Export Subsidies and Timing of Decision-Making

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1 Export Subsdes and Tmng of Decson-Makng Koun Hamada Faculty of Economcs, Ngata Unversty August 22, 2005 Abstract Ths paper examnes how the tmng of decson-makng affects the strategc trade polcy. Extendng the analyss on the strategc trade polcy to the sequental-move game, I show some nterestng results as follows: Frst, t s shown that when the governments decde the subsdes smultaneously before the Stackelberg competton, the leader frm loses ts frstmover advantage. Second, t s shown that under the sequental-move game n whch the government that can subsdze the leader frm decdes the subsdy at frst, the proft of the leader frm s less than that of the follower n the Stackelberg model. JEL classfcaton: D43; F12; L13 Keywords: export subsdy; sequental-move game; Stackelberg competton Correspondng Author: Koun Hamada Faculty of Economcs, Ngata Unversty, 8050 Ikarash 2-no-cho, Ngata-sh , Japan. Tel. and fax: E-mal address: khamada@econ.ngata-u.ac.p I am grateful to Takao Ohkawa, Yasuhro Takarada and Makoto Tawada for helpful comments. The research for ths paper s supported by the Grant-n-Ad for Scentfc Research (KAKENHI from JSPS and MEXT of the Japanese Government. The usual dsclamer apples. 1

2 1 Introducton Ths paper examnes how the tmng of decson-makng affects the strategc trade polcy. I analyze the relatonshp between the dfferent tmng of the decson-makng by exportng frms and ther subsdzng governments and ts mpact on the export subsdy polcy. Although WTO reorganzed from the GATT n 1995 and the FTAs tend to ncrease rapdly nowadays, the export subsdy polcy have yet been practced n many countres as a strategc means to nduce more domestc surplus from exportaton. In the WTO agreements, the export subsdes to the manufactured products are prohbted per se, but as for the agrcultural products, the WTO members are n the very act of negotatng the reducton of the subsdy rate. From the theoretcal pont of vew, snce Brander and Spencer (1985 elucdate the strategc effect of subsdy polcy, many artcles has dealt wth the exportng subsdes n the context of the strategc trade polcy. Usng the thrd country model, Brander and Spencer (1985 analyze the rent-shftng effect of the export subsdy and the strategc nteracton between the export subsdes. They show that the export subsdy functons effectvely to rase the domestc welfare, but t mples that the strategc subsdy choces by both governments n the exportng countres fall nto the prsoner s dlemma. Eaton and Grossman (1986 extend the model of Brander and Spencer (1985 to allow the dfferent conectural varatons that ncludes Cournot case. Although the above two representatve papers and ther successors deal wth the general demand structure and llumnate the strategc aspects on the trade polcy clearly, ther papers have lmted to the analyses of only the stuaton n whch the choces of the strategc varables by the compettve frms are made smultaneously. Extendng the smultaneous-move game to the sequental one on output choce and also subsdy choce, I present a new pont of vew about 2

3 the strategc subsdy polcy that s nfluenced by the tmng of decson-makng. In the actual nternatonal trade polcy, for nstance, t may take place that the governments of the developed countres frst determne the subsdy levels n advance before the governments of the developng countres determne the subsdy levels and vce versa. Because of the dfferent abltes between governments to mplement and enforce the trade polcy, there exsts the tme lag on the subsdy decsons by governments. I ntroduce the dfference on the tmng of decsonmakng on output and subsdy level nto the model. As for the sequental-move game on strategc trade polcy, there are several artcles that t should be referred. In the two-country model, Syropoulos (1994 shows that the governments may choose tarffs sequentally under perfect competton. Colle (1994 shows that the domestc government sets tarff at frst and then the foregn government sets export subsdy under Cournot quantty competton. In the thrd-country model, Arvan (1991 concludes that demand uncertanty may cause the sequental-move of the polcy choce by governments. Shvakumar (1993 ntroduces the export quota and shows that the restrcted quantty competton and demand uncertanty brng the sequental decson of trade polcy by governments. Recently, Ohkawa, Okamura and Tawada (2002 endogenze the tmng of government nterventon under nternatonal olgopoly. Ther paper s closely related wth my paper n the sense that the sequental-move game by governments s analyzed n the thrd-country model. Dfferent from my concern, however, they focus on the relatonshp between the number of frms and the endogenous tmng of the polcy decson by governments and they do not deal wth Stackelberg competton between frms. Comparng between the smultaneous and sequental moves by frms and governments, I show some nterestng results. Frst, when the governments decde the export subsdes smultane- 3

4 ously under the Stackelberg competton, the orgnal leader frm loses ts frst-mover advantage Dfferent from the Cournot model, under the Stackelberg model, the subsdy polcy by the government that can subsdze the leader frm s almost nullfed. Second, under the sequental-move game n whch the government that can subsdze the leader frm decdes the subsdy level at frst, the proft of the leader s less than that of the follower, although the frst-mover advantage of the government s mantaned and the leader produces more than the follower. The paper presents one of the theoretcal foundatons on the sgnfcance that the tmng of polcy decson has on the effectveness of trade polcy. The remander of the artcle s organzed as follows. Secton 2 descrbes the model. Secton 3 derves subsdy, output, proft and domestc welfare n the equlbrum and analyze the relatonshp between the dfferent structures. In Secton 4, I summarze the calculatng results about varables under each case and make the comparatve statcs wth regard to the dfferent structures on tmng. Secton 5 s the concludng remarks. 2 The model Two dentcal frms, one from country and one from country, produce and sell n a thrd country. I consder the mperfect quantty competton model n the thrd country àlabrander and Spencer (1985. Both frms produce only for the thrd market. They produce homogeneous goods. The frm n country ( s denoted by the ndex (respectvely. Frm (frm produces quantty q (resp. q. The total quantty s Q q +q. The nverse demand functon s denoted by P (Q a bq and the constant margnal cost s denoted by c.it s assumed that a>c and b>0. Government that les n country can mplement the per unt 4

