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State aid in the European Union: The prohibition of subsidies in an integrated market
International Journal of Industrial Organization 18 (2000) 867–884 www.elsevier.com / locate / econbase
State aid in the European Union: The prohibition of subsidies in an integrated market David R. Collie* Cardiff Business School, Cardiff University, Aberconway Building, Colum Drive, Cardiff CF1 3 EU, UK Accepted 30 October 1998
Abstract The effect of prohibiting state aid in an integrated market is analysed in a symmetric Cournot oligopoly model where one firm is located in each member state. Subsidies are financed by distortionary taxation so there is a trade-off between the deadweight loss from the oligopolistic distortion and that from distortionary taxation. It is shown that there exists a range of values for the opportunity cost of government revenue where member states want to give subsidies and where the multilateral prohibition of subsidies would increase aggregate welfare. Furthermore, this range of values is shown to include plausible estimates of opportunity cost. 2000 Elsevier Science B.V. All rights reserved. Keywords: Distortionary taxation; European Union; Oligopoly; State aid JEL classification: L13; L40; L52
1. Introduction Article 92(1) of the EC treaty states that ‘‘any aid granted by a member state or through state resources in any form whatsoever which distorts or threatens to distort competition by favouring certain undertakings or the production of certain goods shall, in so far as it affects trade between member states, be incompatible
* E-mail address: [email protected] (D.R. Collie) 0167-7187 / 00 / $ – see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S0167-7187( 98 )00051-4
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with the common market’’.1 However, although this statement seems unambiguous, it does not amount to an absolute prohibition of state aid since there are a number of exceptions to this general rule.2 Member states are required to notify the European Commission of any proposed state aid so that the Commission can determine whether the aid qualifies for exemption.3 The Commission also keeps existing aid under constant review and requires member states to provide it with annual reports. The extent of state aid in the European Union can be seen from Table 1, which shows state aid to industry as a percentage of value added for the EC12 from 1990 to 1994 together with 3 year averages for the individual member states for 1990–92 and 1992–94. Looking at these figures it is hard to disagree with the European Commission (1997b) in its latest survey on state aid when it says that ‘‘the volume of aid in the Community is massive’’. It goes on to say that the survey reflects ‘‘the determined will of the Community to eliminate distorting aid that is incompatible with the internal market and to keep overall aid levels under control’’. Clearly, faced with the desire of the member states to grant state aid, the European Commission is struggling to achieve its objective. The purpose of this paper is to provide an explanation for the desire of member states to grant state aid to their firms and the desire of the Commission to prohibit or, at least, to limit state aid. Although many analysts would explain this situation by appealing to political economy arguments, this paper will attempt to provide a purely economic explanation based upon welfare maximising governments. Throughout this article, state aid will be modelled as a production subsidy that has the effect of reducing the recipient firm’s marginal cost of production. A perfectly competitive model cannot really explain the situation since there is no incentive for the member states to give subsidies to their firms as the effect would be to
1 An explanation of the rules applicable to state aid is given in European Commission (1997a) and the rules themselves are detailed in European Commission (1995). 2 Article 92(2) lists three types of state aid that are always compatible with the common market: firstly, ‘‘aid having a social character, granted to individual consumers, provided that such aid is granted without discrimination related to the origin of the products concerned’’; secondly, ‘‘aid to make good the damage caused by natural disasters or exceptional circumstances’’; thirdly, ‘‘aid to regions of the Federal Republic of Germany disadvantaged by the division’’, but since the reunification of Germany in October 1990 this category has become obsolete. Article 92(3) lists four types of state aid that may be exempted by the European Commission. Article 92(3)(a) refers to ‘‘aid to promote the economic development of areas where the standard of living is abnormally low or where there is serious underemployment’’. Article 92(3)(b) refers to ‘‘aid to promote the execution of an important project of common European interest or to remedy a serious disturbance in the economy of a member state’’. Article 92(3)(c) covers ‘‘aid to facilitate the development of certain economic activities or of certain economic areas, where such aid does not adversely affect trading conditions to an extent contrary to the common interest’’. Article 92(3)(d) refers to ‘‘aid to promote culture and heritage conservation’’, and there is an Article 92(3)(e) that allows further categories of aid that may be exempted to be added if proposed by the European Commission. 3 Firms that receive aid that has not been notified to the Commission may have to repay this aid if the Commission decides that the aid is incompatible with the common market.
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Table 1 State aid to industry as a percentage of value added % EC12
1990 4.0
1991 3.6
1992 3.9
1993 4.2
%
1990–92
1992–94
Belgium Denmark Germany Greece Spain France Ireland Italy Luxembourg Netherlands Portugal United Kingdom EC12
7.9 1.9 3.5 12.5 2.1 2.7 2.7 8.9 3.5 2.5 4.6 1.4 3.8
4.8 2.8 4.8 10.5 1.7 3.3 3.5 8.4 2.9 2.1 4.4 0.8 4.0
1994 3.8
Source: Fifth Survey on State Aid in the European Union in the Manufacturing and Certain Other Sectors, Com(97) 170.
reduce welfare by introducing a production distortion into the economy.4 With imperfect competition, as in the Cournot oligopoly model considered by Brander and Spencer (1985), the profit-shifting motive would provide an incentive for the member states to give subsidies to their firms. With all member states giving subsidies in the Nash equilibrium some readers might think, by analogy with the Brander and Spencer model, that the outcome will obviously be a prisoners’ dilemma, but they would be wrong! Unlike the Brander and Spencer model, the member states all consume the subsidised products so consumers will benefit from a subsidy war. In fact, in a symmetric model, all member states will subsidise their firms in the Nash equilibrium until price is equal to marginal cost, which will lead to a Pareto-efficient outcome rather than the usual prisoners’ dilemma. All the member states giving subsidies eliminates the deadweight loss due to the oligopolistic distortion. Thus, imperfect competition on its own cannot provide an explanation, but the addition of distortionary taxation as in Neary (1994) does provide a solution to the puzzle.5 4
Although, in the absence of an import tariff, a production subsidy to an industry that was a net importer could be used to improve the terms of trade if the country was large, but this would also imply using a production tax in industries that were net exporters. 5 Collie (1997) analyses the effect of trade bloc formation in a multi-country version of the Brander and Spencer (1985) model with distortionary taxation added as in Neary (1994), and suggests that this model may explain multilateral agreements to limit or prohibit export subsidies.
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With distortionary taxation, the opportunity cost of government revenue exceeds unity due to the marginal welfare cost of taxation, and this reduces the incentive for member states to give subsidies. However, provided the opportunity cost of government revenue is sufficiently low, the member states will still give subsidies in the Nash equilibrium. Then, when all member states reduce subsidies, there may be a welfare gain if the increase in the deadweight loss from the oligopolistic distortion is outweighed by the reduction in the deadweight loss from distortionary taxation. Obviously, provided the opportunity cost of government revenue is sufficiently high, there will be a welfare gain when subsidies are reduced. The main result of this paper is to show that there always exists a range of values for the opportunity cost of government revenue where a prisoners’ dilemma obtains: individual member states want to give subsidies whereas the multilateral reduction or prohibition of subsidies would increase the welfare of all member states. Furthermore, using specific functional forms, it is shown that this range of values for the opportunity cost of government revenue includes the most plausible empirical estimates of opportunity cost. An important assumption that will be employed throughout this article is that of symmetry: all countries and all firms will be assumed to be identical. Despite the obvious asymmetry in the state aid granted by member states shown in Table 1, the assumption of symmetry seems reasonable in a model looking at the aggregate welfare gains from the prohibition of subsidies given the analytical convenience of this assumption. Without this assumption, the explicit welfare comparison between the Nash equilibrium in production subsidies and prohibition would only be possible by assuming linear demand. The layout of the paper is as follows: Section 2 presents the basic Cournot oligopoly model, then the Nash equilibrium in subsidies is derived in Section 3. The welfare effects of a reduction in subsidies from the Nash equilibrium levels and of a complete prohibition of subsidies are analysed in Section 4. Some examples with specific functional forms are considered in Section 5, then the conclusions are presented in Section 6.
