W NN = W NP + W PN for those values of a and n such that: PN
810 þ 1278n þ 84n2 68n3 1359a 1407na 4n2 a þ 68n3 a þ 252a2 þ 222na2 12n2 a2 9a3 9na3 ¼ 0: The value of the parameter n that solves the preceding equation is: nPI1 ¼
1 102ða 1Þ
1 2ð21 a 3a Þ þ G H þ 459ða 1ÞI 2
! 1=3 1=3 þðH þ 459ða 1ÞIÞ ;
where G = 6 6 94 2 13 71 0 3a + 82 5 79a2 11 75 7a3 + 4 95a4, H = 1 05 0 07 32 + 3 20 78 1 60 a 34 52 2 27 2 a2 + 14 36 3 22 5a3 14 27 8 23 a4 34 2 09 a5 + 4 34 7 a6, I = (900495144 3749972868a + 6461427294a2 5949900399a3 + 3174084583a4 1003842935a5 + 187896150a6 20420433a7 + 1238031a8 38637a9 + 486a10)1/2. It can be shown that 2W NN >W NP + W PN if and only if n < nPI1.
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Under partial integration, 2W NN = 2W PP for those values of a and n such that: 45 þ 75n þ 8n2 4n3 72a 80na 4n2 a þ 4n3 a þ 9a2 þ 9na2 ¼ 0: The value of the parameter n that solves the preceding equation is: nPI2 ¼
1 6ða 1Þ
1 2ð2 þ aÞ þ J H þ 459ða 1ÞI
1=3
! pffiffiffi 1=3 þðK þ 3 3ða 1ÞLÞ ;
where J = 241 481a + 271a2 27a3, K = 2629 + 7935a 8391a2 + 3401a3 324a4, L = ( 26 2 44 0 + 1 03 39 5 9a 1 6 47 781a2 + 1353039a3 604926a4 + 143721a5 16605a6 + 729a7)1/2. It can be shown that 2W NN >2W PP if and only if n < nPI2. Under partial integration, W NP + W PN = 2W PP for those values of a and n such that: 90 þ 158n þ 24n2 8n3 137a 161na 16n2 a þ 8n3 a þ 9a2 þ 9na2 ¼ 0: The value of the parameter n that solves the preceding equation is: 0
nPI3
1 1 @48 þ 32a 422=3 M pffiffiffi ¼ 48ða 1Þ N þ 3 6ða 1ÞP ! pffiffiffi 1=3 2=3 þ 2 ðM þ 3 6ða 1ÞPÞ ;
!1=3
where M = 546 + 1053a 542a2 + 27a3, N = 14256 + 41760a 41958a2 + 15232a3 810a4, P = ( 2 2 64 98 4 + 8 30 0 32 4a 11 9 07 09 8a2 + 83 33 9 31a3 28 83 4 20 a4 + 448308a5 30294a6 + 729a7)1/2. It can be shown that W NP + W PN> 2W PP if and only if n < nPI3, where nPI1 < nPI2 < nPI3. A.3 . Full integration Using Lemmas 5, 7 and 8 we obtain that, under full integration, 2W NN>W NP + W PN if and only if n < nFI1, 2W NN>2W PP if and only if n < nFI2, and W NP + W PN >2W PP if and only if n < nFI3, where nFI1>nFI2>nFI3. pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1
1
1 þ 217 126a þ 18a2 ; nFI2 ¼ 1 þ 28 9a ; 4 2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1
3 þ 73 18a : ¼ 4
nFI1 ¼ nFI3
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Economic integration and privatisation under diseconomies of scale Juan Carlos Ba´rcena-Ruiz, Marı´a Begon˜a Garzo´n * Departamento de Fundamentos del Ana´lisis Econo´mico, Universidad del Paı´s Vasco, Avenida Lehendakari Aguirre, 83 48015 Bilbao, Spain Received 14 February 2002; received in revised form 29 October 2003; accepted 23 February 2004 Available online 30 July 2004
Abstract In this paper we analyse whether it should be national governments that decide whether to privatise public firms (non-integration) or whether this decision should be delegated to a supranational authority (economic integration). We assume that two countries form a single market in which there is free trade and that each country has one public firm and n private firms. We show that, if the supra-national authority decides whether or not to privatise public firms, aggregated politically weighted welfare is no less than if the governments take this decision. We also show that aggregated politically weighted welfare is no less if the firms are owned by the governments rather than a supranational authority. D 2004 Elsevier B.V. All rights reserved. JEL classification: L33; Q28; F15 Keywords: International trade; Economic integration; Public firms; Privatisation
1. Introduction In the late 1980s there was a consensus in Western Europe in favour of a mixed economy including both public and private firms. Local and central governments created or purchase firms in a variety of sectors of the economy (including manufacturing and the service sector) for reasons that ranged from ideology to short-term strategic planning. As a result, EU governments own a significant percent-
* Corresponding author. Tel.: +34-94-601-38-15; fax: +34-94-601-37-99. E-mail addresses: [email protected] (J.C. Ba´rcena-Ruiz), [email protected] (M. Begon˜a Garzo´n). 0176-2680/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ejpoleco.2004.02.008
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age of the firms in the different sectors of industry in Europe.1 EU countries have subsequently privatised some of their public firms in recent years. In 1979 the United Kingdom privatised many of its public firms, and more privatisations, albeit on a smaller scale, followed in the rest of the then EC in the 1980s. In the 1990s the creation of the Single Market sparked further privatisation. However, in spite of this privatisation, no consensus was reached among EU governments regarding the number of firms in the different industries that should remain in public hands. Some governments favour going as far as possible with privatisation, while others prefer to continue with public ownership. At one extreme stands the UK, where most public firms have been privatised, and at the other stand Italy and Spain, where public ownership is still a major feature of many industries. The Treaty of Rome is neutral as regards public ownership of firms. This neutrality is the result of the EU’s having to accommodate within it the different levels of state ownership of firms and the different opinions of its member countries. The Treaty does not question the ownership of public firms, but it does indicate that all public sector intervention must be neutral in the sense that it must not affect competition within the Single Market. For instance, there is a ban on state aid that might distort competition between member countries. Parker (1998b, p. 23) argues that in spite of the neutral position maintained by the Treaty of Rome on public ownership, it has been recognised on some occasions that privatisation can be beneficial. For instance, in 1994 the European Commission indicated that the privatisation of public firms could, when governments deemed it compatible with their objectives, help to improve the competitive environment (European Commission, 1994, p. 11). In regard to this last question, it must be said that some countries are reluctant to privatise their state owned firms for fear that many will fall into foreign ownership.2 On the other hand, the individual governments are reluctant to transfer national sovereignty over public firms to Brussels (Parker, 1998b, p. 22). These arguments have led us to wonder from a theoretical viewpoint whether it is welfare-superior for each government to decide whether it privatises its public firms or for a supra-national body to be created that can decide whether to privatise public firms in different countries. For this latter case we also analyse whether ownership of these firms should be passed over to the supra-national authority. The literature that looks at the decision whether to privatise public firms usually considers only one country and one public firm (see for instance De Fraja and Delbono, 1989, 1990; White, 1996; Willner, 2001). This literature has been extended to privatisation decisions when there is international trade (see for instance Fjell and Pal, 1996; Pal and White, 1998), but the extensions continue to consider only one public firm, with firms
1
