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Lobbying and Cournot-Nash competition
Journal of International Economics 35 (1993) 367-376. North-Holland
Lobbying and Cournot-Nash competition Implications for strategic trade policy Michael O. Moore Department of Economics and Elliott School of International Affairs, The George Washington University, 2201 G. St. NW, Washington, DC 20052, USA
Steven M. Suranovic* Department of Economics, The George Washington University, 2201 G. St. NW, Washington, DC 20052, USA Received July 1991, revised version received November 1992
Arguments for strategic trade intervention with Cournot duopolists are reconsidered in a model where domestic firms can lobby for increased subsidies. An export subsidy may not improve national welfare if lobbying costs are included. Even if an optimal positive subsidy exists, the government needs information about lobbying effectiveness in order to correctly implement the program.
1. Introduction One of the most important contributions to international trade theory of the last decade is the incorporation of imperfect competition into the study of optimal trade policy. A number of authors have shown that in a world with oligopolistic industries, free trade may not maximize national welfare. The classic paper by Brander and Spencer (1985) showed that in a model of Cournot behavior between a domestic and foreign firm, a government export subsidy can shift sufficient profits from the foreign duopolist to more than pay for the subsidy. Their work, and others' that followed, have generated much discussion about strategic trade and industrial policy, both among academic observers and policy analysts.l While these studies have outlined circumstances when unilateral trade intervention may increase domestic welfare, a number of caveats have Correspondence to: Michael Moore, Department of Economics, The George Washington University, 2201 G. St. NW, Washington, DC 20052, USA. *We wish to thank Jim Brander, Burkhard Drees and two anonymous referees for helpful comments.
1For a survey of the imperfect competition literature, see Krishna and Thursby (1990). 0022-1996/93/$06.00 © 1993--Elsevier Science Publishers B.V. All fights reserved
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M.O. Moore and S.M. Suranovic, Lobbying and Cournot-Nash competition
emerged. 2 Many authors have alluded to how. lobbying may distort strategic trade policy outcomes. Krugman (1987, p. 141) has written that 'an effort to pursue efficiency through intervention could be captured by special interests and turned into an inefficient redistributionist program'. Similarly, Grossman (1986. p. 65) argues that 'experience has shown that the trade policy apparatus is susceptible to the political pressures ... The risk that any scheme of targeted export promotion would fall prey to much the same special interest pressures is cause for grave concern.' The implicationg of lobbying for strategic trade policy are particularly appropriate since the targeted industries, i.e. those with positive economic profits, are precisely the industries analyzed in the endogenous protection literature) Imperfectly competitive firms may use the excess funds to obtain higher subsidies which may distort the allocation of subsidies granted in a strategic trade program. Therefore, a natural overlap exists between the strategic trade policy literature and the lobbying literature. Despite this, no attempt has been made to formally analyze the implications of including lobbying in a model of strategic trade policy. In this paper we attempt to combine these two literatures. In particular, we extend the analysis of Brander and Spencer (1985) and allow the targeted industry to lobby to increase the production subsidy. Lobbying occurs subsequent to the announcement of the subsidy program, i.e. while the government can precommit to establishing a program, rent-seeking behavior may alter the final level of the subsidy. 4 We find that the argument for strategic trade policy in a model of Cournot duopoly is weakened in two fundamental ways. On the one hand, including the costs of lobbying in the government's objective function means that a subsidy may not raise national welfare. Even when a positive optimal subsidy exists, the government must lower the announced subsidy to compensate for the effects of lobbying. In order to know how much to 'lowbalr, the government must have considerable information about the lobbying effectiveness of the industries in question, thereby further increasing the information requirements necessary to optimally administer an export subsidy program. We find further that a government that ignores the effects of lobbying will generally set a non-optimal subsidy. 2The results are sensitive to the choice variable of the oligopolistic firms [Eaton and Grossman (1986)], the sequence of decisions rGruenspecht (1988)], the degree of market segmentation [Markusen and Venables (1988)], the number of domestic firms [Dixit and Grossman (1986)] and the possibility of retaliation. 3For examples of endogenous protection models with imperfectly competitive markets, see Cassing and Hillman (1985) and Hillman and Urspring (1988). For a review of this literature, see Moore (1990). 4Brander and Spencer allude in a footnote to the importance of credible government precommitment to a subsidy rate. We focus on one reason that governments may not be able to commit to a final subsidy rate, i.e. the presence of lobbying.