2. The model The model is a partial equilibrium analysis of the welfare effects of production subsidies in a Cournot oligopolistic industry located within a single integrated market. Like the Single Market of the European Union, this integrated market was formed by a customs union, consisting of M identical countries, eliminating all barriers to trade and arbitrage between its member states. In each member state, there is a single oligopolistic firm that produces a homogeneous good for sale in the integrated market. Symmetry is assumed so all the firms have identical and constant marginal cost c. The firm in the ith member state receives a production subsidy s i from its government and produces output x i for sale in the integrated
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market. Consumers are identical in all member states, and can be represented by a single representative consumer in each market with an indirect utility function that is linearly separable: U 5V(P) 1 I where P is the consumer price and I is income. With perfect arbitrage and no trade barriers, there will be a uniform consumer price in all member states. By Roy’s identity, consumption in each market is given by y 5 2 ≠V/ ≠P, so total consumption in the integrated market is Y 5 My 5 2 M ≠V/ ≠P, and this can be inverted to obtain the aggregate inverse demand function: P 5 P(Y), where it is assumed that the demand curve is downward sloping, P9 , 0. The model can be viewed as a two stage game where the national governments set production subsidies to maximise their national welfare at the first stage and the firms compete in a Cournot oligopoly at the second stage. As usual, the game is solved by backwards induction to obtain the subgame perfect equilibrium, and the first step is to solve the final stage of the game where the profits of the firm in the ith member state are:
pi 5 (P 2 c 1 s i )xi , i 5 1,M.
(1)
In the Cournot equilibrium of the final stage of the game, the M firms simultaneously and independently set their outputs to maximise their profits given the production subsidies set by the national governments. Assuming an interior solution, where all firms produce some positive quantity, the first-order conditions for a Cournot equilibrium are: ≠pi / ≠x i 5 P 1 x i P9 2 c 1 s i 5 0, i 5 1,M.
(2)
The second-order conditions for profit maximisation are assumed to hold so that ≠ 2 pi / ≠x 2i 5 2P9 1 x i P0 , 0, and it will also be assumed that the outputs of the firms are strategic substitutes according to the definition of Bulow et al. (1985) so that ≠ 2 pi / ≠x j ≠x i 5 P9 1 x i P0 , 0. This implies that the reaction functions of the firms are all downward sloping and that the Cournot equilibrium is unique as well as being stable. The comparative static results for the effects of the production subsidies can be obtained by totally differentiating the first-order conditions for profit maximisation (2) to obtain: (P9 1 x i P0)dX 1 P9 dx i 1 ds i 5 0, i 5 1,M.
(3)
Summing (3) over all the M firms, then noting that Y 5 X 5 o im51 x i and that dX 5 o mi 51 dx i yields
O ds . M
((M 1 1)P9 1 XP0)dX 5
i
(4)
i 51
Hence, the effect of a production subsidy given by the ith member state on total production is ≠X / ≠s i 5 2 1 /D . 0 and on price is ≠P/ ≠s i 5 2 P9 /D , 0, where D 5 (M 1 1)P9 1 XP0 , 0. Substituting these results into (3), it can be shown that
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the effect of a production subsidy given by the ith member state on the output of its firm and the output of the rest of the industry is ≠x MP9 1 (X 2 x i )P0 ]i 5 ]]]]] . 0, ≠s i DP9 ≠(X 2 x i ) (M 2 1)P9 1 (X 2 x i )P0 ]]] 5 ]]]]]]] , 0. ≠s i DP9
(5)
These derivatives can be signed by noting that the assumption that outputs are strategic substitutes implies that (M 2 1)P9 1 (X 2 x i )P0 , 0. Hence, a production subsidy increases the output of the firm in the member state giving the subsidy, reduces the output of the rest of the industry, leads to an increase in total industry output and a reduction in the market price. For later reference, if all member states set the same production subsidy then the comparative statics for a change in this common subsidy can easily be shown to be ≠X / ≠s 5 2 M /D . 0 and ≠P/ ≠s 5 2 MP9 /D , 0. All member states increasing their subsidies by the same amount will increase total industry output and lead to a reduction in the market price.
3. Nash equilibrium in subsidies Although all member states are in the customs union, it seems reasonable to assume that each member state is concerned to maximise its own national welfare and attaches no weight to the welfare of the other member states. Thus, ignoring questions of income distribution, the welfare of each member state is given by the sum of consumer surplus and producer surplus less the cost of the production subsidy. To capture the fact that the government revenue to pay the production subsidy will typically be raised by some form of distortionary taxation, the opportunity cost of government revenue will be allowed to exceed unity as in Neary (1994). Thus, the cost of the production subsidy includes the deadweight loss imposed by the distortionary taxation used to finance the subsidy; hence, the welfare of the ith member state can be written as Wi 5V(P) 1 pi 2 ls i x i 5V(P) 1 (P 2 c)x i 2 ( l 2 1)s i x i ,
(6)
where l is the opportunity cost of government revenue and the term ( l 2 1)s i x i represents the deadweight loss from the distortionary taxation which will be zero if lump-sum taxes are feasible, l 5 1. In the absence of any restriction on state aid to industry, national governments will be free to give production subsidies to their firms and the result will be a subsidy war that can best be modelled as a Nash equilibrium in subsidies. In the Nash equilibrium, the national governments independently and simultaneously set their production subsidies to maximise their national welfare; hence, the first-order conditions for the Nash equilibrium are
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S
D
≠W ≠x ≠x ≠P ]i 5 (x i 2 y)] 1 (P 2 c)]i 2 ( l 2 1) s i ]i 1 x i 5 0. ≠s i ≠s i ≠s i ≠s i
873
(7)
The first term is the terms of trade effect: the subsidy reduces the market price and will worsen (improve) the terms of trade if the member state is a net importer (exporter), (x i 2 y) . ( , )0. The second term is the profit-shifting effect: the subsidy increases the output of the domestic firm thereby shifting profits to the domestic firm. The third term is the deadweight loss effect: increasing the subsidy increases total expenditure on the subsidy and thereby increases the deadweight loss from distortionary taxation as tax revenue has to be increased. Since the model is symmetric, all firms have identical marginal cost and demand is identical in all member states, there will obviously be a symmetric Nash equilibrium where all the national governments set the same subsidy, s i 5 s N , and all the firms produce the same quantity of output, x i 5 x. As production and consumption will be identical in all member states, x 5 y, net exports will be zero and consequently there will be no terms of trade effect in (7) at the symmetric Nash equilibrium. Hence, solving (7) yields the Nash equilibrium production subsidy:
F
G
2 xP9 ( l 2 1)D s N 5 ]] 1 2 ]]]]] . l MP9 1 (X 2 x)P0
(8)
When lump-sum taxes are feasible, l 5 1, the Nash equilibrium subsidy is unambiguously positive, s N 5 2 xP9 . 0, but, with distortionary taxation, the Nash equilibrium subsidy will only be positive if the opportunity cost of government revenue is less than the critical value l S , which is obtained by setting the expression in square brackets in (8) equal to zero: P9 1 (M 2 1)(P9 1 xP0) (P9 1 xP0) l S ; 1 1 ]]]]]]] 5 2 2 ]]]. D D
(9)
Clearly, given the assumption of strategic substitutes, this critical value of opportunity cost is greater than one but less than two. Substituting the Nash equilibrium subsidy (8) into the ith firm’s first-order condition for profit maximisation (2) yields the firm’s price-cost margin:
F
G
2 xP9( l 2 1) D P 2 c 5 ]]]] 1 1 ]]]]] > 0. l MP9 1 (X 2 x)P0
(10)
When lump-sum taxes are feasible, l 5 1, price is equal to marginal cost so the oligopolistic distortion is eliminated and the welfare of the customs union is maximised at the Nash equilibrium in production subsidies. Unusually, the Nash equilibrium in production subsidies yields a Pareto-efficient outcome for the member states rather than the usual prisoners’ dilemma type of outcome. Obviously, in this case, the prohibition of subsidies would reduce the welfare of the customs union and the member states. With distortionary taxation, l . 1, price
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exceeds marginal cost so the oligopolistic distortion is not fully eliminated at the Nash equilibrium in production subsidies. To determine the effect of an increase in the opportunity cost of government revenue on the Nash equilibrium production subsidy, consider the reaction function of the ith member state shown in Fig. 1. This gives the optimal subsidy of the ith member state as a function of the average subsidy set by the other member states, s¯ 5 o j ±i s j /(M 2 1); the reaction function is implicitly given by the firstorder condition for welfare maximisation (7). In the symmetric Nash equilibrium, all the national governments set the same subsidy, s N , which is given by the intersection of the ith member state’s reaction function with the diagonal, s i 5 s N , at A in Fig. 1. The effect of an increase in the opportunity cost of government revenue on the ith member state’s reaction function is obtained by differentiating
Fig. 1. Production subsidy reaction function.
