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The design of industry-specific trade policies and a sequential entry-exit model of international trade Zhang, Anming 1986

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T H E DESIGN OF INDUSTRY-SPECIFIC T R A D E POLICIES AND A SEQUENTIAL ENTRY-EXIT MODEL OF I N T E R N A T I O N A L T R A D E  by  ANMING ZHANG B.Sc, Shanghai Jiao Tong University,  1983  A THESIS S U B M I T T E D IN P A R T I A L F U L F I L M E N T O F T H E REQUIREMENTS FOR T H E D E G R E E OF M A S T E R OF SCIENCE (BUSINESS  ADMINISTRATION)  in T H E F A C U L T Y O F G R A D U A T E STUDIES Faculty of Commerce and Business Administration  We accept this thesis as conforming to the required standard  T H E UNIVERSITY OF BRITISH C O L U M B I A September  1986  © Anming Zhang,  1986  In p r e s e n t i n g  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the  requirements f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make it  f r e e l y a v a i l a b l e f o r r e f e r e n c e and study.  I further  agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by t h e head o f my department o r by h i s o r h e r r e p r e s e n t a t i v e s .  It i s  understood t h a t copying o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l gain  s h a l l n o t be allowed without my  written  permission.  Department o f  (L^&MtM-cfU-  The U n i v e r s i t y o f B r i t i s h 1956 Main Mall Vancouver, Canada V6T 1Y3  Date  Se{fc~>W 3o , ,  3u^,Vg<^ Columbia  AX^^'Sfmr-iorv  ABSTRACT  Conventional trade theory assumes perfect competition among firms and makes on balance a strong case for free trade. A n important observation in the modern international economy is that competition among firms in many industries is imperfectly competitive. These firms, usually few and large, strategically interact with each other and may earn supernormal profits. As shown by the recently growing literature on trade with imperfect competition, allowing for the importance of imperfect competition leads to new insights about causes, effects, and patterns of trade, and has major implications for the analysis of trade policy as well. This study investigates the effects of firms' imperfect competition on trade policy designs and on trade patterns, product variety, and specialization. The thesis consists of two parts. The first part is entitled "The design of industry-specific trade policies" and the second part " A sequential entry-exit model of international trade". The first part of the thesis addresses the following two questions: (l) Whether government intervention can raise the national welfare and how important the effect of intervention would be in raising welfare; and (2) Whether, or when, trade restrictions are first-best policies, and when other policy instruments would achieve the same aims more efficiently. Dixit (1985) has recently undertaken an empirical study of strategic trade policy for a specific industry. The rivalry between the U.S. firms and Japanese firms in the U.S. passenger car market is examined. It is noticed that in Dixit's work, only the numerical (simulation) results are given and evaluated, and only the U.S. government is assumed to be active in policy-making. The purpose of the first part of the thesis is to provide a theoretical treatment of Dixit's model, to discuss the role of policy intervention and compare the importance and efficiency of tariffs vis-a-vis domestic production subsidies under different market structures, and to examine the consequences of allowing Japan to be active in policy-making. The basic results of this part are as follows. First, when the domestic (foreign) firms' conduct has rather significant effects on the market equilibrium relative to the foreign (domestic) firms', policy is usually directed by the domestic (foreign) firms' monopoly in the market, and a domestic production subsidy (a tariff) is usually more important and more efficient than a tariff (a domestic production subsidy). Secondly, allowing Japan to simultaneously pursue its optimal policy can reverse the result of positive U.S. welfare gains from the optimal policies, a result obtained under the condition that Japan adopts complete laissez-faire. Furthermore, Japan does have an incentive to pursue the optimal policy. Thus, The U.S. policy gains are not at all automatic or riskless. This result is obtained by examined the non-cooperative Nash equilibrium in tariff/subsidy for the U.S. and Japan. Thirdly, both countries would nonetheless be better off if they could cooperatively choose policy parameters to maximize the joint welfare rather than non-cooperatively pursue their own optimal policies. The two countries may play a bargaining game.  ii  The purpose of the second part is to examine firms' strategic behaviour in international rivalry, and its effects on trade pattens and on product variety by using a sequential entry-exit model of trade. The paper models an industry consisting of two firms, each in a different country. The two firms are assumed to be able to potentially produce and export two imperfectly substitutable products, to be able to make their entry, exit, and production (quantity, price, etc.) decisions sequentially, and to be able to choose these strategy variables for each country separately. Two four-stage games are constructed and examined. The paper intends to do an exploration of models of international trade. The new feature of our model is that the fixed cost of withdrawing a product is considered as a variable and firms are allowed to exit in response to entry. Three basic results emerge from the second paper. First, firms' strategic behaviour can give rise to two-way trade in identical products which are produced only for trade. The kind of two-way trade can introduce products which would otherwise not be produced in autarky. The non-cooperative solution to the firm's profit-maximizing problem involves such a two-way trade, but each firm may nonetheless be better off if the two firms could agree not to invade each other's home markets. This result is more likely to hold as exit costs are low, as transport costs are small, as products are better substitutes, as competition in identical products is more intense, and as firms are more likely to treat different countries as different markets. Secondly, our model gives mixed results on the issue of whether trade, through intraindustry trade, makes a greater variety of products available to consumers. Whether trade increases or reduces variety depends on the firms' payoffs of various market structures and on the level of entry, exit, and transport costs. Firms' strategic interaction through trade in order to maximize profits can increase or reduce product variety. In the case of Cournot or Bertrand conduct with linear demand, trade would increase product variety. Moreover, changes in variety can be brought about by either an actual flow of trade or a potential for trade. Finally, instead of producing all substitutable products and monopolizing their home markets, firms may specialize in some products and invade each other's countries. So the third result is in favour for intra-industry trade, and it also shows specialization can be independently caused by the rivalry of oligopolistic firms.  iii  TABLE OF  CONTENTS  Abstract Table of Contents List of Tables List of Figures Acknowlegdement  ii iv vi vii viii  Part 1: The design of industry-specific trade policies 1. Introduction  1 •  2  2. The basic model  4  3. Properties of the basic model  9  4. The role of tariffs and production subsidies  22  5. Japanese policy response  34  1) Only Japan is active in policy-making 2) Both the U.S. and Japan are active in policy-making  35 41  6. Concluding remarks  52  Part 2: A sequential entry-exit model of international trade  56  1. Introduction  57  2. A domestic incumbent and a foreign entrant  60  1) 2) 3) 4)  The The The The  fourth-stage subgame third-stage subgame second-stage subgame first-stage subgame  63 68 71 73  3. Two countries  74  4. Trade and product variety  83  a) Trade increases product variety b) Trade reduces product variety  84 86  iv  5. Specialization  89  6. Concluding remarks  91  Notes  94  Bibliograp hy  96  100  Appendix A-l A-2 A-3 A-4 A-5 A-6 A-7 A-8 A-9 A-10 A-ll A-12 A-13 A-14 A-15  100 104 107 108 110 HI 114 116 118 125 129 132 133 134 137  v  LIST OF  TABLES  Table Table Table Table Table Table Table Table Table Table Table  1 Sensitivity analysis for c\ and c% 2 Sensitivity analysis for P\ and P20 3 Sensitivity analysis for Qi and Q o 4 The U.S. holds status quo and Japan pursues an optimal policy 5 Policy calculations, 1979 (only U.S. is active in policy-making) 6 Policy calculations, 1980 (only U.S. is active in policy-making) 7 Nash equilibria in tariff / subsidy, 1979 8 Nash equilibria in tariff / subsidy, 1980 9 The optimal tariff and subsidy rates in the two models 10 Welfare gains in Model 2, 1979 11 Welfare effects of jointly optimal tariff and subsidy schedule, 1979  19 20 21 40 46 46 47 47 48 48 51  Table Table Table Table Table Table Table Table  12 13 14 15 16 17 18 19  69 69 70 70 72 72 78 78  0  0  Stage Stage Stage Stage Stage Stage  3 3 3 3 2 1  2  equilibria under Assumptions in the domestic country, case in the domestic country, case in the domestic country, case subgame under Assumptions subgame under Assumptions  VI  1-9 in the domestic country 14 8 16 1-9 1-9  LIST OF FIGURES  Fig. Fig. Fig. Fig.  1 2 3 4  The optimal tariff and optimal subsidy as functions of c\ The best-response functions: tariff / export subsidy The best-response functions: production subsidy / export subsidy A bargaining game  vii  29 44 44 51  ACKNOWLEDGEMENT  I am very pleased to be able to express my thanks to the members of my thesis committee for their encouragement and advice. Dr. James Brander has provided invaluable assistance and his guidance has been crucial to the completion of the study. I would also like to thank Dr. Barbara Spencer and Dr. Tae Hoon Oum for their helpful comments.  viii  PART 1  T H E D E S I G N OF INDUSTRY-SPECIFIC T R A D E POLICIES  1. I N T R O D U C T I O N Conventional trade theory with perfect competition among firms makes on balance a strong case for free trade. In the modern international business environment, we observe that competition among firms in many world markets is imperfectly competitive. These firms, usually few and large, may thus earn supernormal profits.  From a purely national perspective, policies that could shift this profit from foreign to domestic  firms would be attractive to a government. Current research on trade policy in oligopolistic international markets has indicated that intervention can be beneficial to a country (early work including Brander and Spencer (1984) and (1985), Krugman (1984)). For example, Brander and Spencer (1985) finds in a Cournot duopoly model that an export subsidy can help domestic firms capture a large share of any supernormal profit in the industry. Dixit (1984) extends this result to cases with more than two firms, and finds in a Cournot oligopoly that an export subsidy is optimal as long as the number of domestic firms is not too large. Eaton and Grossman (1986) finds in a Bertrand duopoly that an export tax is optimal. For an importing country, the government would affect not only the competitiveness of domestic firms vis-a-vis foreign firms, but also the welfare of domestic consumers.  