Open economies review 13: 73–86 (2002) c 2002 Kluwer Academic Publishers. Printed in The Netherlands. 

Industrial Concentration Reverses the Timing in a Trade Policy Game MASAYUKI HAYASHIBARA [email protected] Faculty of Economics, Otemon Gakuin University, Nishi-Ai, Ibaraki City, Osaka, 567-8502, Japan

Key words: policy timing, strategic trade policy JEL Classification Numbers:

F12, F13

Abstract Faced with an export subsidy by a foreign government, importing countries have to decide whether they should impose countervailing duties or not. Using a Cournot duopoly model, Collie (Weltwirtschaftliches Archiv 130: 191–209) shows that the subgame perfect equilibrium occurs when the importing country sets its production subsidy and tariff at stage one and the foreign government sets its export subsidy at stage two. That is, an importing country will choose to commit itself not to use countervailing duties. In this paper, we extend Collie’s duopoly model to the case of a Cournot oligopoly and show that the country in which industry is less concentrated tends to emerge as the Stackelberg leader.

Introduction The strategic trade and industrial policy literature has established various propositions concerning the effects of alternative policies on outputs, prices and welfare.1 Recent arguments tend to maintain that both policy tools and the timing of trade policy are determined endogenously. Faced with an export subsidy by a foreign government, importing countries have to decide whether they should impose countervailing duties or not. A pioneering paper by Collie (1994) shows that in the model of a two-country, four-stage trade policy game, an importing country will choose to commit itself not to use countervailing duties. This conclusion is based on the premise that, on the one hand, the home government can use a production subsidy to correct domestic distortions and/or a tariff to extract profit from a foreign firm by improving home terms of trade. On the other hand, the foreign government can use an export subsidy to shift profit from a home firm to a foreign firm. Endogenous timing is modeled using the extended game with observable delay proposed by Hamilton and Slutsky (1990). At stage zero each government chooses the timing of its policy between stage one or two. The outcome will be one of the following three equilibria: a simultaneous-move trade policy game, a Stackelberg game with the home government as a leader, and a Stackelberg

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game with the foreign government as a leader. Taking both governments’ policies as given, at stage three two firms, one in each country, supply a perfectly substitutable good into the home market in a Cournot fashion. Proposition 1 by Collie shows that the subgame perfect equilibrium occurs when the home government sets its production subsidy and tariff at stage one and the foreign government sets its export subsidy at stage two. However, we actually see countervailing duties put in use quite often. Wong and Chow (1997) rationalize the use of countervailing duties by introducing demand uncertainty into Collie’s framework. This paper is concerned with whether Collie’s Proposition 1 in the duopoly model is applicable in the case of a Cournot oligopoly.2 Here, we will consider a possible case of the reversal of policy timing. In general, the number of firms in an industry will affect trade and industry policy. Then in a Cournot oligopoly, the subgame perfect equilibrium is as follows. (1) The home government sets a production subsidy and a tariff at stage one and the foreign government sets an export subsidy at stage two, if the number of foreign firms is less than or equal to that of home firms. (2) If the number of foreign firms is greater at least by one than that of home firms, then the foreign government sets a zero export subsidy at stage one. In addition, at stage two the home government responds with a production subsidy and a tariff. In other words, the country with less-concentrated industry tends to emerge as the Stackelberg leader. Collie’s duopoly case applies to (1). Here, to clarify the situation that applies to this study, we need to compare equilibria for two games. The first is the simultaneous-move equilibrium, and the other is the equilibrium for the endogenous timing game, where each government gets the opportunity to choose its policy between stage one and stage two. If the number of foreign firms is less than or equal to that of home firms, then in the simultaneous-move equilibrium, the home government sets a production subsidy and tariff and the foreign government sets an export subsidy. The sequential equilibrium occurs when the home government sets a lower production subsidy and lower tariff at stage one, and the foreign government responds by setting a higher export subsidy at stage two. The home tariff revenue and total export subsidy for the foreign country increase and the welfare of each country, as well as world welfare, goes up. Next, consider the case in which the number of foreign firms is greater at least by one than that of home firms. In the simultaneous-move equilibrium, the home government sets a production subsidy and tariff and the foreign government sets an export tax. That is, export discouragement by the foreign government raises foreign welfare. In the sequential equilibrium, the foreign government sets a zero export subsidy (tax) at stage one, and the home government responds to it by setting a lower production subsidy and higher tariff at stage two. The overall effect of retaliation encourages the foreign government to expand its exports. Again, the home tariff revenue increases and the total export tax for the foreign country decreases to zero, and the welfare of each country, as well as world welfare, goes up.