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(7), while holding constant the subsidies set by all the other national governments, which yields ds ≠ 2Wi ≠ 2Wi ≠ 2Wi ≠x i ]i 5 2 ]] ]] ]] , 0, where 5 2 s i ] 1 x i , 0, 2 dl ≠l ≠s i ≠s i ≠l ≠s i ≠s i
Y
S
D
(11)
and the second-order condition for welfare maximisation implies that ≠ 2Wi / ≠s 2i , 0. Since ds i / dl , 0, the effect of an increase in the opportunity cost of government revenue is to shift the reaction function of the ith member state downwards from f Ai to f Bi in Fig. 1; hence, there is a reduction in the Nash equilibrium production subsidy from s AN to s BN so ds N / dl , 0. Note that this result guarantees the uniqueness of the critical value of opportunity cost, l S , derived above in Eq. (9). The main results of this section are summarised in the following proposition: Proposition 1. The Nash equilibrium production subsidy is positive if the opportunity cost of government revenue is less than l S , and an increase in the opportunity cost leads to a reduction in the Nash equilibrium production subsidy. For each government, the optimum subsidy is given by equating the marginal benefit of the subsidy with its marginal cost. The marginal benefit of the subsidy is the sum of the terms of trade effect and the profit shifting effect while the marginal cost is the deadweight loss from the distortionary taxation required to finance the subsidy. Provided the marginal cost of the subsidy (the opportunity cost of government revenue) is sufficiently low, the Nash equilibrium production subsidy will be positive and all governments will subsidise their firms. An increase in the opportunity cost of government revenue increases the marginal cost of the subsidy and will lead all governments to set lower subsidies which will lead to a reduction in the Nash equilibrium production subsidy.
4. The prohibition of subsidies Having derived the Nash equilibrium in production subsidies, the next step is to derive the welfare effect on the customs union of a reduction in subsidies by all the national governments and then to assess the welfare effect of prohibiting subsidies. Since all member states are assumed to be identical, they all set the same Nash equilibrium production subsidy and if they all reduce their subsidies by the same amount then they will all continue to set the same subsidy. Hence, for these welfare comparisons, the welfare of the customs union can be considered to be a function of a common production subsidy set by all the national governments. With a common production subsidy, the welfare of all member states will be equal
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and the aggregate welfare of the customs union is simply obtained by summing the welfare of the member states:
OW 5 MV(P) 1 (P 2 c)X 2 ( l 2 1)sX. M
V5
i
(12)
i 51
The welfare effect of a reduction in subsidies by all national governments can be assessed by differentiating aggregate welfare with respect to the common production subsidy, which yields ≠V ≠P ≠X ] 5 (Y 2 X)] 1 hP 2 c 2 ( l 2 1)sj] 2 ( l 2 1)X. ≠s ≠s ≠s
(13)
Using the first-order conditions for welfare maximisation (7), together with the comparative static results for the effects of a common production subsidy derived in Section 3, to evaluate this derivative at the Nash equilibrium yields ≠V N (M 2 1)(P9 1 xP0) ]] 5 2 ( l 2 1)X ]]]]] < 0. ≠s MP9 1 (X 2 x)P0
(14)
When lump-sum taxes are feasible, l 5 1, aggregate welfare of the customs union is maximised since the Nash equilibrium subsidies yield a market price equal to marginal cost; hence, this derivative is equal to zero. With distortionary taxation, l . 1, this derivative is negative so if all member states reduce their subsidies then there will be an increase in the aggregate welfare of the customs union and of all the member states. This is because, for a small reduction in the subsidies evaluated at the Nash equilibrium, the reduction in the deadweight loss from distortionary taxation exceeds the increase in the deadweight loss from the oligopolistic distortion. This result leads to the following proposition: Proposition 2. With distortionary taxation, l . 1, a reduction in production subsidies by all member states, evaluated at the Nash equilibrium, will increase the aggregate welfare of the customs union and of all the member states. This shows that a small reduction in subsidies, evaluated at the Nash equilibrium, will increase aggregate welfare of the customs union, but it does not imply that prohibiting subsidies will yield higher welfare for the customs union than in the Nash equilibrium. To demonstrate that the prohibition of subsidies may be beneficial, consider Fig. 2 which shows aggregate welfare when subsidies are prohibited, V P, and in the Nash equilibrium in subsidies, V N , as functions of the opportunity cost of government revenue. Aggregate welfare when subsidies are prohibited is independent of opportunity cost since with no subsidies there is no deadweight loss from distortionary taxation required to finance the subsidies. When lump-sum taxes are feasible, the Nash equilibrium is Pareto-efficient and aggregate welfare in the Nash equilibrium is obviously higher than aggregate
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Fig. 2. Welfare comparison of Nash equilibrium with prohibition of Subsidies.
welfare when subsidies are prohibited. When opportunity cost is equal to the critical value, l 5 l S , the Nash equilibrium subsidy is equal to zero so aggregate welfare in the Nash equilibrium is identical to aggregate welfare when subsidies are prohibited. The slope of aggregate welfare in the Nash equilibrium is obtained by totally differentiating (11) with respect to opportunity cost and evaluating at the Nash equilibrium: dV N ≠V N ds N ≠V N ≠V N ds N ]] 5 ]] ] 1 ]] 5 ]] ] 2 s N X. dl ≠s dl ≠l ≠s dl
(15)
For l . 1, the first term is positive since ≠V N / ≠s , 0 and ds N / dl , 0 while the second term is negative if the Nash equilibrium subsidy is positive. At the critical
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value of opportunity cost, l 5 l S , the Nash equilibrium subsidy is zero so the second term vanishes leaving the first term which is unambiguously positive; hence, aggregate welfare in the Nash equilibrium is positively sloped at l 5 l S and therefore must be ‘‘U’’ shaped as shown in Fig. 2.6 Consequently, there must be some value of opportunity cost, l P, that is lower than the critical value of opportunity cost, l S , where aggregate welfare is the same in the Nash equilibrium as when subsidies are prohibited, V N ( l P ) 5 V P for 1 , l P , l S . Thus, for values of opportunity cost greater than l P but less than l S , the Nash equilibrium subsidy is positive and prohibiting subsidies yields higher welfare for all member states in the customs union than in the Nash equilibrium; this leads to the following proposition: Proposition 3. There exists a range of values for the opportunity cost of government revenue, l P , l , l S , where the Nash equilibrium production subsidy is positive and aggregate welfare (and that of each member state) is higher when subsidies are prohibited than in the Nash equilibrium. This proposition demonstrates that there always exists a range of values for the opportunity cost of government revenue where the Nash equilibrium subsidy is positive and the prohibition of subsidies yields higher welfare than in the Nash equilibrium. For these values of opportunity cost, the deadweight loss from distortionary taxation in the Nash equilibrium exceeds the increase in the deadweight loss from the oligopolistic distortion when subsidies are prohibited. The situation is a prisoners’ dilemma where each member state has an incentive to give subsidies but all member states are worse-off in the Nash equilibrium than under prohibition. Thus, this model provides an economic rationale for the EC regulations on state aid that attempt to control subsidies. It explains both the incentive for welfare maximising governments to give subsidies and the desire of the EU to prohibit subsidies.
5. Examples: linear and constant elasticity demand functions To illustrate the practical relevance of these results, the critical values of the opportunity cost of government revenue will be calculated for the two most common functional forms: linear and constant elasticity demand functions. Before looking at these examples some recent estimates of the opportunity cost of
6
For very high values of opportunity cost, l . l S , all governments tax their firms in the Nash equilibrium and aggregate welfare is increasing in opportunity cost. In this case, taxing the oligopolistic industry is the most efficient method of raising revenue for the member states; hence, welfare in the Nash equilibrium is higher than when subsidies (and taxes) are prohibited.
