Resolved: That the United States should substantially change its federal agricultural policy.

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Source: American Journal of Agricultural Economics, Feb 2001 v83 i1 p209.


Full Text COPYRIGHT 2001 American Agricultural Economics Association

If the main justification for agricultural export subsidies is that they reduce government costs of deficiency payments, then the 1996 farm legislation would make U.S. export subsidies largely unnecessary. An additional argument advanced in favor of export subsidies is that their aggressive use by one country will cause competing countries to reduce or discontinue their own subsidies. This argument is explored by means of a Nash equilibrium in which countries choose both a base subsidy level and a response to competitors, and by a consistent conjectures equilibrium. Little support is found for the argument.

Key words: agricultural policy, EEP, export subsidies, strategic interactions.

During the period of the mid 1980s to the mid 1990s, export subsidies became an increasingly important part of U.S. farm policy. In fact, expenditures on the Export Enhancement Program (EEP) exceeded $1 billion in FY 1993. The enduring popularity of export subsidies has been a source of puzzlement to economists (see R. Paarlberg, for example). Economists argue that governments could provide more assistance to farmers at the same cost to consumers if the money spent on export subsidies were spent instead on direct subsidies to farmers. Anania, Bohman, and Carter present a strong argument along these lines.

Several papers have found circumstances under which export subsidies might be justified. Abbott, Paarlberg, and Sharples show that export subsidies can improve welfare in the exporting country if they are implemented in a discriminatory way, reducing prices in countries with relatively elastic demands. Abbott and Kallio show how export subsidies may complement other policies intended to support producers when the exporting country has market power in the world market. Another possible explanation for the popularity of export subsidies is advanced by Alston, Carter, and Smith (1993, 1995). They show that export subsidies may be justified because they reduce the budgetary costs of the price support program.

There is an additional argument which is frequently heard in debates about agricultural export subsidies, but which has not been fully analyzed by economists. Supporters of the EEP program argue that to discontinue its use would be tantamount to "unilateral disarmament" in the war for international market share in agricultural trade. In other words, export subsidies are a useful tool of trade strategy-the use of export subsidies by the United States will restrain the use of export subsidies by foreign competitors (notably the European Union (EU)). The EEP program was sold as a strategic tool. The law authorizing the EEP program as part of the 1990 Farm Legislation states that the purpose of the program is "to discourage unfair trade practices by making U.S. agricultural commodities competitive." In addition, the notice in The Federal Register (June 7, 1991, Section 1494) implementing the EEP program lists among the objectives: "to discourage unfair trade practices by other countries" and "to encourage other countries to undertake serious negotiations on agricultural trade problems." The same Federal Register notice requires the administration of the program to consider the "contribution... in Furthering... negotiating strategy of countering competitors' subsidies."

The present paper develops a model in which the strategic aspects of export subsidies can be considered explicitly. The model shows how the exports of a country depend on its subsidies, and on the level of subsidies by the other country. The optimal decision by the United States about whether and how intensively to use export subsidies depends on both the level of EU subsidies and the way that EU policy makers react to changes in the U.S. subsidy level.

The paper uses two approaches to examine the validity of the strategic interactions argument: (a) a Nash equilibrium in which each country optimally chooses a base level and a reaction and (b) a "consistent conjectures" equilibrium (proposed by Bresnahan) in which the reaction of each policy maker is measured as the slope of the reaction function. The consistent conjectures approach has been used widely in analysis of export subsidies for industrial products (Eaton and Grossman, Brander and Spencer, and Tanaka, for example). [1] In these papers, the exporting industry is assumed to be imperfectly competitive, and the government's objective is to maximize domestic firm profits net of the subsidy. The agricultural export subsidies take place in a different economic environment: the exporting industry is competitive, but the existence of domestic programs to support domestic prices creates a possible role for export subsidies.

In the first part of the paper, producer prices and output are assumed to be established by legislatively mandated producer support prices. This corresponds to the policy situation prior to the Federal Agricultural Improvement and Reform Act (FAIR) of 1996, and after the EU's Common Agricultural Policy (CAP) reform of 1992. [2] The theoretical model shows that in the pre-1995 policy environment, the trade strategy argument cannot by itself justify export subsidies. In a Nash equilibrium, the optimal reaction is shown to be zero. In the consistent conjectures equilibrium, use of export subsidies could be optimal if the policy maker conjectured that the opposing country would "back down" in the face of such subsidies. However, the model also shows that such a conjecture is never consistent with optimizing behavior on the part of the opposing policy maker. In the absence of government inefficiencies, it is never rational for one government to reduce its subsidies in the response to an increase in subsidies by t he other government. However, if government decision makers put a higher weight on government expenditures than on consumer welfare (as posited by Alston, Carter, and Smith 1993), the trade strategy argument becomes theoretically feasible: there are conditions under which a government will rationally reduce its export subsidies in response to an increase in the subsidies by the competing country.

A simulation model demonstrates that actual levels of export subsidies in 1993 can be replicated by the model with reasonable assumptions about demand elasticities, and the welfare weight assigned to government expenditures is consistent with published estimates of the welfare losses associated with government transfers. However, the simulation shows that here too the trade strategy argument is not valid: a rational policy maker will increase subsidies in response to an increase in subsidies by the competing policy maker.

These results suggest that the principal motivation for export subsidies historically has been to reduce the budgetary costs of the price support program. But the FAIR Act of 1996 effectively eliminated target prices and acreage restrictions in favor of income supplements -- thereby invalidating the assumption that output is predetermined by policy choices. [3] Are export subsidies still justifiable under the new policy regime? That question is addressed in the last part of the paper. Optimal export subsidies are zero, not only for the United States but also for the European Union in many simulations.

