This paper discusses the timing and the optimal trade policy in the presence of oligopolisitic industries and free entry. Collie (1994) proved that an importing government should not commit a countervailing duty in response to a foreign export subsidy. We show that his main conclusion does not always hold, since the timing, as well as the optimal trade policy, depends on the number of firms in both countries and the characteristic of the industry, i.e. no entry or free entry.

Tsuyoshi Toshimitsu

English

Research Papers in Economics

 
DISCUSSIONç PAPERç SERIES 
 
 
 
 
Discussion paper No.20 
 
 
ON THE ENDOGENOUS TIMlNG IN TRADE POLICY GAMEɿ 
A GENERAL CASE 
 
 
 
Tsuyoshi Toshimitsu 
Kwansei Gakuin University 
 
 
 
 
 
October 1997 
 
 
 
 
 
 
 
 
 
 
 
SCHOOL OF ECONOMICS 
KWANSEIç GAKUINç UNIVERSITY 
 
1-155 Uegahara Ichiban-cho 
Nishinomiya 662-8501, Japan ON THE ENDOGENOUS TIMING IN TRADE POLICY GAME:  A GENERAL CASE 
Tsuyoshi TOSHIMITSU* 
Abstract 
This  paper  discusses  the  timing and  the  optimal  trade  policy  in 
the  presence  of  oligopolistic  industries  and  free  entry.  Collie 
(1994)  proved  that  an  importing  government  should  not  commit  a 
countervailing  duty  in  response  to  a  foreign  export  subsidy.  We 
show  that  his  main  conclusion  does  not  always  hold,  since  the 
timing,  as  well  as  the  optimal  trade  policy,  depends  on  the 
number  of  firms  in  both  countries  and  the  characteristic  of  the 
industry,  i.e.  no  entry  or  free  entry. 
»  Associate Professor  of  Economics 
School  of Economics 
Kwansei  Gakuin University 
1-155,  Uegahara  Ichibanchyo,  Nishinomiya,  662,  Japan 
Phone  (0798)54-6440 
Fax  (0798)51-0944 
E-mail.z95016@kwansei.ac.jp 
-1-1.  INTRODUCTION 
A player  can  determine  its  timing  (or  the  order  of  its  action) 
as  well  as  its  action.  As  to  this  issue,  Hamilton  and  Slutsky 
(1990)  have  proved  the  endogenous  timing of  action  in  the  duopoly 
game  under  perfect  information.  Albaek  (1990)  has  also  shown  that 
there  can  be  a  unique  natural  Stackelberg  equilibrium  under 
incomplete  information.  Applying  the  endogenous  timing  game  to 
trade  policy  games.  Collie  (1994)  has  shown  that  there  is  such  a 
unique  Stackelberg  equilibrium  that  an  importing  (=  domestic) 
government,  being  a  leader,  uses  an  import  tariff  policy  and  an 
exporting  (=  foreign)  government,  being  a  follower,  uses  an 
export  subsidy  policy  and  that  the  domestic  government  benefits 
from  a  larger  export  subsidy  than  in  a  Nash  equilibrium,  while 
the  foreign  government  benefits  from  a  lower  import  tariff  than 
in  a  Nash  equilibrium.  Therefore,  his  main  suggestion  is  that  the 
domestic  government  should  not  commit  a  countervailing  duty  in 
response  to  a  foreign  export  subsidy.  It  means  that  the  domestic 
government  should be  a  leader,  not  a  follower. 
It  is  assumed  in  Collie  (1994)  that  the  number  of  firms  in  both 
countries  is  identical.  But,  it  was  shown  in  Dixit  (1984)  that 
the  optimal  trade  policy  is  an  export  subsidy  (tax)  if  the  number 
of  exporting  firms  is  relatively  smaller  (larger)  than  that  of 
importing  firms.  Because  the  slope  of  the  reaction  functions  of 
both  governments  depends  on  the  number  of  firms  in  both 
countries,  the  results  about  the  timing,  as  well  as  the  optimal 