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government revenue will be briefly reviewed so that the practical relevance of the critical values in these examples can be assessed. Since studies usually report estimates for the marginal welfare cost (MWC) of public funds, it should be noted that the opportunity cost of government revenue is given by l 5 1 1 MWC. Recently, Snow and Warren (1996) derived a general analytical formula for the marginal welfare cost of public funds and used it to reconcile disparities among the reported estimates of MWC. For the case when distortionary taxation is used to finance a transfer payment (such as a production subsidy), they report estimates for the MWC ranging from 0.195 to 0.236, which implies values for the opportunity cost of government revenue from 1.195 to 1.236.7 Thus, a value for the opportunity cost of government revenue equal to 1.2 seems perfectly plausible and this figure should be borne in mind when assessing the practical relevance of the critical values in the following examples. The first example to be considered is the simplest possible case of linear demand where the aggregate inverse demand function is P 5 a 2 b Y, and it is fairly straightforward to show that the Nash equilibrium production subsidy is: s N 5 (a 2 c)h(2M 1 1) 2 l(M 1 1)j /L,
(16)
where the denominator is positive, L 5 lM 2 1 ( l 2 1)(2M 1 1) . 0. The Nash equilibrium subsidy is positive if the term in curly brackets is positive; hence, the critical value of opportunity cost where the Nash equilibrium subsidy is zero is: M 1 l S 5 1 1 ]] 5 2 2 ]]. M 11 M 11
(17)
This critical value of opportunity cost is equal to 5 / 3 when there are two member states and asymptotically approaches 2 as the number of member states increases. Given the estimates of the opportunity cost of government revenue, it seems unlikely that member states will be deterred from giving subsidies as a result of having to finance them with distortionary taxation. Further straightforward, but messy, derivations yield the aggregate welfare in the Nash equilibrium and when subsidies are prohibited: M(M 1 2) V P 5 ]]]]2 (a 2 c)2 , 2b (M 1 1)
l 2 M 2 (M 2 1 2( l 2 1)(M 1 1)) V N 5 ]]]]]]]]] (a 2 c)2 . 2bL 2
(18)
7 See Table 1 of Snow and Warren (1996) for the case of non-exhaustive government spending p 5 0, where they report the results of Browning (1987), Stuart (1984) and Ballard (1990) together with their own estimates based on their Eq. (18) and the parameters used in the earlier studies.
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The critical value of opportunity cost l P is obtained by equating these two expressions and solving for opportunity cost. There are three possible solutions: l 5 l S is one solution, but obviously not the appropriate solution, and the other two solutions are two roots of a quadratic, one of which is less than unity while the other is greater than unity. Since opportunity cost must exceed unity, the appropriate solution is the larger of these two roots: ]]]]]]]]]] 2M 2 1 5M 1 2 1œ(M 1 2)(2M 1 1)(2M 2 2 3M 1 2) l 5 ]]]]]]]]]]]]]]]. 4M(M 1 1) P
(19)
The two critical values of opportunity cost, l S and l P, are plotted together in Fig. 3 as a function of the number of member states in the customs union. For values of the opportunity cost between the two critical values, l P , l , l S , the Nash equilibrium production subsidy is positive and the prohibition of subsidies will increase the aggregate welfare of the customs union and of all the member nations. It can be seen that there is a wide range of values where this is the case and, when
Fig. 3. Critical values of opportunity cost: linear demand.
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there are more than a few member states, it includes the estimated values of the opportunity cost of government revenue. The second example to be considered is the case of constant elasticity demand where the aggregate inverse demand function is P 5 Y 21 / h and the elasticity of demand equal to h. To ensure that the assumption that outputs are strategic substitutes is satisfied, it will be assumed that h . 1 /(M 2 1), which implies that the firms’ reaction functions are downward sloping in the symmetric Cournot equilibrium but they are not everywhere downward sloping. It is straightforward to derive the Nash equilibrium production subsidy but the resulting expression is very messy and will not be reported, but it can be used to derive the critical value for the opportunity cost of government revenue that makes the Nash equilibrium subsidy equal to zero: (M 2 1)(Mh 2 1) 1 h l S 5 1 1 ]]]]]]. M(Mh 2 1)
(20)
With two member states, the critical value is equal to 2 when the elasticity of demand is equal to 1 and is decreasing in the elasticity of demand, approaching 7 / 4 as the elasticity of demand becomes very large. As the number of member states becomes very large, the critical value asymptotically approaches 2. For the smallest value of the elasticity of demand consistent with strategic substitutes, h 5 1 /(M 2 1), the critical value is equal to 2 and it is decreasing in the elasticity of demand as can be seen by differentiating (20): ≠l S 21 ]] 5 ]]]]2 , 0. ≠h M(Mh 2 1)
(21)
Having derived the Nash equilibrium subsidy, it can be used to derive aggregate welfare in the Nash equilibrium which can then be used to calculate the critical value of opportunity cost such that prohibition yields the same welfare as in the Nash equilibrium, V N ( l P ) 5 V P. This problem cannot be solved analytically, but can be solved numerically using Mathematica for different values of the elasticity of demand and the results can then be plotted. Fig. 4 shows the two critical values of opportunity cost when the elasticity of demand is equal to 2 as a function of the number of member states.8 Clearly, there is a wide range of values for the opportunity cost of government revenue where the Nash equilibrium subsidy is positive and the prohibition of subsidies will be welfare improving for all the member states in the customs union. With more than four member states in the customs union, this range of values includes the estimates for the opportunity cost of government revenue. Hence, with both linear and constant elasticity demand, the estimates of opportunity cost suggest that the results of this paper are
8
Similar results are obtained for other values of the elasticity of demand.
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Fig. 4. Critical values of opportunity cost: constant elasticity of demand equal to 2.
practically relevant and that the prohibition of subsidies will be welfare improving for the customs union.
6. Conclusions The aim of this paper was to provide an economic explanation for the desire of the member states to grant state aid to their firms and the desire of the European Commission to prohibit or, at least, to limit state aid in the internal market. The desire of the member states to give subsidies can easily be explained by profitshifting in oligopolistic industries, but this does not explain the desire of the Commission to prohibit subsidies since the welfare of the customs union would be maximised in a symmetric Nash equilibrium in subsidies. All the member states giving subsidies yields a Pareto-efficient outcome where price is equal to marginal cost and the oligopolistic distortion is eliminated. However, if the subsidies have to be financed by distortionary taxation, which implies an opportunity cost greater than unity, then the desire of the Commission to limit or prohibit subsidies can be explained. Prohibiting subsidies results in an increase in the deadweight loss from
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the oligopolistic distortion but this is outweighed by the decrease in the deadweight loss from distortionary taxation if the opportunity cost of government revenue is sufficiently large, but a large enough value of opportunity cost will deter the member states from giving subsidies in the first place. The main contribution of this paper was to show that there always exists a range of values for the opportunity cost of government revenue where individual member states want to give subsidies and where the multilateral prohibition of subsidies would increase the welfare of all member states. Furthermore, this range of values was shown to include plausible estimates of opportunity cost. Therefore, although the Nash equilibrium in subsidies may yield a Pareto-efficient outcome if lump sum taxes are feasible, the likely outcome is a prisoners’ dilemma for plausible values of opportunity cost. This article has ignored non-economic explanations for state aid such as the desire of governments to shore up uncompetitive domestic firms and to protect employment in certain sectors for political reasons. With the assumption of symmetry so that all firms are equally efficient, this obviously important issue cannot really be addressed in this model.9 However, when state aid is motivated by political rather than economic factors, the argument for the prohibition of state aid is undoubtedly strengthened. The conclusion of the paper has great practical relevance as it suggests that the European Union could gain by taking stronger action to limit or even to prohibit state aid. This could be achieved by the European Commission setting ceilings for the level of state aid in individual member states and then reducing these ceilings over time until state aid was significantly reduced or even eliminated. The Commission seems to agree since the conclusion of the latest survey of state aid notes that ‘‘(A)s well as being a source of distortion of competition, the observed high levels of state aid risk to endanger the efficient functioning of the internal market’’ and that ‘‘(T)his situation will certainly induce the Commission to look for means that could further increase the efficiency and strictness of its state aid controls’’.10
Acknowledgements Presented to the EARIE conference at Copenhagen in August 1998, and to workshops at Cardiff Business School and the University of Antwerp (UFSIA). I
9
In fact, if profit-shifting was the motive for intervention then the member states with the most competitive firms would be expected to give the largest amount of state aid, but this does not seem to be what is observed. 10 European Commission (1997b) (p. 39).
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would like to thank the participants, especially Wilfried Pauwels, and a referee for their insightful comments.
