Playing favorites: welfare effects when strategic trade policy is set to favor producers.

I. Introduction

Governments routinely use international trade policies to assist their domestic industries. While the official explanations for such policies may rely on infant-industry or national-security arguments, or on the use of unfair trade practices by other countries, it is commonly acknowledged that such protection is often politically motivated. In particular, commercial interests often convince the government to enact policies that transfer resources to firms and away from consumers or taxpayers. A large academic literature studies the extent to which various interest groups can influence the design of trade policy.(1) These analyses often conclude that governmental "favoritism" of commercial interests has a detrimental effect on overall national welfare. The fact that this favoritism exists in spite of its presumed harmful overall effect is often attributed to differences in the amounts of political influence wielded by competing interest groups.

At the same time, another vast literature investigates a different (non-political) process by which governments may establish active international trade policy. This literature analyzes the strategic aspect of trade policy design in markets containing a small number of firms. While results vary across models, a common conclusion (expressed simply) is that a single government that seeks to raise domestic national surplus may have an incentive to employ active trade policy. When two (or more) opposing governments both impose such policies, however, this literature often concludes that both national surpluses fall.(2)

In this note, we draw together these two approaches by considering the strategic trade policy choices of a government that sets its policy to maximize an objective function that differs from national surplus. In a non-strategic setting, attributing a non-surplus-maximizing motive to a nation's government would be expected to reduce that nation's equilibrium surplus. We use a model derived from Brander and Spencer [5], however, to show that this conclusion need not hold in a setting that involves a strategic relationship between governments.

In our model, two firms located in different countries export to a third-country market. Each government has an incentive to subsidize its firm's exports. The export subsidies affect domestic interest groups in opposite ways - firms gain; taxpayers lose. We assume that a government chooses its subsidy to maximize a function that may place more weight on the profit that its firm derives from exporting than it places on the cost to its taxpayers of subsidizing those exports; this pattern may be due to various internal political pressures.

We show that if a country's government designs its policy while "overweighting" firm interests, that country can experience a larger equilibrium true national surplus (weighting profit and tax cost equally) than it would experience if its government acted to maximize that surplus. True surplus is increased because firm profit rises by more than does taxpayer cost. Such an outcome is possible only in a strategic setting in which the overweighting of profit by one government changes the equilibrium action of the other government.

If both governments in our model overweight profit, both countries experience lower true national surplus than in the standard Brander-Spencer model. We show that such a "prisoners' dilemma" outcome may be difficult to escape in the absence of coordinated action. More specifically, a "reform" in a single country that causes its government's objective function to more closely resemble true national surplus may decrease that country's equilibrium surplus.

Our results imply that the explanation for why governments adopt policies that favor commercial interests need not rest entirely on the view that firms have sufficient political influence to convince governments to favor them even at a possible cost to national welfare. Rather, we show that in a strategic setting the existence of favoritism can be self-reenforcing. A government that acts to favor commercial interests can increase, albeit inadvertently, its country's true surplus.

Using a different model, Panagariya and Schiff [23] independently derive a result related to ours. Their paper considers export-tax-setting governments that act to maximize either tariff revenue or national welfare. Panagariya and Schiff allow their governments to possess only one of two possible objective functions, and assume that both governments have the same objective. Thus, they do not consider the effect of a marginal change in the extent to which one government's objective function corresponds to national welfare.(3)

II. Model

The model used in this paper follows the simplest version of a model developed by Brander and Spencer [5]. We assume the existence of two firms (producing homogeneous goods), each of which is located in a different country: firm i is located in country i, i = 1, 2. Each firm sells its product in a potentially-profitable third-country market. In order to focus solely on trade policy, the model assumes that there are no domestic markets within either of the exporting countries. Brander and Spencer show that when governments in such a model set policy in a noncooperative manner, each government has an individual incentive to subsidize sales by its home firm.(4) While these subsidies are costly to the country's taxpayers, they encourage its firm to capture a larger share of the export market, and can thus raise firm profit enough to increase national surplus. When both countries impose export subsidies, however, both suffer as a result.(5)

To simplify the computations found below, we assume that the third-country demand curve is linear, namely p = b - [x.sub.1] - [x.sub.2], where [x.sub.i] is the output of firm i, and that each firm operates with private marginal costs of production that are constant at unity. We also use a graphical approach, detailed below, to discuss whether our results carry over to cases of nonlinear demand. The firm in country i receives a specific subsidy of [s.sub.i] [greater than] 0 from its home government (financed through tax collections) for each unit [x.sub.i] it sells. Firm i thus maximizes [[Pi].sub.i] = (b - [x.sub.i] - [x.sub.j] - 1 + [s.sub.i])[x.sub.i].