M.O. Moore and S.M. Suranovic, Lobbying and Cournot-Nash competition
369
The rest of the paper is organized in the following way. In section 2 we develop the general analytical framework. In section 3 we consider the effects of lobbying in the one-industry case, both when the government takes lobbying into account and also when it ignores lobbying activities. Concluding remarks and possible extensions are in section 4. 2. The model In this section we extend the original Brander-Spencer framework to allow lobbying for a subsidy by a domestic industry. We assume that the industry consists of one domestic and one foreign firm. The industry exports its product entirely to a third market, s We assume that the domestic and foreign firms play a Cournot-Nash game to determine output levels. We assume that the government initiates a subsidy program the purpose of which is to shift profits from foreign to domestic firms. The program might involve the creation of a new government agency such as a Ministry of International Trade and Industry. The agency's mission is to determine the size of the optimal subsidy for the eligible industry. We assume that the domestic firm learns of its eligibility when the program is announced. The government announces the likely per unit subsidy, s, that the firm will receive. However, the final subsidy rate will be determined only after the firm has had an opportunity to lobby for a larger subsidy? We imagine that the government's initial announced subsidy is its 'best-guess' of the optimal subsidy based on readily available information. The domestic firm's lobbying activity aims to increase the subsidy, perhaps beyond the national optimum. Lobbying uses resources, L, diverted from the production of goods and hired at the wage rate, w. The more resources devoted to lobbying, the higher the firm's subsidy, ceteris paribus. We describe the total unit production subsidy by the function
S==_s+~(L),
(I)
where s is the initial government subsidy and a(L) is the lobbying-affected component of the subsidy rate. 7 The variable subsidy component, a(L), is increasing in the firm's own lobbying effort. Sln this way we avoid the complications of welfare effects for domestic consumers as a result of a change in prices. 6The analysis below will demonstrate that national welfare would be higher if the government did not allow lobbying to affect the subsidy rate. We assume that this is not a credible 'threat', because of political considerations not explicitly modeled. 7This formulation is applicable in a two-stage process whenever a policy proposal is announced and the final outcome is susceptible to lobbying efforts. For example, the executive branch may propose an initial subsidy (s), while ¢ is that part of the subsidy affected by lobbying in the legislature. There is, therefore, a lobbying game in the background which we have not explicitly raodeled.
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M.O. Moore and $.M. Suranovic, Lobbying ~.nd Cournot-Nash competition
The model is constructed as a two-stage game. In the first stage the government announces the subsidy program. The announcement includes a list of eligible firms and the initial per unit subsidy, s, for the firm. The domestic government chooses the initial subsidy level s to maximize total domestic profits, U, net of subsidy payments and lobbying costs: (2)
U=-~-(s+~(L))x,
where n is the profit of the firm. The government will pick s taking the profit-maximizing decision of the firm into account. This will ensure that the equilibrum is subgame perfect. In the second stage the firm chooses a production level (x) and lobbying effort (L) to maximize its own profit, n: = t,(x + y ) x
-c(x) + Is + a(L)]x -
wL,
(3)
where y is the output of the foreign competitor, s is the initial subsidy chosen by the government in stage one (both assumed fixed by the domestic firm), and c(x) is variable cost. 3. Effects of government intervention We will consider two scenarios about government behavior, each of which depends on the information used in its decision. A 'smart' government will take full account of the lobbying activity that will occur in stage 2. A 'naive' government will choose the subsidy without regard to the effect of subsequent lobbying activity. Case 1. Smart government. The first-order conditions for the domestic firm are a ~x=p~x + p-c~ + Is + ~r(L)] < O,
(4)
nL=~LX--w
(5)
Condition (5) is the Kuhn-Tucker condition for lobbying. If the costs of lobbying (w) were sufficiently high or if the industry's lobbying effectiveness (trL) were sufficiently low, then lobbying would not occur and the model reduces to the original Brander-Spencer model. We will assume in the subsequent analysis that (5) holds with equality for L >0 so that a positive level of lobbying occurs. The sufficient second-order conditions for profit maximization requires SSubscripts denote partial derivatives throughout.
M.O. Moore and S.M. Suranovic, Lobbying and Cournot-Nasb competition
371
that nxx <0, nLt. <0, and gxxal.,Ix - a2>'O. With these satisfied, we implicitly define the optimal values for the choice variables and label them ~ and L. The foreign competitor will choose y to maximize n* = p(x + y ) y - c*(y),
(6)
which yields the following first- and second-order conditions, respectively: (7)
n*fpyy+p-c~=O,
* -- pyyy + 2p - c .* rcy~
<0.
(8)
Again assuming sufficient second-order conditions yields the optimal value p. Own marginal profit effects of output changes are assumed to be larger than cross effects so that
n*,< n~*y.
(9)
The reaction of the domestic output to changes in the value of s can be determined by total differentiation of (4), (5) and (7). Using these simultaneously insures that both production and lobbying decisions are adjusted optimally to changes in the value of s. If the equilibrium is stable, then it can be shown that A
0R
~cs= OS
,
- aLLXn. > 0 d
(10)
and
Ls-- oL = OLnvv< 0, ds
(11)
A
9 These results mean that where A = --aLn.+ar.LX[nx,,nyy--rcyxnxy]
(12) Os
A
The government's objective function is: max U :-- n(Sc, y,L; s, w)-(s + cr(L))yc.