5 export subsdy, s 0. The proft of frm s denoted by π (q,q ; s,s (P (Q c + s q = (P (Q e q. The surplus of country s denoted by G (s,s, whch conssts of the proft from the exportng frm mnus the cost of the export subsdy: G (s,s π (q,q ; s,s s q. Government maxmzes ths surplus. The soluton concept s the subgame perfect equlbrum. The tmng of the game s as follows: 1st stage: Governments choose subsdy levels smultaneously or sequentally. 2nd stage: Frms choose output levels smultaneously or sequentally. Subsdy polces can be commtted by both governments and can be observed by both frms before the competton stage n advance. 3 The analyss In ths secton, I examne the subsdy, the output, the proft and the domestc welfare n the equlbrum. As the frst step, I solve the subgame at the second stage. At frst, I examne the Cournot quantty competton. Then I proceed to consder the Stackelberg duopoly. 3.1 The output choce at the second stage Cournot competton Gven the subsdes (s,s, both frms maxmzes ther profts. The frst-order condton for frm to maxmze the proft s as follows: π =(a b(q + q e bq =0. 1 The reacton functon of frm s q = R (q = a bq e. By solvng the ntersecton of the reacton functons, 1 The subscrpt of the proft denotes the partal dervatve by q. Because of the concavty of the proft functon wth regard to q, the second-order condton s satsfed throughout the followng analyss. 5

6 the Cournot output level s obtaned as follows: (q C (s,s,q C (s,s =( a 2e + e, a 2e + e. (1 If there s no subsdy, the Cournot outcome s as follows: (q C(0, 0,qC (0, 0 = ( a 2c +c, a 2c +c. The total quantty s Q C = 2a e e, the prce s P (Q C = a+e +e 3, and the proft margn s P (Q C e = a 2e +e 3 = bq C. The Cournot proft s calculated as follows: (π C (s,s,π C (s,s =(b(q C 2,b(q C 2 =( (a 2e + e 2 9b, (a 2e + e 2. (2 9b Stackelberg competton Under the Stackelberg competton, I consder that frm s the Stackelberg leader and frm s the follower wthout loss of generalty. Antcpatng the reacton functon of frm, frm maxmzes the followng obectve: π (q,r (q. The f.o.c. s π +π R (q = 0. The Stackelberg output pars are as follows: (q S (s,s,q S (s,s =( a 2e + e, a 3e +2e. (3 For (1 and (3 to be postve, t s assumed that a 2c + c > 0 and a 3c +2c > 0. Wth no subsdy, the Stackelberg outcome s as follows: (q S(0, 0,qS (0, 0 = ( a 2c +c, a 3c +2c. It s well-known that q C (s,s <q S (s,s and q C (s,s >q S (s,s (s,s. The total quantty s Q S = 3a 2e e and the prce s P (Q S = a+2e +e 4. It s satsfed that Q S >Q C and P (Q C >P(Q S. The proft margn s P (Q S e = a 2e +e 4 = b 2 qs and P (Q S e = a 3e +2e 4 = bq S. The proft under the Stackelberg competton s calculated as follows: (π S (s,s,π S (s,s =( b 2 (qs 2,b(q S 2 =( (a 2e + e 2 6, (a 3e +2e 2. (4

7 It s satsfed that π C (s,s <π S (s,s and π C (s,s >π S (s,s (s,s. For the followng analyss, I present the comparatve statcs: qc (s,s s = 2, qc (s,s s = 1, q S (s,s s = 1 b, qs (s,s s = 1, qs (s,s s = 3 and qs (s,s s = The subsdy decson at the frst stage At the frst stage, government maxmzes the domestc surplus, that s, max s 0 G (s,s π (q,q ; s,s s q. The f.o.c. for government s as follows: G (s,s = π (q,q ; s,s q q s =0, (5 s s s f s 0 (nteror soluton. If G (s,s s < 0, the soluton s s = 0 (corner soluton. 2 I classfy the dfferent tmng of the decson-makng between frms and between governments nto fve cases. In Case A and Case B, I examne the unlateral and the blateral nterventon by government(s under the Cournot competton. In Case C and Case D, I examne the unlateral and the blateral nterventon by government(s under the Stackelberg competton. In Case E, the stuaton n whch all players sequentally decde s analyzed. In the followng subsecton, I nvestgate all cases n turn. See Fgure 1. The superscrpts, C and S, stand for Cournot and Stackelberg equlbrum respectvely. Fgure 1 around here A. unlateral nterventon under Cournot competton Frst, I examne the unlateral nterventon case n whch only government subsdzes under the Cournot competton. As s = 0, government maxmzes G C (s, 0. By solvng the f.o.c., 2 Throughout the followng analyss, the s.o.c. s satsfed and the soluton s unque and stable. 7

8 the optmal subsdy level s obtaned as follows: s uc = a 2c + c. (6 4 The Cournot output s as follows: (q C (suc, 0,q C (suc, 0 = ( a 2c + c, a 3c +2c [=(q S (0, 0,qS (0, 0]. (7 Ths result s summarzed mmedately n the followng proposton. Proposton 1. Under the Cournot competton, the unlateral nterventon by government changes the market structure from the Cournot duopoly to the Stackelberg one n whch frm s the leader. Ths proposton s ust a corollary of Proposton 3 n Brander and Spencer (1985. The optmal subsdy has the proft-shftng effect and moves the Cournot competton to the Stackelberg leader-follower poston. It s mmedately shown that q C(suC, 0 >q C(0, 0 and qc (suc, 0 < q C (0, 0. As a result of the unlateral subsdy, the proft of frm that s subsdzed by the government rases, that s, π C (s uc, 0(= π S (0, 0 >π C (0, 0 and π C (s uc, 0(= π S (0, 0 < π C (0, 0. Also, t s obvous that the surplus n country ( expands (resp. contracts by the subsdy of government, that s, G C (s uc, 0(= max s G C (s, 0 > G C (0, 0 and G C (s uc, 0(= π C (s uc, 0 <G C (0, 0(= π C (0, 0. B. blateral nterventon under Cournot competton I analyze the blateral nterventon under the Cournot competton. I examne the smultaneous and sequental decson of subsdy n turn. 8