Thus, policy instruments may also  include domestic production subsidies or taxes, often referred to as industrial policies. Eaton and Grossman (1986) theoretically classifies policy intervention under three circumstances:  (1) When foreign firms earn  pure profits and firms are competing in the home market, the home country can capture some of this profit with a tariff; (2) When prices of home products remain above marginal costs in the home market, the home country can achieve a welfare gain with a domestic antitrust policy or a production subsidy; and (3) When the home firms compete too much with each other in their exporting activities, the home country can gain with an export tax.  2  In the design of industry-specific trade policies, the following two questions are important: (1) Whether intervention with free trade can raise the national welfare; and (2) If it can, whether or when it is the first-best policy, and when other policy instruments would achieve the same aims more efficiently. Dixit (1985) has recently undertaken an empirical study on strategic trade policy for a specific industry. The U . S . passenger car market is chosen and the rivalry between U.S. and Japanese firms is examined. Only the U.S. government is assumed to be active in policy-making. The policy instruments are a tariff on Japanese firms and/or a production subsidy to U.S. firms, and the latter is considered as an imperfect proxy for an antitrust policy. The policy perspective is that of U.S. social welfare. The model is constructed in the following way: in the first stage, governments simultaneously choose policies that are credible to their firms; in the second stage, firms simultaneously choose their output levels and the industrial equilibrium is then determined. One helpful aspect of the U.S. car market is that exports of U.S. cars are negligible, and hence we can simply assume that the entire market for U.S. firms' outputs is at home. In this simple case, the production subsidy (tax) and the export subsidy (tax) are identical. We can further avoid the complexity introduced by the possible two-way trade in an oligopolistic world market: a country simultaneously exports and imports the same good. The second part of my M.Sc. thesis discusses the two-way trade using a sequential entry-exit model. Dixit then applies his model to the U.S. car market for 1979 and 1980, which are the most recent years with reasonably free trade for which data are available. The broad findings are : (1) The market was much more competitive in 1980 than in 1979, and the case for strategic trade and antitrust policies was therefore weaker in 1980; and (2) The aggregate economic gains to the U.S. are quite small with tariffs, and the role of domestic antitrust policies or production subsidies is more significant than that of tariffs. In Dixit (1985), only the numerical results for the particular cases of 1979 and 1980 are given and evaluated.  Consequently, for the demand and cost figures used, the paper provides examples in which  3  interventionist trade policy for the U.S. automobile industry can raise national welfare, and suitable antitrust measures to bring domestic prices closer to marginal costs are quantitatively more important and more efficient than tariffs in raising U.S. social welfare. It is of some interest, however, to see whether we can extract some general conclusions from the established model. This also seems necessary in view of probably unreliable data.  The purpose of this paper is to provide a theoretical treatment to the basic model, to  discuss the role of policy intervention and compare the importance and efficiency of tariffs vis-a-vis domestic production subsidies under different market structures, and to examine the consequences of allowing Japan to be active in policy-making. The paper is organized as follows. Section 2 briefly describes the basic model established in Dixit (1985). Section 3 shows a number of properties of this model. Section 4 is based on a slightly different model through which we discuss the role of tariffs and domestic production subsidies and compare the relative importance and efficiency of tariffs and production subsidies under different market structures.  Section 5  extends the basic model, where U.S. is active in policy-making while Japan takes a laissez-faire position, into the environment where Japan is active in making policies. Two cases are examined there. One of them is the case where only Japan is active in pursuing the profit-shifting policy, and the other is the case where both the U.S. and Japan are active in policy-making. In the second case, the Nash equilibria in tariff/subsidy for U.S. and Japan are examined, and the results are compared with those from the basic model. Section 6 provides concluding remarks.  2. THE BASIC MODEL For computational simplicity, demand functions are assumed to be linear.  U.S. and Japanese cars are  assumed to be imperfect substitutes for each other, but perfect substitutes within each country. Let the  subscripts 1 and 2 denote U.S. and Japanese cars respectively, and Pi, P and Q , Q denote the prices and 2  t  2  the total quantities respectively. Then the following demand functions are considered,  Qi = < * i= a  Q  2  2  where all the parameters are positive, and PiP  - pP  + P 1  P1P1 + 1P2  l  2  (1  (2)  2  — 7 > 0. 2  2  The corresponding inverse demand functions are,  Pi = ai & , ( ? , -kQ  (3)  2  P  2  = a  2  - kQi - b Q 2  (4)  2  Again, all the parameters are positive and 6^2 — fc > 0. 2  The demand parameters in (1) and (2) or (3) and (4) are estimated using each year's prices and quantities as well as assumed elasticities. We can show (see Appendix 1) that,  o,  =  1)P  (e, +  (5)  10  02 = ( e , + 1)P  (6)  20  ,  _ Piu(e Pu)Qiu  +  2  ' ~  eP Q ) 1  2li  20  e Q PQ ie2  lu  (  0  , ^ 2 0 (l 0 e  + 2 f 2 u Q 2 o ) e  PluQlU  lO)  2=  eie Q PQ 2  2l)  5  '  u  K  '  k =  ( e 2  ~ ' e  "  ) P l o P 2  (9)  where P Q i ) — PiuQiu + P20Q20;  Pyu,  a n  d Qiu, Q20 are the actual prices and quantities for the year under consideration;  ei is the overall price elasticity of demand for passenger cars in the U.S.; and e is the elasticity of substitution between U.S. and Japanese cars, and e > t\ > 0. 2  2  For the central case in which t\ = 1 and e = 2, system (5)-(9) becomes, 2  01 =  2 P  1  (10)  0  a = 2^0  (11)  2  6 1  ^ 2  W^P~Ql  _  _ P2o{PloQlO  ~  ( 1 2 )  + 2.P ()Q u) 2  2Q P(? 20  , „,  2  1 0  *=  '  ( ) 14  As shown in Appendix 2, the variables in the model are not sensitive to the changes of elasticities e and e : x  2  the percent change of the variables from base are less than those of ei or e . We shall assume &\ = 1 and 2  e = 2 when system (5)-(9) is used. 2  From (10) and (11), we have,  dai  =  2 d P  i  0  and  6  d a  2  =  2 d P  2  u  T h e r e f o r e , an error in price d a t a will double the estimated error in a\ and o . T h i s instability could be one 2  of s h o r t c o m i n g s of the current m e t h o d of e s t i m a t i n g d e m a n d  parameters.  T h e inverse d e m a n d f u n c t i o n s (3) and (4) can be regarded as c o m i n g from an aggregate utility f u n c t i o n ,  U ( Q  with ^  = P , and  =  i  1  , Q  2  )  =  a  1  Q  +  l  a  2  Q  2  i(6,Q  -  2  +2  k Q  1  Q  +  2  b  2  Q  2 2  )  JV  T h e relevant policies for the U . S . are a tariff, t, on Japanese firms and a p r o d u c t i o n subsidy, s, to U . S . firms. Denote c  t  to be the unit p r o d u c t i o n cost of U . S . firms, and c  the J a p a n e s e unit p r o d u c t i o n cost plus  2  the u n i t t r a n s p o r t cost to the U . S . market. T h e m a r g i n a l costs C i and c  are assumed as constants.  2  C o n s i d e r one U . S . firm. Its profit, given the credible government subsidy, is [ P i — C i + s)q\ (fixed cost is not considered).  T h e firm chooses o u t p u t level q\ to m a x i m i z e its profit, giving the following  first-order  condition,  P  l  - c,  , + s  dP,  q\—f-  +  = 0  (15)  dq[  and  dq\  where  qj(j  =  2,3,...,ni) are  firms' outputs (imports).  ^  firms,  =  T h e term  j^ - = —b 1  firms r e m a i n s u n c h a n g e d ;  ]  d  the other U . S . firms' o u t p u t s , and  l  Q  2  ^  q?(j  d  q  \  = l,2,...,n ) 2  are foreign (Japanese)  represents the firm's belief about the effect on its price if it sells  another u n i t , t a k i n g into account its conjecture foreign  d q \  about the o u t p u t responses of the other home firms and  if the firm adopts the C o u r n o t strategy: it assumes that the o u t p u t of other  = 0 if the firm adopts the c o m p e t i t i v e strategy: it believes that it can sell as  m u c h o u t p u t as it likes at the going price.  7  Aggregate the first-order conditions over all n  U . S . firms, we have,  t  Pi  where V i = &i/rii  —  (J2'jLi  df*")/"'  l}  '  1  s  *  n e  i n the case of C o u r n o t c o n d u c t .  a  c, + s -  -  88  r e  S * a  ; e  = 0  Q i V ,  (16)  version of the conjectural v a r i a t i o n p a r a m e t e r .  It equals  It is n u m e r i c a l l y smaller if the oligopoly is more c o m p e t i t i v e t h a n  t h a t , and zero in the case of perfect c o m p e t i t i o n . T h e effects of the U . S . firms' oligopolistic conduct on the m a r k e t e q u i l i b r i u m are thus channelled t h r o u g h V\.  S i m i l a r l y , for the J a p a n e s e firms, we have,  P  The  parameter V  2  -  2  c  -  2  t -  Q  2  V  0  =  2  (17)  can be similarly i n t e r p r e t e d . W e shall assume Vi and V  2  For each year, Vi and V  2  are positive in this p a p e r .  are d e t e r m i n e d by eqs. (16)—(17) using the observed prices, quantities, costs,  tariff and s u b s i d y . T h e degree of c o m p e t i t i o n i m p l i e d would thus be different for different observed figures used. F o r e x a m p l e , it m a y vary from one year to another.  A s long as Vi a n d V o b t a i n e d f r o m eqs. (3),  2  have been d e t e r m i n e d , the e q u i l i b r i u m prices P i , P  (4),  (16),  and (17)  2  and quantities Q i , Q  for any given policy configuration (t,s)  2  (suppose ci and c  can be  2  have  been already g i v e n ) . T h e U . S . social welfare can then be c a l c u l a t e d , which is the s u m of the U . S . consumer s u r p l u s , the U . S . firms' profits, and the government tariff revenue and subsidy cost,  W  By  =  [ U ( Q i , Q  2  )  -  P  i  Q  i  -  P  2  Q  2  )  +  (Pi  -  c,  +  s)Qi  +  ( t Q  2  -  s Q i )  (18)  perfectly a n t i c i p a t i n g firms' b e h a v i o u r , the U . S . government, before firms choose their o p t i m a l o u t p u t  levels, chooses the o p t i m a l tariff a n d / o r the o p t i m a l subsidy rates to m a x i m i z e the national welfare. 8  3. PROPERTIES OF T H E BASIC M O D E L A s was m e n t i o n e d , the e q u i l i b r i u m quantities Q  l  Q  t  a n d the e q u i l i b r i u m prices P , P  2  t  2  c a n be o b t a i n e d  f r o m (3), (4), (16), a n d (17) for any given p o l i c y configuration (t,s). T h e y t u r n out to b e ,  Q i  =  ^ ( ( f > 2  + V ) ( a , - c, +  < ? 2 = -^((<>i + V i ) ( a  where £ > = ( ( ) , + K , ) ( b  2  + V )- k 2  2  s)  2  P  l  P  2  a  2  k { a  2  -  c  2  -  (19)  t))  - c - t) - fc(a, - c, + s))  2  (20)  2  = a, -  =  -  b i Q , -  -  fcQ,  -  b  k Q  2  Q  2  2  (21)  (22)  > 0.  F r o m (19)-(22), we can carry out the c o m p a r a t i v e statics of the e q u i l i b r i u m quantities a n d prices with respect to changes in tariffs a n d subsidies. T o the tariff, we have,  d Q x  k  dt  d Q  D  bi + V i  2  dt  d P  kVi  x  1H=-D d P  < 0  D  2  at  =  b {bx 2  >  0  +K!)-fc  2  z?  T h u s , a tariff has the following effects: (1) shifting profits away f r o m the J a p a n e s e firms ( as Q i f, Q (2) i m p r o v i n g the U.S. terms-of-trade ( as ^ f - - 1 = -  2  J. ),  < 0 ), (3) i n d i r e c t l y r e d u c i n g the domestic  d i s t o r t i o n ( as Q i j ), (4) m a y b e decreasing the U.S. consumer surplus ( as P\ f ), a n d (5) f u r t h e r d i s t o r t i n g 9  trade ( as Q  2  I, P  welfare w o r s e n i n g .  2  T )• T h e first three effects are welfare i m p r o v i n g for the U . S . while the last two  are  In our case where d e m a n d functions are assumed to be linear, we shall see shortly that  the net effect on the U . S . welfare is positive if the tariff is o p t i m a l l y chosen.  E a t o n and G r o s s m a n (1986)  discusses the general case.  