(13)
The government chooses s, taking into account the domestic firm's production and lobbying decisions as well as the responses of the foreign rival. 9Stability of the sytem requires that the product of the slopes of the reaction curves is less than one. The domestic reaction curve, defined inclusive of lobbying, is derived from eqs. (4) and (5). The foreign reaction curve is derived from eq. (7).
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M.O. Moore and S.M. Suranovic, Lobbying and Cournot-Nash competition
After some manipulation, the first-order condition becomes
us= : pxS,s - [s +
wL =o.
(14)
In c~rder to determine whether a small subsidy will improve national welfare, we evaluate (14) when s=O: Us,. =o= ~p.~s-(a(L))~s-
wLs.
(15)
From (10), (I1) and (12), we know that ~s>0, Ls>0 and ~,<0, so that (15) may be positive or negative. If positive, then the profit shifted from the foreign rival ($p~,) as a result of a subsidy will exceed the marginal cost of increased lobbying (¢(L)Yc,+wL~). However, if (15) is negative, then any subsidy program will necessarily reduce welfare. This demonstrates that the existence of lobbying can negate the potential benefits of a strategic export subsidy. As expected, the higher are the direct costs of rent-seeking (w), the less likely that the introduction of the subsidy program will be welfare-improving. In the subsequent analysis, we will assume that the subsidy program will be beneficial, even when lobbying exists. This assumption implies that (15) is positive so that a small subsidy will improve national welfare as defined by (13). Using (14), we can solve for the optimal initial subsidy announced by the government:
rL,l
(16)
where sms= px~ [YJXs]. The expression ssis is of the same form as the optimal subsidy derived in Brander and Spencer. When no lobbying occurs, the expression has the same value at the optimum. With lobbying, the functional forms of ~s and ~s differ from those derived in Brander and Spencer so that ssis can be smaller or larger than the original optimal subsidy when lobbying opportunities are absent. Substituting (16) into (1), we find that total per ur.it subsidies after the domestic industry lobbies in the second period are
S =--g+ ¢r(L)=sa/S- w [ ~ ].
(17)
Since the government takes full account of the subsequent lobbying activity that will raise the subsidy, it will 'lowball' the announced initial subsidy by just enough to ensure that the total subsidy reaches the national optimum. In fig. 1 we plot welfare as defined by (2) against the total per unit subsidy. The highest curve, A, represents welfare when there is no lobbying. Uo is the
M.O. Moore and S.M. Suranovic, Lobbying and Cournot-Nash competition
373
Uo
\
Z
O
.
I
I--<[
C
Z
s°
FINAL
Sm
UNIT SUBSIDY Fig. 1
level of welfare if there is no subsidy program. The optimal subsidy as derived in Brander and Spencer equals s o and the subsidy program is beneficial. If lobbying occurs, national welfare net of lobbying costs will lie below curve A. Welfare is necessarily lower relative to the Brander and Spencer case since lobbying costs are incurred~ In fig. 1 we have drawn curve B under the assumption that the total subsidy under lobbying is less than s °. However, the final total subsidy under lobbying may be greater than or less than sO.1° As drawn, welfare is still higher than if there were no subsidy 1°This ambiguity can be seen explicitly using the special case of linear demand function~ The difference between the optimal subsidy of Brander and Spencer and that given by (17) is
- -L~,j is the optimal production level under Brander and Spencer. Given the results shown in (10), (11) and (12), the sign of this expression is ambiguous since ~ is greater than x NL. w h e r e XNL
374
M.O. Moore and S.M. Suranovic, Lobbying and Cournot-Nash competition
program. While a subsidy program in the presence of lobbying can be beneficial, this result depends not only on government knowledge about profit-shifting potential but also on its knowledge of firm lobbying abilities as well as lobbying costs. Even if we accept government omniscience, a subsidy program may not be worthwhile. As the cost of lobbying (w) rises, the welfare contour shifts down. If w were high enough, welfare might be described by curve C. In this case the optimum lies below Uo, and the subsidy program would reduce welfare.