9 B-1. smultaneous decson of subsdy Consder the smultaneous decson of subsdes (s,s by both governments. Gven s, government maxmzes G C (s,s =π (q C (s,s,q C (s,s ; s,s s q C. Lke Case A, the f.o.c. s arranged as s = b 2 qc = a 2e +e 6. The reacton functon s derved as s = R (s = s +a 2c +c 4. The subsdy level n the equlbrum s obtaned as follows: s bcc = a 3c +2c. (8 5 Substtutng ths subsdy level, the Cournot output n the equlbrum s obtaned: (q C (sbcc,s bcc,q C (sbcc,s bcc =( 2(a 3c +2c 5b, 2(a 3c +2c. (9 5b Comparng the subsdy under the unlateral and blateral cases, the lemma s derved. Lemma 1. The subsdy under the unlateral nterventon s larger than under the blateral nterventon. That s, s uc >s bcc. Ths lemma mples that under the blateral nterventon, there s the strategc nteracton about the subsdy settng between governments and as a result, the mpact on whch the subsdy affects the output choce of the frm s smaller than under the unlateral nterventon. Then I compare the output levels under the unlateral and blateral nterventons. Proposton 2. Under the Cournot competton, (a the output level of frm ( under the blateral nterventon s smaller (resp. larger than under the unlateral nterventon by government. That s, q C (suc, 0(= q S (0, 0 >qc (sbcc,s bcc, q C (suc, 0(= q S(0, 0 <qc (sbcc,s bcc. (b when each frm has almost dentcal cost, the output level under the blateral nterventon s larger than under no nterventon. That s, f a 8c +7c > 0, 3 q C (0, 0 <qc (sbcc 3 If the cost s dentcal, ths condton s satsfed.,s bcc. 9

10 Ths proposton mples that by strategc substtutes on output competton, subsdzng by rval government results n the output reducton of the own frm. As the reacton functons of both frms shft outwards by subsdzng blaterally, as a result, the output competton under the blateral nterventon becomes more severe than wthout nterventon. As for the proft of the frm, as π C = b(q C 2, the relaton about the proft sze s mmedately obtaned. By Proposton 2, t s obtaned that π C (s uc π C (s bcc,s bcc, 0 >π C (s bcc. When the cost s almost dentcal, π C (0, 0 <π C (s bcc,s bcc and π C (s uc, 0 <,s bcc. They mply that subsdzng by government ( makes the proft of frm larger (resp. smaller and the blateral nterventon makes the profts of both frms larger than wthout nterventon. Fnally, I examne the effect of the subsdy on the surplus. By drect calculaton, t s obtaned that G C (0, 0 = (a 2c +c 2 9b, G C (s uc and G C (s bcc,s bcc G C (s bcc G C (s bcc = 2(a 3c +2c 2 25b, 0 = (a 2c +c 2, G C (s uc, 0 = π C (s uc, 0 = (a 3c +2c 2. It s necessarly satsfed that G C (s uc, 0 >G C (0, 0 and,s bcc >G C (s uc, 0. If the cost s almost dentcal, t s satsfed that G C (0, 0 >,s bcc. The blateral nterventon falls nto the prsoner s dlemma for governments. Ths s ust a corollary of Proposton 5 n Brander and Spencer (1985. See Table 1. Proposton 3. Under the Cournot competton, when each frm has almost dentcal cost, the surplus under the blateral nterventon s smaller than under no nterventon. That s, the blateral nterventon falls nto the prsoner s dlemma for governments. Table 1 around here B-2. sequental decson of subsdy Next I consder the sequental decson of subsdy as the sequental-move game for governments. Government decdes s at frst and then government decdes s after observng s. 10

11 The follower government decdes the subsdy s = R (s = s +a 2c +c 4 gven s. Government nduces ths reacton and solves the followng maxmzaton problem: max s 0 G C (s,r (s. Solvng the f.o.c., I obtan the subsdy levels as follows: s bsc = a 3c +2c 3 = R (s bsc = a 4c +3c. (10 6 By substtutng (s bsc, the Cournot output s obtaned as follows: (q C (sbsc,q C (sbsc = ( a 3c +2c, a 4c +3c. (11 For q C > 0, t s assumed that a 4c +3c > 0 throughout the followng analyss. Comparng the subsdy levels under the unlateral and blateral cases, I obtan the lemma. Lemma 2. The subsdy under the unlateral nterventon s smaller than that of the leader government under the blateral nterventon when the cost s almost dentcal. The subsdy under the unlateral nterventon s larger than that of the follower government under the blateral nterventon. That s, s uc <s bsc f a 6c +5c > 0 and s uc >s bsc. Dfferent from Case B-1, when the sequental decson of subsdy s made by governments under the blateral nterventon, the subsdy of the frst-mover government s larger and that of the follower government s smaller than under the unlateral case. Then I compare the output levels under the unlateral and blateral nterventons. Lemma 3. Under the Cournot competton, (a whether the output of frm under the blateral sequental nterventon s smaller than under the unlateral nterventon by government depends on the relatve szes of the frm s cost. That s, q C (suc, 0 q C(sbSC c c. When the cost s almost dentcal, the output of frm under the blateral nterventon s 11

12 smaller than under the unlateral nterventon by government. That s, f a 7c +6c > 0, q C (suc, 0 <q C(sbSC. When the cost s almost dentcal, the output of frm under the blateral nterventon s smaller than under the unlateral nterventon by government. That s, f a 6c +5c > 0, q C (0,suC >q C(sbSC. (b When the cost s almost dentcal, the output of frm under the blateral nterventon s larger than under no nterventon. That s, f a 5c +4c > 0, q C(0, 0 <qc (sbsc. Whether the output of frm under the blateral nterventon s smaller than under no nterventon depends on the relatve szes of the frm s cost.that s, q C(0, 0 qc (sbsc c c. As a corollary of ths lemma, under the dentcal costs, t s satsfed that q C (suc, 0 = q C (sbsc and q C (0, 0 = qc (sbsc. When the cost s dentcal, the output of frm under the blateral nterventon by government s equal to that under the unlateral nterventon by government. And also the output of frm under the blateral nterventon by government s equal to that under no nterventon. The subsdy polcy by the government has two effects on output. The one s to shft the reacton functon outwards and have the home frm the advantage on output competton under strategc substtutes. The second s to adust to compettve dstorton by the cost dfference. If the cost s dentcal, the second effect does not appear and the output s adusted at the level of the Stackelberg leader by subsdzng. As for the proft of the frm, the relaton about the proft sze s mmedately obtaned wth π C = b(q C 2. By Lemma 3, t s obtaned that π C (s uc, 0 π C (s bsc fc c, π C (s uc, 0 <π C (s bsc fa 7c +6c > 0, and π C (0,s uc >π C (s bsc f a 6c +5c > 0. Moreover t s satsfed that π C (0, 0 <π C (s bsc fa 5c +4c > 0, 12