S i m i l a r l y , to the subsidies, we have,  9 Q i  b  =  +  2  V  2  ds  D  ds  dP  D  i»i(6 + Va) ~  _  t  fc  2  2  d s  <  0  D  ds  D  A s we can see, a s u b s i d y has the direct role of r e d u c i n g the domestic d i s t o r t i o n (as Q\ ], P\ { ) a n d indirect role of s h i f t i n g profits f r o m J a p a n e s e firms (as  Q  2  [). B u t meanwhile, trade m a y be d i s t o r t e d (as Q  2  \).  A g a i n , as is to be s h o w n , the net effect on the U . S . welfare is positive for the case u n d e r consideration if the s u b s i d y is o p t i m a l l y chosen.  W e t u r n now to the discussions of o p t i m a l policies. E q s . (19)-(22) i n d i c a t e that the e q u i l i b r i u m quantities a n d prices are functions of (t,s). H e n c e , a c c o r d i n g to (18),  the total U . S . welfare is also a function of  (t,s). C a l c u l a t i o n s show,  W ( t , s )  =  -J-(-tfi<  2  -  K  2  t s  -  K  3  s  2  +  K  4  t  +  K  5  s )  +  W(0,0)  (23)  where  Ki  =  + 2 K i ) ( M - k ) + 63V, + 2 ^ ( 6 , + Vi) ) 2  3  K  2  =  k ^ b ^ r , - k  2  ) + { 2 b  10  2  l  + V  2  1  ) V  2  )  (24)  (25)  K z  Ub {b b 2  =  1  2  k  2  )  fc(ft V,- 6,V )(o, - c,) + ((6, +  K <  =  K „  =  2  {(b  2  2  +  V  2  )  2  V i  -  k  2  V  2  ) (  a  b V (2b  +  1  V  l  2  )  2  V  2  +  2  -  k  V  2  2  (26)  ) )  V i ) ( a  (27)  2  - c,) +fc(6,V - 6 K,)(a - c ) 2  i  2  2  2  (28)  and W(0,0) is the total welfare when both t and s are set at zero, that is, U.S. adopts complete laissez-faire. That Ki > 0, K  2  > 0, and K  z  > 0 can be readily seen from (24), (25), and (26) respectively. Further,  we can discuss different optimal policy configurations (t,s) by using (23). In particular, the following three policy configurations are of interest and are to be analysed. 1) The optimal tariff  (t*,0)  When one of the policy instruments, the subsidy, is not available but the tariff can be optimally chosen, for any t the total welfare is,  W { t , s )  =  W { t , 0 ) =  - ^ l ~ K  t  l  2  +  K  4  t ) +  W { 0 , 0 )  (29)  with d W l t . O )  d  2  W ( t , 0 ) d t  1  ,  2 K D  2  1  < 0.  2  The optimal tariff, t*, can be obtained from the first-order condition, giving  -k where K \ and K level  W ( t * , 0 )  4  (30)  are given by (24) and (27) respectively. Substituting (30) into (29), we obtain the welfare  under the optimal tariff. VV((*,0) is the maximal welfare when only the tariff instrument is  11  available. 1 W ( t * , 0 ) =  —  K  ^  t  *  )  2  +  (31)  W ( 0 , 0 )  It c a n be easily seen from (31) that  W ( t ' , 0 )  >  W ( 0 , 0 ) ,  W { t * , 0 )  =  W ( 0 , 0 )  and  iff  t*  =  0.  where " i f f " means "if a n d only i f .  2) T h e o p t i m a l s u b s i d y ( 0 , s * )  W h e n the tariff i n s t r u m e n t is not available b u t the subsidy can be o p t i m a l l y chosen, we can similarly calculate the o p t i m a l subsidy as well as the c o r r e s p o n d i n g m a x i m a l welfare. T h e y are,  S  =  2K~  < > M  and  ^(°> *) = - ^ # ( 0 s  2  3  respectively.  +W(0,0)  Therefore,  W ( 0 , s ' )  >  W ( 0 , 0 ) ,  W ( 0 , s * )  =  W ( 0 , 0 )  3) T h e o p t i m a l tariff a n d subsidy (t**,s**)  12  and  iff  s ' = 0 .  (33)  W h e n b o t h the tariff and the subsidy instruments  are available, the welfare function is that of  (23).  T h e first-order c o n d i t i o n s are,  d W ( t , s )  1  d W { t , s )  1  a  = 7 ^ ( - - 2 i - 2 A S + A ) = 0. f t  3  a s  T h e second-order conditions  ,  D  5  2  are,  d  2  W ( t ,  s  )  2 ^  =  9 W(t,s)  2if  2  d s  c3 W(<, )9 iy(<, ) 2  S  T h e i n e q u a l i t y 4 i f i . / i f — K\ 3  W ( t , s ) is strictly  concave.  2  S  d  2  W ( t , s ) d  2  D  2  <  0,  1  W [ t , s )  > 0 is proved in A p p e n d i x 3.  3  2  F r o m the second-order  conditions, we see that  T h e r e f o r e , the point ( f * * , s * * ) which satisfies the first-order conditions is the  u n i q u e m a x i m i z i n g solution to W ( t , s ) , and  «" = "II \ K , K  2KiK$  =  s  *  Z  — v  v  -  K  2  I"  (34)  K2K4  IF*—  () 35  In p a r t i c u l a r , it can be shown that  and  W ( t * ' , s " )  >  W(t*,0),  W { t * * , s * * )  =  W ( t * , 0 )  13  iff  s**  =  0.  T h e proof is not hard. If s** / 0, => (t**,s**) # (**,0), =*> tV(<**,s**) > W ( r , 0 ) because (<**,s**) is the unique m a x i m i z i n g  = f,  p o i n t ; if s*' = 0, => i f / i f 5  (i**,s**) = (r,0), =>  W { t ' \ s * ' )  4  = #2/2*1,  => <** = ffi-fjgj = ^^-K^JK'  =  = W(<*,0). S i m i l a r l y , we have that,  W ( i * * , s * * ) > W(0,s*),  and  W(t**,s**) =  iff <** = 0.  W { 0 , f )  T h e foregoing discussions have proved the f o l l o w i n g result,  R e s u l t  1.  F o r the basic m o d e l of section  2,  the o p t i m a l tariff and the o p t i m a l p r o d u c t i o n subsidy are  each welfare i m p r o v i n g (relative to complete laissez-faire) if i m p l e m e n t e d separately; b u t an o p t i m a l policy package involves b o t h tariffs and p r o d u c t i o n subsidies.  In the o p t i m a l tariff and the o p t i m a l subsidy formulas,  t  = — — 2tf,  and  s = 2 K  the signs of t* a n d s* depend, respectively, on the signs of K  t  R e s u l t  2.  3  and K  b  because K\ > 0, K  3  If the d e m a n d parameters are estimated using eqs. (10)-(14), and 2  Q  i  0  >  > 0. We have,  Piu,  2 Q  2  o  >  -Fao,  then t*  Proof  >0  and  s* > 0.  A p p e n d i x 4 shows that if the conditions are satisfied, then  and s* > 0.  Q . E . D .  14  K  4  >  0 and  K $  >  0. Therefore,  t*  > 0  It is noted that if both Vi and V are zero, then from (27) and (28) both i f and K 2  4  b  are zero, and thus  t* = 0, s* = 0, and <** = s** = 0. In words, if competition is perfect, laissez-faire is the optimal policy for U.S..  But in general, as Result 2 indicates, the optimal policy includes a positive tariff or a positive  production subsidy if only one policy instrument is available.  It is interesting to examine how large the welfare gains that are available from the pursuit of an optimal tariff. When a domestic production subsidy or antitrust policy is not available, the gain from using the optimal tariff over free trade is  A ,u t  =  W [ t * , 0 )  —  W(0,0). When the subsidy or antitrust policy is available,  the contribution of the tariff over what is possible with the optimal subsidy is given by A , t  W(0,s*).  = W (f* ,s**) —  We have,  Result 3.  If t " > 0 and s** > 0, then  (i) 0 < A  ts>8  < A,, t  0  (ii) A o/a: < A , < aAs.O, where A,, = W(0,s*) Sj  Proof  i8  t  0  0  W(0,0),  a  =  4K,K /Kl > 3  1.  (i) Rearranging (34), (35) and substituting for t* and s*, we have,  4K K V V  -  3  4K K t  2K K s* 2  -  3  4if /f s* 1  s  1KIK V 2  3  4K K t  z  K\  Kl  3  (36)  (37)  Solve for t* and s*, t'  =  K  2  t**  (38)  +  s* = s** +  K  2  2 K  15  (39) 3  If <**  > 0 and s** > 0, then f r o m (38)  and  > <**  > 0  t"  A  ( 8  ,  =  W ( t " ,  =  J  ~  D  2  D  2  s  p  1  (  -  K  S  i  " )  (  t  -  4 K i K  )  A K  -  2  4 K  3  and  s* > s** >  K  t " s "  2  [  '  t  3  K  2  (  J  t  t  ^  -  K  3  - (s*) ) + 2  ( { s * * ) -  2 K  +  F r o m (31),  T h a t is, A ,,, t  (ii)  If t"  A , t  <  0  =  - ^ K ^ t * )  A  t "  +  K  &  ( s "  -  s*))  2  3  and the last equality follows by using  0.  t  K  )  1 3  where the second from the last equality follows by using (39) Therefore, A , . , >  0.  W ( 0 , s * )  "  \  (39),  2  .  Thus,  At.o-  > 0 and s** > 0, then f r o m (36)  and  (37),  4tf tf <* -  2 K  4 K ! K  2 K i K  1  3  3  s *  -  2  K  3  2  s *  >  0  t '  >  0  that is,  2 K  3  t*  16  K  2  (34).  F r o m (31)  a n d (33),  we have,  A ,u 8  T h e n use  Kl( lY a  =  (40),  4if i if  3  Therefore, A „ , / a 0  < At,u <  a  A ,„  K  t  2  A,, . 0  In the r e m a i n i n g of this section, we consider the effects of c h a n g i n g the m a r g i n a l costs C] and c  2  on the  o p t i m a l tariff and the o p t i m a l subsidy.  In the basic m o d e l , the aggregate conjectural variations are related to the m a r g i n a l costs,  V,  where  P  l  l  y  ,  F  2 0  , and  Q i o ,  Q  2  ~  =  o ,  a  c  i  +  s  u  ,  and  PM — 2 ~ ' u c  V  =  2  before, are the a c t u a l prices and quantities in a year; s  s  0  and  t  0  a c t u a l s u b s i d y a n d tariff. T h u s ,  W  x  = dci  1 — Q i  d V  1  2  and  — d c  U  2  ,  Q20  i n d i c a t i n g t h a t the lower the m a r g i n a l costs, the higher degree of implicit m o n o p o l y in the m a r k e t .  T h e following result arises from the basic m o d e l ,  Result 4.  If the d e m a n d parameters are estimated using eqs. (10)-(14), then  ds* dci  17  are the  °f  & = £l  Pro  = iklfc  <  0 if  l£f"  <  0  (  as  ^  > 0).  That  < 0 is proved in A p p e n d i x 5.  | f f  Q.E.D. Result 4 shows that for a lower domestic unit cost, c o r r e s p o n d i n g to a higher degree of i m p l i c i t collusion a m o n g the domestic firms, a higher subsidy level can be justified when only the subsidy policy is i m p l e m e n t e d .  In f £ = fall of c  2  would cause b o t h K\  on the sign of  {^ \l^° K  2  and 2K\  are also met in s i g n i n g  1  = 2(6,  + V , )  2  ^ -  < 0. So a  rising, and whether the o p t i m a l tariff t* rises or falls would depends  — i)KjJ^c* ^ , an expression w h i c h is c o m p u t a t i o n a l l y h a r d to sign. S i m i l a r situations  at*  1979  < 0 c a n be similarly shown. B u t now ^ f f ^  that ^  a *  and T ^ - . T h u s , we instead c a r r y out a sensitivity analysis for c i a n d c  2  using  d a t a of the U . S . car m a r k e t . T h e results are contained in T a b l e 1.  Table  T h r e e observations  1  is  inserted  here.  are obvious f r o m T a b l e 1.  1) B o t h t* and s* are negatively related to c , }  c , suggesting that for lower m a r g i n a l costs, c o r r e s p o n d i n g 2  to a higher degree of implicit m o n o p o l y in the m a r k e t , greater government  intervention can be justified.  2) B o t h t* and s* are sensitive to the domestic unit cost c i . O f t h e m , the o p t i m a l subsidy is p a r t i c u l a r l y sensitive to c . t  F o r instance, a 5% decrease in c, f r o m base would cause a 50%  increase in s* from base. O n  the o t h e r h a n d , the o p t i m a l subsidy s* is not sensitive to the change of the foreign m a r g i n a l cost c , while 2  the o p t i m a l tariff t* is very sensitive to the change of c : 2  increase in t* f r o m base.  a 5% decrease in c  In view of the relationship between  c,  and V  lt  c  2  2  from base would cause a 20% and V ? , the tariff seems more  closely related to the competitiveness of foreign firms whereas the o p t i m a l subsidy seems m o r e closely related to the c o m p e t i t i v e n e s s  of domestic  firms.  T h i s point is also s u p p o r t e d  by the following t h i r d  observation  f r o m T a b l e 1.  3)  In the c o l u m n O P T - T S  welfare, a fall of c  lt  component  of T a b l e 1 where tariff a n d subsidy are jointly chosen  to m a x i m i z e  the  corresponding to an increase in i m p l i c i t collusion of U . S . firms, would cause the subsidy  of the o p t i m a l policy package, s**,  to rise and the tariff c o m p o n e n t  18  t** to fall.  