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This paper is organized as follows: In Section 1, a basic model is presented. Section 2 deals with national welfare under an exogenously determined sequence of policy moves. The main proposition regarding the endogenous determination of policy timing is derived in Section 3. Section 4 provides a summary and conclusion. 1.

Basic model

We consider a two-country model in which n h identical home firms and n f identical foreign firms compete in the domestic market in a Cournot fashion. The numbers of firms are fixed. The home government maximizes national welfare through a production subsidy and a tariff, and the foreign government maximizes national welfare (net profit) through an export subsidy. The game considered here has four stages, as follows: Stage 0: Stage 1: Stage 2: Stage 3:

Each government independently chooses its policy stage The leader country sets its policy variables The follower country sets policy variables Firms choose outputs in a Cournot fashion.

The subgame perfect equilibrium is obtained by a process of backward induction. Thus, endogenous timing is modeled using the extended game with observable delay proposed by Hamilton and Slutsky (1990). 1.1.

Demand for goods

The home country’s household utility function U (Q, z) is differentiable and strictly concave in Q, U (Q, z) = aQ − bQ 2 /2 + z = u(Q) + z, 0 < a and 0 < b,

(1)

where Q is the total consumption of the homogenous good and z denotes consumption of the numeraire good. From the first order condition for utility maximization by a household, we obtain the linear inverse demand function: p = a − bQ,

(2)

where p stands for the product price and p = du(Q)/dQ holds. Defining the consumer surplus as C S = U − ( pQ + z), substitution obtains C S = bQ 2 /2 > 0. 1.2.

Production

Consider the third stage of the game. Taking the governments’ policies as given, each home firm and foreign firm produces x and y, respectively. Thus

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Q = n h x + n f y holds. Let cx and c y be the constant marginal costs of the home firm and the foreign firm. In order to satisfy the interior solution, it is assumed that foreign firms have a cost advantage, but not to such an extent that the production by home firms is completely driven away. That is, there exists some positive value k for the marginal cost of foreign firms, such that, 0 < k < c y < cx . k depends on the marginal cost of home firms, the number of firms, and the coefficients for the demand function, and will be defined formally in Section 2.3. The gross profit of each firm is: πx = ( p − cx + s)x, π y = ( p − c y − t + e)y, where s, t and e denote a specific production subsidy to a home firm, a tariff on imports levied by the home government and an export subsidy to a foreign firm provided by the foreign government, respectively. Under Cournot competition, assuming an interior solution, the first order condition (the reaction function) for the profit maximization by each firm will be: ( p − cx + s) − bx = 0, and ( p − c y − t + e) − by = 0.

(3)

Solving the equations in (3) for Cournot–Nash outputs obtains: x(s, t, e) = {(a − c y − t + e) − (n f + 1)(cx − c y −s − t + e)}/(b ) y(s, t, e) = {(a − cx + s) + (n h + 1)(cx −c y − s − t + e)}/(b ) where = n h + n f + 1. Furthermore, the Cournot price will be: p(s, t, e) = {a + (cx − s)n h + (c y + t − e)n f }/ . The above results summarize the output and price at the third stage in terms of policy variables s, t and e. 1.3.

Comparative statical effects on production and price

First, the effects of the small change in c y on output and price are: d x/dc y = n f /(b ) > 0, dy/dc y = −(n h + 1)/(b ) < 0, d p/dc y = n f / > 0. Second, the effects of a production subsidy can be obtained as: dx/ds = (n f + 1)/(b ) > 0,

dy/ds = −n h /(b ) < 0,

d p/ds = −n h / < 0.

An increase in s encourages home production but discourages foreign production. A production subsidy will increase total supply and thus reduce the price.

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Third, the effects of a tariff change can be the same as those of c y . Fourth, the effects of an export subsidy are opposite those of a tariff. 1.4.

National welfare

The national welfare of the home country is assumed to be the sum of the consumer surplus, total gross profit of home firms and net government revenue. Net government revenue is defined as T = tn f y − sn h x, and the home country welfare is summarized as: SW(s, t, e) = C S + ( p − cx + s)n h x + T = u(Q) − cx n h x − pn f y + tn f y.