See, for instance, Parker (1998a) and McGowan (1993). Parker (1998b, p. 36) indicates that EU countries fear that the privatisation of their public firms will lead to a loss of national control over major industries, and that this has led some countries to limit the percentage of privatised firms that can be acquired by foreign investors. For instance in Belgium sales have usually taken place on the basis of a preselection of investors rather than through public share offers. In Spain, the privatisation processes staged in the 1980s involved the sale of minority share packages because the government did not wish to relinquish control of the firms involved. 2
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selling their products in a single country. The literature does not analyse whether it should be the government of each country or a supra-national authority that decides whether public firms in the different countries should be privatised. To consider this question, we consider two countries that form a single market in which there is free trade. Each country has one public firm and n private firms, which produce a homogeneous good with the same technology. If a public firm is owned by a government, its objective function is the politically weighted welfare or political benefit of that country, which includes the consumer and producer surpluses of the country. If the public firms are owned by a supra-national authority, the objective function is aggregate political benefit of the countries. We consider three possibilities: the first is that each public firm is owned by one government, which decides whether to privatise it or not (non-integration). In the second case there is a supra-national authority, which decides whether or not to privatise public firms, but these firms are owned by the governments (partial integration). In the third and final case there is a supra-national authority, which owns the public firms and decides whether these firms are privatised (full integration). For simplicity and in order to concentrate on whether or not the decision to privatise should be delegated to a supra-national authority, we do not here consider income other than profits of public firms within their countries, that can affect the decision whether to privatise (in this regard, see Willner, 1999). Nor do we consider decisions made by politicians to achieve political objectives (Boycko et al., 1996, analyse this question), the existence of economies of scale (see Estrin and de Meza, 1995), differentiation in the goods produced by the firms (see Cremer et al., 1991), the fact that public firms are directed by managers (this question is analysed by Barros, 1995; Willner and Parker, 2000; White, 2001), mergers between private and public firms (see Ba´rcena-Ruiz and Garzo´n, 2003), the regulation of public firms (see Bo¨s, 1998) or partial privatisation (see Matsumura, 1998). Comparing the non-integration and partial integration cases, when the consumer and producer surpluses have the same weight in political benefit, we find that, if the number of private firms is small enough, no public firm is privatised in either case (since market competition would be greatly reduced). Aggregate political benefit of the two countries would therefore be the same in both cases. If the number of private firms is large enough, aggregate political benefit is greater if countries integrate partially: under nonintegration the governments decide whether to privatise for strategic reasons, but under partial integration the supra-national authority decides whether or not to privatise for reasons of efficiency. As a result, aggregate political benefit is greater in the latter case than in the former. Under partial and full integration the decision whether to privatise is delegated to a supra-national authority. However, in the former case, the public firms are owned by the governments, while in the latter they are owned by the supra-national authority. A comparison of these two cases shows that if the number of private firms is small (high) enough, neither public firm is (both are) privatised, so aggregate political benefit is the same in both cases. When there is an intermediate number of private firms, that political benefit is greater under partial integration than under full integration. The intuition is that, in the latter case, the public firms are more aggressive (produce more) than in the former
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case (since their objective functions are aggregate political benefit), and this reduces producers’ surpluses excessively even though it increases the surplus of consumers. When consumer surplus has a greater weight than producer surplus in political benefit, aggregate political benefit is no less under partial integration than under non-integration. Under partial integration political benefit is also no less than under full integration since, in this last case, public firms are excessively aggressive. We also compare the marginal cost of the public firm with the market price. De Fraja and Delbono (1989) show, considering one public firm and one country, that the marginal cost of the public firm equals the market price. Fjell and Pal (1996), by considering that there are both domestic and foreign private firms, show that the marginal cost of the public firm exceeds the market price. We show that under non-integration the marginal cost of the public firm exceeds (equals) the market price if consumer surplus has a greater (the same) weight than producer surplus in political benefit. Under full integration, the marginal cost of the public firm is lower than the market price if and only if the weight of the consumer surplus in political benefit is low enough. The paper is organised as follows. Section 2 presents the model. Section 3 shows the results obtained under non-integration when the political weights are equal. Section 4 shows the results obtained under integration when the political weights are equal. Section 5 compares the results obtained in the preceding sections. Section 6 studies the case in which political weights differ. Conclusions are drawn in Section 7.
2. The model We consider a single market comprising two countries, A and B. In each country there is one public firm, denoted by 0, and n private firms (n z 1). All firms produce a homogeneous good. For simplicity, we assume that there is free trade, there are no transportation costs and there is no possibility of discriminating between consumers from different countries. Therefore, consumers in both countries can buy the product from either a domestic or a foreign firm. The public firm of each country can be privatised, and this decision can be taken by the governments or by a supra-national authority. Therefore, three cases arise. In the first case, each public firm is owned by a government, which decides whether to privatise (nonintegration). In the second case, there is a supra-national authority, which decides whether or not to privatise public firms, but firms are owned by the governments (partial integration). In these two cases, we assume that, if a public firm is privatised, it is acquired by domestic investors, so that there are then n + 1 private firms in that country.3 In the third case, there is a supra-national authority, which owns the public firms and decides whether to privatise (full integration). The inverse demand function for the product in country k is: p = a 2yk (k = A, B), where p is the price for the good in the world market and yk is the amount of the good sold 3
We consider this assumption since, as pointed out in ,Footnote 2, EU countries fear that the privatisation of their public firms will lead to a loss of national control over major industries (see Parker, 1998b, pp. 36 – 37). It can be shown that the main results of the paper hold if we permit public firms to be acquired by foreign investors.