trade  policy,  are  not  necessarily  identical  to  those  of  Collie 
(1994),  if  the  number  of  firms  in  each  country  is  not  identical, 
or  if  it  is  allowed  to  be  free  entry. 
Generalizing  the  model  of  Collie  (1994),  we will  reconsider  the 
-2-s'n ]  (Note  that  N,  N*  is  omited)  .  We  will  give W =  W[tn  ,  s* f  ]  . 
Then,  from  (13)  and  (17*),  it  holds  that  W >  Wn  .  Also,  taking 
into  account  that  (16)  is  negative  at  a  Nash  equilibrium,  and 
(17),  W1  >  W. Thus,  W1  >  Wn  .  Next,  from  (8),  it  will  be  denoted 
that  Wf  =  W[tf  ,  s*  '  ]  =  W[t[s*  '  ]  ,  s*  '  ]  ,  and  that  Wn  =  W[tn  ,  s' n  ]  = 
W[t[s*n],  s*n].  Thus,  taking  into  account  (7)  (or  (8)),  (9), 
(13),  and  (17*),  it  holds  that  Wn  >  Wf  .  Therefore,  we  obtain 
(18). 
Similarly,  as  to  (18*),  first,  it  will  be  denoted  that  W1  = 
W[s-'t  tf  ]  ,  and  W* n  =  W*[s*n,  tn ]  .  We  will  give  W'  =  W*[s'n, 
tf  ]  .  Then,  from  (13*)  and  (17),  it  holds  that  W  '  >  W* n  .  Also, 
taking into  account  that  (16*)  is  negative  at  a  Nash  equilibrium, 
and  (17*),  W  '  >  W  '  .  Thus,  W*  '  >  Wn.  Next,  from  (8*),  it  will 
be  denoted  that  W* f  =  W'  [ s'  f  ,  t1  ]  =  W*  [ s*  [  t1  ]  ,  t1  ]  ,  and  that W  n 
=  W*[s'n,  tn ]  =  W[s-[tn],  tn  ]  .  Thus,  taking  into  account  (7*) 
(or  (8*)),  (9*),  (13*),  and  (17),  it  holds  that  W'f  >  W  n  . 
Therefore,  we  obtain  (18*).  Q.E.D. 
Appendix 4.  Proof  of  Lemma  8. 
As  to  (36*),  first,  taking  into  account  (30),  and  (33*),  and 
evaluating  (35*)  at  the  Nash  equilibirum,  the  sign  of  (35*)  is 
negative.  Thus,  s*n  ( =  0)  >  s*•  .  Also,  if  the  foreign  government 
is  a  follower,  as  shown  above,  it  will  use  a  free  trade  policy  as 
in  the  Nash  equilibrium.  Thus,  s'n  =  s*f  =0. 
Secondly,  as  to  (36),  it  has  been  shown  that  t1  =  tn  .  Also, 
taking  into  account  (30)  and  s'n  (=  0)  >  s*  '  ,  it  holds  that  tn  = 
t[s'n],  and  V  =  t[s*'].  Thus,  tn  >  tf  .  Q.E.D. 
-29-References 
Albaek,  Svend,  1990,  Stackelberg Leadership  as  a  Natural  Solution 
under  Cost  Uncertainty,  Journal  of  Industrial  Economics,  38, 
355-347. 
Collie,  David,  1991,  Export  Subsidies  and Countervailing Tariffs, 
Journal  of  International  Economics,  31,  309-324. 
Collie,  David,  1994,  Endogenous  Timing  in  Trade  Policy  Games: 
Should  Governments  Use  Countervailing  Duties  ?  Weltwirtschaft-
liches  Archiv,  130,  191-209. 
Dixit,  A.  K.,  1984,  International  Trade  Policy  for  Oligopolistic 
Industries,  Economic  Journal,  94,  1-16. 
Hamilton,  Jonathan  H.  and  Steven  M.  Slutsky,  1990,  Endogenous 
Timing  in  Duopoly  Games:  Stackelberg  or  Cournot  Equilibria, 
Games  and Economic Behavior,  2,  29-46. 
-30-

Endogenous Timing in Duopoly Games: Stackelberg or Cournot Equilibria,

Endogenous Timing in Trade Policy Games: Should Governments Use Countervailing Duties ?

Export Subsidies and Countervailing Tariffs,

International Trade Policy for Oligopolistic Industries,

Stackelberg Leadership as a Natural Solution under Cost Uncertainty,

ON THE ENDOGENOUS TIMlNG IN TRADE POLICY GAMEFA GENERAL CASE

http://192.218.163.163/RePEc/pdf/kgdp20.pdf

ON THE ENDOGENOUS TIMlNG IN TRADE POLICY GAMEFA GENERAL CASE

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