(4)

Considering the third-stage competition and taking the foreign subsidy as given, the home government chooses a production subsidy and a tariff, so as to maximize home welfare. By partially differentiating SW with respect to policy variables, and substituting the comparative statical results into the reaction functions of the home government in the policy game, ∂SW/∂s = 0 and ∂SW/∂t = 0, gives: ∂SW/∂s = {( p − cx )(n f + 1) − n f (t − by)}n h /(b ) = {(a − cx )(2n f + 1) − (cx − c y )n f (n f − n h ) − n h (2n f + 1)s −n f (2n h + 1)t − n f (n f − n h )e}n h /(b 2 ) = 0

(5)

and ∂SW/∂t = {( p − cx )n h − (n h + 1)(t − by)}n f /(b ) = [(a − c y )(2n h + 1) + (cx − c y )n h (n h − n f ) − n h (2n h + 1)s −{(n f + 2(n h + 1)2 }t + {(n h + 1)2 − n h n f }e]n f /(b 2 ) = 0.

(6)

Under the reaction functions for the home government, relations s = bx and t = by hold. Notice that if n h = n f , then the coefficient for e in ∂SW/∂s = 0 vanishes. The national welfare of the foreign country can be defined as the net profit of the foreign firms, that is: SW (s, t, e) = ( p − c y − t)n f y.

(7)

The reaction function of the foreign government in the policy game is characterized in a similar fashion. The first order condition is: ∂SW /∂e = ( p − c y − t)n f ∂ y/∂e + n f y∂( p − t)/∂e = 0. Reference to the comparative statical results obtains:

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∂SW /∂e = {( p − c y − t)(n h + 1) − n f by}n f /(b ) = [{(a − cx ) + (cx − c y )(n h + 1) − sn h − t (n h + 1)}ε −e2n f (n h + 1)]n f /(b 2 ) = 0,

(8)

where ε = n h +1−n f . On the reaction function for the foreign government, relation e = byε/(n h + 1) holds. 1.5.

Free trade equilibrium

For later reference, the free trade outputs and national welfare for each country are shown. The superscript FT denotes the free trade variable. Putting s = t = e = 0 yields: x F T = {(a − c y ) − (n f + 1)(cx − c y }/(b ) y F T = {(a − cx ) + (n h + 1)(cx − c y )}/(b ). In addition, the free trade price is: p F T = (a + cx n h + c y n f )/ . Finally, the free trade national welfare for each country can be denoted as: SWF T = {(3n f + n h + 2)n h (a − cx )2 + (n f − n h )n f (a − c y )2 +(2n f + 1)n f n h (cx − c y )2 }/(2b 2 ),

(9)

and: SW F T = n f {(a − cx ) + (n h + 1)(cx − c y )}2 /(b 2 ). 2.

(10)

National welfare under alternative policy timing

Having knowledge of the third-stage Cournot competition among firms, each government chooses the timing of its policy game. In this section, the national welfare of each country under the exogenously determined sequence of policy moves is shown. At stage zero of the game, each government decides independently to take the first move or the second. If one government, for example the home government, chooses the first move and the other chooses the second, then the policy game becomes a sequential one with the home government playing the Stackelberg leader. If both governments choose the same move, then the policy game is a simultaneous one. In our setup, without uncertainty, the equilibrium outcome in two kinds of subgames, one in which two governments take the first move and the other in which two governments take the second move, are observationally equivalent.

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2.1.

The simultaneous-move (Nash) policy game

If both governments choose the same stage of the policy game, by solving the reaction functions (5), (6) and (8) simultaneously for s, t, and e, the following relations are obtained: s S = (a − cx )/n h − (cx − c y )n f (n h + 1)/(n h ) = bx S > 0 t S = (cx − c y )(n h + 1)/ = by S > 0 e S = (cx − c y ) ε/ .

(11)

The superscript S denotes a simultaneous-move policy game. The level of national welfare in each country will be: SW S = [(a − cx )2 2 + 2n f (n h + 1)2 (cx − c y )2 ]/(2b 2 ),

(12)

SW S = (n h + 1)n 2f (cx − c y )2 /(b 2 ).

(13)

and

Given simultaneous-move policy equilibrium, the home government sets its production subsidy and tariff and the foreign government sets an export subsidy which may be positive, negative, or zero, according to whether ε = n h + 1 − n f is positive, negative, or zero. In the case of a duopoly with n h = 1 and n f = 1, the home tariff is twice as large as the foreign export subsidy, as shown by Collie (1994). 2.2.

The case in which the home government plays the Stackelberg leader

In this case, first by solving ∂SW (s, t, e)/∂e = 0 in (8) for e, the reaction function of the foreign government at the second stage is obtained as a function of s and t: e(s, t) = {a − cx + (n h + 1)(cx − c y ) − n h s − (n h + 1)t}ε/{2n f (n h + 1)}.