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in country k. The X world inverse demand Xnfunction for the product is: p = a yA yB, where n yA þ yB ¼ qA0 þ q þ q þ q . Let qki denote the amount of the good that Ai B0 i¼1 i¼1 Bi the firm i located in country k, firm ki, sells in the single market (k = A, B; i = 0, 1,. . ., n). The consumer surplus in country k, denoted by CSk, is: CSk=( yk)2, k = A, B. As is usually assumed in literature on mixed oligopoly (see, for example, De Fraja and Delbono, 1989, 1990), firms have the same technology, represented by the following cost function: C( qki)=( qki)2, k = A, B; i = 0,. . ., n.4 The profit function of firm ki is: pki ¼
a qA0
n X j¼1
qAj qB0
n X
! qBj qki q2ki ; i ¼ 0; . . . ; n; k ¼ A; B
ð1Þ
j¼1
We consider governments as seeking to maximize politically weighted welfare or political benefit. The objective function of government k includes Xn consumer surplus CSk and producer surplus in country k, PSk. The latter is PSk ¼ p . We use a linear i¼0 ki function for political benefit:5 Wk ¼ aCSk þ PSk ; 1Va < 2; k ¼ A; B:
ð2Þ
We propose a three stage game with the following timing. In the first stage, the decision is whether public firms should be privatised by governments or a supra-national authority. In the second stage, under non-integration, the two governments decide simultaneously whether to privatise their public firms; under economic integration, the supra-national authority decides whether to privatise the two public firms, only one of them or neither of them. In the third stage, each firm decides its output level. We solve the game by backward induction to obtain a subgame perfect Nash equilibrium.
3. Non-integration In this section we assume that each government decides whether to privatise its public firm. Given that there are two public firms that can be privatised, one in each country, there are four subgames that, by symmetry, can be reduced to three. These three subgames are the following: neither of the governments privatises (denoted by superscript NN), each government privatises (denoted by superscript PP), and one government does not privatise while the other government does; in this last case, we use the superscript NP to denote the country that does not privatise and the superscript PN to denote the other. Next we analyse each of the different subgames. 4 It can be shown that if the cost function is given by C( qki) = c( qki)2, the main results of the paper hold; i. e. the results of the paper are robust to changes in parameter c. 5 We assume that a < 2 to ensure that private firms produce a positive output level. We consider that a z 1 to ensure that the consumer surplus has a weight that is no less than the producer surplus in political benefit (see also Matsumura, 1998). If a < 1 our results can change and ‘‘non-realistic’’ equilibria can arise, since the ‘‘excessively low’’ weight of the consumer surplus distortions the objective function of public firms.
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3.1. Neither government privatises In the third stage of the game, the private firm ki chooses the output level, qki, that maximizes its profit function; the public firm 0 owned by government k chooses the output level, qk0, that maximizes its political benefit. Then: Lemma 1 . Under non-integration, when neither government privatises, the output level of firms, the consumer surplus, the profit of firms, the producer surplus and the political benefit in each country are, respectively: qNN 0 ¼
að3 nð1 aÞÞ að3 aÞ ; qNN ; ¼ i 15 þ 4n 3a 15 þ 4n 3a
CSNN ¼ pNN 0 ¼ PSNN ¼ W NN ¼
a2 ð3 þ 2nÞ2 ð15 þ 4n 3aÞ
; pNN ¼ i 2
2a2 ð3 aÞ2 ð15 þ 4n 3aÞ2
a2 ð3 n þ naÞð6 þ n 3a naÞ ð15 þ 4n 3aÞ2
;
;
a2 ð9ð2 aÞ n2 ð1 aÞ2 þ nð15 6a a2 ÞÞ ð15 þ 4n 3aÞ2 a2 ð18 þ nð15 þ 6a a2 Þ n2 ð1 6a þ a2 ÞÞ ð15 þ 4n 3aÞ2
;
; i ¼ 1; . . . ; n
ð3Þ
Using the output levels obtained in Lemma 1, we can compare the market price and the marginal cost of the public firm. We show the result in the following lemma. Lemma 2. Under non-integration, when neither government privatises, the marginal cost of the public firm equals the market price if and only if a = 1. The marginal cost of the public firm exceeds the market price if 1 < a < 2. This lemma shows that the marginal cost of the public firm equals the market price if the consumer and producer surpluses have the same weight in political benefit (a = 1). If a = 1, each public firm chooses the output level that maximises the political benefit of its government, taking into account that the consumer surplus has the same weight as the producer surplus in political benefit.6 6 Given the symmetry existing in this case, we obtain the same result as De Fraja and Delbono (1989) although we consider that there are two public firms instead of one. When the political weights differ, we find that the marginal cost of the public firm exceeds the market price. This result is also obtained by Fjell and Pal (1996) considering an industry with one public firm, m domestic private firms and n foreign private firms. In their model, for a given amount of total private firms’ output, the output level of the public firm is greater if some output comes from foreign firms, since foreign firms’ profit is not included in political benefit; therefore the producer (consumer) surplus has a lower (greater) weight in political benefit. As a result, they obtain that the public firm’s marginal cost equals the price only if n = 0. In our paper, when a increases, the output level of the public firms increases since the weight of the consumer surplus is greater; as a result, the marginal cost of the public firms exceeds the price.
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3.2. Only one government privatises Suppose that firm 0 in country A is sold to domestic investors. At the third stage, each of the 2n + 1 private firms chooses the profit-maximising output level, while qB0 maximises government B’s political benefit function. Then: Lemma 3. Under non-integration, when only one government privatises, the output level of firms, the consumer surplus, the profit of firms, the producer surplus and the political benefit in each country are, respectively: qNP 0 ¼
að6 2nð1 aÞ þ aÞ að6 aÞ PN ; qNP ; i ¼ qj ¼ 30 þ 10n 3a 30 þ 10n 3a
CSNP ¼ CSPN ¼ pNP 0 ¼
a2 ð6 þ 5nÞ2 ð30 þ 10n 3aÞ2
;
2a2 ð6 þ n 2a naÞð6 2n þ a þ 2naÞ ð30 þ 10n 3aÞ2
PN pNP i ¼ pj ¼
PSNP ¼
W PN ¼
ð30 þ 10n 3aÞ2
;
2a2 ð2ð18 3a a2 Þ þ nð30 a 4a2 Þ 2n2 ð1 aÞ2 Þ ð30 þ 10n 3aÞ2
PSPN ¼ W NP ¼
2a2 ð6 aÞ2
;
2a2 ð1 þ nÞð6 aÞ2 ð30 þ 10n 3aÞ2
;
;
a2 ð4ð18 þ 6a a2 Þ þ nð60 þ 58a 8a2 Þ n2 ð4 33a þ 4a2 ÞÞ ð30 þ 10n 3aÞ2 a2 ð2ð36 þ 6a þ a2 Þ þ 2nð36 þ 18a þ a2 Þ þ 25n2 aÞ ð30 þ 10n 3aÞ2
i ¼ 1; . . . ; n; j ¼ 0; . . . ; n:
;
; ð4Þ
If one public firm is privatised, it reduces its output level ( q0PN < q0NN), since its objective function is now its profit. But this reduction in output is not compensated by a sufficient variation in the output level of the other public firm ( q0PN + q0NP < 2 q0NN), since the objective function of the latter comprises only the political benefit of its country. As a result, the industry output level decreases after the privatisation of a public firm. In this PN case, p0NP>pNP i = pj if and only if a < ((6 + 2n)/(3 + 2n)); as market competition decreases following privatisation, the profit of the public firm increases more than the profit of the private firms if the parameter a is low enough, since the weight of the consumer surplus in social welfare is low enough.