The recent administration of the EEP program is consistent with the model. EEP bonuses were suspended in the 1996-1998 period, when the FAIR provisions were in place. The proposed [4] reintroduction of EEP bonuses in late 1998 coincided with a period in which the "marketing loan" provisions of the FAIR Act were in place for wheat. Under these marketing loan provisions, farmers receive a minimum support price, and the government makes up the difference between the support price and a lower market price. When marketing loans are in effect, the "pre-FAIR" model is the appropriate one, since again the U.S. government has an incentive to use export subsidies to reduce government program costs by increasing domestic consumer prices. Thus, it may be reasonable to keep the EEP program "on the books" but dormant for lengthy periods of time when the market prices are above support prices. [5]

Export Subsidies when Domestic Price Is Fixed by a Price Support Program

This section develops a model of optimal export subsidies in which farm level prices and outputs are fixed by predetermined policy choices (such as target prices). The question addressed by the analysis which follows might be better stated as: Given that we are going to support farm prices at a certain level, is there any appropriate role for export subsidies in the policy mix? Taking farm output as fixed simplifies the policy analytics: producer price and output (and thus producer surplus) is the same under all circumstances. This model would be appropriate to evaluate the administration of the EEP in a period when target prices (prices received by farmers) are established by legislation, or by previously taken and unalterable administrative action. [6] In reality, decisions about how aggressively to use the EEP program are made in exactly that context: farm support programs and output are established and the decisions concerning the EEP are made subsequently. Modeling the EEP program in this way is consiste nt with the Alston, Carter, and Smith paper (1993); but has been criticized by Gardner. [7]

This section's model consists of two exporting countries: In the numerical example later in the paper, Country A will be referred to as the United States, and country B as the European Union. In each country, a domestic support program establishes a price received by farmers, [[P.sup.p].sub.n], and thereby a quantity supplied [S.sub.n], in each country n = A, B. Each country will also operate an export subsidy program, which establishes a price differential [[delta].sub.n] between the world price [P.sub.w] and a (higher) domestic price paid by consumers, [P.sub.n].

Denote demand curves for the commodity in country A, country B, and the world as functions of the quantities consumed (Q) in each market:

[P.sub.A] = [P.sub.A]([Q.sub.A])

[P.sub.B] = [P.sub.B]([Q.sub.B])

[P.sub.w] = [P.sub.w]([Q.sub.w]).

Under the conditions described above, the objective of the policy maker establishing an optimal level of export subsidies is to maximize the weighted sum of consumer surplus (CS) minus government expenditures on deficiency payments (DP) and on export subsidies (ES) for country A:

[Max.sub.[[delta].sub.A]] [[phi].sub.A] = [[alpha].sub.A] CS - DP - ES,


CS = [[[integral].sup.[Q.sub.A]].sub.0] [P.sub.A](Q)dQ - [P.sub.A]([Q.sub.A])[Q.sub.A]

DP = [[[P.sup.p].sub.A] - [P.sub.A]([Q.sub.A])][S.sub.A]

ES = [[P.sub.A]([Q.sub.A]) - [P.sub.w]([Q.sub.w])]([S.sub.A] - [Q.sub.A]).

We begin by ignoring the possibility of a strategic interaction. The first order condition for an optimum is

d[[phi].sub.A]/d[[delta].sub.A] = [partial][[phi].sub.A]/[partial] [Q.sub.A] d[Q.sub.A]/d[[delta].sub.A] + [partial][[phi].sub.A]/[partial][Q.sub.w] d[Q.sub.w]/d[[delta].sub.A] [less than or equal to] 0

d[[phi].sub.A]/d[[delta].sub.A] [[delta].sub.A] = 0.

Defining [P'.sub.A] = d[P.sub.A]/d[Q.sub.A] and [P'.sub.W] = d[P.sub.W]/d[Q.sub.W], the condition for a non-zero export subsidy is

[(1 - [[alpha].sub.A])[P'.sub.A][Q.sub.A] + ([P.sub.A] - [P.sub.W])]d[Q.sub.A]/d[[delta].sub.A] + ([S.sub.A] - [Q.sub.A])[P'.sub.W]d[Q.sub.W]/d[[delta].sub.A] = 0.

Equation (1) can be written in elasticity terms as

(2) [([[alpha].sub.A] - 1)[[xi].sub.A] + 1 - [r.sub.A]]d[Q.sub.A]/d[[delta].sub.A] - [[xi].sub.W][X.sub.A][r.sub.A]d[Q.sub.W]/d[[delta].sub.A] = 0,

where [[xi].sub.A] is the inverse of the elasticity of domestic demand in country A:

[[xi].sub.A] = -d[P.sub.A]/d[Q.sub.A][Q.sub.A]/[P.sub.A] [greater than] 0;

[[xi].sub.W] is the inverse of the elasticity of demand in the world export market:

[[xi].sub.W] = -d[P.sub.W]/d[Q.sub.W][Q.sub.W]/[P.sub.W] [greater than] 0;

[x.sub.A] is the share of the world export market that is supplied by country A: [x.sub.A] = ([S.sub.A] - [Q.sub.A])/[Q.sub.W] [less than or equal to] 1; [r.sub.A] is the ratio of the world price to the domestic consumer price in country A: [r.sub.A] = [P.sub.W]/[P.sub.A] [less than or equal to] 1.

Two familiar results follow. The first result is that under "ordinary" assumptions, export subsidies are not justified. If [[alpha].sub.A] = 1 (consumer welfare is not given less weight than government costs by the policy maker), then at the point of zero export subsidy (where [r.sub.A] = 1), the first order condition (2) becomes


which is negative (since quantity sold on the world market increases as A's export subsidy increases, ceteris paribus) implying optimal export subsidy is zero.

A second familiar result is attributable to Alston, Carter, and Smith (1993), who show that inefficiencies in government taxation and spending may provide a justification for export subsidies. In the context of the model above, the Alston, Carter, and Smith argument is incorporated by allowing [[alpha].sub.A] [less than] 1. Now the necessary condition for a non-zero export subsidy (2) becomes

(3) [([[alpha].sub.A] - 1)[[xi].sub.A] + 1 - [r.sub.A]]d[Q.sub.A]/d[[delta].sub.A]

+ [[xi].sub.W][X.sub.A][r.sub.A](-d[Q.sub.W]/d[[delta].sub.A]) = 0.

At the point of zero export subsidies ([r.sub.A] = 1), the first term is positive and the second term is negative. For any level of [alpha], as domestic demand becomes more inelastic (so [[xi].sub.A] grows larger) or as world demand becomes more elastic (so [[xi].sub.W] approaches zero), conditions improve for positive levels of optimal export subsidy, as suggested by Alston, Carter, and Smith.

Export Subsidies as a Strategic Tool: Another Justification

A principal objective of this paper is to analyze another justification that has been put forward for export subsidies: that export subsidies serve a strategic purpose of influencing policy choices by competitors. As Sumner points out, "It may seem ironic that one of the more compelling arguments in favor of trade distortions is to eliminate distortions. This argument applies where export subsidies used by one country increase the costs for other countries' export subsidies and other distorting trade policies. ... In particular, if by driving down world prices, export subsidy costs are increased for one's competitors, the result is an added incentive for multilateral trade disarmament" (Sumner, p. 2.18). This argument appears, not just in the legislative and administrative record cited in the introduction, but also in the economics literature on agricultural export subsidies. For example, Seitzinger and Paarlberg say that the EEP program "was an offensive stance against export subsidies employed by the EC" (p . 445). Likewise, Anania, Bohman, and Carter recognize: "A final theoretical argument for export subsidies is ... the intent of reducing other exporter (i.e., EC) subsidies" (p. 535).