(14)

By substitution, SW(s, t, e(s, t)) are obtained. Maximizing home welfare SW(s, t, e(s, t)) with respect to s and t gives two equations for the first order condition: dSW(s, t, e(s, t))/ds = n h {(a − cx )(2n h + 3) − (cx − c y )(n h + 1) − n h (2n h + 3)s −(2n h + 1)(n h + 1)t}/{4b(n h + 1)2 } = 0

(15)

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and dSW(s, t, e(s, t))/dt = {(a − cx )(2n h + 1) + (cx − c y )(n h + 1) − n h (2n h + 1)s − (2n h + 3) × (n h + 1)t}/{4b(n h + 1)} = 0.

(16)

Solving the equations in (15) and (16) for s and t yields s H = bx H and t H = bn f y H / (n h + 1). In fact, the policy variables of each government, when the home government is the Stackelberg leader, have the values: s H = {2(a − cx ) − (n h + 1)(cx − c y )}/(2n h ) = bx H > 0 t H = (cx − c y )/2 = bn f y H /(n h + 1) > 0 eH = ε(cx − c y )/(2n f ).

(17)

That is, the home government sets its production subsidy cum tariff at stage one, and the foreign government sets an export subsidy which may be positive, negative, or zero, according to whether ε = n h + 1 − n f is positive, negative, or zero, at stage two. Note that the optimal value of the tariff is not dependent on the number of firms. After some manipulation, home and foreign welfare calculations under the policy game with the home government playing the Stackelberg leader are: SWH = {2(a − cx )2 + (n h + 1)(cx − c y )2 }/(4b)

(18)

SW H = (n h + 1)(cx − c y )2 /(4b).

(19)

and

2.3.

The case in which the foreign government plays the Stackelberg leader

This case applies to the counter vailing duties allowed by the GATT (the General Agreement on Tariffs and Trade) and the WTO (the World Trade Organization). The response by the home government is optimal given the export subsidy set by the foreign government, and the foreign government anticipates the optimal response by the home government when it sets an export subsidy at stage one. By a procedure analogous to that in the preceding section, the reaction functions for the home government are obtained as: s(e) = {2(a − cx ) − n f (cx − c y + e)}/(2n h ),

(20)

t (e) = (cx − c y + e)/2.

(21)

and

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That is, the home government responds to an increase in the foreign export subsidy by increasing its tariff and by reducing its production subsidy. The home government’s countervailing tariff will reduce foreign welfare and the reduction in the production subsidy will increase foreign welfare. The overall effects of an export subsidy may be ambiguous. For welfare maximization by the foreign government in the first stage, put dSW (s(e), t (e), e)/de = {by(s(e), t (e), e) − e}n f /(2b) − n f y(s(e), t (e), e)/2 = −n f e/(2b) = 0.

(22)

Solving (22) for e yields: eF = 0.

(23)

That is, for linear demand the optimal export subsidy by the foreign government is zero. Using (23), the optimal subsidy and tariff calculations for the home government are: s F = {2(a − cx ) − (cx − c y )n f }/(2n h ) = bx F > 0 and t F = (c y − cx )/2 = by F > 0. In this equilibrium, the foreign government sets a zero export subsidy at stage one and the home government responds to it by setting its production subsidy and tariff at stage two. Note that the value of the tariff is the same as that of t H and is not dependent on the number of firms. The welfare calculations for each country can be shown as: SWF = {2(a − cx )2 + n f (cx − c y )2 }/(4b)

(24)

SW F = n f (cx − c y )2 /(4b).

(25)

and

This subgame can be used to examine the use of countervailing duties by the home government in response to the foreign expor t subsidy. In order to satisfy the interior solution in all the cases considered, F T, S, H and F, we assume hereafter that: k = max[cx − 2(a − cx )/(n h + 1), cx − (a − cx )/n f ] < c y < cx , must hold.

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Payoff for policy game (home welfare, foreign welfare). Foreign government choice

Home government choice

3.

Stage 1 Stage 2

Stage 1

Stage 2

(SWS , SW∗S ) (SWF , SW F )

(SWH , SWH ) (SWS , SW S )

Determination of policy timing

Thus far we have investigated the subgame perfect equilibrium with an exogenously given sequence of policy moves. However, we need to find the best outcome of the policy games for each government if the timing of the policy is determined endogenously. At stage zero, each government chooses its policy timing by comparing its national welfare (payoff ) in relation to each strategy. This is summarized in Table 1. For the welfare of the home country, we have: SWS − SWH = −(n h + 1)(cx − c y )2 ε 2 /(4b 2 ) ≤ 0.