13 and π C (0, 0 π C (s bsc fc c. When the cost s almost dentcal, the frm that s subsdzed by the leader government prefers the unlateral nterventon to the blateral one when the frm s cost s hgher than the rval s and vce versa. On the other hand, the frm that s subsdzed by the follower government always prefers the blateral nterventon to the unlateral nterventon by the rval government, although ths frm always prefers the unlateral nterventon by ts home government to the blateral nterventon. Comparng no nterventon wth blateral one, frm always prefers the blateral nterventon to no nterventon, although the frm prefers the blateral nterventon to no nterventon f the cost s lower and vce versa. Fnally, I examne the effect of the subsdy on the surplus. By drect calculaton, t s obtaned that G C (s bsc = (a 3c +2c 2 1 that G C (s uc and G C (s bsc = (a 4c +3c 2, 0 >G C (0, 0 and G C (s bsc = (a 3c +2c 2 1 If the cost s almost dentcal, G C (s bsc G C (0, 0 >G C (s bsc <G C (s uc 1. It s necessarly satsfed >G C (0,s uc = (a 3c +2c 2., 0, G C (0, 0 >G C (s bsc and are obtaned. Dfferent from Case B-1, when the cost s almost dentcal, the leader government chooses to ntervene and the follower government chooses not to ntervene. The frst-mover advantage of government on the choce of subsdy can deter the rval follower government from exercsng the subsdy. I state ths result n the followng proposton. See Table 2. Proposton 4. Under the Cournot competton, when the cost s almost dentcal, the surplus under the blateral nterventon s smaller than under no nterventon. In the equlbrum, the result s that only the leader government ntervenes and the follower government does not ntervene. The prsoner s dlemma under the blateral nterventon does not occur. 13

14 Table 2 around here C. unlateral nterventon under Stackelberg model I proceed to examne the unlateral nterventon under the Stackelberg model. C-1. unlateral nterventon of government I examne the case n whch government whose frm s the Stackelberg leader ntervenes. As s = 0, government maxmzes G S (s, 0 = π (q S(s, 0,q S(s, 0; s, 0 s q S. Solvng the f.o.c., I obtan that the subsdy s zero, s us = 0. The Stackelberg output n the equlbrum s as follows: (q S (s us, 0,q S (s us, 0[= (q S (0, 0,q S (0, 0] = ( a 2c + c, a 3c +2c. (12 In Case C, another corollary of Prop. 3 n Brander and Spender (1985 s derved. The optmal subsdy moves to the Stackelberg leader-follower poston. Proposton 5. Under the Stackelberg competton n whch frm s the leader, the unlateral nterventon by the government of the leader frm s of no use. That s, there s no subsdy. Ths proposton s ust a corollary of Proposton 3 n Brander and Spencer (1985. The optmal subsdy has the proft-shftng effect and moves the Cournot competton to the Stackelberg leader-follower poston. leader frm has nothng to do. Under the Stackelberg competton, the government of the The proft of frm that s not subsdzed by the government s π S (s us, 0 = π S (0, 0 = b 2 (qs 2 and π S (s us, 0 = π S (0, 0 = b(q S2. The surplus s G S (s us, 0 = G S (0, 0 = π S (0, 0 and G S (s us, 0 = π S (0, 0. 14

15 C-2. unlateral nterventon of government I examne the case n whch government whose frm s the Stackelberg follower ntervenes. As s = 0, government maxmzes G S (0,s =π (q S(0,s,q S(0,s ; 0,s s q S. By solvng the f.o.c., the subsdy level s as follows: s us The Stackelberg output n the equlbrum s as follows: (q S (0,suS,q S (0,suS = a 3c +2c. (13 3 =( a 4c +3c, a 3c +2c. (14 Ths output level s equvalent to that n Case B-2. The followng proposton s obtaned. Proposton 6. Under the Stackelberg competton n whch frm s the leader, the unlateral nterventon by the government of the follower frm yelds the same result on output as the blateral sequental nterventon under Cournot competton n whch government frst moves and then government moves. That s, (q S (0,suS,q S (0,suS =(q C (sbsc,q C(sbSC. Ths proposton mples that the subsdy of the government works as f t changes the competton mode from Stackelberg to Cournot. The optmal subsdy mproves the Stackelbergfollower poston to the Cournot one. Even f frm s the Stackelberg follower the optmal subsdy by government makes the dsadvantage of follower reduce to some extent. Substtutng (14 nto π S (s,s = b 2 (qs 2 and π S (s,s =b(q S 2, the proft of the frm s mmedately obtaned: π S (0,s us = (a 4c +3c 2 1 that π S (s us, 0 = (a 2c +c 2 >π S (0,s us and π S (s us, 0 = (a 3c +2c 2 and π S (0,s us = (a 3c +2c 2. It s shown Fnally, the surplus s obtaned that G S (0,s us =π S (0,s us = (a 4c +3c 2 1 <π S (0,s us. <G S (s us, 0 = π S (s us, 0 = (a 2c +c 2, and G S (0,s us =b(q S2 s us q S = (a 3c +2c 2 1 >G S (s us, 0 = π S (s us, 0 = (a 3c +2c 2. When the cost s dentcal, the followng proposton s obtaned: 15

16 Proposton 7. Consder the Stackelberg competton n whch frm s the leader. Suppose that the cost s dentcal. When the government of the follower frm unlaterally ntervenes, the proft of the follower frm (the leader frm s larger (resp. smaller than that of the leader frm (resp. the follower frm when the government of the leader frm unlaterally ntervenes. That s, π S (0,s us = (a c2 >π S (s us, 0 = (a c2, π S (0,s us = (a c2 1 <π S (s us, 0 = (a c2. When government unlaterally ntervenes, the welfare of government ( s smaller than that of government (resp. when government unlaterally ntervenes. That s, G S (0,s us = (a c2 1 <G S (s us, 0 = (a c2, G S (0,s us = (a c2 1 <G S (s us, 0 = (a c2. Note that ths proposton also holds when the cost s almost dentcal. Although t looks at frst glance that the leader frm may enoy hgher proft when the government of the leader frm can subsdze than that of the follower when ts government can subsdze, the above proposton shows that ths vew s not correct. Ths mplcaton s derved from the fact that government does not subsdze at all because the advantage of the Stackelberg leader has already acqured by frm n Case C-1. On the other hand, ths ntuton s correct when the welfare s consdered. Even f the government makes the follower frm recover the frst-mover advantage by nterventon, t takes an extra cost to subsdze t. D. blateral nterventon under Stackelberg model I examne the blateral nterventon under Stackelberg model. Both governments ntervene. D-1. smultaneous decson of subsdy I consder the smultaneous decson of subsdy. Government whose frm s leader max- 16