Firm i's reaction function, which gives its profit-maximizing output (derived assuming [x.sub.j] is constant), is

[x.sub.i] = (b - 1 - [x.sub.j] + [s.sub.i])/2.

Using the reaction functions of the two firms reveals that a Nash equilibrium in quantities the output of Firm i is

[Mathematical Expression Omitted].

Using the standard definition, national surplus equals firm profit minus subsidy cost, or

[G.sub.i]([s.sub.i]) = [x.sub.i] (b - [x.sub.i] - [x.sub.j] - 1 + [s.sub.i]) - [s.sub.i][x.sub.i] = [x.sub.i] (b - 1 - [x.sub.i] - [x.sub.j]).

This paper investigates how national surplus is affected when government policy is designed to maximize a function other than [G.sub.i]. In particular, we assume that each government may be subject to domestic political pressures that lead it to maximize a function that places greater weight on the firm component of national surplus than it places on the taxpayer component. Various possible justifications for such government behavior have been offered in the literature. One is that firms (or their unionized work force) might have more ability to influence government payoffs (perhaps through offers of campaign support) than do taxpayers (or consumers) who might be less able to organize and influence government due to problems of free riding.(6) As discussed below, profit-overweighting in a strategic setting may be self-perpetuating once begun.

Baldwin [1] shows that the policy outcome from a process in which "policy makers choose tariffs to stay elected," and "industry groups lobby," can be obtained directly from a model in which a government maximizes an objective function that "gives 'too much' weight to profits." We denote the weight given to profit in the government's objective function as [w.sub.i] [greater than or equal to] 1. We leave the political process within a country unmodeled, and treat [w.sub.i] as an exogenous constant that affects government behavior. Government i is thus modeled as setting its export subsidy [s.sub.i] to maximize(7)

[Mathematical Expression Omitted].

One can interpret [Mathematical Expression Omitted] as representing the outcome of a domestic political process in which firms and taxpayers have opposing interests.(8)

Substituting equilibrium firm outputs (1) into [Mathematical Expression Omitted] and differentiating with respect to [s.sub.i] (while holding [s.sub.j] constant) produces the reaction function of government i(9)

[s.sub.i] = (b - 1 - [s.sub.j])(4[w.sub.i] - 3)/[4(3 - 2[w.sub.i])]. (2)

The second-order condition for a maximum of [Mathematical Expression Omitted] is 4(2[w.sub.i] - 3)/9 [less than] 0, which is satisfied for [w.sub.i] [less than] 3/2). (10)

We first investigate the case in which one country, say country 2, places equal weight on profit and taxpayer cost, so that [w.sub.2] = 1. If [w.sub.1] = 1 also holds, our model reduces to the basic Brander-Spencer model. The equilibrium when [w.sub.1] = [w.sub.2] = 1 can be illustrated in Figure 1, in which each straight line is a firm reaction function and each curve is the locus of all the output levels at which Country i earns a given level of true national surplus [G.sub.1].(11) When neither government subsidizes its firm's exports, the firm reaction functions are [Mathematical Expression Omitted] and [Mathematical Expression Omitted], and equilibrium output is represented by point a. In the Brander-Spencer model, each government has an incentive to subsidize its firm in order to shift out its reaction function. In the case of country 1, the government subsidizes its firm in an attempt to shift the outcome along Firm 2's reaction function to a point such as b, where Country 1 earns a greater true national surplus than it earns at a. When both countries place a weight of unity on firm profit, and both subsidize exports, the firms' reaction functions are shifted out to [Mathematical Expression Omitted] and [Mathematical Expression Omitted] and the Nash equilibrium is at point c, where each country earns a lower national surplus than it earned at a.

The Nash equilibrium export subsidies, when demand is linear and [w.sub.2] is fixed at unity, can be computed by equating the governments' reaction functions. The equilibrium subsidies are

[s.sub.1] = (b - 1)(4[w.sub.1] - 3)/(17 - 12[w.sub.1]) [s.sub.2] = (b - 1)(5 - 4[w.sub.1])/(17 - 12[w.sub.1]). (3)

When [w.sub.1] = [w.sub.2] = 1 holds, [Delta][s.sub.1]/[Delta][w.sub.1] [greater than] 0. A country that overweights firm profit will increase the subsidy it offers its firm for two reasons - the subsidy creates a direct transfer from taxpayers to the firm and, by altering the reaction function, it improves the firm's relative position in the export market.(12) Furthermore, [w.sub.1] = [w.sub.2] = 1 also implies [Delta][s.sub.2]/[Delta][w.sub.1] [less than] 0. This inequality holds because of the strategic game between the governments. An increase in [w.sub.1] alters the game by making more "credible" government 1's commitment to aggressive efforts to promote exports (i.e., to impose high subsidies). In equilibrium, this increased credibility causes government 2 to reduce its subsidy.