References Ballard, C.L., 1990. Marginal efficiency cost calculations. Journal of Public Economics 41, 263–276. Brander, J.A., Spencer, B.J., 1985. Export subsidies and international market share rivalry. Journal of International Economics 18, 83–100. Browning, E.K., 1987. On the marginal welfare cost of taxation. American Economic Review 77, 11–23. Bulow, J.I., Geanakoplos, J.D., Klemperer, P.D., 1985. Multimarket Oligopoly: Strategic substitutes and complements. Journal of Political Economy 93, 488–511. Collie, D.R., 1997. Bilateralism is good: trade blocs and strategic export subsidies. Oxford Economic Papers 49, 504–520. European Commission, 1995. Competition Law in the European Communities, Vol. IIA: Rules Applicable to State Aid. Office for Official Publications of the European Communities, Luxembourg. European Commission, 1997a. Competition Law in the European Communities, Vol. IIB: Explanation of the Rules Applicable to State Aid. Office for Official Publications of the European Communities, Luxembourg. European Commission, 1997b. Fifth Survey on State Aid in the European Union in the Manufacturing and Certain Other Sectors, Com(97) 170. Office for Official Publications of the European Communities, Luxembourg. Neary, J.P., 1994. Cost asymmetries in international subsidy games: should governments help winners or losers?. Journal of International Economics 37, 197–218. Snow, A., Warren, R.S., 1996. The marginal cost of funds: theory and evidence. Journal of Public Economics 61, 289–305. Stuart, C., 1984. Welfare costs per dollar of additional tax revenue. American Economic Review 74, 352–362.
State aid in the European Union: The prohibition of subsidies in an integrated market David R. Collie* Cardiff Business School, Cardiff University, Aberconway Building, Colum Drive, Cardiff CF1 3 EU, UK Accepted 30 October 1998
Abstract The effect of prohibiting state aid in an integrated market is analysed in a symmetric Cournot oligopoly model where one firm is located in each member state. Subsidies are financed by distortionary taxation so there is a trade-off between the deadweight loss from the oligopolistic distortion and that from distortionary taxation. It is shown that there exists a range of values for the opportunity cost of government revenue where member states want to give subsidies and where the multilateral prohibition of subsidies would increase aggregate welfare. Furthermore, this range of values is shown to include plausible estimates of opportunity cost. 2000 Elsevier Science B.V. All rights reserved. Keywords: Distortionary taxation; European Union; Oligopoly; State aid JEL classification: L13; L40; L52
1. Introduction Article 92(1) of the EC treaty states that ‘‘any aid granted by a member state or through state resources in any form whatsoever which distorts or threatens to distort competition by favouring certain undertakings or the production of certain goods shall, in so far as it affects trade between member states, be incompatible
* E-mail address: [email protected] (D.R. Collie) 0167-7187 / 00 / $ – see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S0167-7187( 98 )00051-4
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with the common market’’.1 However, although this statement seems unambiguous, it does not amount to an absolute prohibition of state aid since there are a number of exceptions to this general rule.2 Member states are required to notify the European Commission of any proposed state aid so that the Commission can determine whether the aid qualifies for exemption.3 The Commission also keeps existing aid under constant review and requires member states to provide it with annual reports. The extent of state aid in the European Union can be seen from Table 1, which shows state aid to industry as a percentage of value added for the EC12 from 1990 to 1994 together with 3 year averages for the individual member states for 1990–92 and 1992–94. Looking at these figures it is hard to disagree with the European Commission (1997b) in its latest survey on state aid when it says that ‘‘the volume of aid in the Community is massive’’. It goes on to say that the survey reflects ‘‘the determined will of the Community to eliminate distorting aid that is incompatible with the internal market and to keep overall aid levels under control’’. Clearly, faced with the desire of the member states to grant state aid, the European Commission is struggling to achieve its objective. The purpose of this paper is to provide an explanation for the desire of member states to grant state aid to their firms and the desire of the Commission to prohibit or, at least, to limit state aid. Although many analysts would explain this situation by appealing to political economy arguments, this paper will attempt to provide a purely economic explanation based upon welfare maximising governments. Throughout this article, state aid will be modelled as a production subsidy that has the effect of reducing the recipient firm’s marginal cost of production. A perfectly competitive model cannot really explain the situation since there is no incentive for the member states to give subsidies to their firms as the effect would be to
1 An explanation of the rules applicable to state aid is given in European Commission (1997a) and the rules themselves are detailed in European Commission (1995). 2 Article 92(2) lists three types of state aid that are always compatible with the common market: firstly, ‘‘aid having a social character, granted to individual consumers, provided that such aid is granted without discrimination related to the origin of the products concerned’’; secondly, ‘‘aid to make good the damage caused by natural disasters or exceptional circumstances’’; thirdly, ‘‘aid to regions of the Federal Republic of Germany disadvantaged by the division’’, but since the reunification of Germany in October 1990 this category has become obsolete. Article 92(3) lists four types of state aid that may be exempted by the European Commission. Article 92(3)(a) refers to ‘‘aid to promote the economic development of areas where the standard of living is abnormally low or where there is serious underemployment’’. Article 92(3)(b) refers to ‘‘aid to promote the execution of an important project of common European interest or to remedy a serious disturbance in the economy of a member state’’. Article 92(3)(c) covers ‘‘aid to facilitate the development of certain economic activities or of certain economic areas, where such aid does not adversely affect trading conditions to an extent contrary to the common interest’’. Article 92(3)(d) refers to ‘‘aid to promote culture and heritage conservation’’, and there is an Article 92(3)(e) that allows further categories of aid that may be exempted to be added if proposed by the European Commission. 3 Firms that receive aid that has not been notified to the Commission may have to repay this aid if the Commission decides that the aid is incompatible with the common market.
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Table 1 State aid to industry as a percentage of value added % EC12
1990 4.0
1991 3.6
1992 3.9
1993 4.2
%
1990–92
1992–94
Belgium Denmark Germany Greece Spain France Ireland Italy Luxembourg Netherlands Portugal United Kingdom EC12
7.9 1.9 3.5 12.5 2.1 2.7 2.7 8.9 3.5 2.5 4.6 1.4 3.8
4.8 2.8 4.8 10.5 1.7 3.3 3.5 8.4 2.9 2.1 4.4 0.8 4.0
1994 3.8
Source: Fifth Survey on State Aid in the European Union in the Manufacturing and Certain Other Sectors, Com(97) 170.
reduce welfare by introducing a production distortion into the economy.4 With imperfect competition, as in the Cournot oligopoly model considered by Brander and Spencer (1985), the profit-shifting motive would provide an incentive for the member states to give subsidies to their firms. With all member states giving subsidies in the Nash equilibrium some readers might think, by analogy with the Brander and Spencer model, that the outcome will obviously be a prisoners’ dilemma, but they would be wrong! Unlike the Brander and Spencer model, the member states all consume the subsidised products so consumers will benefit from a subsidy war. In fact, in a symmetric model, all member states will subsidise their firms in the Nash equilibrium until price is equal to marginal cost, which will lead to a Pareto-efficient outcome rather than the usual prisoners’ dilemma. All the member states giving subsidies eliminates the deadweight loss due to the oligopolistic distortion. Thus, imperfect competition on its own cannot provide an explanation, but the addition of distortionary taxation as in Neary (1994) does provide a solution to the puzzle.5 4
Although, in the absence of an import tariff, a production subsidy to an industry that was a net importer could be used to improve the terms of trade if the country was large, but this would also imply using a production tax in industries that were net exporters. 5 Collie (1997) analyses the effect of trade bloc formation in a multi-country version of the Brander and Spencer (1985) model with distortionary taxation added as in Neary (1994), and suggests that this model may explain multilateral agreements to limit or prohibit export subsidies.
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With distortionary taxation, the opportunity cost of government revenue exceeds unity due to the marginal welfare cost of taxation, and this reduces the incentive for member states to give subsidies. However, provided the opportunity cost of government revenue is sufficiently low, the member states will still give subsidies in the Nash equilibrium. Then, when all member states reduce subsidies, there may be a welfare gain if the increase in the deadweight loss from the oligopolistic distortion is outweighed by the reduction in the deadweight loss from distortionary taxation. Obviously, provided the opportunity cost of government revenue is sufficiently high, there will be a welfare gain when subsidies are reduced. The main result of this paper is to show that there always exists a range of values for the opportunity cost of government revenue where a prisoners’ dilemma obtains: individual member states want to give subsidies whereas the multilateral reduction or prohibition of subsidies would increase the welfare of all member states. Furthermore, using specific functional forms, it is shown that this range of values for the opportunity cost of government revenue includes the most plausible empirical estimates of opportunity cost. An important assumption that will be employed throughout this article is that of symmetry: all countries and all firms will be assumed to be identical. Despite the obvious asymmetry in the state aid granted by member states shown in Table 1, the assumption of symmetry seems reasonable in a model looking at the aggregate welfare gains from the prohibition of subsidies given the analytical convenience of this assumption. Without this assumption, the explicit welfare comparison between the Nash equilibrium in production subsidies and prohibition would only be possible by assuming linear demand. The layout of the paper is as follows: Section 2 presents the basic Cournot oligopoly model, then the Nash equilibrium in subsidies is derived in Section 3. The welfare effects of a reduction in subsidies from the Nash equilibrium levels and of a complete prohibition of subsidies are analysed in Section 4. Some examples with specific functional forms are considered in Section 5, then the conclusions are presented in Section 6.