(26)

Thus if ε = 0 then SWS < SWH , but if ε = 0 then SWS =SWH . Second, in SWS − SWF = εn f (3n h + n f + 3)(cx − c y )2 /(4b 2 ),

(27)

SWS − SWF has the same sign as that of ε. As for foreign welfare, first: SW H − SW S = ε(n h + 1 + 3n f )(n h + 1)(cx − c y )2 /(4b 2 ),

(28)

and the sign of (SW H − SW S ) is the same as that of ε. Second, since: SW S − SW F = −n f (cx − c y )2 ε 2 /(4b 2 ) ≤ 0,

(29)

if ε = 0 then SW S < SW F , but if ε = 0 then SW S = SW F . From the above argument, we can see that if n h +1−n f > 0, then SWS −SWH < 0 and SWS − SWF > 0 hold, thus, setting policy at stage one is a dominant strategy for the home government. Besides, SW H − SW S > 0 holds, which implies that setting trade policy at stage two is the optimal response by the foreign government. If n h + 1 − n f < 0, then the reverse is true. Proposition 1. In the case of a Cournot oligopoly, the subgame perfect equilibrium of the trade policy game is as follows. (1) The home government sets its

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production subsidy and tariff at stage one and the foreign government sets its export subsidy at stage two, if n h +1 > n f . (2) If nh + 1 < n f , the foreign government sets a (maximum) zero export subsidy at stage one and the home government sets its production subsidy and tariff at stage two. (3) If n h + 1 = n f holds, then each government will be indifferent to the timing of the policy game, and the foreign export subsidy is zero. In other words, the country with less-concentrated industry tends to emerge as the Stackelberg leader. In each case, through a production subsidy, the product price in the domestic market has to be equal to the marginal cost of the home firms, and it takes a common value, p = cx . So home welfare can be determined as: SW = u(Q c ) − cx Q c + tn f y = C S(Q c ) + tn f y, where Q c = (a − cx )/b is also a common value in the three cases. Then home welfare is higher, given the larger tariff revenue that depends upon the relative number of home firms. Because foreign welfare can be rewritten as: SW = (cx − c y − t)n f y, world welfare, W, simply defined as SW + SW will be: W = SW + SW = C S(Q c ) + (cx − c y )n f y. We can also show that the best sequence is the one that maximizes both foreign export subsidies and world welfare. According to this proposition, a comparison of tariffs and export subsidies yields: t S − t H = (cx − c y )ε/(2 ), t H − t F = 0 and eS − eH = −(cx − c y )ε2 /(2n f ) ≤ 0, eS − eF = (cx − c y )ε/ , eH − eF = (cx − c y ) ε/(2n f ). Further, combining these results gives: (t H − eH ) − (t S − eS ) = −(n h + 1)(cx − c y )ε/(2n f ), (t H − eH ) − (t F − eF ) = −(cx − c y )ε/(2n f ), (t S − eS ) − (t F − eF ) = −(cx − c y )ε/(2 ). Again, compare equilibria for two games. The first is the simultaneous-move equilibrium, and the other is the equilibrium for the endogenous timing game,