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Lemma 4. Under non-integration, when only one government privatises, the marginal cost of the public firm is lower than the market price if and only if a < a*, where a*< ((6 + 4n)/(5 + 4n)), 1 < a*< 2. This lemma shows that the market price is greater than the marginal cost of the public firm if the parameter a is low enough (a < a*). This is due to the fact that when one public firm is privatised, that firm reduces its production, which is not compensated by a sufficient variation in the output level of the other public firm, so the output of industry decreases after privatisation. If a is high enough (a z a*), as the output level of the public firm increases with a, the reduction in the output level of the privatised firm is compensated by a sufficient variation in the output level of the other public firm. Therefore, in this last case the marginal cost of the public firm exceeds the price. 3.3. The two governments privatise In this case, each government privatises its public firm, which is acquired by domestic investors. Therefore, in each country there are n + 1 private firms. Each private firm chooses the output level that maximizes its profit function. Then: Lemma 5. Under non-integration, when the two governments privatise, the output level of firms, the consumer surplus, the profit of firms, the producer surplus and the political benefit in each country are, respectively: qPP i ¼
a a2 ð1 þ nÞ2 PP 2a2 ; CSPP ¼ ; pi ¼ ; 2 5 þ 2n ð5 þ 2nÞ ð5 þ 2nÞ2
PSPP ¼
2a2 ðn þ 1Þ ð5 þ 2nÞ2
; W PP ¼
a2 ðn þ 1Þð2 þ a þ naÞ ð5 þ 2nÞ2
; i ¼ 0; . . . ; n:
ð5Þ
Once we have solved the different subgames, we proceed to solve stage two. We analyse first the case in which the consumer and the producer surpluses have the same weight in political benefit (a = 1). Next, in Section 6, we shall study whether the results are robust to changes in parameter a. 3.4. The decision by the governments whether to privatise By using Lemmas 1, 3 and 5 we can compare the consumer and producer surpluses obtained in the different subgames when a = 1. This comparison is useful for studying the decision by governments whether to privatise. Lemma 6. Under non-integration, CSNN>CSNP = CSPN>CSPP and PSPP>PSNP>PSPN >PSNN. Given that each public firm chooses the output level that maximizes the political benefit of its government, it is more aggressive in the product market than private firms (i.e. its output level is greater). As a result, the highest industry output level is obtained when there
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are two public firms in the market and the lowest industry output level is obtained when all firms are private. Therefore, as the consumer surplus increases with industry output level, we obtain that CSNN>CSNP = CSPN>CSPP. The lowest (greatest) producer surplus is obtained when there are two (no) public firms in the market since the greatest (lowest) industry output level is obtained in that case. When only one government privatises, the producer surplus takes an intermediate value. As we saw in Lemma 3, q0NN>q0PN and 2q0NN>q0PN + q0NP. As a result, the level of industry output decreases after the privatisation of one public firm. Thus, producer surplus is lower when there are two public firms than when there is only one and, in this last case, producer surplus is lower than when all firms are private. When there is only one public firm in the market, producer surplus is greater in the country that owns that firm (PSNP>PSPN) since, as we saw in Lemma 3, when a = 1, the public firm makes a greater profit than the private PN firms (p0NP>pNP i = pj ). Next we solve the second stage of the game under non-integration. The following result is obtained. Proposition 1. Under non-integration, if n>na only one government privatises while if n V na neither government privatises, where na = 13.0316. 2
2
ð369þ102n10n Þ , which is Proof. From Lemmas 1, 3 and 5 we obtain that W NN W PN ¼ a8ð3þnÞ 2 ð27þ10nÞ2 positive if and only if n < na = 13.0316. Therefore, if one government does not privatise, the other government privatises (does not privatise) if n >na (n V na). On the other hand, a2 ð113þ54nþ4n2 Þ W NP W PP ¼ ð5þ2nÞ , which is positive for all n. Thus, if one government privatises 2 ð27þ10nÞ2 the other government does not privatise. 5
We consider first the decision taken by one government when the other government does not privatise. When parameter n is great enough (n >na), if one government does not privatise the other government privatises (W PN >W NN). In this case, the producer surplus has a greater weight than the consumer surplus in political benefit since the competition in the product market is high enough (and CSNN>CSPN while PSNN < PSPN). When n is low enough (n V na), if one government does not privatise nor does the other (W NN >W PN). In this case, consumer surplus has a greater weight than producer surplus in political benefit since the competition in the product market is low enough. The decision taken by one government when the other government privatises remains to be analysed. In this case, independently of n, when one government privatises, the other government does not (W NP>W PP). Lemma 6 shows that, when there is only one public firm in the market, the strategic behaviour of the public firm results in greater producer surplus in the country that owns that firm (PSNP>PSPN). This implies that, although PSNP is lower than PSPP, the difference between PSNP and PSPP is small. On the other hand, CSNP is greater than CSPP and the difference between CSNP and CSPP is great since the strategic behaviour of the public firm affects the consumer surplus of both countries equally. Thus, the difference between CSNP and CSPP is greater than the difference between PSPP and PSNP. As a result of the preceding arguments, we find that, when n is low enough (n V na), neither government privatises its public firm. When n is high enough (n>na), only one government privatises, and therefore there are two equilibria; in this case, the government
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that does not privatise has greater political benefit than the other government, but both governments are better off than if neither public firm is privatised. It must be noted that, in this case, firms are never both privatised.7
4. Economic integration In this section we assume that there is a supra-national authority. We consider two types of economic integration: partial and full. 4.1. Partial integration Under partial integration a supra-national authority decides whether public firms are privatised, but the firms are owned by governments. In this case, when a = 1, the following result is obtained. Proposition 2. Under partial integration, if nc < n the supra-national authority privatises both public firms; if nb < n V nc the supra-national authority privatises only one; and if n V nb neither firm is privatised, where nb = 1.5917 and nc = 1.8364.8 2
2