To compute country 1's true national surplus with [w.sub.2] = 1 but with [w.sub.1] [greater than] 1 possible, equations (3) and (1) and the true formula for [G.sub.i] are used to produce

[Mathematical Expression Omitted].

Clearly, [Mathematical Expression Omitted]. Assuming linear demand, therefore, the introduction of profit overweighting by the government of country 1 increases that country's true equilibrium national surplus. Note that the beneficial effect on true surplus of profit overweighting is limited, since [Mathematical Expression Omitted] achieves its maximum value at [w.sub.1] = 13/12.

Figure 1 can be now used to illustrate why non-surplus-maximizing behavior by a nation's government can raise that nation's equilibrium true surplus. Remember that the weight a government puts on profit affects the equilibrium export subsidy, which in turn affects the location of the firm reaction function. An increase in [w.sub.1] causes Firm 1's reaction function in Figure 1 to shift out and Firm 2's reaction function to shift down. As the formulae above suggest, such shifts have the potential to move the intersection of the two reaction functions to a point like e in the figure. At point e, [x.sub.1] is greater than, [x.sub.2] is less than, and [G.sub.1] is greater than the values held by each parameter at point c. Thus, as Government 1 begins to overweight profit, the consequent fall in [s.sub.2] makes it possible for Country 1's true national surplus to rise.

As [w.sub.1] continues to rise, the government's effort to maximize [Mathematical Expression Omitted] eventually causes the two reaction functions to cross at a point above the [Mathematical Expression Omitted] curve. In this situation, [G.sub.1] falls because the rise in [x.sub.1] + [x.sub.2] reduces the market price of the export good by enough to overwhelm Firm 1's increased market share.

Figure 1 makes clear that, starting in a situation in which both [w.sub.i] terms equal unity, an increase in [w.sub.i] can raise [G.sub.i] whenever firm reaction functions are downward-sloping. Thus, the result derived above is not limited to the case of linear demand, but rather holds whenever firm reaction functions both slope down and are shifted in the manner described above when a government overweights profit. The figure also makes clear that the existence of a strategic game between the two governments is crucial to the result. If an increase in [w.sub.1] has no effect on the subsidy set by government 2, the "credible commitment" argument detailed above is irrelevant. If [s.sub.2] is unaffected, then [Mathematical Expression Omitted] is not shifted, and point e cannot fall under [Mathematical Expression Omitted]; profit overweighting thus cannot raise true national surplus.

Returning to the case of linear demand, we now consider the case in which both governments may overweight profit. Substitution reveals that, with linear demand, the Nash-equilibrium government subsidy levels as a function of the governments' weights on profits are

[Mathematical Expression Omitted].

There exists an interior stable equilibrium for this particular game, with [Mathematical Expression Omitted] and [Mathematical Expression Omitted], if and only if [w.sub.k] [less than or equal to] 5/4 for k = i, j.(13) We assume that this condition holds.

To compute true national surplus when governments overweight profit, we use (4) and (2) to obtain [Mathematical Expression Omitted], and substitute this expression into the formula for [G.sub.i] to produce

[Mathematical Expression Omitted].

To determine the effect that an increase in the degree of government i's commercial favoritism has on the equilibrium true national surplus of country i, we differentiate [Mathematical Expression Omitted] to produce

[Mathematical Expression Omitted].

Evaluating (5) when both governments design policy giving equal but arbitrary weight to profit yields: [Mathematical Expression Omitted]. Anytime the two countries originally design trade policy while placing the same weight on profit, therefore, an exogenous increase in the weight that government i gives to profit will increase its country's true national surplus.(14) Again, the existence of a strategic game between the governments drives this result. If [s.sub.2] is fixed at any value, an increase in [w.sub.1] could not raise [G.sub.1], as can be demonstrated by substituting (2) and an arbitrary fixed [Mathematical Expression Omitted] into (1), and then substituting into the formula for true national surplus.