Case 2. Naive government. In this case we assume that the government initiates a subsidy program by announcing an initial subsidy, but does not take subsequent firm lobbying into account. ", his situation might arise if the government did not have sufficient information about lobbying. An alternative interpretation is that a government ministry announced the program but a legislature, susceptible to lobbying, steps in to alter the subsidy rate. The government's objective function from (13) is optimized presuming L =0, which is the same problem solved by the government in Brander and Spencer. The government would choose an initial subsidy, s = s°. Lobbying in the second period results in a higher final subsidy, S~=s°+~(L). If the optimal subsidy under lobbying, ~, is less than s°, then the naive government will necessarily over-subsidize and welfare will be less than optimal. However, if ~ > s °, then it is conceivable that lobbying could raise the final subsidy to the optimal level. In this case, the naive government may blunder into the correct subsidy. 5. Conclusion
In this paper we have analyzed the impact of lobbying in a model of Cournot duopoly. We assume that the government cannot precommit to a level of subsidies and that lobbying effort by the targeted export industries can increase the per unit subsidy beyond the level announced by the government in the first period. As expected, the presence of lobbying weakens the argument for strategic trade subsidies designed to capture profits from rival foreign firms. Three results stand out. First, the inclusion of lobbying costs in the national welfare function means that a unilateral incentive no longer necessarily exists for the government to provide a subsidy to the domestic Cournot competitor; lobbying costs may overwhelm the profits captured from foreigners. Secondly, even if a positive optimal subsidy exists, a government that correctly anticipates the effects of lobbying will set a lower subsidy in the first stage to compensate for the lobbying in the second. National welfare will necessarily be lower than that achieved under Brander and Spencer because of the resources lest to lobbying. Finally, a government
M.O. Moore and S.M. Suranovic, Lobbying and Cournot-Nash competition
375
that does not account for rent-seeking behavior will most likely either overor under-subsidize and further reduce welfare. Additional complications are likely to arise if multiple industries are eligible for a strategic export subsidy. If these industries lobby for additional subsidies, then all of the caveats identified above hold for each industry. Secondly, the government will need even more information in order to implement a welfare-improving subsidy program. For example, one industry's lobbying may affect another industry's ability to secure a higher subsidy. Consequently, the government would need to understand the nature of the lobbying 'game' among industries. A further problem may occur if the targeted industries have differential political clout. For example, a relatively influential industry may receive a higher-than-optimal subsidy on the basis of political clout rather than profit-shifting potential. 11 This framework could also be extended to Bertrand competition as well as models with more complicated market structures. Many of the basic points derived in this paper are likely to hold. 12 Strategic trade programs of most types will induce rent-seeking behavior by firms eager for higher profits. The welfare costs of the resultant lobbying will generally lessen the benefits of such export programs, even if the government can fully anticipate these activities. Furthermore, the information needed by the government to compensate for the distortionary effects of lobbying may be very extensive and not readily available. l tDixit and Grossman (1986) have already identified one scenario when the argument for intervention is weaker for export subsidies in a multiple-firm case. In their study, many industries compete for the use of a inelastically-suppli~! specialized factor used in production. Support for one firm can result in profit decreases in the other sectors. The firms modeled in this study do not share such a specialized factor. 12Moore and Suranovic (1992) analyze a similar model using Cournot-Stackelberg, Bertrand-Stackelberg and Bertrand-Nash firm behavior.
References Brander, J.A. and B.J. Spencer, 1985, Export subsidies and international market share rivalry, Journal of International Economics 18, 83-100. Cassing, J. and A. Hillman, 1985, Political influence motives and the choice between tariffs and quotas, Journal of International Economics 19, 279-300. Dixit, A.K. and G.M. Grossman, 1986, Targeted export promotion with several oligopolist industries, Journal of International Economics 21,233-250. Eaton, J. and G.M. Grossman, 1986, Optimal trade and industrial policy under oligopoly, Quarterly Journal of Economics, 383--406. Grossman, G., 1986, Strategic trade promotion: A critique, in: P. Krugman, ed., Strategic trade policy and the new international economics (MIT Press, Cambridge, MA) 47-68. Gruenspecht, H., 1988, Export subsidies for differentiated products, Journal of International Economics 24, 331-344. Hillman, A. and H. Urspring, 1988, Domestic politics, foreign interests and international trade policy, American Economic Review 51, 59-79. Krishna, K. and M. Thursby, 1990, Trade policy with imperfe-t competition: A selective surwy, in: C. Carter, A. McCalla and J. Sharpies, eds.~ Imperfect competition and political economy (Westview Press, Boulder, CO) 9-36.
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M.O. Moore and S.M. Suranovic, Lobbying and Cournot-Nash competition
Krngman, P., 1987, Is free trade passe?, Journal of Economic Perspectives 1, 131-144. Markusen, J. and A. Venables, 1988, Trade policy with increasing returns and imperfect competition, Journal of International Economics 24, 299-316. Moore, M., 1990, New developments in the political economy of protectionism, in: C. Carter, A. McCalla and J. Sharpies, eds., Imperfect competition and political economy lWestview Press, Boulder, CO) 143-168. Moore, M. and S. Suranovic, 1992, Lobbying, incomplete information and optimal trade policy under imperfect competition, George Washington University, Department of Economics Discussion Paper D-92905.