T h u s , in the  TABLE 1 S E N S I T I V I T Y ANALYSIS FOR C1 AND C2 IN THE CENTRAL C A S E , (PERCENT CHANGE FROM BASE)  OPT-TARI OPT-SUBS C1 T S  -5 10.13  C1 T S  C1 T S  £  OPT-TS  24.76  -2.500 -1.680 27.29  OPT-TARI OPT-SUBS  OPT-TS  -23.76  OPT-TARI OPT-SUBS  OPT-TS  -46.52  OPT-TARI OPT-SUBS  OPT-TS  5  2.503  -5 28.90 .1642  OPT-TARI OPT-SUBS  OPT-TS  -2.500 10.55 ^  2.500  5 3.359 -51.28  -5 20.79  C2 T S  -2.500  2.500 1.680 -26.19  5 -1 1.04  C2 T S  C2 T S  OPT-TARI OPT-SUBS  2.500 -5.400  C1 T S  C2 T S  50.51  -5 -3.359 55.67  -2.500 5.174  -5  OPT-TS  -5  1.289  -2.500 14.66 .0864  OPT-TARI OPT-SUBS  OPT-TS  2.500 -10.91  -2.500  -1.371  2.500 -15.15 -.0963  OPT-TARI OPT-SUBS  OPT-TS  5 -22.24  2.500  5 -2.833  5 -30.87 -.2044  1979  TABLE 2 S E N S I T I V I T Y ANALYSIS FOR P10 AND P20 IN THE CENTRAL CASE, (PERCENT CHANGE FROM BASE)  OPT-TARI OPT-SUBS P10 T S  P10 T S  P10 T S  to O  P 1  T S  0  P20 T S  P20 T S  P20 T S  P20 T S  -5 -11.66  OPT-TS  -51.03  -5 3.581 -56.15  OPT-TARI OPT-SUBS  OPT-TS  -2.500 -5.553  -5  -26.04  -2.500 1.749 -28.66  OPT-TARI OPT-SUBS  OPT-TS  2.500 5.073  -2.500  27.02  2.500 -1.672 29.73  OPT-TARI OPT-SUBS  OPT-TS  5 9.727  2.500  54.95  5 -3.271 60.45  OPT-TARI OPT-SUBS  OPT-TS  -5 -27.82  5  -3.379  -5 -36.78 -.2896  OPT-TARI OPT-SUBS  OPT-TS  -2.500 -13.66  -5  -1.628  -2.500 -18.05 -.1374  OPT-TARI OPT-SUBS  OPT-TS  2.500 13.27  -2.500  1.525  2.500 17.52 .1258  OPT-TARI OPT-SUBS  OPT-TS  5 26.23  2.500  5 2.964  5 34.61 .2425  1979  TABLE 3 S E N S I T I V I T Y ANALYSIS FOR 010 AND 020 IN THE CENTRAL CASE, (PERCENT CHANGE FROM BASE)  010 T S  010 T S  010 T S  010 T S  020 T S  OPT-TARI OPT-SUBS  OPT-TS  -5 .4404  -5 .0629 .0695  OPT-TARI OPT-SUBS  OPT-TS  -5 -.0369  -2.500 -.0180  .2155  -2.500 .0307 .0339  OPT-TARI OPT-SUBS  OPT-TS  2.500 .0171  -2.500  -.2067  2.500 -.0294 -.0324  OPT-TARI OPT-SUBS  OPT-TS  5 -.4052  5 -.0575 -.0634  OPT-TARI OPT-SUBS  OPT-TS  5 .0333  -5 .0350  2.500  -5 -.4257  OPT-TARI OPT-SUBS Q20 T S 020 T S  020 T S  -2.500 .0175  OPT-TS  - .21 19  -2.500 -.0301 -.0332  OPT-TARI OPT-SUBS  OPT-TS  2.500 -.0175  -2.500  -5 -.0604 -.0666  2.500 .2102  2 .500 .0300 .0331  OPT-TARI OPT-SUBS  OPT-TS  5  5 .0598 .0660  5 .0350  .4186  1979  o p t i m a l p o l i c y package, the subsidy becomes quantitatively more significant while the tariff less. T h e similar s i t u a t i o n h a p p e n s as c  2  falls.  W h e n foreign firms become more collusive, <**  would rise r a p i d l y while s**  would r e m a i n almost u n c h a n g e d .  S i m i l a r observations  can be found in T a b l e 2 where the sensitivity analysis for the a c t u a l prices is  c o n d u c t e d . F u r t h e r m o r e , it is noted t h a t ,  Vi  U s i n g 1979  \ Q i  V i )  P  i  0  \  Q  i  0  V i )  c,  '  '  d a t a , we calculate,  QioVi  T h a t is, a  0  1%  change of  Q10V1  P  1  0  or  Ci  ( P  2  o  Q20V2  '  Q20V2  or c ) from base would, a p p r o x i m a t e l y , cause a 2  10% (7.5%)  change  in Vj (V ) f r o m base. Hence the aggregate conjectural variations are very sensitive to the price or cost data. 2  T h e p r a c t i c a l matter of the above sensitivity analysis is in the design of g o o d policies. T h e difficulty in finding  accurate cost and price i n f o r m a t i o n would make the profit-shifting policy less a t t r a c t i v e in practice.  F i n a l l y , the sensitivity analysis for a c t u a l quantities (see T a b l e 3) shows that neither the tariff n o r the s u b s i d y is sensitive to the q u a n t i t y variables. M o r e o v e r , the quantity d a t a are relatively easy to collect and are m u c h less volatile t h a n the d a t a for either costs or prices.  4. T H E R O L E O F T A R I F F S A N D P R O D U C T I O N S U B S I D I E S  In section 3 we have d e m o n s t r a t e d several properties of the basic m o d e l .  (1) A tariff has a direct role of  s h i f t i n g p u r e profit away f r o m foreign frims to domestic firms and an indirect role of r e d u c i n g domestic d i s t o r t i o n , whereas a p r o d u c t i o n subsidy has a direct role of r e d u c i n g domestic distortion and an indirect  22  role of shifting profit. (2) The optimal tariff and the optimal subsidy are each welfare improving (Result 1). (3) T h e higher the degree of implicit collusion of domestic firms is, the larger the production subsidy is required (Result 4). The simulation results also show the positive relations between the optimal tariff level and the degree of firms' implicit monopoly in the market; moreover, the subsidy (tariff) seems more closely related to how collusive the domestic (foreign) firms are (Table 1).  It is noted that the formulas for the optimal tariff t* and the optimal subsidy s* involve both the marginal costs c, and the aggregate conjectures V,. In the basic model V, is related with c,- through  Vi -  Pio  —  — Ci  +s  0 V  ,  P  =  2  VlO  20  —  c— •  2  t[,  V 2 0  This would make the comparative statics of t* and s* with respect to changes in C i and c computationally 2  too complex to do. Partly for this reason, we shall in this section slightly change the basic model by assuming that the conjecture V (V ) is independent of the cost c (c ). So the effect of the domestitic (foreign) firms' x  2  x  2  conduct on the market equilibrium is assumed to be independent of the change in the marginal cost of domestic (foreign) firms. In the case of Cournot conduct, K,- = &,/«,- (i=l,2), and hence our assumption means that the exogenous number of firms n, would not be affected by changes in the marginal cost c,which may be brought by an exogenous technology advance. This is similar to the model of Brander (1981), Brander and Spencer (1983), and Dixit (1984), in that firms in each country follow Cournot behaviour and the number of firms in each economy is arbitrarily fixed.  The equilibrium quantities and prices are given by (19)-(22) and are functions of c , c for given t, s, x  and V , V - We consider the following three different policy configurations (t,s): x  2  (i) complete laissez-faire (0,0), IV = W (c\ ,c )\ 0  (ii) the optimal tariff  (t*,0),  f = t'(c c ), lt  2  2  and W =  W ( ,c );  (iii) the optimal subsidy (0, s*), s* = s*[ci, c ), and W = 2  23  t  Cl  2  W,(ci, c ). 2  2  When marginal costs are exogenously changed, it would be expected that the monopoly power that is collectively possessed by domestic (foreign) firms in the market might also be changed. We define,  (41)  4>i=fo(ci,c )=H—^ 2  = * (ci,c ) =  h  2  ^  2  —  -  (42)  <j>i {4> ) is an index which is assumed to measure the monopoly power collectively possessed by domestic 2  (foreign) firms in the market. It is noted that in a single product and monopolized industry, <f> =  is the  Lerner Index of monopoly power. In the following analysis we shall variate the domestic marginal cost C, while hold the foreign marginal cost c fixed (Note 1). 2  Result 5. (i)  (ii)  Proof  In complete laissez-faire,  d + i l d c x  d<j> /dc 2  2  <  0;  >  0.  (i)  dc\  dci  = £<*> =  d h  3c,  =  / P, -  d  9c, V F,  C l  P  -  (  b  +  ^  +  b  x  b  -  2  k) 2  >  0  \  ,  /  c,dP,/dc, P  (Pi  ^  dc\  -  c  2  1  ) ( b  l  V  + 6,b - k ) + PiV,(b + 2  2  2  P  24  2  2  D  V  2  )  (ii) Similarly, we have d P  W  2  9c,  d<j>  ~  _  2  dci  2  > 0  D  k V  ~  2  c  > 0  2  P % D  Q . E . D .  Thus, as the domestic marginal cost falls, the domestic firms would increase their monopoly power while the monopoly power possessed by the foreign firms would be reduced. We do not yet know whether, and when, the overall market becomes less or more competitive. For this purpose we would like to compare the rate of increase in  with the rate of decrease in  <p  x  that is, compare  <f> , 2  the algebraic complexity, we shall instead compare | ^ v ^ i / ^ i | with c  and  <j>  2  =  P  2  —  c  2  =  P <t> 2  2  \d<j>i/dci  \d<f> /dc \, 2  l  | with where  \d<j> /dc \-  <j>\  2  =  2  P\  —  To avoid  =  Pi<j>i  It is easy to show that  + V2W1  (f>2  dci  <0  D  dcj> _ kV dci ~ ~)T 2  >  2  0  Therefore,  d<t>  2  iff  dci  Yl V~  > 2  fc b  2  +  (43) V  2  Condition (43) holds when the effect of the domestic firms' collusive conduct on the market outcome is sufficiently large.  If the market structure is such that condition (43) holds, the rate of increase in the  monopoly power possessed by the domestic firms firms, as their marginal cost falls, would be greater than the rate of decrease in the monopoly power of foreign firms. It is suspected in this case that intervention  25  would be more important and, since the domestic monopolistic distortion becomes a more serious problem, the role of subsidies would be more significant than that of tariffs. We now examine this suspicion. From the optimal tariff (30) and the optimal subsidy (32), we have  i ^ £ ( £ ) - - i ^ - ' " >  and 9s  (45)  dc  Thus, dt* <  0  iff  b  h  2  V i  6,V  -  >  2  0  iff  i  and 9  S*  —  n <  0  iff  (6  +  2  V  2  )  2  V  o -  l  k  2  V  2  >  0  iff  dci  YL v  2  fc (fc + v ) 2  >  2  2  ( 4 7 )  2  It can be easily shown that if bj > k (Note 2), then  bi  62"  Therefore, when condition (46)  bi  >  k >  b  2  holds, i . e . , V i / V  k  +  V  2  >  (6 + 2  >  2  bi/b , 2  k.  26  2  V  2  )  2  both conditions (43)  (  and (47)  4  8  )  will hold, given  F u r t h e r , let  A t , o = &t,u(ci,c )  = W (d,c )  -  W (c,,c )  = A,, (c ,c ) = lV,(c,,c ) -  ^(cj.cz)  2  A,,  0  0  1  t  2  2  0  2  2  that is, A , o a n d A , , u are welfare gains from the o p t i m a l tariff a n d t h e o p t i m a l s u b s i d y over t  complete  laissez-faire, respectively. F r o m (31) a n d (33), we have  A  '.o=f^('*)  and  2  A.. =^( *) 0  2  8  Then  d A , u _ K± t  K^dt*_ _ K4 ar  ,d£_ _  Similarly, 9As,0 _ K 5c,  5  9s*  ~ IP JC~I  We know from Result 2 that if t h e d e m a n d parameters are estimated A u , 2 Q o > P20, then i f 2  sign as d t * / 5 c , and  5  (  ds*/dc , respectively. x  T h e foregoing discussions have shown the following result,  Result  6.  If V  x  / V  (i) 1 3 0 , / S d l  2  >  bi/b  a n d f>, >  2  k,  then  > |a^/a,| 2  and 2 Q ,  0  >  (t* > 0) and tf > 0 (s* > 0). T h u s 9 A , / a , a n d 0 A , , / d c , have the same  > 0  4  using eqs. (10)-(14),  c  ;  (ii) d i V d c , < 0 and ds*/dc < 0; x  (iii) if t* > 0 a n d s* > 0, then 9 A , / d c , < 0 and 9 A „ . / 0 c , f  0  o  27  < 0.  u  C  o  The crucial condition of Result 6 is that  V\/V  >  2  b  l  / b  or  2  V  x  / b i  >  V  2  / b  2  ,  which may be interpreted  as the domestic firms' collusive conduct exerts more influences on the market equilibrium than the foreign firms'. In the case of Cournot conduct, the condition V1/61 >  V  2  / b  2  is equivalent to the condition  n\  <  n  2  ,  that is, there are fewer domestic firms in the market. Result 6 says that if the market structure is such that  Vi/bi  >  V  2  / b  2  ,  a fall of the domestic marginal  cost would increase the monopoly power possessed by the domestic firms. This is more than offset by the decrease of the foreign firms' monopoly power in the market (Result 6, (i)). As was suspected, higher tariff and subsidy rates are required in the optimal policy (Result 6, (ii)). As a result, greater welfare gains over complete laissez-faire can usually be achieved (Result 6, (iii)). As for the relative importance and efficiency of the optimal tariff vis-a-vis the optimal subsidy, we have Result 7, R e s u l t 7.  If  V  x  / V  2  >  61/62 and 6, >  k,  then  ds* dci  >  dt* dci  The proof is given by Appendix 6. When the monopoly power gained by the domestic firms is more than that lost by the foreign firms (as the result of a fall of C i ) , Result 6 shows that both the optimal tariff t* and the optimal subsidy s* would rise. Now Result 7 further indicates that the rate of increase in s* is greater than the rate of increase in t*. In other words, when domestic monopoly becomes a major problem, the value of an optimal production subsidy would rise faster than the value of an optimal tariff if each policy instrument is implemented separately, suggesting that in a sense, the subsidy becomes more important than the tariff. Because both t* and s* are linear functions of c i (from (30) and (32)), the situation can be depicted using Figure 1 where both t* and s* are assumed to be positive.  28  where  Vi _!_>  ..  Vo _2_  , * t  >  0  >  s  ,  >  0  Figure 1 The optimal t a r i f f and optimal subsidy as functions of c,  29  Figure  1  is  inserted  here.  F r o m Results 6 a n d 7, the following corollary can be d e r i v e d ,  Corollary (i)  1.  if  If  V i / V  >  2  b  1  / b  2  ,  b  >  x  k,  V  0, a n d s* > 0, then for any given c ,  >  2  is such a point that s * ( c j ) = <*(c?), then for any c , , 0 < c < x  min(Fi ,c"), 0  s * ( c i ) > <*(c,);  (ii)  if b  2  > k ( N o t e 2), for any c,, 0 < c  <  t  d c  Proof  (i)  (ii)  min(Fi ,Ci), 0  >  x  dci  It c a n be seen f r o m F i g u r e 1.  