17 mzes the followng obectve: Gven s, G S (s,s =π (q S(s,s,q S(s,s ; s,s s q S. By the f.o.c., the reacton functon s s bcs = R (s bcs = 0. Government whose frm s the follower maxmzes the followng obectve: Gven s, G S (s,s =π (q S (s,s,q S (s,s ; s,s s q S. By the f.o.c., the reacton functon s s bcs of the reacton functon. Note that s bcs = s us s bcs = 0 and s bcs =0,s bcs = s us = R (s bcs = 2s +a 3c +2c 3. I solve the ntersecton = a 3c +2c. (15 3 = a 3c +2c 3. The optmal Stackelberg output level s obtaned as follows: (q S (sbcs,s bcs,q S (sbcs,s bcs =( a 4c +3c, a 3c +2c. (16 It s satsfed that q S (sbcs,s bcs =q S (0,suS and q S (sbcs,s bcs =q S(0,suS. In the case of the smultaneous decson of subsdy levels, the subsdy polcy of the government to the leader frms does not work. Dfferent from the Cournot model, under the Stackelberg model, the subsdy polcy of the government of the leader frm s nullfed. In Case D-1, the Stackelberg leader and follower behave as f they do n Case C-2. Proposton 8. Consder the Stackelberg competton n whch frm s the leader. The result n the equlbrum under Case D-1 s the same as that under Case C-2. The government whose frm s the leader does not subsdze ts frm. Also the proft and the welfare are the same as that under Case C-2. See also Table 3. D-2. sequental decson of subsdy (s s I examne the sequental decson of subsdy under whch the government of the Stackelberg leader moves at frst and then the government of the follower decdes s. Observng s, the 17

18 follower government decdes the subsdy s = R (s. Government whose frm s the follower maxmzes the followng obectve: Gven s, G S (s,s =π (q S (s,s,q S (s,s ; s,s s q S. By drect calculaton, the reacton functon s obtaned as s bss = R (s bss = 2s +a 3c +2c 3. The reacton functon s obtaned by the same procedure as n Case D-1. The leader government nduces ths reacton and solves the followng maxmzaton problem: G S (s,r (s = π (q S (s,r (s,q S (s,r (s ; s,r (s s q S (s,r (s. By the f.o.c., the followng equalty s obtaned: s = b 4 q = a 2(c s +(c R (s 8. Under the sequental decson, the optmal subsdy level s as follows: s bss = a 4c +3c, s bss 8 = R (s bss = a 5c +4c. (17 4 Note that f the cost s almost dentcal, s bss >s bss, that s, the subsdy to the follower s larger than that to the leader. Substtutng s, the Stackelberg output level s obtaned as follows: (q S (s bss,s bss, q S (s bss,s bss =( a 4c +3c, 3(a 5c +4c. (18 Note that when the cost s almost dentcal, the output of the leader s larger than that of the follower, q S (sbss,s bss >q S(sbSS,s bss. As for the proft, because t s satsfed that (π S,π S = ( b 2 (qs 2,b(q S 2, the proft s calculated as π S (s bss,s bss = (a 4c +3c 2 and π S (s bss,s bss = 9(a 5c +4c 2 6. When the cost s dentcal, t s worth notng that π S (s bss,s bss = (a c2 <π S (s bss In other words, the proft of the follower s larger than that of the leader.,s bss = 9(a c2 6. By G S = π S s q, the welfare s calculated as follows: G S (s bss,s bss = (a 4c +3c 2 G S (s bss,s bss = 3(a 5c +4c 2 6 and. When the cost s dentcal, t s satsfed that G S (s bss,s bss = (a c 2 >G S (s bss,s bss = 3(a c2 6. Wth regard to the socal welfare, the welfare of the leader 18

19 government s larger than that of the follower under the dentcal cost. The above result s summarzed n the followng proposton. Proposton 9. Consder the Stackelberg competton n whch frm s the leader. In the symmetrc equlbrum under Case D-2, the proft of the leader s less than that of the follower. The welfare of the leader government s larger than that of the follower government. Although the leader produces more than the follower, the government of the leader subsdzes less than that of the follower. As a result, t s shown that the proft of the leader s less than that of the follower and the welfare of the frst-mover government s larger than that of secondmover government. The result that the proft of the leader s smaller s a new vewpont that s obtaned from consderng the tmng of subsdy polcy. Further by comparng the surplus under no nterventon wth that under Case D-2, t s obtaned that G S (0, 0 = (a 2c +c 2 > G S (s bss,s bss = (a 4c +3c 2 and G S (0, 0 = (a 3c +2c 2 >G S (s bss,s bss = 3(a 5c +4c 2 6 f the cost s almost dentcal. Thus I am n the poston to state the followng proposton. Under the blateral nterventon, both governments obtan fewer surpluses than under no nterventon. Proposton 10. Under the Stackelberg competton n whch frm s the leader, when the cost s almost dentcal, the surplus under the blateral nterventon n Case D-2 s smaller than under no nterventon. That s, the blateral nterventon falls nto the prsoner s dlemma. D-3. sequental decson of subsdy (s s Fnally, I examne the sequental decson of subsdy under whch the government of the Stackelberg follower moves at frst and then the government of the leader decdes s. Ths s 19

20 the adverse case of Case D-2 wth regard to the tmng of the decson-makng by governments. Observng s, the follower government decdes the subsdy s = R (s. The follower government whose frm s the leader maxmzes the followng obectve: Gven s, G S (s,s = π (q S (s,s,q S (s,s ; s,s s q S. The reacton functon s sbss same procedure as the leader government n D-1 Case. = R (s bss = 0. Ths s the The leader government nduces ths and solves the followng maxmzaton problem wth substtutng s bss = R (s bss = 0: max s 0 G S (0,s =π (q S(0,s,q S(0,s ; 0,s s q S(0,s. Under the sequental decson, the optmal subsdy level s as follows: s bss =0,s bss = a 3c +2c. (19 3 Substtutng s, the Stackelberg output level s obtaned as follows: (q S (s bss,s bss, q S (s bss,s bss =( a 4c +3c The equlbrum n ths case s the same as Case D-1 (and also C-2 case., a 3c +2c. (20 Proposton 11. Consder the Stackelberg competton n whch frm s the leader. The result n the equlbrum under Case D-3 s the same as that under Case D-1 (and also Case C-2. The government whose frm s the leader does not subsdze ts frm. In ths case, the follower subsdy setter n the country where there s the Stackelberg leader frm has nothng to do, by the same reason as Case D-1 and C-2. Also the proft and the welfare are the same as that under Case D-1 and C-2. I compare the proft and the welfare n Case D-2 wth that n Case D-3. When the cost s dentcal, the followng nequaltes are satsfed: π S (s bss G S (s bss,s bss,s bss <G S (s bss <π S (s bss,s bss,s bss <G S (s bss 20 <π S (s bss,s bss,s bss <π S (s bss,s bss, and <G S (s bss,s bss. See also Table 3.