As a preliminary look at the validity of this argument, we add, to the above model, "strategic interaction" terms: the response of country B's export subsidy to changes in country A's subsidy, or [[delta].sub.BA] = d[[delta].sub.B]/d[[delta].sub.A].

The necessary condition (1) for export subsidies by country A now becomes

(4) [(1-[[alpha].sub.A]) [P'.sub.A][Q.sub.A] + ([P.sub.A] -- [P.sub.w])]

x [[partial][Q.sub.A]/[partial][[delta].sub.A]+[partial][Q.sub.A]/[part ial][[delta].sub.B][[delta].sub.BA]]+([S.sub.A]-[Q.sub.A]) [P'.sub.w]

x [partial][Q.sub.w]/[partial][[delta].sub.A]+[partial][Q.sub.w]/[parti al][[delta].sub.B][[delta].sub.BA]]=0.

Examination of (4) reveals that for certain values of [[delta].sub.BA], [partial][Q.sub.A]/[partial][[delta].sub.B], [partial][Q.sub.w]/[partial][[delta].sub.B] it is mathematically possible for the optimal [[delta].sub.A] to be positive, even when [[alpha].sub.A] = 1. The question is whether the mathematical possibility will hold in reality. The algebra in (4) is consistent with the verbal argument presented above: negative values of the interaction term [[delta].sub.BA] are necessary to imply that export subsidies are optimal; a negative [[delta].sub.BA] means that by increasing its export subsidy, country A can persuade policy makers in B to reduce exports subsidies by B.

Nash Equilibrium with Strategic Interaction Terms

We begin by considering the possibility of strategic interactions explicitly. In particular, assume that each country announces not a flat level, but chooses a base level, and a strategic response to its opponent's base level. [8] Thus country A chooses [[[delta].sup.0].sub.A] and [[delta].sub.AB], country B chooses [[[delta].sup.0].sub.B] and [[delta].sub.AB], and

[[delta].sub.A] = [[[delta].sup.0].sub.A]+ [[delta].sub.AB] [[[delta].sup.0].sub.B]

[[delta].sub.B] = [[[delta].sup.0].sub.B] + [[delta].sub.BA] [[[delta].sup.0].sub.B]

The objective of country A, as above, is [[phi].sub.A] ([[delta].sub.A], [[delta].sub.B]). Country A chooses [[[delta].sup.0].sub.A] and [[delta].sub.AB] to maximize that objective, taking the choices of B as fixed. The first order conditions for country A are

d[[phi].sub.A]/d[[[delta].sup.0].sub.A] = [partial][[phi].sub.A]/[partial][[delta].sub.A] [partial][[delta].sub.A]/[partial][[[delta].sup.0].sub.A] + [partial][[phi].sub.A]/[partial][[delta].sub.B] [partial][[delta].sub.B]/[partial][[delta].sup.0].sub.A] [less than or equal to] 0

d[[phi].sub.A]/d[[[delta].sup.0].sub.A] [[[delta].sup.0].sub.A]=0

d[[phi].sub.A]/d[[delta].sub.AB] = [partial][[phi].sub.A]/[partial][[delta].sub.A] [partial][[delta].sub.A]/[partial][[delta].sub.AB]+ [partia][[phi].sub.A]/[partial][[delta].sub.B] [partial][[delta].sub.B]/[partial][[delta].sub.AB]=0



[partial[[phi].sub.A]/[partial][[delta].sub.A]+[partial][[phi].sub.A] /[partial][[delta].sub.A][[delta].sub.BA] [less than or equal to] 0

[partial][[phi].sub.A]/[partial][[delta].sub.A] [[[delta].sup.0].sub.B] [less than or equal to] 0.

For country B, the analogous first order conditions are

[partial][[phi].sub.B]/[partial][[delta].sub.B] + [partial][[phi].sub.B]/[partial][[delta].sub.A] [[delta].sub.AB] [less than or equal to] 0

[partial][[phi].sub.B]/[partial][[delta].sub.B] [[[delta].sup.0].sub.A] [less than or equal to] 0.

These four conditions describe the Nash equilibrium. The equilibrium is "rationalizable" (in the terminology of Bernheim and Pierce): each player announces a credible level and reaction to the opponent's announcement; each player believes that his opponent is following a similar calculation of the optimum.

The solution to the above is [[delta].sub.AB] = [[delta].sub.BA] = 0 and [partial][[phi].sub.A]/[partial][[delta].sub.A] [less than or equal to] 0 and [partial][[phi].sub.B] [less than or equal to] 0. In other words, the analysis collapses to the simple case described above (with the optimum described in (3)) and there is no strategic interaction. The Nash equilibrium approach provides no support for the strategic interactions argument for export subsidies.

Consistent Conjectures Equilibrium

A second way to examine the possibility of a strategic interaction utilizes the concept of consistent conjectures proposed by Bresnahan. When demand curves are linear, the earlier model can be solved explicitly. [9] Let

[P.sub.A] = [a.sub.0] - a[Q.sub.A] [P.sub.B]=[b.sub.0] - b[Q.sub.B]

[P.sub.w] = [w.sub.0] - w[Q.sub.w] = [w.sub.0] - w.

x [[S.sub.A]- [Q.sub.A] + [S.sub.B] - [Q.sub.B]].

The demand curves can be solved for [Q.sub.A],[Q.sub.B], and [Q.sub.w] as functions of export subsidies [[delta].sub.A]

and [[delta].sub.B],

[Q.sub.A] = 1/ab + aw + bw

x [[A.sub.0] - (b + w)[[delta].sub.A] + w[[delta].sub.B]]

[Q.sub.A] = 1/ab + bw + bw

x [[A.sub.0] - (b + w)[[delta].sub.A] + w[[delta].sub.B]]

[Q.sub.w] = 1/ab + aw + bw

x [[W.sub.0] + b[[delta].sub.A] + a[[delta].sub.B]],


[A.sub.0] = [a.sub.0][a.sup.-1] [ab + bw + aw] -b[[w.sub.0] - w([S.sub.A] + [S.sub.B]) +([wa.sup.-1][a.sub.0] + [wb.sup.-1][b.sub.0])]

= [a.sub.0][b + w] - b[[w.sub.0] - w x([S.sub.A] + [S.sub.B])] + [wb.sub.0]

[B.sub.0] = [b.sub.0][a + w] - a[[w.sub.0] - w x ([S.sub.A] + [S.sub.B])] + [wa.sub.0]

[W.sub.0] = [ab + aw + bw] x ([S.sub.A] + [S.sub.B]) - ([A.sub.0] + [B.sub.0]),

The necessary condition (4) for export subsidies to be optimal for country A can be rewritten

(5) [a[[[alpha].sub.A][Q.sub.A] - [S.sub.A]] + [[delta].sub.A]][- (b + w) + w[[delta].sub.AB]]/ab + bw + aw -([S.sub.A] - [Q.sub.A]) = 0.