ð153þ42nþ34n Þ Proof. From Lemmas 1, 3 and 5 we obtain that W NP þ W PN 2W NN ¼ a4ð3þnÞ , 2 ð27þ10nÞ2 2
2
4a ð19þ3nþ4n Þ , which is positive if and only if n>nb = 1.5917; 2W PP W NP þ W PN ¼ ð5þ2nÞ 2 ð27þ10nÞ2 2
2
a ð9þ2nþ2n Þ , which is which is positive if and only if n>nc = 1.8364; 2W PP 2W NN ¼ 4ð3þnÞ 2 ð5þ2nÞ2 positive if and only if n>nd = 1.6794. 5
The intuition underlying this result is the following. When the number of private firms is low enough (n V nb), as the competition in the product market is also low enough, the privatisation of either of the public firms causes a reduction in the consumer surplus that is greater than the increase in the producer surplus. Thus, in this case neither public firm is privatised by the supra-national authority. When n is great enough (n>nc), the competition in the product market is also great enough, and thus both public firms are privatised, since the reduction in the consumer surplus is compensated by an increase in the producer surplus. As a result, in this case the supra-national authority privatises both public firms. When the number of private firms takes an intermediate value (nb < n V nc) the supranational authority privatises only one public firm. Under partial integration, although it is the supra-national authority that decides whether to privatise public firms, these firms are owned by governments; thus, each public firm maximizes the political benefit of its government. This means, as we have seen in Lemma 3, that, if one public firm is 7 The result obtained here is different from that obtained by De Fraja and Delbono (1989). They consider only one country and one public firm, so they cannot obtain the result in which only one public firm is privatised since this result is driven by strategic reasons. 8 To obtain this proposition, we assume that firms have the following cost function: C( qki) = c( qki)2, where c = 1. In this case, the supranational authority privatises only one public firm if nb = 1.5917 < n V nc = 1.8364; in this zone, n is not an integer. However, there exist values of parameter c such that in the zone in which the supranational authority privatises only one public firm, n is an integer. For example, if c = 3/7, then nb = 1.0270 < n V nc = 2.099.
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privatised, the reduction in its output level is not compensated by a sufficient increase in the output level of the other public firm (since its objective function comprises only the political benefit of its country).9 In this interval, although the consumer surplus decreases after the privatisation of one public firm, this reduction is compensated by an increase in the producer surplus (since, as we have seen in Lemma 3, the profit of the public firm rises). This means that, when the number of private firms takes an intermediate value, only one public firm is privatised by the supra-national authority. It has to be noted that, as the two countries are identical, either of the two public firms could be privatised. 4.2. Full integration Under full integration there is a supra-national authority which owns the public firms and decides whether they are privatised. If neither public firm is privatised, the two public firms choose the output level that maximises the aggregate political benefit of the two governments. In this case, if a = 1, we obtain the following result. Lemma 7. Under full integration, when neither government privatises, the output level of the firms, the consumer surplus, the profit of the firms, the producer surplus and political benefit in each country are, respectively: qNN 0 ¼
að3 2nð1 aÞÞ að2 aÞ ; qNN ; ¼ i 18 þ 4n 6a 9 þ 2n 3a
CSNN ¼ pNN 0 ¼
a2 ð3 þ 2nÞ2 4ð9 þ 2n 3aÞ
; pNN ¼ i 2
2a2 ð2 aÞ2 ð9 þ 2n 3aÞ2
;
a2 ð27 18a 4nðn þ 3Þð1 aÞ2 Þ
PSNN ¼ W NN ¼
4ð9 þ 2n 3aÞ2 a2 ð27 18a þ 4nð5 2a a2 Þ 4n2 ð1 aÞ2 Þ 4ð9 þ 2n 3aÞ2
;
a2 ð9ð3 aÞ þ 4nð5 þ a a2 Þ 4n2 ð1 3a þ a2 ÞÞ 2ð9 þ 2n 3aÞ2
; i ¼ 1; . . . ; n:
ð6Þ
If both public firms are privatised, we obtain the same result as in Lemma 5, since all firms are private. Finally, if there is only one public firm, it chooses the output level that maximises the aggregate political benefit of the two countries. In this case, we obtain the following result.10 9 NN In fact, under partial integration, qNP if and only if n < 1.5. If the objective function of the public 0 >q0 firm is the aggregate political benefit of the two countries, when one public firm is privatised the other public firm increases its output level (as much as possible) to compensate for the reduction in the output level of the privatised firm. 10 When a = 1, we consider the same model as De Fraja and Delbono (1989), since they assume only one country and one public firm.
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Lemma 8. Under full integration, when only one government privatises, the output level of firms, the consumer surplus in each country, the profit of firms, the aggregate producer surplus and the aggregate political benefit are, respectively: qNP 0 ¼
að2 þ a 2nð1 aÞÞ að3 aÞ PN ; qNP ; i ¼ qj ¼ 14 þ 4n 3a 14 þ 4n 3a
CSNP ¼ CSPN ¼ pNP 0 ¼
a2 ð5 þ 4nÞ2 4ð14 þ 4n 3aÞ2
;
a2 ð2 2n þ a þ 2naÞð7 þ 2n 4a 2naÞ
PN pNP i ¼ pj ¼
ð24 þ 4n 3aÞ2 2a2 ð3 aÞ2 ð14 þ 4n 3aÞ2
PSNP þ PSPN ¼ W NP þ W PN ¼
;
; i ¼ 1; . . . ; n; j ¼ 0; . . . ; n;
a2 ð32 13a 2a2 þ nð26 4a 6a2 Þ 4n2 ð1 a2 Þ ð14 þ 4n 3aÞ2
;
a2 ð64 a 4a2 þ 4nð13 þ 8a 3a2 Þ 8n2 ð1 4a þ a2 ÞÞ 2ð14 þ 4n 3aÞ2
:
ð7Þ
We analyse first the case in which the consumer and the producer surpluses have the same weight in political benefit (a = 1). In Section 6 we shall study whether the results are robust to changes in parameter a. Proposition 3. Under full integration, if n>nd the supra-national authority privatises both public firms while if n V nd neither of them is privatised, where nd = 1.6794. 2
2
a ð27þ2nþ4n Þ , Proof. From Lemmas 5, 7 and 8 we obtain that W NP þ W PN 2W NN ¼ 4ð3þnÞ 2 ð11þ4nÞ2 2
2
ð23þ12nþ8n Þ which is positive if and only if n>n/ = 2.3600; 2W PP W NP þ W PN ¼ a2ð5þ2nÞ , 2 ð11þ4nÞ2 2
2
a ð9þ2nþ2n Þ which is positive if and only if n>nh = 1.1040; 2W PP 2W NN ¼ 4ð3þnÞ , which is 2 ð5þ2nÞ2 positive if and only if n>nd = 1.6794. 5
The difference between partial and full integration is that in the latter case public firms choose the output level that maximises the aggregate political benefit of the two countries, while in the former case each public firm chooses the output level that maximizes the political benefit of its government. Thus, when only one public firm is privatised, under full integration the other public firm increases its output level (as much as possible) to compensate for the reduction in the output level of the privatised firm;11 under partial integration the other public firm behaves strategically and, thus, its output level is lower than under full integration. If the supra-national authority privatises only one public firm, the privatised firm reduces its output level, while the other public firm increases its output level. However, 11
NN It can be shown that, under full integration, qNP 0 >q0 for all n.