F o r m (i),  s*{ci)  >  for  t*{ci)  c  i  |9A./3ci| \ d A  t  / d  C  l  0 < c, < m i n ( F  t  (b  =  +  2  V  2  fc(6 V,  \  {b  2  + k ( b  - k  -  2  >  f  V  2  V  2  x  )  b  2  -  x  ,cJ).  l u  V  2  V  2  s * {  2  2  C  l  )  <*(c,)  )  k  - b , V  2  Hence  V  2  )  > 1  the last inequality holds as long as b > k a n d b > k. x  2  Q . E . D .  T h e r e f o r e , when domestic  m o n o p o l y becomes a m a j o r p r o b l e m , the o p t i m a l subsidy rate tends to be  greater t h a n the o p t i m a l tariff rate. subsidy over laissez-faire  M o r e o v e r , the rate of increase in the welfare gain f r o m the o p t i m a l  tends to be greater than that of increase f r o m the o p t i m a l tariff, suggesting  in this case a p r o d u c t i o n subsidy is m o r e efficient in raising the welfare t h a n a tariff.  30  that  It is noted that the c o n d i t i o n V /V t  Results The  Vi/V2  > f>,/f>  2  2  (in C o u r n o t , n , < n2)  6, 7 and C o r o l l a r y 1. A s was mentioned earlier, if b > k, then bi/b  +  V2) 2.  It can be similarly shown that in the case where  0<  t  case where  Vt/V  < k /(b  + V)  2  2  2  > bi/b  2  or  2  has been analysed.  2  V /Vi  > [b + V ) /k ,  2  2  2  2  plays a c r u c i a l role in deriving  2  > kj[b  2  + V ) > k /(b 2  2  2  the results just reverse those reported in Results  2  6, 7 and  C o r o l l a r y 1. T h e proofs are similar. T o save space, we shall omit the proofs and only state the results.  Result  If  8.  V IV 2  > (b + V ) /k  X  2  (i) \d^/d \ <  2  2  and  2  bi > k, then  \dh/dc \;  Cl  l  (ii) dt*/dci > 0, ds*/dc  > 0;  x  (iii) if t* > 0 and s* > 0, then SAt.u/dc, > 0 and aA,, /9cj > 0. 0  Result  If  9.  V2/K1 > (b + V ) /k , 2  2  2  b > k, and b > k, then  2  x  2  dt* dci  Corollary 2. (i) if  If  V /Vi 2  V ) /k ,  > (f> +  2  2  2  >  ds* dci  6, > k, t* > 0, and s* > 0, then for any given c ,  2  2  t*(c°), then for any  is such a point that s*(c") =  C i ,  cj <  Ci <  Pm,  «*(ci) > « * ( c i ) ;  (ii) if b  2  > k, then for any c  lt  < c  x  <  dA  tl0  dci  The  interpretation  >  9A,,o  dci  of these results can be similarly given except that the tariff a n d the subsidy have  reversed their positions. W h e n the market structure is such that the effect of the foreign f i r m s ' conduct on  31  the m a r k e t o u t c o m e is r a t h e r significant relative to that of the domestic firms', a fall of domestic m a r g i n a l cost would reduce the m o n o p o l y power possessed b y the foreign firms, a reduction which is more significant t h a n t h e i n c r e m e n t of m o n o p o l y power gained by the domestic firms. In a sense, the overall market would b e c o m e more c o m p e t i t i v e . B o t h the o p t i m a l tariff and subsidy rates would thus fall, so as t h e welfare gains from  using t h e o p t i m a l policy.  O n the other h a n d , a rise of domestic m a r g i n a l cost w o u l d increase the  foreign firms' m o n o p o l y power, an increase which is more t h a n offset by the r e d u c t i o n of the domestic m o n o p o l y power.  firms'  So t h e overall market would become less c o m p e t i t i v e a n d the foreign f i r m s ' m o n o p o l y  w o u l d b e the major p r o b l e m . In this case more intervention is called for and by doing so, more welfare gains can be achieved. F u r t h e r m o r e , the rate of increase in the o p t i m a l tariff t* is greater t h a n that in the o p t i m a l subsidy s*, and t* tends to be greater t h a n s*. M o r e o v e r , the rate of increase i n welfare gains from t* tends to be greater t h a n that f r o m s*. T h e s e suggest that the tariff i n s t r u m e n t is now more i m p o r t a n t and more efficient t h a n the subsidy.  T h e case in w h i c h  (i)  k / ( b  2  +  V  2  )  <  V  V  l  l  / V  / V  2  is between  2  <  b  1  / b  b  1  / b  2  and  k  2  / { b  +  2  V  2  )  2  is briefly discussed as following.  2  F r o m conditions (43), (44), and (45), we have  d<f>  2  (49)  d c i  —  > 0  (50)  a c i  ds*  ^ - <  ,  4  (51)  n  OCi  It m a y be interesting to compare this case with the case where  V  l  / V  2  >  b i / b  2  .  In b o t h cases, the increase  in t h e d o m e s t i c firms' m o n o p o l y power outweighs the decrease in the foreign firms' m o n o p o l y power as the d o m e s t i c m a r g i n a l cost falls. In the case of  V \ / V  2  >  b i / b  32  2  ,  b o t h the o p t i m a l subsidy a n d tariff rates would  rise. In the current case where T h u s as the ratio of Vi /V  2  Vi/V < bi/b , 2  2  the subsidy would still rise but the tariff would instead f a l l .  is falling, the foreign f i r m s ' c o n d u c t would be exerting more a n d more influences  on the m a r k e t o u t c o m e relative to the domestic  firms'.  T h i s is first reflected in the change of tariff rates in  that the tariff rate falls as the foreign firms become c o m p e t i t i v e despite that the overall m a r k e t becomes less c o m p e t i t i v e , suggesting that tariffs are more closely related to how foreign firms behave in the m a r k e t .  (ii) k /(b + v )- < vjv 2  2  2  2  < k/(b + v ) 2  2  We have, d  h  d(j> d h  ,  2  (  5  2  )  dci  —  > 0  (53)  —  < 0  54)  S i m i l a r l y , a comparison of this case with the case where 0 <  Vi/^2 <  k  2  / ( b  2  +  V  2  )  2  suggests t h a t  p r o d u c t i o n subsidies are more closely related to how domestic firms behave in the m a r k e t .  B y c o n d u c t i n g the sensitivity exercises of 0,-, t*, s * , A , o , and A , t  8  u  with respect to Cj, we have shown in  this section several interesting results c o n c e r n i n g the role of tariffs and p r o d u c t i o n subsidies. W h e t h e r the tariff and subsidy rates should be raised or lowered depends on whether the overall market becomes less or m o r e c o m p e t i t i v e . T h i s is in t u r n closely related to the initial market s t r u c t u r e : c o n d u c t exerts more or less effects on the market e q u i l i b r i u m t h a n the foreign firms'  whether the d o m e s t i c firms'.  c o n d u c t has rather significant effects on the market e q u i l i b r i u m , the domestic  firms'  W h e n the d o m e s t i c firms'  m o n o p o l y is  usually the major issue, and a p r o d u c t i o n subsidy is usually more i m p o r t a n t and more efficient t h a n a tariff. O n the other h a n d , when the foreign firms' c o n d u c t has rather significant effects on the market e q u i l i b r i u m , the foreign firms' m o n o p o l y is usually the m a j o r issue, and a tariff usually becomes more i m p o r t a n t and more efficient t h a n a p r o d u c t i o n subsidy.  33  5. J A P A N E S E POLICY RESPONSE In the analysis u p to this p o i n t , it has been assumed that the foreign (i.e., Japanese) government pursues a laissez-faire p o l i c y a n d only the d o m e s t i c (i.e., U . S . ) government is active in p o l i c y - m a k i n g . if we depart f r o m this a s s u m p t i o n ? Here we consider two cases separately.  W h a t happens  O n e is the case where the U . S .  government p u r s u e s the status quo policy, with the M F N tariff $ 1 0 0 per car on Japanese i m p o r t s and a zero p r o d u c t i o n s u b s i d y to U . S . firms, while J a p a n is active in p o l i c y - m a k i n g . T h e other is the case where b o t h governments are active in m a k i n g policy.  We assume that the policy i n s t r u m e n t for J a p a n in this context  is an export s u b s i d y or an export tax, and the policy perspective is the J a p a n e s e welfare which is the s u m of J a p a n e s e  firms'  profit f r o m e x p o r t i n g to the U . S . market and Japanese g o v e r n m e n t ' s subsidy cost (or tax  revenue).  Since part of Japanese firms' o u t p u t is in the d o m e s t i c (Japanese) m a r k e t , we must assume a segmentedm a r k e t s p e r c e p t i o n a d o p t e d by the Japanese firms in order to separate o u r U . S . market f r o m the market  and focus on the U . S . m a r k e t .  Segmented markets arise when firms treat different countries as  different m a r k e t s in that they choose their strategy Japanese  (exporting)  firm.  Japanese  variables for each m a r k e t separately.  Its profit in the U . S . market is  subsidy f r o m the J a p a n e s e government (if s  ( P  2  -  c  2  + s  2  —  t  1  ) q  2  where s  ,  C o n s i d e r one  2  is the export  turns out to be negative, it is interpreted as the export  2  <i is the tariff i m p o s e d by the U . S . government. T h e firm chooses its export level q  2  tax),  to m a x i m i z e its profit  from e x p o r t i n g ,  P  S u p p o s e t h a t there are n  2  2  such Japanese  P-2  —  C  +  2  firms.  ~  Aggregate over t h e m ,  C + S 2  0  So  2  - U - QV =0 2  34  2  (55)  where V  has the same m e a n i n g as that in p r e v i o u s sections.  2  B y c o m b i n i n g (55)  with previous eqs. (3), (4), and  Pi  P  2  Pi  where s  x  =  a,  =  a  -  -  2  biQt  - k Q  - kQx -  + s ,  ci  (16),  is the U.S. domestic p r o d u c t i o n subsidy, V  -  Q  2  QiVx  and V  x  b  (3)  2  (4)  2  0  =  (16)  are the aggregate version of c o n j e c t u r a l v a r i a t i o n  2  p a r a m e t e r s , we can determine the e q u i l i b r i u m quantities a n d prices, given policy p a r a m e t e r s t  ly  1) O n l y J a p a n  J  A  P  = 100 and s  x  x  = 0.  T h e J a p a n e s e welfare  is,  W  where  2  is a c t i v e i n p o l i c y - m a k i n g  In the first case where only J a p a n is active in p o l i c y - m a k i n g , t  W  s , , and s .  W  J  A  P  =  W  J  A  P  e x p o r t s u b s i d y (tax)  [ s  s  2  2  ) .  J  A  F  =  ( P  - c  2  2  -  100+  s  2  ) Q  - s  2  2  Q  2  T h e c o m p a r a t i v e statics of quantities and prices with respect to the  (56)  Japanese  are,  d s  d_P d s  1  D  2  J  =  t  l  +  V  i  )  b  2  -  k  2 <  o  D  2  d Q d s  k  x  U  2  dPi —  1  d s  k V -  =  -  —  1  D  2  a) Effects on Japanese welfare  35  -  ,  x  <  0  ,  (60)  T h e c o m p a r a t i v e static effect of the J a p a n e s e export subsidy (tax) on J a p a n e s e welfare is,  d W —  T h e first t e r m in librium P negative:  > [c  2  d W  J  A  P  j d s  J  A  ,  F  =  OS2  (  dQ  d P  2  P  2  -  c  2  100)-^+ Q  -  2  - ^ -  2  (61)  " S o  <IS2  indicates that an e x p o r t subsidy is desirable to J a p a n because in equi-  2  + 100) and a subsidy would e x p a n d Japanese exports (from (57)). B u t the second term is  2  a subsidy w o u l d lower t h e price charged by Japanese producers (from (58)) and might thus lower  their profits.  A n e x p o r t tax works in just an opposite w a y : it is h a r m f u l f r o m v i e w p o i n t of the first t e r m  but desirable f r o m v i e w p o i n t of the second t e r m . In this example,  d  W  2  J  A  P =  2  ds?,  a p o i n t , s , at w h i c h the  first-order  2  {s* )  W  JAP  >  2  W  J  d Q  d P  2  d s  2  2  <  d s  because  o  '  2  c o n d i t i o n is satisfied, is the unique w e l f a r e - m a x i m i z i n g p o i n t ,  A  F  and  ( 0 )  W  J  A  P  { s *  2  )  =  W  J  A  P  ( 0 )  iff s = 0. 2  In w o r d s , we have  Result  10.  T h e o p t i m a l export subsidy (tax) s  2  is w e l f a r e - i m p r o v i n g (relative to complete  laissez-faire)  for J a p a n .  Solving  d W  J  A  P  / d s  .  =  2  =  0 for  s' , 2  ((&i + Vi)(a2 - c - 100) - fc(oi 2  2(b,  5 2  Because 2(6, + V i M ^ i  we have  +M  2  +V )(b V 1  2  l  - ^ ) > 0 and (b, + V i ) ( a 2  36  2  C l  ) ) ( ( t , + V.)(K 2 -  bb t  +  2  b ) +k)  -k) 2  - c - 100) - fc(a, - C j ) = 2  2  2  (  D Q  2  0  >  0  (from (20)),  '  we have  s*.  <  0  iff  [ b  + V  1  ) [ V  l  - b  2  )  2  +  k  2  < 0  iff  a n d we t h u s o b t a i n the following result,  Result  1 1 .  