Plugging the expression for [Q.sub.A] into (5) and rearranging yields

(6) -[k.sub.1] - [k.sub.2][[delta].sub.A] + [k.sub.3][[delta].sub.B] + [-[k.sub.4] + [k.sub.5][[delta].sub.A] + [k.sub.6][[delta].sub.B]][[delta].sub.BA] = 0,


[k.sub.1] = [S.sub.A] bw - [A.sub.0]/ab + aw + bw (ab(1 - [[alpha].sub.A]) + bw + aw (1 - [[alpha].sub.A]))

[k.sub.2] = (b + w) x (1 + (ab(1 - [[alpha].sub.A]) + bw + aw (1 - [[alpha].sub.A]))/ab + aw + bw)

[k.sub.3] = [k.sub.5] = w(ab(1 - [[alpha].sub.A]) + bw + aw(1 - [[alpha].sub.A]))/ab + aw + bw

[k.sub.4] = aw [S.sub.A] - [[alpha].sub.A]aw[A.sub.0]/ab+aw+bw

[k.sub.6] = [[alpha].sub.A][aw.sup.2]/ab+aw+bw .

Country B's optimization problem yields a similar first order condition, which can be written as

(7) -[j.sub.1] + [j.sub.2] [[delta].sub.A] - [j.sub.3][[delta].sub.B] + [-[j.sub.4] + [j.sub.5][[delta].sub.A] + [j.sub.6][[delta].sub.B]][[delta].sub.AB] = 0


[j.sub.1] = [S.sub.B]aw - [B.sub.0]/ab+aw+bw (ab(1 - [[alpha].sub.B]) + aw +bw (1 - [[alpha].sub.B]))

[j.sub.2] = [j.sub.6] = w(ab(1 - [[alpha].sub.B]) + aw + bw(1 - [[alpha].sub.B]))/ab+aw+bw

[j.sub.3] = (a + w) (1 + (ab(1 - [[alpha].sub.B])+aw+bw(1 - [[alpha].sub.B]))/ab+aw+bw)

[j.sub.4] = aw[S.sub.B] - [[alpha].sub.B]aw[B.sub.0]/ab+aw+bw

[j.sub.5] = [[alpha].sub.B][bw.sup.2]/ab+aw+bw.

From (6) and (7), the consistent conjectures equilibrium is calculated as follows. First, solve (6) and (7) for the reaction functions as the optimal subsidy of one country as a function of the other country's subsidy:

(8) [[[delta].sup.*].sub.A] = -[k.sub.1] - [k.sub.4][[delta].sub.AB] + [[k.sub.3] = [k.sub.6][[delta].sub.AB]][[delta].sub.B]/[k.sub.2] - [k.sub.5][[delta].sub.BA]

(9) [[[delta].sup.*].sub.B] = -[j.sub.1] - [j.sub.4][[delta].sub.AB] + [[j.sub.2] + [j.sub.5][[delta].sub.AB]][[delta].sub.A]/[j.sub.3] - [j.sub.6][[delta].sub.AB].

Next measure the optimal reaction of one country to the other country's subsidy as the slope of the reaction function, with respect to the opponent's subsidy:

(10) [[[delta].sup.*].sub.AB] = d[[[delta].sup.*].sub.A]/d[[delta].sub.B] = [k.sub.3] + [k.sub.6][[delta].sub.BA]/[k.sub.2] - [k.sub.5][[delta].sub.BA]

(11) [[[delta].sup.*].sub.BA] = d[[[delta].sup.*].sub.B]/d[[delta].sub.A] = [j.sub.2] + [j.sub.5][[delta].sub.AB]/[j.sub.3] - [j.sub.6][[delta].sub.AB].

The consistent conjectures equilibrium requires [[delta].sub.n] = [[[delta].sup.*].sub.n] and [[delta]] = [[[delta].sup.*]] for m and n = (A, B). Equations (8)-(11) give us four equations in four unknowns, which can be solved sequentially, using (10) and (11) to solve for the interaction terms, and then (8) and (9) for the optimal subsidies.

Equation (8) shows that country A's optimal decision depends on country B's subsidy and B's reaction to A. In effect, country B recognizes that it can influence country A's export subsidy in two ways: (1) Country A's decision is influenced by B's announced level of subsidy and (2) country A's decision is influenced by B's reaction to A's subsidy. This second point is the essence of the strategic trade argument for EEP: the level of my subsidy is influenced by my beliefs about how my opponent will respond to my subsidy. The requirement that [[delta]] = [[[delta].sup.*]] simply means that my beliefs are based on knowledge of my opponent's objective and confidence in his rationality. This method of incorporating strategic response is less sophisticated than a full dynamic game theory treatment. But it has the virtue of allowing us to incorporate the trade strategy argument into a familiar model of export subsidies. [10]

From the consistent conjectures equilibrium, we can ask two questions: (a) Is a strategic reaction alone (i.e., in the absense of unbalanced weighting in the policy objective function, or assuming [[alpha].sub.n] = 1) enough to justify export subsidies? (We will show that the answer is no.) (b) Given realistic values for demand elasticities and policy weights on consumer surplus, are we likely to observe a negative strategic reaction in reality?

Strategic Reaction as a Stand-Alone Justification for Export Subsidies

First, to examine whether or not the strategic reaction argument serves as a separate "stand-alone" justification for export subsidies, rewrite (4) for the case where [[alpha].sub.A] = 1 (thus eliminating the government budget argument) but where [[delta].sub.BA] [neq] 0:

(12) [[delta].sub.A][-b(b + w) + w[[delta].sub.BA]] - ([S.sub.A] - [Q.sub.A])

x w[b + a[[delta].sub.BA]] [less than or equal to] 0 or

-(b + w)[[delta].sub.A] - ([S.sub.A] - [Q.sub.A])wb + w

x [[[delta].sub.A] - ([S.sub.A] - [Q.sub.A])a][[delta].sub.BA] [less than or equal to] 0.