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although the objective function of the public firm is the aggregate political benefit, this last firm cannot increase its output level enough to compensate for the reduction in the output of the industry, since its production costs are quadratic. Moreover, given that the production costs are quadratic, it is cheaper to produce a given output level using two public firms than using one. Therefore, the supra-national authority never privatises only one public firm. As a result of the preceding arguments, when the parameter n is low enough (n V nd), neither public firm is privatised. However, if n>nd, the supra-national authority privatises both firms since competition in the product market is great enough.
5. Comparison between the three types of integration when political weights are equal In this section we solve the first stage of the game. Comparing the aggregate political benefit in the three types of integration, we obtain the following results. Proposition 4. When political weights are equal, the aggregate political benefit under partial integration is no less than under non-integration. This proposition states that non-integration is (weakly) dominated by partial integration. By comparing Propositions 1 and 2, we find that, if n V nb, the aggregate political benefit is the same under partial integration as under non-integration, since in both cases neither public firm is privatised. When n>nb, under non-integration, the governments decide, for strategic reasons, whether their public firms are privatised or not. However, under partial integration there is a supra-national authority that decides, for reasons of efficiency, whether the public firms are privatised. As a result, if n >nb, aggregate political benefit is greater under partial integration than under non-integration, and the political benefit of each government could increase if the decision regarding privatisation were delegated to a supra-national authority. If nb < n V nc, under partial integration only one public firm is privatised, while under non-integration neither of them is privatised, and aggregate political benefit is greater in the first case. In this interval, under non-integration, given that the country that privatises obtains a lower political benefit than the other country (W NN >W PN ), neither of the two governments wants to privatise. Under partial integration, given that n takes an intermediate value, the supra-national authority privatises only one public firm. As in this interval W NP >W NN > W PN, the country that privatises would prefer not to delegate the decision whether to privatise to a supra-national authority (this country would prefer not to privatise). But, as W NP + W PN > 2W NN, the country that privatises could be compensated by the other country by way of a monetary transference, and both countries would obtain greater political benefit under partial integration than under non-integration. If nc < n V na, under partial integration both public firms are privatised, while under nonintegration neither of them is privatised, and the aggregate political benefit is greater in the first case. In this interval, as W NN < W PP, the two governments obtain a greater political profit by delegating the decision whether to privatise to a supra-national authority. Finally, when n>na, under partial integration both public firms are privatised while under non-integration only one is, and aggregate political benefit is greater in the first
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case. In this interval W NP > W PP and, thus, the government that owns the public firm would not want to privatise it. But, as W NP + W PN < 2W PP, this government could be compensated by the other government by way of a monetary transference, and both countries would obtain a greater political benefit under partial integration than under non-integration. Now that we have compared non-integration and partial integration, let us compare partial and full integration. Proposition 5. When political weights are equal, aggregate political benefit under partial integration is no less than under full integration.12 This proposition states that full integration is (weakly) dominated by partial integration. By comparing Propositions 2 and 3, we find that, if n V nb, aggregate political benefit is the same in both cases, since in neither case is either public firm privatised. Given that consumer surplus has the same weight as producer surplus in political benefit and that there are no asymmetries in the model,13 the output levels of both the public firms and the private firms (and, thus, the consumer and producer surpluses) are the same under partial and full integration. If n>nc, both public firms are privatised in both cases and, thus, the aggregate political benefit is also the same. It only remains to compare the two types of integration in the interval nb < n V nc. In this interval, as Proposition 2 shows, under partial integration only one public firm is privatised since the aggregate political benefit is greater than if the two public firms are privatised or if neither of them is privatised. In this interval, under full integration, the supra-national authority privatises both public firms (if nd < n V nc) or neither of them (if nb < n V nd). And it must be noted that when there are two public firms in the market, aggregate political benefit is the same in the two types of economic integration; if all firms are private, the same aggregate political benefit is also obtained in both cases. Therefore, in this interval, partial integration generates a greater aggregate political benefit than full integration.14 In the interval nb < n V nd, under full integration neither public firm is privatised while under partial integration only one public firm is privatised. If neither public 12 If we allow partial privatisation of public firms (see Matsumura, 1998; Ba´rcena-Ruiz and Garzo´n, 2003), the supra-national authority would choose the percentage of the shares of the public firms that is held by governments (under partial integration) or by the supranational authority (under full integration). In both cases, the supra-national authority chooses partially to privatise public firms (and, thus, we have semi-public firms). There is a greater aggregate political benefit under full integration than under partial integration since, in the first case, the supra-national authority can choose the level of ‘‘aggressiveness’’ of the public firms by choosing the percentage of the shares of the public firms that it wants to hold (the lower this percentage is, the lower the output level of the semi-public firms). 13 When consumer surplus has a different weight than producer surplus in political benefit, aggregate political benefit is different under partial and full integration. 14 An alternative explanation for this result is the following. In the interval nb < n V nc, if there are two public firms in the market, as under full integration these firms maximise aggregate political benefit, the competition in the product market is excessively high. In this interval, if the two public firms are privatised, under full integration the competition in the product market is excessively low. Under partial integration, in this interval, as the supranational authority privatises only one public firm and the other public firm maximises the political benefit of its government, the competition in the product market takes an intermediate level. Therefore, in this interval, a greater aggregate political benefit is obtained under partial integration than under full integration.