21 E. wholly sequental decson Fnally, I examne the wholly sequental decson. I consder the blateral nterventon of sequental decson-makng: s q s q. The equlbrum s solved by backward nducton. At the 4th stage, the f.o.c. for proft maxmzaton of frm gven (s,q,s s as follows: π =(a b(q +q e bq = 0. The reacton functon s q = R s(q,s = a bq e. Note that ths reacton functon does not depend on s drectly. At the 3rd stage, the subsdy decson by government s determned by maxmzng the followng obectve, G (s,q,s,r s (q,s. By solvng the f.o.c., the soluton s corner, s bs solved as follows: Gven s, nducng s bs = 0. At the 2nd stage, the output choce by frm s = 0 and q = R s(q, 0 = a bq c, the frm maxmzes the proft functon π (q,r s (q, 0; s, 0. The f.o.c. s the same as the Stackelberg equlbrum wthout any subsdy: q = R s (s = a 2e +c = q S (s, 0, and q = R (q, 0 = a 3c +2e = q S (s, 0. At the 1st stage, the subsdy decson by government s determned by the same procedure as C-1 case. That s, there s no subsdy, s = 0. In the equlbrum, (s bs,s bs =(0, 0, (21 (q bs,q bs =( a 2c + c It s satsfed that (q bs,qbs = (qs (0, 0,qS (0, 0., a 3c +2c. (22 The proft and the welfare s as follows: π S (0, 0 = G S (0, 0 = (a 2c +c 2 and π S (0, 0 = G S (0, 0 = (a 3c +2c 2. 4 The comparson In ths secton, I compare the dfferent structures wth regard to the tmng of the decsonmakng on the subsdy by governments and the output by the frms. Before proceedng to 21

22 the analyss, t s convenent to dgest the equlbrum outcome under the dfferent tmng of the decson-makng n the table. See Table 3. In order to fgure out the output level n the equlbrum graphcally, see also Fgure 2 and 3. 4 Table 3 around here Fgure 2 and 3 around here By Table 3, I can examne how the dfferent structures about the tmng of the decsonmakng by frms and governments affects the effcency of the subsdy polcy. Throughout the followng comparson, I lmt the argument on the stuaton n whch the cost s dentcal. I show the several notceable comparsons as the followng propostons. 5 Proposton 12. Consder the unlateral nterventon of the government. When the frm faces the Cournot competton, the proft s larger than when t competes as the Stackelberg leader and t s equal to that when t competes as the Stackelberg follower. That s, π C (s uc, 0 = π S (0,s us = (a c2 >π S (s us, 0 = (a c2. Ths proposton mples that although t looks at frst glance that the Stackelberg leader has more advantage than under Cournot competton, ths mpresson s not correct. If the unlateral nterventon of the government (and no nterventon of the rval government s guaranteed, the frm prefers to compete n the Cournot way rather than become the Stackelberg leader. The reason s that the government has nothng to do under the Stackelberg competton, but as the government under the Cournot competton subsdzes the frm, the acquston of ths subsdy rases the frm s proft. Whereas, the proposton also mples that the Stackelberg 4 For smplfcaton, I llustrate only the case n whch the cost s dentcal. 5 Although I do not compare the welfare n the thrd country, t s worth notng that the thrd country s welfare s reduced by the sze of total quantty, Q. 22

23 follower recovers the compettve poston from the Stackelberg follower to the Cournot and t can compete on equal terms wth the rval frm by subsdzaton of the government. Next I compare the profts between two compettve forms under the blateral nterventon. At frst, I compare Case B-1 wth Case D-1. Proposton 13. Consder the blateral smultaneous nterventon of the governments. When the frm faces the Cournot competton, the proft s larger than when t competes as the Stackelberg leader. The proft under the Cournot competton s smaller than when t competes as the Stackelberg follower. That s, π S (s bcs,s bcs = (a c2 1 <π C (s bcc,s bcc = 4(a c2 25b <π S (s bcs,s bcs = (a c2. Ths proposton s the extensve verson of Proposton 12 to the blateral nterventon. Although t looks at frst glance that the Stackelberg leader has more advantage than under Cournot competton, the frm prefers to compete n the Cournot way rather than become the Stackelberg leader and moreover prefers to become the follower. The reason s smlar to that of Proposton 12. Under the blateral smultaneous nterventon, the government that has the Stackelberg leader does not have any nfluence to change the market structure. As both governments under the Cournot competton subsdze the frm, ther subsdes nfluence market structure and rase the frm s profts. Whereas, the Stackelberg follower s fully supported by ts government. It can compete on more advantageous terms than the rval frm n Case D-1. Ths proposton suggests the followng mportant asserton on the trade polcy: When governments can ntervene n ts domestc frm wth a certan polcy nstrument n advance, the dfference of the compettve mode between frms such as Cournot or Stackelberg competton does not necessarly nfluence the frm s advantage on the competton. Even f a frm s the 23

24 Stackelberg follower n the thrd-market, the subsdzaton by the government can get rd of the compettve dsadvantage entrely. Fnally, I compare Case B-2 wth Case D-2 and D-3. Proposton 14. Consder the blateral sequental nterventon of the governments. Suppose that government frst moves. ( When frm faces the Cournot competton, the proft s larger than when t competes as the Stackelberg leader. The proft of frm under the Cournot competton s smaller than when t competes as the Stackelberg follower. That s, π C (s bsc = (a c2 >π S (s bss,s bss = (a c 2 and π C (s bsc = (a c2 9b <π S (s bss,s bss = 9(a c2 6. ( When frm faces the Cournot competton, the proft s equvalent when t competes as the Stackelberg follower. The proft of frm under the Cournot competton s larger than when t competes as the Stackelberg leader. That s, π C (s bsc =π S (s bss,s bss = (a c2 and π C (s bsc = (a c2 9b >π S (s bss,s bss = (a c Part ( n ths proposton states as follows: Under the blateral sequental nterventon, lke the smultaneous nterventon, the frm prefers to compete n the Cournot way rather than become the Stackelberg leader. On the other hand, the frm prefers to become the follower rather than compete n the Cournot way. At frst glance, t seems that the change of decson structure from Case B-2 to D-2 gves the frm that becomes the Stackelberg leader more advantage about output choce. However, ths proposton mples that ths shft of decson structure does not brng any advantage and n the contrary, the proft of the leader frm decreases. On the other hand, the frm that becomes the Stackelberg follower acqures more proft than under 6 Note that the ndex of s nterchanged wth that of n Case D-3, because government frst moves and frm s the Stackelberg follower. 24