The first two terms in (12) are always negative. In the third term, using [[delta].sub.A] = [P.sub.A] - [P.sub.W], we see that [[delta].sub.A] - a([S.sub.A] - [Q.sub.A]) = [[a.sub.0] - a[S.sup.A]] - [P.sub.W]. The term [[a.sub.0] - [aS.sup.A]] - [P.sup.W] shows the difference between the domestic price and the world price that would exist if country A did not export any output. For a natural exporter (a country that would export the commodity if the world were free of export subsidies), this term is negative. Under that assumption, the third term in (12) will have a sign opposite to the sign of [[delta].BA]. If [[delta].sub.BA] is non-negative, then all three terms in (12) are non-positive, and the optimal policy for country A is to eliminate the export subsidy. In other words: if raising the export subsidy in country A causes country B to either raise or keep unchanged its export subsidy, then country A should reduce its export subsidy as much as possible.

As noted earlier, this is the "trade strategy justification": If an increase in the export subsidy offered by country A will cause country B to reduce its export subsidy, [[delta].BA] [less than] 0, then export subsidies may be an appropriate policy tool for country A. (They "may be" -- but are not necessarily -- appropriate, because the positive third term in (12) must be large enough to offset the first two negative terms.)

To investigate whether or not the strategic reactions argument is a stand-alone justification for export subsidies, we examine whether the condition [[delta].sub.BA] [less than] 0 can hold in the consistent conjectures equilibrium. To do this, we rewrite (10) and (11) for the case where [[alpha].sub.A] = [[alpha].sub.B] = 1,

[[[delta].sup.*].sub.AB] = [k.sub.3] + [k.sub.6][[[delta].sup.*].sub.BA]/[k.sub.2] - [k.sub.5][[[delta].sup.*].sub.BA]

[[[delta].sup.*].sub.BA] = [j.sub.2] + [j.sub.5][[[delta].sup.*].sub.AB]/[j.sub.3] - [j.sub.6][[[delta].sup.*].sub.AB],

with the j's and k's being the j's and k's above evaluated at [[alpha].sub.A] = [[alpha].sub.B] = 1. Note that [j.sub.2] = [j.sub.6] = [k.sub.6] all are referred to as [j.sub.2] below and [k.sub.3] = [k.sub.5] = [j.sub.5] all are referred to as [k.sub.3] below. The result is a quadratic equation (dropping *'s for notational convenience) [11]:

[[delta].sub.AB] = [k.sub.3][j.sub.3] + [j.sub.2][j.sub.2]/[k.sub.2][j.sub.3] - [[k.sub.3][j.sub.2]] - [[k.sub.2][j.sub.2] + [k.sub.3][k.sub.3]][[delta].sub.AB] or

-[[k.sub.2][j.sub.2] + [k.sub.3][k.sub.3]][[[delta].sup.2].sub.AB]

+ [[k.sub.2][j.sub.3] - [k.sub.3][j.sub.2]][[delta].sub.AB]

- [[k.sub.3][j.sub.3] + [j.sub.2][j.sub.2]] = 0.

The parameters [[k.sub.2][j.sub.2] + [k.sub.3][k.sub.3]], [[k.sub.2][j.sub.3] - [k.sub.3][j.sub.2]], and [[k.sub.3][j.sub.3] + [j.sub.2][j.sub.2]] are all positive. (The j's k's used here are all positive. Positivity of [[k.sub.2][j.sub.3] - [k.sub.3][j.sub.2]] can be proven by looking at the definitions above, and noting that all the a's, b's, c's, and w's are positive.) Therefore both roots of the quadratic must be positive. (In the case where the square root term is subtracted, the fraction is a negative number over a negative number. In the case where the square root term is added, the amount under the square root sign is less than [[[k.sub.2][j.sub.3]-[k.sub.3][j.sub.2]].sup.2], so the fraction is still a negative over a negative.) For a country's conjecture about its opponent's reaction to be consistent with known optimizing behavior, the conjecture must be that the opponent will increase its subsidy in response to an increase in our subsidy.

The above proves that the argument that export subsidies can be justified solely as a tool of "trade strategy" is not valid. The expectation that country B will reduce its subsidies in response to more aggressive use of subsidies by country A is not consistent with optimizing behavior by country B. The last two sentences are true under the assumption that [[alpha].sub.n] = 1, that is, under the assumption that there is no "budget savings" justification for export subsidies in either country A or country B.

An Empirical Investigation of Strategic Reactions Prior to 1996

Next we examine the more general case where [[alpha].sub.n] [neq] 1 and where [[delta]] [neq] 0. The question of whether export subsidies may be justified under these circumstances is not an issue. As shown above (following Alston, Carter, and Smith 1993) export subsidies can be justified when policy makers put less weight on consumer surplus than on government expenditures. The question of interest here is whether it is reasonable for one country to expect that more aggressive use of subsidies will cause its competitor to back down. In the terminology of this model, can we find realistic circumstances in which [[delta]] [less than] 0. We will see that it is theoretically possible. However, when we find levels of parameters that are consistent with reasonable estimates of elasticities and government inefficiencies, we see that [[delta]] [greater than] 0 for these levels. By finding parameter values that are consistent with historically observed levels of export subsidies, this exercise al so serves to calibrate the simulation model for later sections in which we examine optimal export subsidies under the post-1995 domestic policy environment.

The solution to (8)-(11) above shows the consistent conjectures equilibrium. Examination of (10) and (11) shows that there are parameter values at which [[delta].sub.AB] [less than] 0 and/or [[delta].sub.BA] [less than] 0. The important question is whether the interaction can be negative at parameter values which are realistic.

To answer this question, we attempt to find parameter values consistent with the observed levels of prices, domestic consumption, and exports for the United States and the European Union in 1993. "World" demand is drawn using the world price and the combined quantities of U.S. and EU exports.

[Graphic omitted]To set parameters of the model, we need estimates of demand elasticities (which give us a's, b's, and w's) and an estimate of [[alpha].sub.A] and [[alpha].sub.B]. Demand elasticities for wheat (the principal commodity subsidized by the United States) are thought to be less than one, and domestic demand is probably more inelastic than world or export demand. As explained above, we expect [[alpha].sub.n] to be less than or equal to one. One way to motivate the [alpha] [less than or equal to] 1 assumption is to assume that the decision maker prefers to have farm price supports paid by consumers, where the cost is less transparent, than by taxpayers. The desire reduce government costs of farm programs might be especially strong in periods of high and controversial federal budget deficits, such as occurred during the 1980-1995 period. Alston, Carter, and Smith (1993) provide an explanation for [[alpha].sub.n] [less than] 1 that has a basis in economic theory. They appeal to the literature in public finance which makes the point that there are welfare losses associated with government programs to tax and subsidize even when those programs do not directly distort prices. The size of these welfare losses is usually thought to be in the 20-30% range--equivalent to an [alpha] of 0.70-0.80.