2. The model The model is a partial equilibrium analysis of the welfare effects of production subsidies in a Cournot oligopolistic industry located within a single integrated market. Like the Single Market of the European Union, this integrated market was formed by a customs union, consisting of M identical countries, eliminating all barriers to trade and arbitrage between its member states. In each member state, there is a single oligopolistic firm that produces a homogeneous good for sale in the integrated market. Symmetry is assumed so all the firms have identical and constant marginal cost c. The firm in the ith member state receives a production subsidy s i from its government and produces output x i for sale in the integrated
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market. Consumers are identical in all member states, and can be represented by a single representative consumer in each market with an indirect utility function that is linearly separable: U 5V(P) 1 I where P is the consumer price and I is income. With perfect arbitrage and no trade barriers, there will be a uniform consumer price in all member states. By Roy’s identity, consumption in each market is given by y 5 2 ≠V/ ≠P, so total consumption in the integrated market is Y 5 My 5 2 M ≠V/ ≠P, and this can be inverted to obtain the aggregate inverse demand function: P 5 P(Y), where it is assumed that the demand curve is downward sloping, P9 , 0. The model can be viewed as a two stage game where the national governments set production subsidies to maximise their national welfare at the first stage and the firms compete in a Cournot oligopoly at the second stage. As usual, the game is solved by backwards induction to obtain the subgame perfect equilibrium, and the first step is to solve the final stage of the game where the profits of the firm in the ith member state are:
pi 5 (P 2 c 1 s i )xi , i 5 1,M.
(1)
In the Cournot equilibrium of the final stage of the game, the M firms simultaneously and independently set their outputs to maximise their profits given the production subsidies set by the national governments. Assuming an interior solution, where all firms produce some positive quantity, the first-order conditions for a Cournot equilibrium are: ≠pi / ≠x i 5 P 1 x i P9 2 c 1 s i 5 0, i 5 1,M.
(2)
The second-order conditions for profit maximisation are assumed to hold so that ≠ 2 pi / ≠x 2i 5 2P9 1 x i P0 , 0, and it will also be assumed that the outputs of the firms are strategic substitutes according to the definition of Bulow et al. (1985) so that ≠ 2 pi / ≠x j ≠x i 5 P9 1 x i P0 , 0. This implies that the reaction functions of the firms are all downward sloping and that the Cournot equilibrium is unique as well as being stable. The comparative static results for the effects of the production subsidies can be obtained by totally differentiating the first-order conditions for profit maximisation (2) to obtain: (P9 1 x i P0)dX 1 P9 dx i 1 ds i 5 0, i 5 1,M.
(3)
Summing (3) over all the M firms, then noting that Y 5 X 5 o im51 x i and that dX 5 o mi 51 dx i yields
O ds . M
((M 1 1)P9 1 XP0)dX 5
i
(4)
i 51
Hence, the effect of a production subsidy given by the ith member state on total production is ≠X / ≠s i 5 2 1 /D . 0 and on price is ≠P/ ≠s i 5 2 P9 /D , 0, where D 5 (M 1 1)P9 1 XP0 , 0. Substituting these results into (3), it can be shown that
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the effect of a production subsidy given by the ith member state on the output of its firm and the output of the rest of the industry is ≠x MP9 1 (X 2 x i )P0 ]i 5 ]]]]] . 0, ≠s i DP9 ≠(X 2 x i ) (M 2 1)P9 1 (X 2 x i )P0 ]]] 5 ]]]]]]] , 0. ≠s i DP9
(5)
These derivatives can be signed by noting that the assumption that outputs are strategic substitutes implies that (M 2 1)P9 1 (X 2 x i )P0 , 0. Hence, a production subsidy increases the output of the firm in the member state giving the subsidy, reduces the output of the rest of the industry, leads to an increase in total industry output and a reduction in the market price. For later reference, if all member states set the same production subsidy then the comparative statics for a change in this common subsidy can easily be shown to be ≠X / ≠s 5 2 M /D . 0 and ≠P/ ≠s 5 2 MP9 /D , 0. All member states increasing their subsidies by the same amount will increase total industry output and lead to a reduction in the market price.
3. Nash equilibrium in subsidies Although all member states are in the customs union, it seems reasonable to assume that each member state is concerned to maximise its own national welfare and attaches no weight to the welfare of the other member states. Thus, ignoring questions of income distribution, the welfare of each member state is given by the sum of consumer surplus and producer surplus less the cost of the production subsidy. To capture the fact that the government revenue to pay the production subsidy will typically be raised by some form of distortionary taxation, the opportunity cost of government revenue will be allowed to exceed unity as in Neary (1994). Thus, the cost of the production subsidy includes the deadweight loss imposed by the distortionary taxation used to finance the subsidy; hence, the welfare of the ith member state can be written as Wi 5V(P) 1 pi 2 ls i x i 5V(P) 1 (P 2 c)x i 2 ( l 2 1)s i x i ,
(6)
where l is the opportunity cost of government revenue and the term ( l 2 1)s i x i represents the deadweight loss from the distortionary taxation which will be zero if lump-sum taxes are feasible, l 5 1. In the absence of any restriction on state aid to industry, national governments will be free to give production subsidies to their firms and the result will be a subsidy war that can best be modelled as a Nash equilibrium in subsidies. In the Nash equilibrium, the national governments independently and simultaneously set their production subsidies to maximise their national welfare; hence, the first-order conditions for the Nash equilibrium are
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S
D
≠W ≠x ≠x ≠P ]i 5 (x i 2 y)] 1 (P 2 c)]i 2 ( l 2 1) s i ]i 1 x i 5 0. ≠s i ≠s i ≠s i ≠s i
873
(7)
The first term is the terms of trade effect: the subsidy reduces the market price and will worsen (improve) the terms of trade if the member state is a net importer (exporter), (x i 2 y) . ( , )0. The second term is the profit-shifting effect: the subsidy increases the output of the domestic firm thereby shifting profits to the domestic firm. The third term is the deadweight loss effect: increasing the subsidy increases total expenditure on the subsidy and thereby increases the deadweight loss from distortionary taxation as tax revenue has to be increased. Since the model is symmetric, all firms have identical marginal cost and demand is identical in all member states, there will obviously be a symmetric Nash equilibrium where all the national governments set the same subsidy, s i 5 s N , and all the firms produce the same quantity of output, x i 5 x. As production and consumption will be identical in all member states, x 5 y, net exports will be zero and consequently there will be no terms of trade effect in (7) at the symmetric Nash equilibrium. Hence, solving (7) yields the Nash equilibrium production subsidy:
F
G
2 xP9 ( l 2 1)D s N 5 ]] 1 2 ]]]]] . l MP9 1 (X 2 x)P0
(8)
When lump-sum taxes are feasible, l 5 1, the Nash equilibrium subsidy is unambiguously positive, s N 5 2 xP9 . 0, but, with distortionary taxation, the Nash equilibrium subsidy will only be positive if the opportunity cost of government revenue is less than the critical value l S , which is obtained by setting the expression in square brackets in (8) equal to zero: P9 1 (M 2 1)(P9 1 xP0) (P9 1 xP0) l S ; 1 1 ]]]]]]] 5 2 2 ]]]. D D
(9)
Clearly, given the assumption of strategic substitutes, this critical value of opportunity cost is greater than one but less than two. Substituting the Nash equilibrium subsidy (8) into the ith firm’s first-order condition for profit maximisation (2) yields the firm’s price-cost margin:
F
G
2 xP9( l 2 1) D P 2 c 5 ]]]] 1 1 ]]]]] > 0. l MP9 1 (X 2 x)P0
(10)
When lump-sum taxes are feasible, l 5 1, price is equal to marginal cost so the oligopolistic distortion is eliminated and the welfare of the customs union is maximised at the Nash equilibrium in production subsidies. Unusually, the Nash equilibrium in production subsidies yields a Pareto-efficient outcome for the member states rather than the usual prisoners’ dilemma type of outcome. Obviously, in this case, the prohibition of subsidies would reduce the welfare of the customs union and the member states. With distortionary taxation, l . 1, price
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exceeds marginal cost so the oligopolistic distortion is not fully eliminated at the Nash equilibrium in production subsidies. To determine the effect of an increase in the opportunity cost of government revenue on the Nash equilibrium production subsidy, consider the reaction function of the ith member state shown in Fig. 1. This gives the optimal subsidy of the ith member state as a function of the average subsidy set by the other member states, s¯ 5 o j ±i s j /(M 2 1); the reaction function is implicitly given by the firstorder condition for welfare maximisation (7). In the symmetric Nash equilibrium, all the national governments set the same subsidy, s N , which is given by the intersection of the ith member state’s reaction function with the diagonal, s i 5 s N , at A in Fig. 1. The effect of an increase in the opportunity cost of government revenue on the ith member state’s reaction function is obtained by differentiating
Fig. 1. Production subsidy reaction function.