T h e necessary a n d sufficient c o n d i t i o n for J a p a n to adopt an o p t i m a l export tax, rather than  an o p t i m a l e x p o r t subsidy, is that the domestic firms behave sufficiently c o m p e t i t i v e l y in e x p o r t i n g  activities  such t h a t c o n d i t i o n (63) holds.  In the C o u r n o t case, V,- = 6,/n,-, a n d c o n d i t i o n (63) is thus equivalent to  (n, + l)6,fr »  2  >  [  n  i  +  1  )  M  2  _  n  2  i  k  2  ( ) 64  Obviously, (n, + 1)6,6 (rc, + 1)6, 6  2  2  - n,  > 1. k  2  T h e r e f o r e , we derive the following corollary f r o m Result 11,  Corollary  3.  In the case of C o u r n o t c o n d u c t , the necessary a n d sufficient condition for J a p a n to adopt  an e x p o r t tax is that the n u m b e r of domestic necessary c o n d i t i o n for J a p a n to adopt  firms is so large that c o n d i t i o n (64) h o l d s .  an export t a x is that the n u m b e r of the domestic  In particular, firms  a  is greater  than one.  W h e n there is only one domestic  firm,  an export subsidy is often desirable for an e x p o r t i n g  country  ( B r a n d e r a n d Spencer (1985)). So if firms' rivalry is along the C o u r n o t line, the o p t i m a l trade policy for an  37  e x p o r t i n g c o u n t r y changes f r o m an e x p o r t subsidy to an export tax as the n u m b e r of domestic firms increase f r o m one to such a level that c o n d i t i o n (64) holds. S i m i l a r results have been p r o v i d e d by D i x i t (1984).  If the d e m a n d p a r a m e t e r s are estimated 2(c  2  + 100), or P  2 0  —c  2  using eqs. (10)-(14),  it can be easily shown that if P  < c + 200, t h e n c o n d i t i o n (63) holds a n d therefore s 2  2  m  <  < 0. So if the price charged by  the domestic firms does not deviate f r o m their m a r g i n a l cost significantly, an export tax would be o p t i m a l for J a p a n . T h i s is certainly the case for the U . S . car m a r k e t in 1979 and 1980.  Result  11 also confirms the analysis of E a t o n a n d G r o s s m a n (1986) in that when h o m e firms fail to  collude a m o n g themselves in e x p o r t i n g , t h e h o m e c o u n t r y can gain by restricting e x p o r t s , a n d can do so by means of an e x p o r t t a x .  b) Effects on the U . S . welfare  N e x t consider the effects of an export subsidy (tax) by J a p a n on the U . S . welfare,  us  w  vs,  s w  S2)  (u{Q Q )  =  lt  3  -  P i Q i  P2Q2) +  -  (P> - c , ) Q , +  100Q  2  and d W  — dsn  u  s  dPn.  do,  = (Pi -  os  2  dQn  Q2-~ + as  2  1  0  0  " 7 ^  as  (65)  2  T h e first term implies that an export subsidy is h a r m f u l to U . S . because the U . S . f i r m s ' o u t p u t level would be lowered (from (59)) and the U . S . domestic distortion would therefore be worsened. T h e other two terms show the benefit of an export revenues.  s u b i d y to U . S . due to lower price of i m p o r t s (from (58)) a n d higher tariff  O n c e a g a i n , the effects of a Japanese export  J a p a n e s e export s u b s i d y .  38  tax on the U . S . welfare are opposite to those of a  Substituting s  2  of (62)  for s  2  in W  W  u  u  2  ( s *  s  [ s ) , we have  s  )  2  -  W  u  ( 0 )  s  =  $  -£(K s 6  +  2  K  7  (66)  )  where  K  6  K  7  =  (fc (6i + K , )  2  2  -  = |(6 (6i + K , ) 3  6,fc )(a 2  -  2  + 100(6! + IM((6, + K , ) ( 6  2  c  -  2  100)  + V) -  2U  2  -  -  6.A; ) >  0,  2  fc((6,6  - fc ) + V , ( 2 6 2  2  was shown in (63)  or (64),  2  k ) + Q 2  2 0  6 V 2  1  -  Q  w  W  u  s  { 0 )  )  k + 100(6, + V , ) ) , a n d if the d e m a n d  a positive s ,  e  and K  are positive in this case.  7  i.e., an o p t i m a l e x p o r t subsidy, c o u l d be justified if the  2  d o m e s t i c (Japanese) firms are able to behave rather collusive. If this is the case, than  Cl  2  p a r a m e t e r s are e s t i m a t e d u s i n g eqs. (10)-(14), then K-, > 0. T h u s , b o t h K  As  + K ))(o, -  2  fc ).  2  A p p e n d i x 7 shows that A > = I > ( C ? ( 6 , 6  -  2  W  u  s  [ s  2  )  would be greater  (from (66)). In other wards, b o t h countries can gain f r o m the J a p a n e s e s u b s i d y policy.  In most situations, however, an export tax would be e x p e c t e d .  T h i s is because, as has been shown, if  there are several h o m e firms e n g a g i n g in e x p o r t i n g , it is generally desirable to increase t h e i r tacit collusion with one a n o t h e r .  When s  W  u  s  2  is negative, we have  ( s *  2  ) - W  u  s  ( 0 ) =  S  ^ ( K  6  S  ;  +  K  7  )  >  0  iff  ( -  S  2  ) > ^ .  A  U  6  In w o r d s , b o t h countries would gain f r o m the Japanese export tax if and only if ( — s ) > 2  Table  4  t  s  inserted  KJ/KQ.  here.  T a b l e 4 shows the results w h e n U . S . takes the status quo while J a p a n pursues the o p t i m a l export policy, u s i n g d a t a for 1979  and 1980.  A s was p r e d i c t e d , an o p t i m a l tax is i m p l i e d . T h e tax rates are quite sizable:  39  Table 4 U.S. holds the status quo policy and Japan pursues policy  an optimal export  1979  1980  Laissezfaire  Optimal export subs idy  Laissezfaire  Optimal export subsidy  0  -1005  0  -1109  Pi $  5951  5962  6407  6417  P  $  4000  4813  4130  5135  million  8.341  8.511  6.581  6.811  Q2 m i l l i o n  1.546  0.955  1.819  1.003  $billion  0.773  0.295  0.418  0.127  $billion  4.596  4.786  2.020  2.164  27.91  26.80  24.84  23.35  155  95  182  100  0  -0.959  0  -1.112  32.66  31.68  27.04  25.61  0.773  1.254  0.418  1.239  Gain over L a i s s e z - f a i r e $raillion U.S.  0  -980  0  -1430  Japan  0  481  0  821  S *  $/car  2  Qi  2  Japan p r o f i t U.S. p r o f i t  U.S. Consu. S u r p l .  $billion  U.S. T a r i f f Rev. $ r a i l l i o n Japan Subsidy Cost U.S. W e l f a r e Japan W e l f a r e  $billion  $billion Sbillion  40  a b o u t 30% expressed relative to the m a r g i n a l cost of J a p a n e s e firms. B y levying the tax J a p a n could achieve a significant welfare gain: a 62% a n d a 200% increase in its welfare for 1979 and 1980 respectively. M o s t of the gains is a t t r i b u t e d to the tax revenues.  O n the other h a n d , U . S . c o u l d suffer losses as the result of the  J a p a n e s e e x p o r t tax: about one billion dollar for 1979 a n d 1.4 billion for 1980. M o s t of the losses is in the f o r m of the depressing U . S . c o n s u m e r surplus. F i n a l l y , a c o m p a r i s o n of the results between the two years suggests that the more c o m p e t i t i v e the market is a n d in p a r t i c u l a r , the more c o m p e t i t i v e the J a p a n e s e firms are a m o n g themselves, the more effective the export tax would be for J a p a n .  2)  B o t h U.S.  and Japan  are active  in policy-making  W h a t h a p p e n s if b o t h governments are active in p o l i c y - m a k i n g ?  W e would examine the n o n - c o o p e r a t i v e  N a s h e q u i l i b r i u m in tariff a n d / o r subsidy for U . S . a n d J a p a n in which each country is assumed to choose its p o l i c y p a r a m e t e r s given those of the other country. A s discussed earlier, the e q u i l i b r i u m quantities and prices can be d e t e r m i n e d by eqs. (3), (4), (16), a n d (55),  Pi  P  Pi  P  2  -  2  =  <*i  =  a  2  -  b i Q i  -  k Q  - c , +s,  c  2  -  ti  +  -  -  x  b  k Q  2  (3)  Q  2  (4)  2  =0  - Q x V ,  s  2  +  Q  2  V  2  (16)  =  0  (55)  where the aggregate versions of conjectural variations are d e t e r m i n e d using the actual quantites ( Q i o , Q o ) , 2  prices  ( P m , P  2  o ) ,  a n d tariff and subsidy figures (tj = 1 0 0 , 6 ! = 0,  s  2  =  0). ( < i , S i ; s ) = ( 1 0 0 , 0 , 0 ) is referred 2  to as the status q u o a n d is to be c o m p a r e d with the N a s h e q u i l i b r i u m tariff a n d subsidy. T h e U . S . welfare  41  f u n c t i o n is W  u  s  =  =  W  u  s  ( t  , s  l  { U ( Q i , Q  l  s  ]  2  )  ) - P  2  l  Q  - P  i  2  Q  2  )  +  - c ,  (Pi  + s  l  ) Q  l  ( t  +  1  Q  2  - s  1  Q  1  ) .  W h e n b o t h ti a n d Si c a n be o p t i m a l l y chosen by the U . S . g o v e r n m e n t , t h e first-order conditions are,  us  d W  dti  us  d W  = 0 :  = 0  H i t !  +  H  2  S  l  +  H  3  s  2  =  G ,  (67)  +  H  b  S  l  +  H  6  s  2  =  G  (68)  2  dsi  Since t h e expressions of parameters  H i a n d G , are not very i n f o r m a t i v e in the current context, they will  be given in A p p e n d i x 8. E q s . (67) a n d (68) define t h e U . S . best-response functions for each export tax s  2  chosen by J a p a n .  T h e J a p a n e s e welfare f u n c t i o n is  d W  J  A  —  = o s  Hi  and G  3  P  0  :  Hjtx  +  //  8  s,  +  H  9  s  2  =  G  3  (69)  2  are given in A p p e n d i x 8. E q . (69) defines the Japanese best-response function for each pair of  tariff a n d s u b s i d y  ( < i , S i )  chosen by the U . S . g o v e r n m e n t .  S o l v i n g eqs. (67), (68), a n d (69) simultaneously using C r a m e r ' s rule gives the n o n - c o o p e r a t i v e N a s h e q u i l i b r i u m in tariff a n d subsidy for U . S . and J a p a n .  T h e cases, where only one of the two U . S . policy i n s t r u m e n t s is available, c a n be similarly analysed.  (i) If only the tariff i n s t r u m e n t is available, then eq. (67) w i t h S j = 0 gives the U . S . best-response function,  #,t,  +  H  3  42  s  2  =  G ,  (70)  whereas eq. (69)  w i t h S i = 0 gives the Japanese best-response f u n c t i o n ,  ff *i + 7  Figure  2  is  H  s  9  =  2  G  (71)  3  inserted  here.  F i g u r e 2 is d e p i c t e d using 1979 d a t a for the U.S. car m a r k e t . It can be seen from the figure that b o t h best-response f u n c t i o n s are u p w a r d sloping, suggesting certain relations between tariffs and export subsidies (for example, c o u n t e r v a i l i n g is usually desirable to a c o u n t r y ) . A s J a p a n switches f r o m s u b s i d i z i n g to t a x i n g e x p o r t s , U.S. should reduce the tariff rates. A s U.S. raises the tariff rates, J a p a n should reduce its tax rates on e x p o r t s .  W i t h different slopes, the intersection indicates the N a s h e q u i l i b r i u m in tariff by U.S. and export  subsidy (tax)  by J a p a n .  (ii) If only the p r o d u c t i o n subsidy i n s t r u m e n t is available for U.S., then eq. (68)  with t  x  = 0 gives the  U.S. best-response f u n c t i o n ,  H  whereas eq. (69)  +  H  6  s  2  =  G  (72)  2  w i t h t = 0 gives the Japanese best-response f u n c t i o n , x  H  The  s i  5  8  S  +  l  H  9  s  2  =  G  (73)  3  N a s h e q u i l i b r i u m i n s u b s i d y / s u b s i d y for U.S. and J a p a n is the solution of eqs. (72)  Figure  S  is  inserted  F i g u r e 3 is d e p i c t e d using the same d a t a as in F i g u r e 2.  and  (73).  here.  It can be seen from Figure 3 that S i and s  2  are almost i n d e p e n d e n t with each other. T h e U.S. government can choose its o p t i m a l p r o d u c t i o n subsidies  43  Figure  2  The best-response f u n c t i o n of U.S. using tarriffs ( t ^ ) and t h e best-response f u n c t i o n of Japan using export s u b s i d i e s (s >. 2  U.S.  best-response function  1  0  1 1 1  1 1  1  t Japan  best-response funct ion  F i g u r e 4: The best-response f u n c t i o n of U.S. using production s u b s i d i e s ( s ^ ) and the bestresponse f u n c t i o n of Japan using e x p o r t subsidies ( s ) • 2  44  w i t h o u t referring very m u c h to the J a p a n e s e export subsidy levels.  In this e x a m p l e the U . S . o p t i m a l pro-  d u c t i o n s u b s i d y is r a t h e r stable in the sense that it won't change m u c h under the J a p a n e s e p u r s u i t of the optimal policy.  N e x t , we e x a m i n e the n u m e r i c a l results f r o m this two-active-player  m o d e l , called M o d e l 2 , and compare  t h e m with the results f r o m the m o d e l in which only U . S . is active in p o l i c y - m a k i n g . T h e latter m o d e l is to be referred to as M o d e l 2 . T a b l e 5 and 6 are the r e p r o d u c t i o n s of T a b l e 5 and 4 , respectively, of D i x i t ( 1 9 8 5 ) using M o d e l 1 ( N o t e 3 ) . T a b l e 7 and 8 are the c o r r e s p o n d i n g results f r o m M o d e l 2 .  