In table 1, the first row shows a simulation in which domestic demand elasticities are 0.28 in both the United States and the European Union, world demand has an elasticity of 0.59, and the [alpha]'s in both countries are about 0.77. These assumptions (which are in the range of elasticities found in the literature) exactly replicate the 1993 situation described above. If these are the correct levels of elasticities and [alpha]'s, and if the model is an appropriate representation of government decision making, then the decisions actually taken in 1993 were optimal decisions.

Notice, however, that at these parameter values, [[delta]] [greater than] 0 for both countries. (For example in simulation 1, a $1 increase in the export subsidy by country A causes a 4.2 [cts.] increase in the export subsidy of country B.) This suggests that export subsidies are not having the desired trade strategy impact. In fact, at the 1993 optimum, if the United States increases its use of the EEP program, the EU's optimal response is to increase its own subsidies. Scenarios 2-4 show that this conclusion is not affected by changes in the base scenario. Each scenario shows alternative values of elasticities and [alpha]'s that are consistent with optimality of 1993 decisions. In every case, [[delta]] is positive.

This analysis suggests that EEP during the pre-1996 period was not an effective tool of trade strategy. The argument that aggressive use of EEP would force the EU to back away from using export subsidies is not supported by this analysis. If EEP was justified, it was as a means of reducing budgetary costs of price supports and stock costs. This finding is consistent with the observation of Seitzinger and Paarlberg that the EU responded to the EEP program by increased efforts to protect their markets.

Export Subsidies After the FAIR Act of 1996

The elimination of price supports in the FAIR Act of 1996 appears (at first glance) to have substantially eliminated the justification for the EEP program. If reducing domestic program costs is the driving motivation behind EEP, then the FAIR Act (to a considerable extent) eliminates this motivation by eliminating target prices and deficiency payments. With the FAIR Act system of income payments regardless of price levels, EEP no longer can serve the purpose of reducing government costs. Before rushing to this conclusion, we should recognize that the above model is changed in some fundamental ways by the FAIR Act. This section modifies the above model to incorporate the substitution of income supplements for price supports in the United States. The model of this section applies to FAIR Act provisions when market prices are above the loan rate and, when, therefore, the marketing loan provisions of FAIR are not in effect. When the market price falls below the support price, farmers can repay their loans (cash a dvanced at the support price level) by paying the prevailing market price. In these circumstances, the effective producer price is set by government action, the government program incurs a loss, and the model presented the section above is the appropriate model.

Under FAIR country A (the United States) has prices determined with a supply and demand curve:

[P.sub.A] = [a.sub.0] - a[Q.sub.A]

[S.sub.A] = [s.sub.0] + s[P.sub.A]

For the United States in this policy context, the export subsidy influences producer price and producer surplus as well as consumer surplus and government costs. The policy maker's objective is to

(13) [Max.sub.[[delta].sub.A]] [[delta].sub.P] PS + [[alpha].sub.c] CS - GE,

Where producer surplus is

PS = 1/2([P.sub.A] + [S.sub.0]/S) ([S.sub.0] + S[P.sub.A])

= [[s.sup.2].sub.0]/2[S.sub.1] + [S.sub.0][P.sub.A] + 1/2s[[P.sup.2].sub.A],

consumer surplus is

CS = 1/2 [([a.sub.0] - [P.sub.A]).sup.2]/a,

government expenditure is

GE = [[sigma].sub.A][E.sub.A],

and where [[alpha].sup.C] and [[alpha].sup.P] are the relative weights put on producer and consumer surplus by government A.

The European Union retains a policy of establishing producer prices through a government support program. Thus, the exports of country B (the European Union) are modelled as above.

Under these circumstances, the first order condition that must hold if positive export subsidies are optimal for country A takes the form

(14) [h.sub.1] + [h.sub.2][[delta].sub.A] + [h.sub.3][[delta].sub.B] + [[h.sub.4] + [h.sub.5][[delta].sub.A] + [h.sub.6][[delta].sub.B]][[delta].sub.BA] = 0,


[h.sub.1] = [[alpha].sub.P][f.sub.1]([s.sub.0] + s[f.sub.0]) - [[alpha].sub.C]/a [f.sub.1] ([a.sub.0] - [f.sub.0]) - [S.sub.0] - [a.sub.0]/a + [f.sub.0] sa + 1/a

[h.sub.2] = [[alpha].sub.P][[f.sup.2].sub.1]s + [[alpha].sub.C]/a[[f.sup.2].sub.1] - 2[sa + 1]/a [f.sub.1]

[h.sub.3] = [h.sub.5] = [[alpha].sub.P][f.sub.1][f.sub.2]S[[alpha].sub.C]/a[f.sub.1][f.sub.2] - sa + 1/a [f.sub.2]

[h.sub.4] = [[alpha].sub.P][f.sub.2]([s.sub.0] + s[f.sub.0]) - [[alpha].sub.c]/a [f.sub.2]([a.sub.0] - [f.sub.0]

[h.sub.6] = [[alpha].sub.P][[f.sup.2].sub.2]s + [[alpha].sub.C]/a[[f.sup.2].sub.2],

and where, for notational ease,

[f.sub.0] = [w.sup.0]ab - wb[s.sub.0]a + [a.sub.0]wb + wa([b.sub.0] - b[S.sub.B])/ab + wb + wa + wsab

[f.sub.1] = ab + aw/ab + wb + wa + wsab

[f.sub.2] = -aw/ab + wb + wa + wsab

The similar condition for country B is

(15) [g.sub.1] + [g.sub.2][[delta].sub.A] + [g.sub.3][[delta].sub.B] + [[g.sub.1] + [g.sub.2][[delta].sub.A] + [g.sub.3][[delta].sub.B]][[delta].sub.AB] = 0,


[g.sub.1] = [[[alpha].sub.B]/b([b.sub.0] - [f.sub.0]) - [S.sub.B]]([f.sub.2] + 1) - [S.sub.B] + [b.sub.0] - [f.sub.0]/b

[g.sub.2] = [g.sub.6] = -([f.sub.1] - 1)/b[[[alpha].sub.B]([f.sub.2] + 1) + 1]

[g.sub.3] = -([f.sub.2] + 1)/b[[[alpha].sub.B]([f.sub.2] + 1) + 2]

[g.sub.4] = [[[alpha].sub.B]/b([b.sub.0] - [f.sub.0]) - [S.sub.B]]([f.sub.1] - 1)

[g.sub.5] = -([f.sub.1] - 1)/b[[alpha].sub.B]([f.sub.1] - 1).