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firm is privatised, the same aggregate political benefit is obtained under full and partial integration. In this last type of integration, when only one government privatises, the aggregate political benefit is greater than if neither government privatises (W NP + W PN >2W NN ). However, when only one government privatises, this government obtains a lower political benefit than if neither government privatises (W PN < W NN). But, as W NP + W PN >2W NN, the government that privatises could be compensated by the other government by way of a monetary transference, and both countries would obtain a greater political benefit under partial integration than under full integration. In the interval nd < n V nc, under full integration both public firms are privatised while under partial integration only one public firm is privatised. It must be noted that if both public firms are privatised the same aggregate political benefit is obtained under full and partial integration. In this last type of integration, if there is one public firm in the market the aggregate political benefit is greater than if all firms are private (W NP + W PN>2W PP). However, if there is only one public firm in the market, the government that does not own the public firm obtains a lower political benefit than if all firms are private (W PN < W PP). But, as W NP + W PN>2W PP, both countries would obtain a greater political benefit under partial integration than under full integration if the government that does not own the public firm is compensated by the other government by way of a monetary transference. By using Propositions 4 and 5, we can solve the first stage of the model when the consumer surplus has the same weight as the producer surplus in political profit. We obtain the following result. Proposition 6. When political weights are equal, the decision whether to privatise the public firms is delegated to a supra-national authority, but the ownership of the public firms is held by governments. Next we consider that the weights attached to the arguments of political benefit are different, in order to analyse whether the results obtained in the preceding sections are robust to changes in the parameter a.
6. Non-integration, partial integration and full integration when political weights differ When political weights differ, under non-integration neither government privatises its public firm if n V nNI1 (zones I and IV in Fig. 1). Only one government privatises if nNI1 < n V nNI2 (zone II in Fig. 1). Finally, both governments privatise if n>max{nNI1, nNI2} (zone III in Fig. 1). The values of nNI1 and nNI2 are collected in Appendix A. When a = 1 (see Proposition 1), given that consumer surplus has the same weight as producer surplus in political benefit, competition in the product market is never high enough for both public firms to be privatised. However, when a>1, both governments privatise if n is high enough, for a given value of a (zone III in Fig. 1). In this case, the weight of producer surplus in political benefit is sufficiently greater than that of consumer surplus and the competition in the product market is high enough for both public firms to be privatised. In zone II, only one government privatises. In zones I and IV of Fig. 1 neither government privatises its public firm since competition in the product market is low enough for all a.
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Fig. 1. Non-integration when political weights differ.
Under partial integration neither public firm is privatised if n V nPI1; the supra-national authority privatises only one if nPI1 < n V nPI3; finally, the supra-national authority privatises both of them if n>nPI3. The values of nPIi (i = 1, 3) are collected in Appendix A. The intuition underlying this result is the same as in Proposition 2. For a given value of a, when the number of private firms increases competition in the product market also increases; thus, if n is low enough neither public firm is privatised, if n takes an intermediate value only one is privatised and if n is large enough both are privatised. Under full integration neither of the public firms is privatised if n V nFI2, whereas the supra-national authority privatises both of them if n>nFI2. The value of nFI2 is shown in Appendix A. The intuition underlying this result is the same as in Proposition 3. Given that the production costs are quadratic, it is cheaper to produce a given output level using two public firms than using one. Therefore, the supra-national authority never privatises only one public firm: it privatises either both or neither. After analysing the three types of integration when political weights differ, we compare them in order to study whether the results obtained in Section 5 are robust to changes in parameter a. We obtain the following result. Proposition 7. When political weights differ, aggregate political benefit under partial integration is no less than under full integration and non-integration. We saw in Section 5 that when a = 1, aggregate political benefit is greater or equal under partial integration than under non-integration. This result is also obtained when a>1, since
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under partial integration there is a supra-national authority, which decides, for reasons of efficiency, whether public firms are privatised. Under non-integration, the government of each country decides, for strategic reasons, whether its public firm is privatised or not. When a = 1, aggregate political benefit is no less under partial integration than under full integration. This result is also obtained when a>1. When a and n are such that the supranational authority privatises both public firms, aggregate political benefit is the same under partial and full integration, since private firms produce the same output level in both cases. When a and n are such that the supra-national authority does not privatise either public firm, aggregate political benefit is greater under partial integration. When a>1, the output level of the public firms is greater under full integration, since public firms are much more aggressive in this case (when a = 1 aggregate political benefit is the same due to the symmetry of the model). When a and n are such that different equilibria are obtained in the two cases, aggregate political benefit is greater under partial integration, since, given that the objective function of public firms is aggregate political benefit, these firms are very aggressive in the product market and, thus, competition in the product market is very high.
7. Conclusions The literature on mixed oligopoly does not analyse whether governments want to delegate the decision whether to privatise public firms to a supra-national authority. To analyse this idea, we consider three possible cases: non-integration, partial integration and full integration. By comparing these three cases, when political weights are equal, we find that aggregate political benefit is no less under partial integration than under full integration or non-integration. In a comparison between non-integration and partial integration, we find that, if the number of private firms is low enough, no public firm is privatised in either case and aggregate political benefit of the two governments is therefore the same in both cases. If the number of private firms is high enough, aggregate political benefit is greater if countries integrate partially. This is due to the fact that, under nonintegration, governments decide whether to privatise for strategic reasons, but under partial integration the supra-national authority decides whether or not to privatise for reasons of efficiency. As a result, aggregate political benefit is greater in the latter case than in the former. A comparison of partial and full integration cases shows that, if the number of private firms is low (high) enough, neither public firm is (both are) privatised, so aggregate political benefit obtained is the same in both cases. When there is an intermediate number of private firms, we find that aggregate political benefit is greater under partial integration than under full integration, even though in the former case each public firm chooses the level of production that maximises the political benefit of its government, while in the latter it chooses the level of production that maximises aggregate political benefit. When consumer surplus has a greater weight than producer surplus in political benefit, we find that aggregate political benefit is no less under partial integration than under nonintegration. Under partial integration, aggregate political benefit is also no less than under full integration, since, in this last case, public firms are excessively aggressive.
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We have not considered asymmetries. For example, we could assume that there is a different number of private firms in each country, that the production function of firms is linear or that the weight that consumer surplus has in political benefit differs from between countries. This could modify the results obtained in the paper, but this issue is left for further research.
Acknowledgements We thank F. van Winden and three referees for helpful comments. Financial support from Fundacio´n Empresa Pu´blica, BEC (2000/0301) and UPV (Subvencio´n a grupos, 2001) is gratefully acknowledged.