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(7), while holding constant the subsidies set by all the other national governments, which yields ds ≠ 2Wi ≠ 2Wi ≠ 2Wi ≠x i ]i 5 2 ]] ]] ]] , 0, where 5 2 s i ] 1 x i , 0, 2 dl ≠l ≠s i ≠s i ≠l ≠s i ≠s i
Y
S
D
(11)
and the second-order condition for welfare maximisation implies that ≠ 2Wi / ≠s 2i , 0. Since ds i / dl , 0, the effect of an increase in the opportunity cost of government revenue is to shift the reaction function of the ith member state downwards from f Ai to f Bi in Fig. 1; hence, there is a reduction in the Nash equilibrium production subsidy from s AN to s BN so ds N / dl , 0. Note that this result guarantees the uniqueness of the critical value of opportunity cost, l S , derived above in Eq. (9). The main results of this section are summarised in the following proposition: Proposition 1. The Nash equilibrium production subsidy is positive if the opportunity cost of government revenue is less than l S , and an increase in the opportunity cost leads to a reduction in the Nash equilibrium production subsidy. For each government, the optimum subsidy is given by equating the marginal benefit of the subsidy with its marginal cost. The marginal benefit of the subsidy is the sum of the terms of trade effect and the profit shifting effect while the marginal cost is the deadweight loss from the distortionary taxation required to finance the subsidy. Provided the marginal cost of the subsidy (the opportunity cost of government revenue) is sufficiently low, the Nash equilibrium production subsidy will be positive and all governments will subsidise their firms. An increase in the opportunity cost of government revenue increases the marginal cost of the subsidy and will lead all governments to set lower subsidies which will lead to a reduction in the Nash equilibrium production subsidy.
4. The prohibition of subsidies Having derived the Nash equilibrium in production subsidies, the next step is to derive the welfare effect on the customs union of a reduction in subsidies by all the national governments and then to assess the welfare effect of prohibiting subsidies. Since all member states are assumed to be identical, they all set the same Nash equilibrium production subsidy and if they all reduce their subsidies by the same amount then they will all continue to set the same subsidy. Hence, for these welfare comparisons, the welfare of the customs union can be considered to be a function of a common production subsidy set by all the national governments. With a common production subsidy, the welfare of all member states will be equal
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and the aggregate welfare of the customs union is simply obtained by summing the welfare of the member states:
OW 5 MV(P) 1 (P 2 c)X 2 ( l 2 1)sX. M
V5
i
(12)
i 51
The welfare effect of a reduction in subsidies by all national governments can be assessed by differentiating aggregate welfare with respect to the common production subsidy, which yields ≠V ≠P ≠X ] 5 (Y 2 X)] 1 hP 2 c 2 ( l 2 1)sj] 2 ( l 2 1)X. ≠s ≠s ≠s
(13)
Using the first-order conditions for welfare maximisation (7), together with the comparative static results for the effects of a common production subsidy derived in Section 3, to evaluate this derivative at the Nash equilibrium yields ≠V N (M 2 1)(P9 1 xP0) ]] 5 2 ( l 2 1)X ]]]]] < 0. ≠s MP9 1 (X 2 x)P0
(14)
When lump-sum taxes are feasible, l 5 1, aggregate welfare of the customs union is maximised since the Nash equilibrium subsidies yield a market price equal to marginal cost; hence, this derivative is equal to zero. With distortionary taxation, l . 1, this derivative is negative so if all member states reduce their subsidies then there will be an increase in the aggregate welfare of the customs union and of all the member states. This is because, for a small reduction in the subsidies evaluated at the Nash equilibrium, the reduction in the deadweight loss from distortionary taxation exceeds the increase in the deadweight loss from the oligopolistic distortion. This result leads to the following proposition: Proposition 2. With distortionary taxation, l . 1, a reduction in production subsidies by all member states, evaluated at the Nash equilibrium, will increase the aggregate welfare of the customs union and of all the member states. This shows that a small reduction in subsidies, evaluated at the Nash equilibrium, will increase aggregate welfare of the customs union, but it does not imply that prohibiting subsidies will yield higher welfare for the customs union than in the Nash equilibrium. To demonstrate that the prohibition of subsidies may be beneficial, consider Fig. 2 which shows aggregate welfare when subsidies are prohibited, V P, and in the Nash equilibrium in subsidies, V N , as functions of the opportunity cost of government revenue. Aggregate welfare when subsidies are prohibited is independent of opportunity cost since with no subsidies there is no deadweight loss from distortionary taxation required to finance the subsidies. When lump-sum taxes are feasible, the Nash equilibrium is Pareto-efficient and aggregate welfare in the Nash equilibrium is obviously higher than aggregate
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Fig. 2. Welfare comparison of Nash equilibrium with prohibition of Subsidies.
welfare when subsidies are prohibited. When opportunity cost is equal to the critical value, l 5 l S , the Nash equilibrium subsidy is equal to zero so aggregate welfare in the Nash equilibrium is identical to aggregate welfare when subsidies are prohibited. The slope of aggregate welfare in the Nash equilibrium is obtained by totally differentiating (11) with respect to opportunity cost and evaluating at the Nash equilibrium: dV N ≠V N ds N ≠V N ≠V N ds N ]] 5 ]] ] 1 ]] 5 ]] ] 2 s N X. dl ≠s dl ≠l ≠s dl
(15)
For l . 1, the first term is positive since ≠V N / ≠s , 0 and ds N / dl , 0 while the second term is negative if the Nash equilibrium subsidy is positive. At the critical
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value of opportunity cost, l 5 l S , the Nash equilibrium subsidy is zero so the second term vanishes leaving the first term which is unambiguously positive; hence, aggregate welfare in the Nash equilibrium is positively sloped at l 5 l S and therefore must be ‘‘U’’ shaped as shown in Fig. 2.6 Consequently, there must be some value of opportunity cost, l P, that is lower than the critical value of opportunity cost, l S , where aggregate welfare is the same in the Nash equilibrium as when subsidies are prohibited, V N ( l P ) 5 V P for 1 , l P , l S . Thus, for values of opportunity cost greater than l P but less than l S , the Nash equilibrium subsidy is positive and prohibiting subsidies yields higher welfare for all member states in the customs union than in the Nash equilibrium; this leads to the following proposition: Proposition 3. There exists a range of values for the opportunity cost of government revenue, l P , l , l S , where the Nash equilibrium production subsidy is positive and aggregate welfare (and that of each member state) is higher when subsidies are prohibited than in the Nash equilibrium. This proposition demonstrates that there always exists a range of values for the opportunity cost of government revenue where the Nash equilibrium subsidy is positive and the prohibition of subsidies yields higher welfare than in the Nash equilibrium. For these values of opportunity cost, the deadweight loss from distortionary taxation in the Nash equilibrium exceeds the increase in the deadweight loss from the oligopolistic distortion when subsidies are prohibited. The situation is a prisoners’ dilemma where each member state has an incentive to give subsidies but all member states are worse-off in the Nash equilibrium than under prohibition. Thus, this model provides an economic rationale for the EC regulations on state aid that attempt to control subsidies. It explains both the incentive for welfare maximising governments to give subsidies and the desire of the EU to prohibit subsidies.
5. Examples: linear and constant elasticity demand functions To illustrate the practical relevance of these results, the critical values of the opportunity cost of government revenue will be calculated for the two most common functional forms: linear and constant elasticity demand functions. Before looking at these examples some recent estimates of the opportunity cost of
6
For very high values of opportunity cost, l . l S , all governments tax their firms in the Nash equilibrium and aggregate welfare is increasing in opportunity cost. In this case, taxing the oligopolistic industry is the most efficient method of raising revenue for the member states; hence, welfare in the Nash equilibrium is higher than when subsidies (and taxes) are prohibited.