As in the pre-FAIR context discussed above, we can examine the validity of the stategic reactions argument either by examining an explicit Nash equilibrium with strategic interactions, or by examining a consistent conjectures equilibrium. If we model strategic interaction as an explicit Nash equilibrium, the optimum is [[delta].sub.AB] = 0. The analysis above uses general first order conditions, and thus applies here just as it applies to the pre-1996 policy environment.

A consistent conjectures equilibrium can be calculated from (14) and (15) using the procedure described above. Once again, we end up with four equations in four unknowns: [[[delta].sup.*].sub.A], [[[delta].sup.*].sub.B], [[[delta].sup.*].sub.AB] = [partial][[[delta].sup.*].sub.A], /[partial][[delta].sub.B], [[[delta].sup.*].sub.BA] = [partial][[[delta].sup.*].sub.B]/[partial][[delta].sub.A]. In the following section, we investigate optimal subsidies in the post-1995 policy environment.

Optimal Subsidies After the FAIR Act of 1996: Consistent Conjectures

[Graphic omitted]What happens if we evaluate optimal subsidies in (14) and (15) using the parameter values that were consistent with optimizing behavior in 1993? The answers are shown in table 2. This table shows the optimal subsidies and strategic reactions for the United States and the European Union under various scenarios. The demand elasticities and [alpha]'s for each scenario correspond to scenario 1 in table 1. The revised model requires two modifications before simulations can be run. First, the revised model requires an assumption about the supply elasticity in country A. Three different levels of supply elasticity are reported. Second, an assumption must be made concerning the weight to be put on producer surplus. Three possibilities are considered. The Alston, Carter, and Smith (1993) argument implies that the important distinction is between government spending and non-government surplus. Thus, one plausible assumption is that the weight on producer surplus should be the same as the weight on consumer surplus. A s econd possibility is that policy makers use export subsidies to pursue their goal of helping farmers. Thus, a plausible assumption is that the weight on producer surplus should be the same as the weight on government expenditures. Third, we examine the case where producer surplus gets a higher weight than government expenditures. [12] For purposes of illustration, we base our comparisons on scenario 1 of table 1, using domestic demand elasticities of 0.28 in both countries, a world demand elasticity of 0.59, and a weight of consumer surplus of 0.77. We will remark briefly on other of the basic scenarios. [13]

Several results from table 2 are worth noting. First, not surprisingly, increasing the weight on producer surplus increases the optimal export subsidy. However, for the elastic supply scenario, optimal subsidies are zero until the weight on producer surplus reaches 1.04. Second, as supply becomes more elastic, the optimal subsidy for the United States is zero. [14] In fact, for many plausible levels of supply elasticity (elasticities greater than 0.35 for a producer weight of 1.1), the optimal subsidy is zero. [15] A third noteworthy aspect of table 2 is that the European Union optimally increases its subsidy in every scenario compared to the 1993 subsidy level of about $48.

For the most part, these results hold if we use other demand-elasticity, consumer-weights scenarios such as described in table 1. For example, under the assumptions of scenario 2 in table 1, with more inelastic domestic demand and a higher weight on consumer surplus, A's optimal subsidy is zero over a wider range of scenarios. Under scenario 3, with a higher elasticity of world demand, the pattern of subsidies is very similar to that shown in table 2.

Although it is possible to construct scenarios in which the United States should optimally continue export subsidies, these scenarios generally require unrealistic assumptions about the supply elasticity, the elasticity of world demand, or weight assigned to producer surplus. Finally note that the "trade strategy" argument fails consistently: if the United States were to increase its subsidy, the optimal response by the European Union is always to increase its subsidy.

Policy Implications and the Relevance of GATT Restrictions

The main implication of the above analysis is that the elimination of the price support program for crops appears to have altered the role of the EEP program. For plausible scenarios of elasticities and welfare weights, the optimal export subsidy for the United States is zero whenever the market price is above the loan rate. We have searched in vain for evidence that EEP is an effective strategic tool in the war with the European Union for world wheat export markets. In the above scenarios, there is never an instance when it is optimal for the European Union to reduce its subsidies in the face of increased U.S. subsidies. Therefore, the main justification remaining (in this model) for export subsidies is that they shift the cost of price support programs from taxpayers to consumers. When the price support program is eliminated, the justification for export subsidies disappears.

The results of this paper focus attention on the role of EEP as a way of reducing the budgetary costs of domestic farm price support programs. This result supports the views of past analysis (Seitzinger and Paarlberg, or Alston, Carter, and Smith, for example). The contribution of this paper is the use of a model that explicitly allows a strategic trade effect--a reduction of subsidies by the European Union in response to export subsidies by the United States.

[Graphic omitted]The result of the models presented here correspond quite closely to the actual administration of EEP since 1995. The use of EEP was suspended from 1996 to 1998. Starting in August 1998, market prices for wheat fell below loan rates, reverting the situation to one more like the pre-FAIR model in this paper. The EEP program for wheat was resurrected in a November 1998 proposal, but no EEP bonuses have actually been awarded since 1995.

In the Uruguay Round of GATT negotiations, reductions in agricultural export subsidies were negotiated. These reductions restricted both the total expenditures on subsidies and the total quantity subsidized. Through 1998, both the United States and the European Union have been able to meet their Uruguay Round obligations without changes in underlying programs. The analysis here suggests that it may be difficult to negotiate further reductions in export subsidies without there first being a change in the CAP price support regime.

Howard Leathers is associate professor of Agricultural and Resource Economics at the University of Maryland, College Park.

(1.) See Paarlberg and Abbott for an application of consistent conjectures to agricultural trade.

(2.) This interpretation is consistent with the Alston, Carter, and Smith paper (1993). However, it should be noted that both the 1985 and 1990 farm legislation contain provisions intended to "decouple" farm production decisions from program prices. The extent to which decoupling has been effective is an unresolved issue. The model presented later in this paper, in which production decisions are tied to market prices and farm programs provide direct income payments to farmers, may be closer in some respects to the pre-1996 legislative environment with effective decoupling.