Since (5) can become negative for [w.sub.i] [greater than] [w.sub.j], there is a limit to the benefit of overweighting profit. Furthermore, joint increases in [w.sub.1] = [w.sub.2] = w always reduce surplus: [Mathematical Expression Omitted]. An increase in profit overweighting in both countries causes each government to increase its subsidy. Both firm reaction functions shift out and intersect at a point like f in Figure 1; each country's national surplus falls.

The above results suggest the following interpretation. As noted earlier, many traditional explanations for why governments often favor commercial interests rely on the view that firms possess more political influence than do taxpayers (or consumers), and are thus able to persuade government to continue to favor them even if this favoritism reduces national welfare. Our analysis, however, shows that in a setting that involves strategic interaction between governments, a government's overweighting of profit can be self-perpetuating since it can inadvertently increase national welfare. This result suggests that in such strategic situations, analysts need not rely as heavily on the view that differing levels of political influence explain the persistence of governmental favoritism.

A related point arises from the result that, while a reduction in [w.sub.i] [greater than] 1 makes the goal of government i correspond more closely to the maximization of national surplus, such a change need not raise national surplus. In fact, starting from a symmetric situation, such a reform will always reduce equilibrium true surplus. This result suggests that, in international markets in which strategic issues are important, we may not be likely to observe many instances of unilateral "reform" in which a country reduces the extent to which its government favors commercial interests. Since such "reform" may well reduce equilibrium national welfare, there is likely to be little political support for continuing it.

To close this section, we note how the assumptions in the model presented above differ from those used by Brander and Spencer [5], Sklivas [25], and Fershtman and Judd [8]. In both the Sklivas and the Fershtman and Judd papers, a principal (specifically, a firm owner) that seeks to maximize its own welfare manipulates the incentives of its agent (specifically, a firm manager). The Brander and Spencer paper, and the literature derived from it, uses a similar approach in which a government manipulates the incentives of an exporting firm. In our model, government i (which in the Brander-Spencer approach is usually assumed to maximize [G.sub.i]) is led by internal political pressures to maximize [Mathematical Expression Omitted]. As prior results suggest, the first-mover in our paper manipulates the incentives of the second-mover. The first-mover does so in order to obtain a higher equilibrium level of [Mathematical Expression Omitted]. Our main result, however, is distinct from the results of the above authors because it indicates that the government can earn a higher [G.sub.i] when it acts to maximize [Mathematical Expression Omitted] than it would earn if it sought to maximize [G.sub.i].(15)

III. Conclusion

This paper considers a model of strategic export subsidization in which a government may maximize an objective function that places a larger weight on the profits of its exporting firm than it places on the costs that those subsidies impose on its taxpayers. Our results show that when the extent to which a government favors firm interests over taxpayer interests rises, that country's equilibrium true national surplus can also rise. This outcome can occur when governments interact strategically because profit-overweighting by one government reduces the export subsidy paid in equilibrium by the other government. In a non-strategic environment, of course, adopting the assumption that a government maximizes a function that differs from national surplus would not be expected to increase that surplus.

The traditional explanation for why governments continue to favor commercial interests is that firms have enough political influence to overwhelm the favoritism's negative effects on national well-being. Our results, however, show that such strong political influence may not be needed. In a strategic environment, favoritism has the potential to increase national welfare rather than reduce it.

If both countries in our model adopt symmetric, non-surplus-maximizing behavior, the equilibrium surpluses of both countries fall. Our model thus indicates that, if governmental favoritism toward commercial interests is widespread, the benefit to similar countries of cooperating in creating international trade policy is larger than some previous theoretical models might suggest.(16) This conclusion follows for two reasons. First, if non-surplus-maximizing government behavior is wide-spread, actual noncooperative strategic trade policies may deviate from the optimal cooperative policies by more than other theoretical models would indicate. Further, as our results show, such non-surplus-maximizing behavior may be unlikely to disappear through unilateral action, since a "reform" that causes the policy-setters of one nation to bring the goals of national policy more in line with the definition of national welfare need not, in a strategic setting, increase that country's actual equilibrium welfare.

1. For a broad sampling of the political-economic trade literature, see: Brock and Magee [6], Bhagwati [2], Hillman [13], Mayer [19], Mayer and Riezman [20], Magee, Brock, and Young [18] and the survey by Hillman [12] as well as the references therein.

2. Much research on strategic trade policy has been based on the work of Brander and Spencer [5]. For some recent extensions of their model, see Gruenspecht [10], Brainard and Martimort [3], Laussel [17], and Hwang and Schulman [15; 16]. For a survey of the strategic trade literature, see Brander [4].