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government revenue will be briefly reviewed so that the practical relevance of the critical values in these examples can be assessed. Since studies usually report estimates for the marginal welfare cost (MWC) of public funds, it should be noted that the opportunity cost of government revenue is given by l 5 1 1 MWC. Recently, Snow and Warren (1996) derived a general analytical formula for the marginal welfare cost of public funds and used it to reconcile disparities among the reported estimates of MWC. For the case when distortionary taxation is used to finance a transfer payment (such as a production subsidy), they report estimates for the MWC ranging from 0.195 to 0.236, which implies values for the opportunity cost of government revenue from 1.195 to 1.236.7 Thus, a value for the opportunity cost of government revenue equal to 1.2 seems perfectly plausible and this figure should be borne in mind when assessing the practical relevance of the critical values in the following examples. The first example to be considered is the simplest possible case of linear demand where the aggregate inverse demand function is P 5 a 2 b Y, and it is fairly straightforward to show that the Nash equilibrium production subsidy is: s N 5 (a 2 c)h(2M 1 1) 2 l(M 1 1)j /L,
(16)
where the denominator is positive, L 5 lM 2 1 ( l 2 1)(2M 1 1) . 0. The Nash equilibrium subsidy is positive if the term in curly brackets is positive; hence, the critical value of opportunity cost where the Nash equilibrium subsidy is zero is: M 1 l S 5 1 1 ]] 5 2 2 ]]. M 11 M 11
(17)
This critical value of opportunity cost is equal to 5 / 3 when there are two member states and asymptotically approaches 2 as the number of member states increases. Given the estimates of the opportunity cost of government revenue, it seems unlikely that member states will be deterred from giving subsidies as a result of having to finance them with distortionary taxation. Further straightforward, but messy, derivations yield the aggregate welfare in the Nash equilibrium and when subsidies are prohibited: M(M 1 2) V P 5 ]]]]2 (a 2 c)2 , 2b (M 1 1)
l 2 M 2 (M 2 1 2( l 2 1)(M 1 1)) V N 5 ]]]]]]]]] (a 2 c)2 . 2bL 2
(18)
7 See Table 1 of Snow and Warren (1996) for the case of non-exhaustive government spending p 5 0, where they report the results of Browning (1987), Stuart (1984) and Ballard (1990) together with their own estimates based on their Eq. (18) and the parameters used in the earlier studies.
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The critical value of opportunity cost l P is obtained by equating these two expressions and solving for opportunity cost. There are three possible solutions: l 5 l S is one solution, but obviously not the appropriate solution, and the other two solutions are two roots of a quadratic, one of which is less than unity while the other is greater than unity. Since opportunity cost must exceed unity, the appropriate solution is the larger of these two roots: ]]]]]]]]]] 2M 2 1 5M 1 2 1œ(M 1 2)(2M 1 1)(2M 2 2 3M 1 2) l 5 ]]]]]]]]]]]]]]]. 4M(M 1 1) P
(19)
The two critical values of opportunity cost, l S and l P, are plotted together in Fig. 3 as a function of the number of member states in the customs union. For values of the opportunity cost between the two critical values, l P , l , l S , the Nash equilibrium production subsidy is positive and the prohibition of subsidies will increase the aggregate welfare of the customs union and of all the member nations. It can be seen that there is a wide range of values where this is the case and, when
Fig. 3. Critical values of opportunity cost: linear demand.
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there are more than a few member states, it includes the estimated values of the opportunity cost of government revenue. The second example to be considered is the case of constant elasticity demand where the aggregate inverse demand function is P 5 Y 21 / h and the elasticity of demand equal to h. To ensure that the assumption that outputs are strategic substitutes is satisfied, it will be assumed that h . 1 /(M 2 1), which implies that the firms’ reaction functions are downward sloping in the symmetric Cournot equilibrium but they are not everywhere downward sloping. It is straightforward to derive the Nash equilibrium production subsidy but the resulting expression is very messy and will not be reported, but it can be used to derive the critical value for the opportunity cost of government revenue that makes the Nash equilibrium subsidy equal to zero: (M 2 1)(Mh 2 1) 1 h l S 5 1 1 ]]]]]]. M(Mh 2 1)
(20)
With two member states, the critical value is equal to 2 when the elasticity of demand is equal to 1 and is decreasing in the elasticity of demand, approaching 7 / 4 as the elasticity of demand becomes very large. As the number of member states becomes very large, the critical value asymptotically approaches 2. For the smallest value of the elasticity of demand consistent with strategic substitutes, h 5 1 /(M 2 1), the critical value is equal to 2 and it is decreasing in the elasticity of demand as can be seen by differentiating (20): ≠l S 21 ]] 5 ]]]]2 , 0. ≠h M(Mh 2 1)
(21)
Having derived the Nash equilibrium subsidy, it can be used to derive aggregate welfare in the Nash equilibrium which can then be used to calculate the critical value of opportunity cost such that prohibition yields the same welfare as in the Nash equilibrium, V N ( l P ) 5 V P. This problem cannot be solved analytically, but can be solved numerically using Mathematica for different values of the elasticity of demand and the results can then be plotted. Fig. 4 shows the two critical values of opportunity cost when the elasticity of demand is equal to 2 as a function of the number of member states.8 Clearly, there is a wide range of values for the opportunity cost of government revenue where the Nash equilibrium subsidy is positive and the prohibition of subsidies will be welfare improving for all the member states in the customs union. With more than four member states in the customs union, this range of values includes the estimates for the opportunity cost of government revenue. Hence, with both linear and constant elasticity demand, the estimates of opportunity cost suggest that the results of this paper are
8
Similar results are obtained for other values of the elasticity of demand.
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Fig. 4. Critical values of opportunity cost: constant elasticity of demand equal to 2.
practically relevant and that the prohibition of subsidies will be welfare improving for the customs union.
6. Conclusions The aim of this paper was to provide an economic explanation for the desire of the member states to grant state aid to their firms and the desire of the European Commission to prohibit or, at least, to limit state aid in the internal market. The desire of the member states to give subsidies can easily be explained by profitshifting in oligopolistic industries, but this does not explain the desire of the Commission to prohibit subsidies since the welfare of the customs union would be maximised in a symmetric Nash equilibrium in subsidies. All the member states giving subsidies yields a Pareto-efficient outcome where price is equal to marginal cost and the oligopolistic distortion is eliminated. However, if the subsidies have to be financed by distortionary taxation, which implies an opportunity cost greater than unity, then the desire of the Commission to limit or prohibit subsidies can be explained. Prohibiting subsidies results in an increase in the deadweight loss from
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the oligopolistic distortion but this is outweighed by the decrease in the deadweight loss from distortionary taxation if the opportunity cost of government revenue is sufficiently large, but a large enough value of opportunity cost will deter the member states from giving subsidies in the first place. The main contribution of this paper was to show that there always exists a range of values for the opportunity cost of government revenue where individual member states want to give subsidies and where the multilateral prohibition of subsidies would increase the welfare of all member states. Furthermore, this range of values was shown to include plausible estimates of opportunity cost. Therefore, although the Nash equilibrium in subsidies may yield a Pareto-efficient outcome if lump sum taxes are feasible, the likely outcome is a prisoners’ dilemma for plausible values of opportunity cost. This article has ignored non-economic explanations for state aid such as the desire of governments to shore up uncompetitive domestic firms and to protect employment in certain sectors for political reasons. With the assumption of symmetry so that all firms are equally efficient, this obviously important issue cannot really be addressed in this model.9 However, when state aid is motivated by political rather than economic factors, the argument for the prohibition of state aid is undoubtedly strengthened. The conclusion of the paper has great practical relevance as it suggests that the European Union could gain by taking stronger action to limit or even to prohibit state aid. This could be achieved by the European Commission setting ceilings for the level of state aid in individual member states and then reducing these ceilings over time until state aid was significantly reduced or even eliminated. The Commission seems to agree since the conclusion of the latest survey of state aid notes that ‘‘(A)s well as being a source of distortion of competition, the observed high levels of state aid risk to endanger the efficient functioning of the internal market’’ and that ‘‘(T)his situation will certainly induce the Commission to look for means that could further increase the efficiency and strictness of its state aid controls’’.10
Acknowledgements Presented to the EARIE conference at Copenhagen in August 1998, and to workshops at Cardiff Business School and the University of Antwerp (UFSIA). I
9
In fact, if profit-shifting was the motive for intervention then the member states with the most competitive firms would be expected to give the largest amount of state aid, but this does not seem to be what is observed. 10 European Commission (1997b) (p. 39).
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would like to thank the participants, especially Wilfried Pauwels, and a referee for their insightful comments.
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