(3.) As noted below, when marketing loan provisions of FAIR are in effect, the assumption is still valid.

(4.) Reintroduction of EEP bonuses was proposed but never implemented in 1998. The renewed interest in EEP coincided with the applicability of the marketing loan provisions, but the ultimate decision was to keep export subsidies at zero.

(5.) This interpretation was suggested by an anonymous reviewer to whom I am indebted.

(6.) The assumption that target prices are equivalent to prices farmers use to decide the level of farm output is in fact an implicit assumption about "decoupling". See footnote 2 above.

(7.) Gardner argues that price support levels and export subsidy levels are determined simultaneously rather than sequentially. Gardner's argument might be valid if applied to a legislative decision in which a level of export subsidies was established along with a level of target price. However, the Alston, Carter, and Smith approach--and the approach of the present paper--does appropriately model the administrative policy decision concerning how aggressively to implement EEP, given that target prices are established.

(8.) Other, more complicated forms of interaction are possible. For example, country A could react to country B's reaction, as well as B's base level. The conclusions drawn from this model are therefore limited in their generality.

(9.) The assumption of linear supply and demand curves is necessary for explicit derivation of a consistent conjectures equilibrium. It should he emphasized that the conclusions drawn in this paper using a consistent conjectures equilibrium apply only to the linear case.

(10.) Abbott and Kallia discuss the pros and cons of using a consistent conjectures model in more detail.

(11.) Of course, the solution to the quadratic is not unique. This is a widely discussed aspect of the "consistent conjectures" equilibrium. In the present case, we are able to calibrate the policy simulation by finding a set of parameters at which one of the possible equilibria is consistent with reality.

(12.) The case of producer surplus having a higher weight than government costs is not unusual in the literature. (See P. L. Paarlberg, for example.) But a rational policy maker would continue to transfer money to producers until the inefficiency of transfers rose to a degree where the weight on producer surplus equaled the weight on government costs. Therefore, there is some question in the author's mind about whether this is a realistic scenario.

(13.) Recall that the basic scenarios in table 1 are ones that rationalize the observed situation in 1993. Thus the different scenarios change both the demand elasticities and the consumer surplus weight.

(14.) An elastic supply curve reduces the effectiveness of an export subsidy because the increases in exports arc offset to a greater degree by increases in production.

(15.) As the weight assigned to producer surplus becomes greater than 1--the welfare weight for government expenditures--then the optimal subsidy of country A grows, and the optimal subsidy of country B declines. This suggests an intriguing possibility: that the strategic game is one in which policy makers do not know the opponent's social welfare function, and that strategic objectives are met by overstating one's true desire to assist producers. This possibility is beyond the scope of the current paper.


Abbott, P.C., and P.K.S. Kallio. "Implications of Game Theory for International Agricultural Trade." Amer. J. Agr. Econ. 78(August 1996)738-44.

Abbott, P.C., P.L. Paarlberg, and J.A. Sharples. "Targeted Export Subsidies and Social Welfare." Amer. J. Agr. Econ. 69(November 1987): 723-32

Alston, J.M., C.A. Carter, and V.H. Smith. "Rationalizing Agricultural Export Subsidies." Amer. J. Agr. Econ. 75(November 1993):1000-1009.

-----. "Rationalizing Agricultural Export Subsidies: Reply." Amer. J. Agr. Econ. 77(February 1995):209-211.

Anania, G., D. Bohman, and C. Carter. "U.S. Export Subsidies in Wheat: Strategic Trade Policy or Expensive Beggar-Thy Neighbor Tactic?" Amer. J. Agr. Econ. 74(August 1992): 534-45.

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Paarlberg, P.L. "When Are Export Subsidies Rational?" Agr. Econ. Res. 36(Winter 1984): 1-7.

Paarlberg, P.L., and P.C. Abbott. "Oligopolistic Behavior by Public Agencies in International Trade: The World Wheat Market." Amer. J. Agr. Econ. 68(August 1986):528-42.

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Pearce, D. "Rationalizable Strategic Behavior and the Problem of Perfection." Econometrica 52(July 1984):1029-50.

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Bull. Econ. Res. 43(1991):259-71.
United States European Union "World"
Price $147/metric ton $158/metric ton $110/metric ton
($4.00 per bushel) ($4.30/bushel) ($3.00/bushel)
Quantity produced 66 million m.t. 98 million m.t.
Quantity exported 34 MMT 33 MMT
Quantity demanded 32 MMT 65 MMT 67 MMT
Scenarios in which Subsidies,
Prices, and Quantities Observed
in 1993 Correspond
to Optimal Decisions by Policy Makers
Demand Demand Weight on
Elasticity in Elasticity in Demand Consumer
Country A Country B Elasticity Surplus in A
Scenario (US) (EU) in World ([[alpha].sub.A])
1 0.28 0.28 0.59 0.77
2 0.1 0.1 0.59 0.91
3 0.28 0.28 1.0 0.83
4 0.28 0.50 0.59 0.77
A's optimal B's Optimal
Weight on Reaction to Reaction to
Consumer a change in a Change in
Surplus in B B's subsidy A's Subsidy
Scenario ([[alpha].sub.B]) [[delta].sub.AB] [[delta].sub.BA]
1 0.77 0.058 0.042
2 0.91 0.012 0.008
3 0.83 0.030 0.021
4 0.59 0.085 0.055
Optimal Export Subsidies After the 1996 Fair Act under different Scenarios
Weight on Optimal
Producer Supply Subsidy
Scenario Surplus Elasticity ([[delta].sup.[A.sup.*]])
1A 0.77 0.2 0
1B 1.0 0.2 0
1C 1.1 0.2 $19.84
1D 0.77 0.1 0
1E 1.0 0.1 $1.91
1F 1.1 0.1 $50.19
1G 0.77 0.05 0
1H 1.0 0.05 $15.98
1I 1.1 0.05 $77.54
B's A's Optimal B's Optimal
Optimal Response to a Response to a
Subsidy Change in B's Change in A's
Scenario ([[delta].sup.[B.sup.*]]) Subsidy Subsidy World Price
1A $57.50 0 0.080 $117.17
1B $57.50 0 0.080 $117.17
1C $54.80 0.054 0.083 $112.89
1D $53.52 0 0.063 $115.65
1E $50.16 0.057 0.063 $115.97
1F $53.58 0.052 0.064 $106.49
1G $51.27 0 0.053 $114.85
1H $49.27 0.057 0.054 $112.88
1I $52.75 0.053 0.054 $102.96

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