Appendix A A.1 . Non integration Using Lemmas 1, 3 and 5 we obtain that, under non-integration, W NN >W PN if and only if n < nNI1, and W NP >W PP if and only if n < nNI2; nNI2>nNI1 if and only if a < 1.7142. The values of nNI1 and nNI2 are shown in Fig. 1, in which we identify four zones. Zone I groups the values of n such as n V min{nNI1, nNI2}. Zone II groups the values of n such as nNI1 < n V nNI2. Zone III groups the values of n such as n>max{nNI1, nNI2}. Finally, zone IV groups the values of n such as nNI2 < n V nNI1. In zones I and IV neither government privatises its public firm. In zone IV there are two equilibria: in one of them both governments privatise and in the other neither government privatises. It can be shown that the second equilibrium Pareto dominates the first. In zone II only one government privatises. Finally, in zone III both governments privatise. Under non-integration, W NN = W PN for those values of a and n such that: 540 108n þ 252n2 þ 100n3 þ 144a þ 273na 332n2 a 100n3 a þ 72a2 þ 48na2 þ 60n2 a2 18a3 9na3 ¼ 0: The value of the parameter n that solves the preceding equation is: 1=3 1 1 2 126 166a þ 30a þ A nNI1 ¼ 150ða 1Þ B þ 675ða 1ÞC ! þ ðB þ 675ða 1ÞCÞ1=3 ; where A = 23976 70407a + 51991a2 5685a3 + 225a4, B = 12643776 31118823a + 27981558a2 13322701a3 + 4210065a4 391500a5 3375a6, C = (320620032 81 9 38 82 2 4a + 73 9 63 85 1 3a2 31 9 70 23 7 1a3 + 1 42 0 06 14 2a4 9 25 11 84 7a5 + 34307145a6 5294493a7 + 224208a8 + 7695a9)1/2.
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It can be shown that W NN >W PN if and only if n < nNI1. Under non-integration, W PN = W PP for those values of a and n such that: 60 þ 12n þ 40n2 þ 16n3 þ 62a þ 51na 36n2 a 16n3 a 9a2 9na2 ¼ 0: The value of the parameter n that solves the preceding equation is: 0 !1=3 1 1 1=3 @20 18a 22 D pffiffiffi nNI2 ¼ 24ða 1Þ E þ 3 3ða 1ÞF ! p ffiffi ffi 1=3 ; þ 22=3 ðE þ 3 3ða 1ÞFÞ
where D = 64 + 297a 261a2 + 27a3, E = 7400 14202a + 5535a2 + 1512a3 243a4, F=(1989312 3265504a 1000260a2 + 4611168a3 2992653a4 + 730458a5 76545a6 + 2916a7)1/2. It can be shown that W NP > W PP if and only if n < nNI2, where nNI2 > nNI1 if and only if a < 1.7142. A.2 . Partial integration Using Lemmas 1, 3 and 5 we obtain that, under partial integration, 2W NN >W NP + W if and only if n < nPI1, 2W NN > 2W PP if and only if n < nPI2 and W NP + W PN > PP 2W if and only if n < nPI3, where nPI1 < nPI2 < nPI3. Under partial integration, 2W NN = W NP + W PN for those values of a and n such that: PN
810 þ 1278n þ 84n2 68n3 1359a 1407na 4n2 a þ 68n3 a þ 252a2 þ 222na2 12n2 a2 9a3 9na3 ¼ 0: The value of the parameter n that solves the preceding equation is: nPI1 ¼
1 102ða 1Þ
1 2ð21 a 3a Þ þ G H þ 459ða 1ÞI 2
! 1=3 1=3 þðH þ 459ða 1ÞIÞ ;
where G = 6 6 94 2 13 71 0 3a + 82 5 79a2 11 75 7a3 + 4 95a4, H = 1 05 0 07 32 + 3 20 78 1 60 a 34 52 2 27 2 a2 + 14 36 3 22 5a3 14 27 8 23 a4 34 2 09 a5 + 4 34 7 a6, I = (900495144 3749972868a + 6461427294a2 5949900399a3 + 3174084583a4 1003842935a5 + 187896150a6 20420433a7 + 1238031a8 38637a9 + 486a10)1/2. It can be shown that 2W NN >W NP + W PN if and only if n < nPI1.
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Under partial integration, 2W NN = 2W PP for those values of a and n such that: 45 þ 75n þ 8n2 4n3 72a 80na 4n2 a þ 4n3 a þ 9a2 þ 9na2 ¼ 0: The value of the parameter n that solves the preceding equation is: nPI2 ¼
1 6ða 1Þ
1 2ð2 þ aÞ þ J H þ 459ða 1ÞI
1=3
! pffiffiffi 1=3 þðK þ 3 3ða 1ÞLÞ ;
where J = 241 481a + 271a2 27a3, K = 2629 + 7935a 8391a2 + 3401a3 324a4, L = ( 26 2 44 0 + 1 03 39 5 9a 1 6 47 781a2 + 1353039a3 604926a4 + 143721a5 16605a6 + 729a7)1/2. It can be shown that 2W NN >2W PP if and only if n < nPI2. Under partial integration, W NP + W PN = 2W PP for those values of a and n such that: 90 þ 158n þ 24n2 8n3 137a 161na 16n2 a þ 8n3 a þ 9a2 þ 9na2 ¼ 0: The value of the parameter n that solves the preceding equation is: 0
nPI3
1 1 @48 þ 32a 422=3 M pffiffiffi ¼ 48ða 1Þ N þ 3 6ða 1ÞP ! pffiffiffi 1=3 2=3 þ 2 ðM þ 3 6ða 1ÞPÞ ;
!1=3
where M = 546 + 1053a 542a2 + 27a3, N = 14256 + 41760a 41958a2 + 15232a3 810a4, P = ( 2 2 64 98 4 + 8 30 0 32 4a 11 9 07 09 8a2 + 83 33 9 31a3 28 83 4 20 a4 + 448308a5 30294a6 + 729a7)1/2. It can be shown that W NP + W PN> 2W PP if and only if n < nPI3, where nPI1 < nPI2 < nPI3. A.3 . Full integration Using Lemmas 5, 7 and 8 we obtain that, under full integration, 2W NN>W NP + W PN if and only if n < nFI1, 2W NN>2W PP if and only if n < nFI2, and W NP + W PN >2W PP if and only if n < nFI3, where nFI1>nFI2>nFI3. pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1
1
1 þ 217 126a þ 18a2 ; nFI2 ¼ 1 þ 28 9a ; 4 2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1
3 þ 73 18a : ¼ 4
nFI1 ¼ nFI3
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