Lobbying and Cournot-Nash competition Implications for strategic trade policy Michael O. Moore Department of Economics and Elliott School of International Affairs, The George Washington University, 2201 G. St. NW, Washington, DC 20052, USA
Steven M. Suranovic* Department of Economics, The George Washington University, 2201 G. St. NW, Washington, DC 20052, USA Received July 1991, revised version received November 1992
Arguments for strategic trade intervention with Cournot duopolists are reconsidered in a model where domestic firms can lobby for increased subsidies. An export subsidy may not improve national welfare if lobbying costs are included. Even if an optimal positive subsidy exists, the government needs information about lobbying effectiveness in order to correctly implement the program.
1. Introduction One of the most important contributions to international trade theory of the last decade is the incorporation of imperfect competition into the study of optimal trade policy. A number of authors have shown that in a world with oligopolistic industries, free trade may not maximize national welfare. The classic paper by Brander and Spencer (1985) showed that in a model of Cournot behavior between a domestic and foreign firm, a government export subsidy can shift sufficient profits from the foreign duopolist to more than pay for the subsidy. Their work, and others' that followed, have generated much discussion about strategic trade and industrial policy, both among academic observers and policy analysts.l While these studies have outlined circumstances when unilateral trade intervention may increase domestic welfare, a number of caveats have Correspondence to: Michael Moore, Department of Economics, The George Washington University, 2201 G. St. NW, Washington, DC 20052, USA. *We wish to thank Jim Brander, Burkhard Drees and two anonymous referees for helpful comments.
1For a survey of the imperfect competition literature, see Krishna and Thursby (1990). 0022-1996/93/$06.00 © 1993--Elsevier Science Publishers B.V. All fights reserved
368
M.O. Moore and S.M. Suranovic, Lobbying and Cournot-Nash competition
emerged. 2 Many authors have alluded to how. lobbying may distort strategic trade policy outcomes. Krugman (1987, p. 141) has written that 'an effort to pursue efficiency through intervention could be captured by special interests and turned into an inefficient redistributionist program'. Similarly, Grossman (1986. p. 65) argues that 'experience has shown that the trade policy apparatus is susceptible to the political pressures ... The risk that any scheme of targeted export promotion would fall prey to much the same special interest pressures is cause for grave concern.' The implicationg of lobbying for strategic trade policy are particularly appropriate since the targeted industries, i.e. those with positive economic profits, are precisely the industries analyzed in the endogenous protection literature) Imperfectly competitive firms may use the excess funds to obtain higher subsidies which may distort the allocation of subsidies granted in a strategic trade program. Therefore, a natural overlap exists between the strategic trade policy literature and the lobbying literature. Despite this, no attempt has been made to formally analyze the implications of including lobbying in a model of strategic trade policy. In this paper we attempt to combine these two literatures. In particular, we extend the analysis of Brander and Spencer (1985) and allow the targeted industry to lobby to increase the production subsidy. Lobbying occurs subsequent to the announcement of the subsidy program, i.e. while the government can precommit to establishing a program, rent-seeking behavior may alter the final level of the subsidy. 4 We find that the argument for strategic trade policy in a model of Cournot duopoly is weakened in two fundamental ways. On the one hand, including the costs of lobbying in the government's objective function means that a subsidy may not raise national welfare. Even when a positive optimal subsidy exists, the government must lower the announced subsidy to compensate for the effects of lobbying. In order to know how much to 'lowbalr, the government must have considerable information about the lobbying effectiveness of the industries in question, thereby further increasing the information requirements necessary to optimally administer an export subsidy program. We find further that a government that ignores the effects of lobbying will generally set a non-optimal subsidy. 2The results are sensitive to the choice variable of the oligopolistic firms [Eaton and Grossman (1986)], the sequence of decisions rGruenspecht (1988)], the degree of market segmentation [Markusen and Venables (1988)], the number of domestic firms [Dixit and Grossman (1986)] and the possibility of retaliation. 3For examples of endogenous protection models with imperfectly competitive markets, see Cassing and Hillman (1985) and Hillman and Urspring (1988). For a review of this literature, see Moore (1990). 4Brander and Spencer allude in a footnote to the importance of credible government precommitment to a subsidy rate. We focus on one reason that governments may not be able to commit to a final subsidy rate, i.e. the presence of lobbying.