T h e following T a b l e 9 are taken f r o m T a b l e 5 and T a b l e 7 where 1 9 7 9 d a t a are used.  Table  9  is  inserted  here.  F r o m M o d e l 1 to M o d e l 2 , the o p t i m a l tariff rate falls by 2 4 % while the o p t i m a l subsidy falls by only 2%.  In the o p t i m a l tariff and subsidy case, the tariff c o m p o n e n t falls from t** = 4 0 7 . 9 to t** = 2 6 8 . 0 while  the subsidy c o m p o n e n t  rises slightly.  A s the result, the ratio of two c o m p o n e n t s ,  o p t i m a l policy package falls significantly: f r o m <**/s** = 6 7 % in M o d e l 1 to t j * / i * s  tariff vs. =  4  3  subsidy, in an  % in M o d e l 2 . T h i s  c o m p a r i s o n d e m o n s t r a t e s that if J a p a n is also assumed to be active in p o l i c y - m a k i n g , the tariff rate may be even f u r t h e r less significant t h a n the p r o d u c t i o n subsidy level for the U . S . auto i n d u s t r y .  Table  1 0  is  inserted  here.  O n e o b v i o u s observation from T a b l e 1 0 is that the U . S . welfare in the N a s h e q u i l i b r i a would be below the level in the status quo where J a p a n is assumed sizable.  to take a laissez-faire  position.  T h e U . S . losses are  T h u s , allowing J a p a n to pursue profit-shifting policy reverses the previous result of positive U . S .  welfare gains f r o m the o p t i m a l policies over complete laissez-faire or status quo shown in M o d e l 1. O n the J a p a n e s e side, however, J a p a n would gain from an o p t i m a l e x p o r t tax over the status quo no m a t t e r what the U . S . policies are.  It would gain most if U . S . takes complete laissez-faire  and least if U . S . chooses b o t h  tariff and s u b s i d y o p t i m a l l y . T h u s , J a p a n clearly has an incentive to pursue this w e l f a r e - i m p r o v i n g policy. T o reduce losses, U . S . also wants to use tariff a n d / o r subsidy.  45  (Part  1)  TABLE 5 POLICY CALCULATIONS FOR THE CENTRAL CASE, 1979 (ONLY US IS ACTIVE IN POLICY-MAKING) MFN-TARI OPT-TARI OPT-SUBS  OPT-TS  T 570.7 407 .9 100 0 S 0 0 670.3 611.0 P1 5951 5956 5342 5400 P2 4381 3882 4216 4000 8341000 8420823 9262589 9248688 01 02 1546000 12689G0 1491184 1261168 JAPAN PROFIT 7.730E8 5.208E8 7. 192E8 5. 144E8 US PROFIT 4.596E9 4.684E9 5.668E9 5.651E9 US CONS SURPL 2.791E10 2.733E10 3.345E10 3.245E10 TARI REV 1.546E8 7.242E8 0 5.144E8 SUBS COST O 0 6.209E9 5.651E9 US WELFARE 3.266E10 3.274E 10 3.291E10 3.297E10 GAIN OVER MFN ($mill1on) 251 U.S. 78 307 0 JAPAN -54 -259 0 -252  TABLE 6 POLICY CALCULATIONS FOR THE CENTRAL CASE, 1980 (ONLY US IS ACTIVE IN POLICY-MAKING) MFN-TARI OPT-TARI OPT-SUBS T  s  P1 P2 01 02 JAPAN PROFIT US PROFIT US CONS SURPL TARI REV SUBS COST US WELFARE GAIN OVER MFN ($m1111on) U.S. JAPAN  OPT-TS  100 298 .4 211.1 0 367 .8 0 0 325.0 6407 6057 6100 6409 4130 4030 4222 4310 6581000 6622102 6970312 6966264 1819000 1672916 1816429 1669874 4.184E8 3.539E8 4.172E8 3.526E8 2.020E9 2.046E9 2.266E9 2.264E9 2.484E10 2.451E10 2.739E10 2.676E10 1.819E8 4.993E8 0 3.526E8 0 0 2.564E9 2.264E9 2.704E10 2.706E10 2.709E10 2.711E10 0 0  16 -65  52 -1  69 -66  TABLE 7 NASH EQUILIBRIA IN TARIFF / SUBSIDY FOR THE CENTRAL C A S E , (BOTH US AND JAPAN ARE ACTIVE IN POLICY-MAKING) STATUS-QUO OPT-TARI OPT-SUBS  1979  OPT-TS  T1 100 432.4 0 268.0 S1 0 0 657.7 620.0 S2 0 -877.4 -970.3 -871.9 P1 5951 5965 5364 5400 P2 4000 4979 4669 4808 01 8 3 4 1 0 0 0 8546167 9409525 9385496 02 1546000 833932 922212 828736 JAPAN PROFIT 7.730E8 2.249E8 2.751E8 2.221E8 US PROFIT 4.596E9 4.825E9 5.849E9 5.819E9 US CONS SURPL 2.791E10 2.663E10 3.230E10 3.183E10 TARI REV 1.546E8 3.606E8 0 2.221E8 US SUBS COST 0 0 6.189E9 5.819E9 JAPAN SUBS COST 0 -7.317E8 -8.948E8 -7.226E8 US WELFARE 3.266E10 3.182E10 3.196E10 3.206E10 JAPAN WELFARE 7.730E8 9.566E8 1.170E9 9.447E8 GAIN OVER STATUS QUO ($mi11 i o n ) US 0 -840 -700 -600 JAPAN 0 184 397 172  TABLE 8 NASH EQUILIBRIA IN TARIFF / SUBSIDY FOR THE CENTRAL C A S E , (BOTH US AND JAPAN ARE ACTIVE IN POLICY-MAKING) STATUS-QUO OPT-TARI OPT-SUBS  1980  OPT-TS  T1 210.7 100 0 120.9 S1 0 0 359.0 334.8 S2 0 -1059 - 1 108 -1057 P1 6407 6418 6076 6100 P2 4130 5191 5035 5099 Q1 6 5 8 1 0 0 0 6823268 7189954 7177489 Q2 1819000 957926 1002442 956132 JAPAN PROFIT 4 . 184E8 1.160E8 1.271E8 1 . 156E8 US PROFIT 2.020E9 2.172E9 2.412E9 2.403E9 US CONS SURPL 2.484E10 2.329E10 2.584E10 2.561E10 TARI REV 1.819E8 2.018E8 0 1.156E8 US SUBS COST 0 0 2 . 581E9 2 . 4 0 3 E 9 JAPAN SUBS COST 0 - 1 . 0 1 4 E 9 - 1 . 1 1 1E9 - 1 . 0 1 1 E 9 US WELFARE 2.704E10 2.566E10 2.567E10 2 .572E10 JAPAN WELFARE 4.184E8 1.130E9 1.238E9 1 . 126E9 GAIN OVER STATUS QUO ($mi11 i o n ) US 0 -1380 -1370 -1320 JAPAN 0 712 820 708  Table 9 The optimal tariff and subsidy rates in the two models Model 1  Model 2  the o p t i m a l tariff  t*  = 570. 7  ti*  - 432.4  the o p t i m a l subsidy  s* - 670. 3  si*  - 657.7  tt**  - 268.0  S i * *  - 620.0  the o p t i m a l t a r i f f and subsidy  t**  = 407. 9  s**  a  661. 0  Table 10 Welfare gains in Model 2, 1979 >  Laissezfaire (0,0)  U.S. p o l i c y ^ ^ ^ C o n f iguration ^ ^ ^ ( t i . S i )  Gains over s t a t u s quo U.S. Japan  MFNTARI (100,0)  the o p t i mal subsidy (0, *) S 1  the o p t i - the o p t i mal t a r i f f mal t a r i f f and sub (ti*,.0> sidy  — ^  $million $million  ^ -1030  -980  -700  -840  -600  578  481  397  184  172  48  It is also f o u n d in T a b l e 10 that the U . S . o p t i m a l subsidy policy would be preferred by b o t h countries to the U . S . o p t i m a l tariff p o l i c y if only one of t h e m can be i m p l e m e n t e d . C o m p a r e d to the tariff, the subsidy would b r i n g less losses t o U . S . whereas more gains to J a p a n .  F i n a l l y , the welfare c o m p a r i s o n s in M o d e l 2 between 1979 a n d 1980 ( T a b l e 7 a n d 8) clearly show t h a t the more c o m p e t i t i v e the market is a n d in p a r t i c u l a r , the more c o m p e t i t i v e the Japanese firms are with one a n o t h e r , the more J a p a n w o u l d gain by t a x i n g e x p o r t s , a n d the more U . S . would lose. F u r t h e r , the Japanese gain is at the expense of the U . S . welfare, especially of the U . S . cousumer s u r p l u s . So for the two countries as w h o l e , it is p o s s i b l e that only loss is left.  If policies c o u l d be chosen to m a x i m i z e the joint welfare, b o t h countries m a y be better off. In other words, ti, S i , a n d s  2  are to be chosen to m a x i m i z e the joint welfare W  W  Since t  t  (ti  J  =  u s  w  +  is the tariff on J a p a n e s e firms by U . S . a n d s  2  d W  J  = 0 and  / d t \  d W  J  J  [ti,  S j , s ), 2  (74)  is the export  — s ) is the t o t a l tax on the Japanese firms, a n d < i and s  maximizing framework. Setting  = W  J A P  w  2  J  subsidy to Japanese firms by J a p a n ,  are actually one variable in this jointly  2  = 0 gives  / d s i  #io(<i - s ) + HuSi 2  = G  4  (75)  and  H i  A g a i n , the expressions of Hi  2  { t i  -  s ) 2  -I-  B  1  3  s  l  =  G  5  (76)  a n d G,- are given in A p p e n d i x 8. T h e o p t i m a l tax o n the Japanese firms by  both g o v e r n m e n t s , ( < i — s ) , a n d the o p t i m a l subsidy to the U . S . firms by the U . S . government, J  2  49  , can be  f o u n d by s o l v i n g eqs. (75)  and (76)  s i m u l t a n e o u s l y . For our p a r t i c u l a r cases at h a n d , we have  1979  :  (t, -  s )  J  = -600.5,  1980  :  (<! -  s )  J  = -254.6,  2  2  s( =  598.5;  = 320.2.  T h a t is, the j o i n t l y o p t i m a l policy involves subsidies to b o t h U . S . and Japanese firms. T h e U . S . firms are s u b s i d i z e d by the U . S . government while the J a p a n e s e firms are either subsidized by b o t h governments, or s u b s i d i z e d by one g o v e r n m e n t and t a x e d by the other. and P  2  =  c. 2  A s the result of this jointly o p t i m a l policy, P  x  — Ci  T h e r e f o r e , the firms are subsidized sufficiently to b r i n g their prices in line with the true  m a r g i n a l costs to solve b o t h domestic and foreign m o n o p o l y p r o b l e m s . It is also worth n o t i n g that complete laissez-faire is n o r m a l l y not jointly o p t i m a l in the oligopolistic market.  Table  Changing t  x  and s  2  11  is  inserted  here.  while keeping their difference at the o p t i m a l level [t  e q u i l i b r i u m quantities and prices, and therefore  x  — s ) 2  J  would leave  the  the o p t i m a l value of joint welfare, u n c h a n g e d , and would  merely transfer revenues f r o m one c o u n t r y to the other. In particular, a fall (rise) of s  2  will raise (lower) the  J a p a n e s e welfare a n d lower (raise) the U . S . welfare. In our framework, the less J a p a n subsidizes its firms, the m o r e U . S . would subsidize the J a p a n e s e firms in this framework, and hence the h i g h e r (lower) the Japanese ( U . S . ) welfare.  C o n s i d e r the case in w h i c h U . S . can use b o t h a tariff and a p r o d u c t i o n subsidy and J a p a n can use an export tax.  Because J a p a n can secure itself a payoff of $.945 billion by p l a y i n g the game non-cooperatively  (see T a b l e 11), to be willing to play the game cooperatively, J a p a n must at least obtain a $.945 billion payoff. In our c o o p e r a t i v e game, the most J a p a n is willing to subsidize its firms is s to a ti '=  2  = $91.75 per car, corresponding  —$508.8 per car U . S . subsidy on the Japanese firms. In this case J a p a n gains nothing over the  non-cooperative outcome.  T h i s h a p p e n s at point B in F i g u r e 4.  50  S i m i l a r analysis applies to the U . S . side:  Table  11  W e l f a r e e f f e c t s o f j o i n t l y optimal t a r i f f >v  Policy State  Status Quo  The Opt'l Subsidy  The Opt'l tariff  Wel-Nv  fare State  >v  and subsidy  schedule,  The J o i n t l y optimal Opt'l t a r i f f and subsidy tariff and t j[»> tl" tl" Sub-508.8 -897.0 -600.5 -703.1 s s = sidy S 2 = s = 0 (OPT-TS) 91.75 -296.5 -102.6 Nash Solution 2  2  j  1979  2  U.S. Welfare $billion  32.66  31.82  31.96  32.06  32.78  32.06  32.61  32.42  Jap. Welfare $billion  .773  .957  1.170  .945  .945  1.665  1.115  1.305  33.43  32.77  33.13  33.01  33.73  33.73  33.73  33.73  Joint Welfare $billion  Japan g a i n over OPT-TS ( $ r a i l l i o n )  _ J u l /  ^  / e—  >v  1  1  \  \  0  A.  1  10  .  u.s ($million)  Figure 4 A b a r g a i n i n g game 51  the most U . S . is w i l l i n g to subsidize the Japanese firms is t = —$897 per car, c o r r e s p o n d i n g to a Japanese x  e x p o r t tax s  2  = —$296.5 per car on the J a p a n e s e firms. O f the $897 U . S . subsidy for each car, $296.5 will  be i n d e e d a c c r u e d to the J a p a n e s e government. T h i s occurs at p o i n t A in F i g u r e 4.  Figure  It is noted that when t  t  solution:  =  —600.5 a n d s  4  2  is  =  inserted  here.  0, both countries would gain over the n o n - c o o p e r a t i v e  U . S . gains a t o t a l of $550 m i l l i o n a n d J a p a n  $170 m i l l i o n (point C in F i g u r e 4).  B u t the N a s h  s o l u t i o n to this b a r g a i n i n g game is at point N in w h i c h b o t h countries achieve the same a m o u n t of gains. In this N a s h s o l u t i o n , U . S . would subsidize the Japanese firms $703.1 p e r car a n d J a p a n w o u l d tax its firms $102.6 p e r car.  In other words, that part of subsidies b e y o n d $600.5 per car would go to the Japanese  g o v e r n m e n t , w h i c h is a k i n d of side p a y m e n t s .  E v e n t h o u g h b o t h countries can be better off by c o o p e r a t i o n , each has an incentive to pursue its own o p t i m a l policies. If the game is played only once, t h e n the self-interest pursuit by each country would lead to a p o o r o u t c o m e for b o t h .  