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where each government gets the opportunity to choose its policy between stage one and stage two. We need to find the best outcome for each government, if the timing of the policy is determined endogenously. Consider the case of n h + 1 > n f first. Referring to Equation (11), in the simultaneous-move equilibrium, the home government sets its production subsidy and tariff and the foreign government sets an export subsidy. On the other hand, in the sequential equilibrium, the home government sets a lower production subsidy and lower tariff at stage one, and the foreign government responds by setting a higher export subsidy at stage two. Alternatively, the value for t − e is minimized, which means that both output y and the foreign export subsidy ey are maximized in the sequential equilibrium. That is, by setting a lower tariff at stage one, the home government creates an incentive for a higher export subsidy by the foreign government. The home tariff revenue and total export subsidy for the foreign country increase and the welfare of each country, as well as world welfare, goes up. Next, consider the case of n h + 1 < n f . In the simultaneous-move equilibrium, the home government sets a production subsidy and tariff and the foreign government sets an export tax. That is, export discouragement by the foreign government raises the foreign welfare. In the sequential equilibrium, the foreign government sets a zero export subsidy (tax) at stage one, and the home government responds to it by setting a lower production subsidy and higher tariff at stage two. Because ds(e)/de = − n f /(2n h ) < 0 and dt (e)/de = 1/2 > 0, the overall level of domestic protection decreases, if n h < n f holds. Thus, the overall effect of retaliation encourages the foreign government to expand its exports. Again, the value for t − e is minimized, the home tariff revenue increases, the total export tax for the foreign country decreases to zero, and the welfare of each country, as well as world welfare, goes up. The larger the tariff revenue, the higher the home welfare. From the two cases considered, we could say that tariff revenue is increasing with the export subsidy, and the outcome of the game is always the one that maximizes the foreign export subsidy ey.3 In this game with endogenous timing, export taxes are never observed as an outcome. Our proposition is a generalization of Collie’s (1994) Proposition 1 in the case of multiple firms. Hwang and Schulman (1993) discussed the implications of adding nonintervention as an explicit policy option to the strategic trade policy models. Here, we will briefly show that even if non-intervention by each government is added to the policy options, the proposition in this paper is not affected in any real sense. Suppose that the game considered is in five stages, with an additional stage prior to stage zero. At stage −1, each government independently chooses its policy type between intervention and non-intervention. Note that we should distinguish non-intervention (free trade policy) from free trade outcome (zero tariff or subsidy rates). In other words, if any government commits to free trade (non-intervention), then there is no choice at stage zero. In a comparison of welfare for both countries, we can report two results. First, by deviating unilaterally from free trade, each country experiences welfare gains, unless ε = 0.

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Second, unilateral intervention can not be superior to mutual intervention. Thus, in the case of a Cournot oligopoly, if n h + 1 > n f , then adding non-intervention to the policy options does not affect the equilibrium policy type. But if n h + 1 < n f holds, then the foreign government will be indifferent to the choice between zero-subsidy intervention and non-intervention. 4.

Summary and conclusion

In this paper, we have shown that in the Cournot oligopoly model where n h home firms and n f foreign firms compete in a home market, the subgame perfect equilibrium policy occurs: (1) when the home government sets a production subsidy and tariff at stage one and the foreign government sets an export subsidy at stage two, if n h + 1 > n f : or (2) when the foreign government sets a zero export subsidy at stage one and the home government sets a production subsidy and a tariff at stage two, if n h + 1 < n f . In other words, the country with less-concentrated industry tends to emerge as the Stackelberg leader. Acknowledgments I would like to thank Tsuyoshi Toshimitsu, Toru Kikuchi, Robert H.N. Parry, Jeffrey Herrick and an anonymous referee for their helpful comments and suggestions. Notes 1. See Brander (1995), Dixit (1984), Eaton and Grossman (1986), and Helpman and Krugman (1989). 2. Toshimitsu (1997) treats the case where the home government uses only an import tariff and a zero production subsidy, as in the second part of Collie (1994). 3. This was pointed out by a referee.

References Brander, J.A. (1995) “Strategic Trade Policy.” In G.M. Grossman and K. Rogoff (eds.) Handbook of International Economics, Vol. 3, Amsterdam: Elsevier. Collie, D.R. (1991) “Export Subsidies and Countervailing Tariffs.” Journal of International Economics 31: 309–324. Collie, D.R. (1994) “Endogenous Timing in Trade Policy Games: Should Governments Use Countervailing Duties?” Weltwirtschaftliches Archiv 130: 191–209. Dixit, A. (1984) “International Trade Policy for Oligopolistic Industries.” Economic Journal Supplement 94: 1–16. Eaton, J. and G.M. Grossman (1986) “Optimal Trade and Industrial Policy Under Oligopoly.” Quarterly Journal of Economics 101: 383–406. Hamilton, J.H. and S.M. Slutsky (1990) “Endogenous Timing in Duopoly Games: Stackelberg or Cournot Equilibria.” Games and Economic Behavior 2: 29–46. Hwang, H.S. and C.T. Schulman (1993) “Strategic Non-Intervention and the Choice of Trade Policy for International Oligopoly.” Journal of International Economics 34: 73–93.

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Helpman, E. and P.R. Krugman (1989) Trade Policy and Market Structure. Cambridge, MA: The MIT Press. Toshimitsu, T. (1997) “On the Endogenous Timing in Trade Policy Game: A General Case.” Kwansei Gakuin University Discussion Paper Series 1997–6. Wong, K.P. and K.W. Chow (1997) “Endogenous Sequencing in Strategic Trade Policy Games Under Uncertainty.” Open Economies Review 8: 353–369.