M.O. Moore and S.M. Suranovic, Lobbying and Cournot-Nash competition
369
The rest of the paper is organized in the following way. In section 2 we develop the general analytical framework. In section 3 we consider the effects of lobbying in the one-industry case, both when the government takes lobbying into account and also when it ignores lobbying activities. Concluding remarks and possible extensions are in section 4. 2. The model In this section we extend the original Brander-Spencer framework to allow lobbying for a subsidy by a domestic industry. We assume that the industry consists of one domestic and one foreign firm. The industry exports its product entirely to a third market, s We assume that the domestic and foreign firms play a Cournot-Nash game to determine output levels. We assume that the government initiates a subsidy program the purpose of which is to shift profits from foreign to domestic firms. The program might involve the creation of a new government agency such as a Ministry of International Trade and Industry. The agency's mission is to determine the size of the optimal subsidy for the eligible industry. We assume that the domestic firm learns of its eligibility when the program is announced. The government announces the likely per unit subsidy, s, that the firm will receive. However, the final subsidy rate will be determined only after the firm has had an opportunity to lobby for a larger subsidy? We imagine that the government's initial announced subsidy is its 'best-guess' of the optimal subsidy based on readily available information. The domestic firm's lobbying activity aims to increase the subsidy, perhaps beyond the national optimum. Lobbying uses resources, L, diverted from the production of goods and hired at the wage rate, w. The more resources devoted to lobbying, the higher the firm's subsidy, ceteris paribus. We describe the total unit production subsidy by the function
S==_s+~(L),
(I)
where s is the initial government subsidy and a(L) is the lobbying-affected component of the subsidy rate. 7 The variable subsidy component, a(L), is increasing in the firm's own lobbying effort. Sln this way we avoid the complications of welfare effects for domestic consumers as a result of a change in prices. 6The analysis below will demonstrate that national welfare would be higher if the government did not allow lobbying to affect the subsidy rate. We assume that this is not a credible 'threat', because of political considerations not explicitly modeled. 7This formulation is applicable in a two-stage process whenever a policy proposal is announced and the final outcome is susceptible to lobbying efforts. For example, the executive branch may propose an initial subsidy (s), while ¢ is that part of the subsidy affected by lobbying in the legislature. There is, therefore, a lobbying game in the background which we have not explicitly raodeled.
370
M.O. Moore and $.M. Suranovic, Lobbying ~.nd Cournot-Nash competition
The model is constructed as a two-stage game. In the first stage the government announces the subsidy program. The announcement includes a list of eligible firms and the initial per unit subsidy, s, for the firm. The domestic government chooses the initial subsidy level s to maximize total domestic profits, U, net of subsidy payments and lobbying costs: (2)
U=-~-(s+~(L))x,
where n is the profit of the firm. The government will pick s taking the profit-maximizing decision of the firm into account. This will ensure that the equilibrum is subgame perfect. In the second stage the firm chooses a production level (x) and lobbying effort (L) to maximize its own profit, n: = t,(x + y ) x
-c(x) + Is + a(L)]x -
wL,
(3)
where y is the output of the foreign competitor, s is the initial subsidy chosen by the government in stage one (both assumed fixed by the domestic firm), and c(x) is variable cost. 3. Effects of government intervention We will consider two scenarios about government behavior, each of which depends on the information used in its decision. A 'smart' government will take full account of the lobbying activity that will occur in stage 2. A 'naive' government will choose the subsidy without regard to the effect of subsequent lobbying activity. Case 1. Smart government. The first-order conditions for the domestic firm are a ~x=p~x + p-c~ + Is + ~r(L)] < O,
(4)
nL=~LX--w
(5)
Condition (5) is the Kuhn-Tucker condition for lobbying. If the costs of lobbying (w) were sufficiently high or if the industry's lobbying effectiveness (trL) were sufficiently low, then lobbying would not occur and the model reduces to the original Brander-Spencer model. We will assume in the subsequent analysis that (5) holds with equality for L >0 so that a positive level of lobbying occurs. The sufficient second-order conditions for profit maximization requires SSubscripts denote partial derivatives throughout.
M.O. Moore and S.M. Suranovic, Lobbying and Cournot-Nasb competition
371
that nxx <0, nLt. <0, and gxxal.,Ix - a2>'O. With these satisfied, we implicitly define the optimal values for the choice variables and label them ~ and L. The foreign competitor will choose y to maximize n* = p(x + y ) y - c*(y),
(6)
which yields the following first- and second-order conditions, respectively: (7)
n*fpyy+p-c~=O,
* -- pyyy + 2p - c .* rcy~
<0.
(8)
Again assuming sufficient second-order conditions yields the optimal value p. Own marginal profit effects of output changes are assumed to be larger than cross effects so that
n*,< n~*y.