25 the prevous Cournot competton. The basc logc of the proposton s smlar to that of Proposton 13, although ths logc s a lttle bt complcated. Under the blateral sequental nterventon, the Stackelberg leader needs less subsdy than f ths frm s engaged n Cournot competton, that s, s bsc = a c 3 >s bss = a c 8, because the frm has already enoyed the frst-mover advantage. Whereas, the Stackelberg follower s supported by ts government wth great care and mproves the compettve poston, that s, s bsc = a c 6 <s bss = a c 4. As a result of the asymmetrc subsdy polcy, t occurs that when both governments subsdze the frm under the Cournot competton, the proft of the leader (the follower s less (resp. more than when they do under the Stackelberg competton. Part ( n ths proposton states as follows: Under the blateral sequental nterventon, when the competton s n the Cournot way, the proft of the frm s equvalent to that when ths frm competes as the Stackelberg follower. Moreover, the frm prefers to compete n the Cournot way rather than become the Stackelberg leader n Case D-3. It mples that when government frst moves, even f the competton form shfts from Cournot to Stackelberg and frm becomes the follower, ts proft does not change. The proft of frm that becomes the leader n place of frm becomes less than under the prevous Cournot competton. The shft of decson structure does not change the proft and only the proft of the frm that becomes the leader decreases. It mples that t s desrable for both frms to shft the compettve mode from the Stackelberg competton under whch the government of the Stackelberg follower frst decdes the subsdy, to the Cournot one under blateral sequental nterventon. Ths shft of the compettve mode avods the excessve subsdy allocaton by governments and saves the subsdy that does not have qute effect on the advantage of the domestc frm n the market. 25

26 These propostons nssts that the dfference n tmng of polcy execute (and announcement by the government affects the proft of the frm and the resultng welfare. And also they nsst that the government should exercse the trade polcy, takng what s the compettve mode between frms nto consderaton. 5 The concludng remarks Ths paper analyzes the relatonshp between the dfferent tmng of the decson-makng by exportng frms and ther subsdng governments and ts mpacts on the export subsdy. Two man results are as follows: Frst, when the governments decde the export subsdes smultaneously n advance under the Stackelberg quantty competton, the orgnal leader n the output competton loses ts frst-mover advantage. Dfferent from the Cournot model, under the Stackelberg model, the subsdy polcy by the government that can subsdze the leader frm s nullfed. Second, under the sequental-move game n whch the government that can subsdze the leader frm decdes the subsdy level at frst, the proft of the leader s less than that of the follower, although the frst-mover advantage s mantaned. I conclude that the tmng of decson-makng affects the effectveness on the export subsdy polcy more sgnfcantly. Although the paper manly focuses on the theoretcal aspect, the results n ths paper are applcable to make some proper suggestons to the actual strategc trade polces. For example, n the realstc context of the nternatonal exportng competton, suppose that there s the leader frm that s the predecessor and les n the domnant poston n the exportng market. When the successor entres and the Stackelberg competton s made, the predecessor government of the leader frm may antcpate the successor s government n decdng the trade polcy. In 26

27 ths stuaton, how does the government mplement the strategc subsdy polcy? Proposton 14 tells us that the predecessor government dares to make ts frm acqure less proft than the rval frm wth the less subsdy than the successor government and should save the subsdy n order to attan more welfare. Moreover, by Proposton 14, t s ndcated that even f the government can choose the tmng of subsdy polcy, t should defend the poston as the frst-mover polcy maker and mantan the frst-mover advantage. On the other hand, Proposton 14 suggests also that n order to brng more proft to the successor frm, ts government should announce the subsdy polcy faster than the rval government of the leader and take the frst-mover advantage f possble. Ths may present one of the reasons that the trade war s trggered. Further extenson n ths paper can be consdered. Frst, the more general model n whch the demand and cost functons have the general forms can be analyzed. Second, product dfferentaton should be analyzed, although the basc results n the above analyss have remaned unchanged. Thrdly, ths result may be extended to strategc complements under whch the optmal trade polcy s to adopt the exportng tarff. 27

28 References [1] Arvan, L., Flexblty versus Commtment n Strategc Trade Polcy under Uncertanty: A Model of Endogenous Polcy Leadershp. Journal of Internatonal Economcs 31, [2] Brander, J.A., Spencer, B.J., Export Subsdes and Internatonal Market Share Rvalry. Journal of Internatonal Economcs 18, [3] Colle, D.R., Endogenous Tmng n Trade Polcy Games: Should Governments Use Countervalng Dutes? Weltwrtschaftlches Archv 130, [4] Eaton, J., Grossman, G.M., Optmal Trade and Industral Polcy under Olgopoly. Quarterly Journal of Economcs 101, [5] Hamada, K., Export Subsdes and Tmng of Decson-Makng: An Extenson to the Sequental-Move Game of Brander and Spencer Model. Dscusson Paper Seres 51, Faculty of Economcs, Ngata Unversty. [6] Hamlton, J.H., Slutsky, S.M., Endogenous Tmng n Duopoly Games: Stackelberg or Cournot Equlbra. Games and Economc Behavor 2, [7] Lahr, S., Ono, Y., Trade and Industral Polcy under Internatonal Olgopoly. Cambrdge Unversty Press, Cambrdge. [8] Ohkawa, T., Okamura, M., Tawada, M., Endogenous Tmng and Welfare n the Game of Trade Polces under Internatonal Olgopoly, n: Woodland, A.D., (Ed., Economc Theory and Internatonal Trade: Essays n Honour of Murray C. Kemp. Edward Elgar, Cheltenham, pp [9] Shvakumar, R., Strategc Trade Polcy: Choosng between Export Subsdes and Export Quotas under Uncertanty. Journal of Internatonal Economcs 35, [10] Syropoulos, C., Endogenous Tmng n Games of Commercal Polcy. Canadan Journal of Economcs 27,