3. Two other related papers analyze models that contain both political and strategic determinants of trade policy. Moore and Suranovic [21] consider a model in which a firm lobbies its government to obtain a larger export subsidy. We differ from Moore and Suranovic by considering interactions between two politically-influenced governments and by showing that non-surplus-maximizing incentives can raise national surplus. Grossman and Helpman [9] analyze a model in which governments design trade policy to maximize their own utility, which depends on both aggregate domestic welfare and the political contributions of special-interest groups. We differ from Grossman and Helpman by employing different assumptions about government incentives and market structure, and again by establishing conditions under which national surplus rises. In another related paper, Hillman and Ursprung [14] consider how the political contributions of strategic firms affect the policy positions taken by political candidates, focusing on how introducing multinational firms alters political outcomes. In their paper, however, there is no strategic competition between governments.

4. We limit our attention to the noncooperative subgame perfect equilibrium considered by Brander-Spencer and most of the strategic trade literature that follows their work; see Brander [4]. It should be noted that in a cooperative equilibrium, both countries do better to impose an export tax, rather than a subsidy, because the tax reduces the extent to which joint output exceeds the monopoly output. An analysis of the conditions under which governments are likely to cooperate is beyond the scope of this paper.

5. The literature using Brander-Spencer-type subsidy models is now vast. While some authors discuss the potential role of lobbyists, nearly all of the formal models assume that governments design policy to maximize national welfare. See Moore and Suranovic [21], however, for a paper in the strategic-subsidy literature that contains an explicitly modeled role for interest groups.

6. Olson's [22] seminal work addresses this issue.

7. Feenstra and Lewis [7] show that an objective like [Mathematical Expression Omitted] can also be derived from a median voter model in which mean capital endowment and median capital endowment differ.

8. It might be possible for a government that weights firms and taxpayers differently to transfer resources between the two groups directly. However, we argue that it is often much easier for governments to rely on indirect methods (such as trade policy) to enact such transfers. Grossman and Helpman [9], along with other authors, make a similar argument. In this paper, we restrict our attention to the use of trade policy as a way of enacting transfers.

9. Throughout this paper we assume that the values of [w.sub.i] are known to both governments.

10. When [w.sub.i] [greater than] 3/2, government i would never stop raising [s.sub.i]; the resulting weighted increase in firm profits (even accounting for the price decrease caused by increased exports) exceeds the cost to taxpayers.

11. Under linear demand, reaction functions of quantity-setting firms are always straight and downward sloping; this situation is illustrated in Figure 1. It is generally assumed in the literature that such reaction functions are downward sloping even in the absence of linear demand; see Helpman and Krugman [11]. Illustrations like Figure 1 are common in the literature; see for example Figure 5.11 in Helpman and Krugman [11].

12. These effects are offset by a reduction in the market price of the export good caused by a rise in joint output.

13. Note that this restriction on the [w.sub.k] values has the effect of restricting the slopes of the governments' reaction functions in subsidy space. Equation (4) gives the optimal subsidy levels when [w.sub.k] [less than or equal to] 5/4. If 5/4 [less than] [w.sub.i] [less than] 3/2 and [w.sub.j] [less than or equal to] 5/4, then the unique equilibrium is [s.sub.i] = b - 1 and [s.sub.j] = 0 (in which case firm outputs are [x.sub.i] = b - 1 and [x.sub.j] = 0). If 5/4 [less than] [w.sub.k] [less than] 3/2 for k = i,j, then there exist three possible equilibria - an unstable interior equilibrium (in which both firms produce positive output) with [Mathematical Expression Omitted] and [Mathematical Expression Omitted], and two corner solutions (in which only one firm produces positive output) with [Mathematical Expression Omitted] and [Mathematical Expression Omitted] or [Mathematical Expression Omitted] and [Mathematical Expression Omitted].

14. This result is consistent with the following suggestion, made independently, by Grossman and Helpman: "a government that is unresponsive to the public interest might actually serve the general voter well [in a trade war], because the self-interested government can credibly commit to a policy of aggressive support for the domestic industry" [9, 694].

15. A related result is that of Rogoff [24]. He shows, in a model of monetary targeting by central banks, that social welfare can be raised by bringing in a "conservative central banker" who minimizes a non-standard social loss function that overweights inflationary losses relative to unemployment losses.

16. This cooperation could take the form of agreements to refrain from using certain trade practices (GATT, for example) or to increase the use of certain policies (export taxes, for example). Of course, the firms in our model will have little interest in seeing international agreements of this type adopted.

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