(9)
The reaction of the domestic output to changes in the value of s can be determined by total differentiation of (4), (5) and (7). Using these simultaneously insures that both production and lobbying decisions are adjusted optimally to changes in the value of s. If the equilibrium is stable, then it can be shown that A
0R
~cs= OS
,
- aLLXn. > 0 d
(10)
and
Ls-- oL = OLnvv< 0, ds
(11)
A
9 These results mean that where A = --aLn.+ar.LX[nx,,nyy--rcyxnxy]
(12) Os
A
The government's objective function is: max U :-- n(Sc, y,L; s, w)-(s + cr(L))yc.
(13)
The government chooses s, taking into account the domestic firm's production and lobbying decisions as well as the responses of the foreign rival. 9Stability of the sytem requires that the product of the slopes of the reaction curves is less than one. The domestic reaction curve, defined inclusive of lobbying, is derived from eqs. (4) and (5). The foreign reaction curve is derived from eq. (7).
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M.O. Moore and S.M. Suranovic, Lobbying and Cournot-Nash competition
After some manipulation, the first-order condition becomes
us= : pxS,s - [s +
wL =o.
(14)
In c~rder to determine whether a small subsidy will improve national welfare, we evaluate (14) when s=O: Us,. =o= ~p.~s-(a(L))~s-
wLs.
(15)
From (10), (I1) and (12), we know that ~s>0, Ls>0 and ~,<0, so that (15) may be positive or negative. If positive, then the profit shifted from the foreign rival ($p~,) as a result of a subsidy will exceed the marginal cost of increased lobbying (¢(L)Yc,+wL~). However, if (15) is negative, then any subsidy program will necessarily reduce welfare. This demonstrates that the existence of lobbying can negate the potential benefits of a strategic export subsidy. As expected, the higher are the direct costs of rent-seeking (w), the less likely that the introduction of the subsidy program will be welfare-improving. In the subsequent analysis, we will assume that the subsidy program will be beneficial, even when lobbying exists. This assumption implies that (15) is positive so that a small subsidy will improve national welfare as defined by (13). Using (14), we can solve for the optimal initial subsidy announced by the government:
rL,l
(16)
where sms= px~ [YJXs]. The expression ssis is of the same form as the optimal subsidy derived in Brander and Spencer. When no lobbying occurs, the expression has the same value at the optimum. With lobbying, the functional forms of ~s and ~s differ from those derived in Brander and Spencer so that ssis can be smaller or larger than the original optimal subsidy when lobbying opportunities are absent. Substituting (16) into (1), we find that total per ur.it subsidies after the domestic industry lobbies in the second period are
S =--g+ ¢r(L)=sa/S- w [ ~ ].
(17)
Since the government takes full account of the subsequent lobbying activity that will raise the subsidy, it will 'lowball' the announced initial subsidy by just enough to ensure that the total subsidy reaches the national optimum. In fig. 1 we plot welfare as defined by (2) against the total per unit subsidy. The highest curve, A, represents welfare when there is no lobbying. Uo is the
M.O. Moore and S.M. Suranovic, Lobbying and Cournot-Nash competition
373
Uo
\
Z
O
.
I
I--<[
C
Z
s°
FINAL
Sm
UNIT SUBSIDY Fig. 1
level of welfare if there is no subsidy program. The optimal subsidy as derived in Brander and Spencer equals s o and the subsidy program is beneficial. If lobbying occurs, national welfare net of lobbying costs will lie below curve A. Welfare is necessarily lower relative to the Brander and Spencer case since lobbying costs are incurred~ In fig. 1 we have drawn curve B under the assumption that the total subsidy under lobbying is less than s °. However, the final total subsidy under lobbying may be greater than or less than sO.1° As drawn, welfare is still higher than if there were no subsidy 1°This ambiguity can be seen explicitly using the special case of linear demand function~ The difference between the optimal subsidy of Brander and Spencer and that given by (17) is
- -L~,j is the optimal production level under Brander and Spencer. Given the results shown in (10), (11) and (12), the sign of this expression is ambiguous since ~ is greater than x NL. w h e r e XNL
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M.O. Moore and S.M. Suranovic, Lobbying and Cournot-Nash competition
program. While a subsidy program in the presence of lobbying can be beneficial, this result depends not only on government knowledge about profit-shifting potential but also on its knowledge of firm lobbying abilities as well as lobbying costs. Even if we accept government omniscience, a subsidy program may not be worthwhile. As the cost of lobbying (w) rises, the welfare contour shifts down. If w were high enough, welfare might be described by curve C. In this case the optimum lies below Uo, and the subsidy program would reduce welfare.