29 government no nterventon nterventon government no nterventon (a 2c +c 2 9b, (a 2c +c 2 9b (a 3c +2c 2, (a 2c +c 2 nterventon (a 2c +c 2, (a 3c +2c 2 2(a 3c +2c 2 25b, 2(a 3c +2c 2 25b Table 1: the socal surplus under no nterventon, Case A and B-1 government no nterventon nterventon government no nterventon (a 2c +c 2 9b, (a 2c +c 2 9b (a 3c +2c 2, (a 2c +c 2 nterventon (a 2c +c 2, (a 3c +2c 2 (a 3c +2c 2 1, (a 4c +3c 2 1 Table 2: the socal surplus under no nterventon, Case A and B-2 29

30 subsdy output prce 1. no-subsdy Cournot nothng ( a 2c +c, a 2c +c 2. no-subsdy Stackelberg nothng ( a 2c +c, a 3c +2c A. unlateral Cournot ( a 2c +c 4, 0 ( a 2c +c, a 3c +2c B. blateral Cournot B-1. smultaneous B-2. sequental C. unlateral Stackelberg ( a 3c +2c 5, a 3c +2c 5 ( 2(a 3c +2c 5b, 2(a 3c +2c ( a 3c +2c 3, a 4c +3c 6 ( a 3c +2c 5b, a 4c +3c C-1. government (0, 0 ( a 2c +c, a 3c +2c C-2. government (0, a 3c +2c 3 ( a 4c +3c, a 3c +2c D. blateral Stackelberg D-1. smultaneous D-2. sequental gov. D-3. sequental gov. (0, a 3c +2c 3 ( a 4c +3c, a 3c +2c ( a 4c +3c 8, a 5c +4c 4 ( a 4c +3c, 3(a 5c +4c (0, a 3c +2c 3 ( a 4c +3c, a 3c +2c E. wholly sequental (0, 0 ( a 2c +c, a 3c +2c proft welfare a+c +c 3 a+2c +c 4 a+2c +c 4 a+2c +2c 5 a+3c +2c 6 a+2c +c 4 a+2c +3c 6 a+2c +3c 6 a+4c +3c 8 a+2c +3c 6 a+2c +c 4 1. no-subsdy Cournot ( (a 2c +c 2 9b, (a 2c +c 2 9b ( (a 2c +c 2 9b, (a 2c +c 2 9b 2. no-subsdy Stackelberg ( (a 2c +c 2, (a 3c +2c 2 ( (a 2c +c 2, (a 3c +2c 2 A. unlateral Cournot ( (a 2c +c 2, (a 3c +2c 2 ( (a 2c +c 2, (a 3c +2c 2 B. blateral Cournot B-1. smultaneous ( 4(a 3c +2c 2 25b, 4(a 3c +2c 2 25b ( 2(a 3c +2c 2 25b, 2(a 3c +2c 2 25b B-2. sequental ( (a 3c +2c 2, (a 4c +3c 2 9b ( (a 3c +2c 2 1, (a 4c +3c 2 1 C. unlateral Stackelberg C-1. government ( (a 2c +c 2, (a 3c +2c 2 ( (a 2c +c 2, (a 3c +2c 2 C-2. government ( (a 4c +3c 2 1, (a 3c +2c 2 ( (a 4c +3c 2 1, (a 3c +2c 2 1 D. blateral Stackelberg D-1. smultaneous ( (a 4c +3c 2 1, (a 3c +2c 2 ( (a 4c +3c 2 1, (a 3c +2c 2 1 D-2. sequental gov. ( (a 4c +3c 2, 9(a 5c +4c 2 6 ( (a 4c +3c 2, 3(a 5c +4c 2 6 D-3. sequental gov. ( (a 4c +3c 2 1, (a 3c +2c 2 ( (a 4c +3c 2 1, (a 3c +2c 2 1 E. wholly sequental ( (a 2c +c 2, (a 3c +2c 2 ( (a 2c +c 2, (a 3c +2c 2 Table 3: the equlbrum result 30

31 Cournot quantty competton A. unlateral nterventon 1st stage gov. Stackelberg quantty competton C. unlateral nterventon C-1. Only gov. ntervenes 1st stage gov. 2nd stage frm frm 2nd stage frm B. blateral nterventon B-1. smultaneous decson-makng 1st stage gov. gov. 2nd stage frm frm B-2. sequental decson-makng gov. 1st stage gov. 2nd stage E. Wholly sequental decson-makng 1st stage 2nd stage frm gov. frm frm gov. frm frm C-2. Only gov. ntervenes 1st stage gov. 2nd stage frm frm D. blateral nterventon D-1. smultaneous decson-makng 1st stage gov. gov. 2nd stage frm frm D-2. sequental decson-makng (gov. moves frst. 1st stage gov. gov. 2nd stage frm frm D-3. sequental decson-makng (gov. moves frst. 1st stage gov. gov. 2nd stage frm frm Fgure 1: decson node 31

32 Cournot competton 1. no nterventon q q =R (q Stackelberg competton 2. no nterventon q q =R (q π =π (q, q a c E(q C, q C π =π (q, q q =R (q 0 a c q q A. unlateral nterventon q =R (q a c E(q S, q S q =R (q 0 a c q C. unlateral nterventon C-1. government q q =R (q a c E(q uc, q uc q =R (q 0 a c q B. blateral nterventon B-1. smultaneous q q =R (q a c C-2. government E(q us, q us q =R (q 0 a c q q q =R (q 2(a c 5b E (q bcc, q bcc q =R (q a c E(q us, q us q =R (q 0 2(a c q 5b q B-2. sequental q =R (q 0 a c q : reacton functon before nterventon : reacton functon after nterventon a c E (q bsc, q bsc q =R (q 0 a c q Fgure 2: reacton functons and equlbrum output levels 32

33 Stackelberg competton (contnued D-1. smultaneous decson-makng q a c q =R (q E (q bcs, q bcs q =R (q 0 a c q D-2. sequental decson-makng (government moves frst. q q =R (q E. Wholly sequental decson-makng q a c q =R (q E(q bs, q bs q =R (q 0 a c q : reacton functon before nterventon : reacton functon after nterventon 3(a c E (q bss, q bss q =R (q q 0 a c q D-3. sequental decson-makng (government moves frst. q =R (q a c E (q bss, q bss q =R (q 0 a c q Fgure 3: reacton functons and equlbrum output levels (contnued 33