Case 2. Naive government. In this case we assume that the government initiates a subsidy program by announcing an initial subsidy, but does not take subsequent firm lobbying into account. ", his situation might arise if the government did not have sufficient information about lobbying. An alternative interpretation is that a government ministry announced the program but a legislature, susceptible to lobbying, steps in to alter the subsidy rate. The government's objective function from (13) is optimized presuming L =0, which is the same problem solved by the government in Brander and Spencer. The government would choose an initial subsidy, s = s°. Lobbying in the second period results in a higher final subsidy, S~=s°+~(L). If the optimal subsidy under lobbying, ~, is less than s°, then the naive government will necessarily over-subsidize and welfare will be less than optimal. However, if ~ > s °, then it is conceivable that lobbying could raise the final subsidy to the optimal level. In this case, the naive government may blunder into the correct subsidy. 5. Conclusion
In this paper we have analyzed the impact of lobbying in a model of Cournot duopoly. We assume that the government cannot precommit to a level of subsidies and that lobbying effort by the targeted export industries can increase the per unit subsidy beyond the level announced by the government in the first period. As expected, the presence of lobbying weakens the argument for strategic trade subsidies designed to capture profits from rival foreign firms. Three results stand out. First, the inclusion of lobbying costs in the national welfare function means that a unilateral incentive no longer necessarily exists for the government to provide a subsidy to the domestic Cournot competitor; lobbying costs may overwhelm the profits captured from foreigners. Secondly, even if a positive optimal subsidy exists, a government that correctly anticipates the effects of lobbying will set a lower subsidy in the first stage to compensate for the lobbying in the second. National welfare will necessarily be lower than that achieved under Brander and Spencer because of the resources lest to lobbying. Finally, a government
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that does not account for rent-seeking behavior will most likely either overor under-subsidize and further reduce welfare. Additional complications are likely to arise if multiple industries are eligible for a strategic export subsidy. If these industries lobby for additional subsidies, then all of the caveats identified above hold for each industry. Secondly, the government will need even more information in order to implement a welfare-improving subsidy program. For example, one industry's lobbying may affect another industry's ability to secure a higher subsidy. Consequently, the government would need to understand the nature of the lobbying 'game' among industries. A further problem may occur if the targeted industries have differential political clout. For example, a relatively influential industry may receive a higher-than-optimal subsidy on the basis of political clout rather than profit-shifting potential. 11 This framework could also be extended to Bertrand competition as well as models with more complicated market structures. Many of the basic points derived in this paper are likely to hold. 12 Strategic trade programs of most types will induce rent-seeking behavior by firms eager for higher profits. The welfare costs of the resultant lobbying will generally lessen the benefits of such export programs, even if the government can fully anticipate these activities. Furthermore, the information needed by the government to compensate for the distortionary effects of lobbying may be very extensive and not readily available. l tDixit and Grossman (1986) have already identified one scenario when the argument for intervention is weaker for export subsidies in a multiple-firm case. In their study, many industries compete for the use of a inelastically-suppli~! specialized factor used in production. Support for one firm can result in profit decreases in the other sectors. The firms modeled in this study do not share such a specialized factor. 12Moore and Suranovic (1992) analyze a similar model using Cournot-Stackelberg, Bertrand-Stackelberg and Bertrand-Nash firm behavior.
References Brander, J.A. and B.J. Spencer, 1985, Export subsidies and international market share rivalry, Journal of International Economics 18, 83-100. Cassing, J. and A. Hillman, 1985, Political influence motives and the choice between tariffs and quotas, Journal of International Economics 19, 279-300. Dixit, A.K. and G.M. Grossman, 1986, Targeted export promotion with several oligopolist industries, Journal of International Economics 21,233-250. Eaton, J. and G.M. Grossman, 1986, Optimal trade and industrial policy under oligopoly, Quarterly Journal of Economics, 383--406. Grossman, G., 1986, Strategic trade promotion: A critique, in: P. Krugman, ed., Strategic trade policy and the new international economics (MIT Press, Cambridge, MA) 47-68. Gruenspecht, H., 1988, Export subsidies for differentiated products, Journal of International Economics 24, 331-344. Hillman, A. and H. Urspring, 1988, Domestic politics, foreign interests and international trade policy, American Economic Review 51, 59-79. Krishna, K. and M. Thursby, 1990, Trade policy with imperfe-t competition: A selective surwy, in: C. Carter, A. McCalla and J. Sharpies, eds.~ Imperfect competition and political economy (Westview Press, Boulder, CO) 9-36.
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Krngman, P., 1987, Is free trade passe?, Journal of Economic Perspectives 1, 131-144. Markusen, J. and A. Venables, 1988, Trade policy with increasing returns and imperfect competition, Journal of International Economics 24, 299-316. Moore, M., 1990, New developments in the political economy of protectionism, in: C. Carter, A. McCalla and J. Sharpies, eds., Imperfect competition and political economy lWestview Press, Boulder, CO) 143-168. Moore, M. and S. Suranovic, 1992, Lobbying, incomplete information and optimal trade policy under imperfect competition, George Washington University, Department of Economics Discussion Paper D-92905.