6. CONCLUDING REMARKS C u r r e n t research on t r a d e policy in the oligopolistic i n t e r n a t i o n a l markets has indicated t h a t intervention w i t h free trade can be beneficial to a country. M a n y theoretical models have been developed in the literature, b u t the a m o u n t of e m p i r i c a l work is rather s m a l l . E m p i r i c a l work is needed in the design of industry-specific trade policies.  In p r a c t i c e ,  we are interested  in not only whether government  intervention can raise the  n a t i o n a l welfare, b u t also how large the policy gains would be. D i x i t ' s work (1985) is essentially an analysis of s i m u l a t i o n m o d e l s a n d is i m p o r t a n t The  technique  in its a t t e m p t to apply new trade theories to a specific industry.  used in D i x i t ' s p a p e r may also have i m p l i c a t i o n s in other similar projects.  s h o r t c o m i n g s of the a n a l y t i c a l m e t h o d has been noted in D i x i t (1985). considered as an i m p o r t a n t research topic.  52  T h e possible  T o try to i m p r o v e the m e t h o d is  It is shown in D i x i t (1985) that U . S . can achieve, although not very impressive, welfare gains by using o p t i m a l interventionist policies in the U . S . a u t o m o b i l e i n d u s t r y , given that J a p a n takes laissez-faire.  This  p a p e r shows t h a t allowing J a p a n to simultaneously p u r s u e o p t i m a l policies can change the result and U . S . m a y suffer sizable welfare losses. M o r e o v e r , J a p a n does have an incentive to pursue the profit-shifting policy. T h u s , the U . S . p o l i c y gains are not at all a u t o m a t i c . Nevertheless, U . S . would suffer more losses if unilaterally a d o p t i n g laissez-faire. It is shown in the p a p e r that b o t h countries w o u l d nonetheless be better off if they c o u l d c o o p e r a t i v e l y choose the policy parameters to m a x i m i z e the joint welfare r a t h e r t h a n non-cooperatively p u r s u e their own o p t i m a l policies. T h e cooperative a p p r o a c h may, however, meet difficulties in real w o r l d . For i n s t a n c e , the countries in a b a r g a i n i n g game m a y be unable to agree on a schedule of revenue division between t h e m . T h a t agreements between nations are enforceable is often a q u e s t i o n . T h e t h i r d party m a y be not sufficiently a u t h o r i t a t i v e or m a y s i m p l y not exist.  F o r these reasons, it m a y be more interesting to  seek a l t e r n a t i v e models in w h i c h cooperation emerges in a tacit fashion between countries. F o r example, the use of repetition or i n c o m p l e t e i n f o r m a t i o n m a y be c o n s i d e r e d .  A n o t h e r question w h i c h is of interest in the design of i n d u s t r y - s p e c i f i c trade policies is whether interv e n t i o n i s t trade policies are the first-best policies, a n d when other policy i n s t r u m e n t s w o u l d achieve same  aims more efficiently.  the  B y working on the U . S . auto industry, D i x i t finds that the role of domestic  a n t i t r u s t policies or p r o d u c t i o n subsidies is q u a n t i t a t i v e l y more significant and more efficient t h a n the role of tariffs. B y using a slightly different m o d e l in this p a p e r , we find that the relative i m p o r t a n c e and efficiency of tariffs and p r o d u c t i o n subsidies are related to the m a r k e t structure, that is, whether the domestic firms' c o n d u c t exerts more effects on the market e q u i l i b r i u m t h a n the foreign f i r m s ' . W h e n the domestic (foreign) f i r m s ' c o n d u c t has more significant effects t h a n the foreign (foreign) firms', the policy is usually directed by the d o m e s t i c (foreign) f i r m s ' m o n o p o l y in the m a r k e t , and a p r o d u c t i o n s u b s i d y (a tariff) is usually more i m p o r t a n t and more efficient t h a n a tariff (a p r o d u c t i o n s u b s i d y ) .  Besides inaccurate i n f o r m a t i o n discussed earlier, information a s y m m e t r y m a y also cast problems in the design of good policies. T h i s is in t u r n related to m o d e l i n g methods in the strategic trade p o l i c y literature.  53  T h e basic p r o b l e m in strategic trade p o l i c y concerns strategic interactions in i n t e r n a t i o n a l trade.  Conven-  t i o n a l t r a d e theory treats all i n d i v i d u a l firms in an i n d u s t r y as price-takers. T h e new trade theory introduces the strategic interaction a m o n g firms in an i m p e r f e c t l y c o m p e t i t i v e international m a r k e t . T h i s new a p p r o a c h to t r a d e p o l i c y usually assumes a sequential structure of the trade g a m e : governments interact a m o n g t h e m selves in the first stage whereas oligopolistic firms, taking g o v e r n m e n t s ' policies as given, interact themselves in the second stage. t h a t between firms at another.  among  In other words, the interaction between governments is at one level while It is possible, however, that one c o u n t r y ' s firms m a y strategically  w i t h a n o t h e r c o u n t r y ' s government a n d / o r their own government.  interact  In D i x i t (1985), the U . S . government's  objective is to m a x i m i z e the U . S . social welfare whereas the objective of the group of J a p a n e s e firms is to m a x i m i z e their own profit. W h e n the J a p a n e s e government adopts complete laissez-faire and the U . S . gove r n m e n t pursues the o p t i m a l policies, U . S . would achieve a welfare gain over the status quo and the Japanese firms  w o u l d suffer a loss, as was shown in T a b l e 5 and 6.  B u t the results in T a b l e 5 and 6 are based on  one of i n f o r m a t i o n a l a s s u m p t i o n , namely the U . S . government has complete i n f o r m a t i o n about the Japanese f i r m s ' cost or at least has the same i n f o r m a t i o n about cost as do the firms. T h i s a s s u m p t i o n is unlikely to be met in reality, since the Japanese firms would be expected to have better information a b o u t their cost t h a n w o u l d t h e U . S . g o v e r n m e n t . A s a result of i n f o r m a t i o n a s y m m e t r y , the Japanese firms m a y collectively have an i n c e n t i v e to conceal cost i n f o r m a t i o n or reveal w r o n g i n f o r m a t i o n in order to pursue their self-interests. T h e strategic use of i n f o r m a t i o n by the J a p a n e s e firms may significantly change the U . S . o p t i m a l policies as well as the design of policies itself. A s a p r a c t i c a l m a t t e r this may presumably make the design of good policies m o r e difficult. It s h o u l d be noted that the t y p e of interaction between the Japanese firms and the U . S . g o v e r n m e n t is n o r m a l l y different f r o m that between a m u l t i n a t i o n a l enterprise and the host government. T h e l a t t e r is the interaction c o n d u c t e d in the host country with foreign direct investment, while the former is the i n t e r a c t i o n c o n d u c t e d in an i n t e r n a t i o n a l e n v i r o n m e n t with trade.  Similarly, the U . S . firms may also  have an incentive to strategically use their cost i n f o r m a t i o n in order to receive a more favorable policy f r o m their g o v e r n m e n t . E x a m i n i n g this incomplete i n f o r m a t i o n game, in which interaction between firms, between  54  g o v e r n m e n t s , a n d between firms and g o v e r n m e n t s are considered, m a y be an interesting area needing f u r t h e r research.  55  PART 2  A SEQUENTIAL ENTRY-EXIT  MODEL  OF I N T E R N A T I O N A L T R A D E  56  1. INTRODUCTION T h e purpose of this p a p e r is to examine f i r m s ' strategic b e h a v i o u r in i n t e r n a t i o n a l market share rivalry as well as its effects on trade p a t t e r n s and p r o d u c t veriety by u s i n g a sequential entry-exit m o d e l of trade. It is observed in an i n d u s t r y that an i n c u m b e n t firm may w i t h d r a w some p r o d u c t s to prevent c o m p e t i t i o n with an a c t u a l entrant from r e d u c i n g profits on other p r o d u c t s . In other words, a m u l t i p r o d u c t i n c u m b e n t m a y exit in response to entry. foreign entrant,  S u c h a reaction would make entry through trade more a t t r a c t i v e to a pontential  a n d invasion is hence more likely to succeed.  A s trade is o p e n e d , the k i n d of interaction  between firms in different countries may thus have an i m p a c t on the type of trade p a t t e r n emerging as well as p r o d u c t variety of c o n s u m p t i o n . In the recently growing literature on trade w i t h imperfect c o m p e t i t i o n , however, there seems no m o d e l which deals with the possible firms' exit in an i n t e r n a t i o n a l rivalry.  This  p a p e r intends to do an exploration of models of i n t e r n a t i o n a l trade by allowing firms to exit in response to entry.  T h e p a p e r models an i n d u s t r y consisting of two firms, each in a different c o u n t r y .  T h e two firms are  a s s u m e d to be able to p o t e n t i a l l y p r o d u c e and export two imperfectly substitutable p r o d u c t s , and may exit f r o m either the h o m e market or the foreign market in response to an entry. to m a k e their entry, exit, and p r o d u c t i o n (quantity, price, etc.) choose separately  these strategy variables for each country.  T h e s e firms are also assumed  decisions sequentially, a n d to be able to  W e examine two four-stage games.  T h e first of  t h e m is the basic case in which the two firms are in a s y m m e t r i c p o s i t i o n : at the first stage, they have equal o p p o r t u n i t y to enter their h o m e markets; at the second stage, they have equal o p p o r t u n i t y to invade the foreign markets; at the t h i r d stage, they make exit choices simultaneously; and at the last stage, they engage in c o m p e t i t i o n in the final i n t e r n a t i o n a l e n v i r o n m e n t . T h e second game differs f r o m the first one in that one of the firms is now able to move first and has the option to enter both p r o d u c t s in b o t h home and foreign m a r k e t s , and at the second stage, the other firm makes entry decisions in b o t h home and foreign markets.  57  T h e c o n s t r u c t e d m o d e l is based on the recent work by J u d d (1985) where s p a t i a l p r e e m p t i o n in a closed e c o n o m y is e x a m i n e d .  T h e sequential e q u i l i b r i u m concept used by J u d d is s i m i l a r to that in Prescott a n d  V i s s c h e r (1977) a n d B r a n d e r a n d E a t o n (1984). B u t in J u d d ' s m o d e l , a f i r m is allowed to exit in response to a rival's entry w h i l e in the other two p a p e r s , an irreversable location or p r o d u c t line decision constitutes a commitment.  J u d d thus d e m o n s t r a t e s  i m p o s s i b l e unless exit costs are h i g h . Lipsey  (1979),  that c r e d i b l e p r e e m p t i o n by a m u l t i p r o d u c t i n c u m b e n t may be  T h i s is in contrast to other papers such as, for example, E a t o n a n d  where exit costs are assumed p r o h i b i t i v e l y high a n d where an i n c u m b e n t firm m a y deter  entry i n t o substitutes by b e i n g the first firm to p r o d u c e t h e p r o d u c t s a n d by c r o w d i n g the p r o d u c t s p e c t r u m sufficiently to leave no niche for p o t e n t i a l  The Krugman  entrants.  work of this p a p e r is also related to the recent literature on trade u n d e r imperfect c o m p e t i t i o n . (1979,  1980,  1981), a n d H e l p m a n (1981),  a m o n g others,  c o m p e t i t i o n m o d e l which i n c o r p o r a t e s an increasing returns-to-scale  examine  t r a d e using a monopolistic  technology. T h e y assume that in equi-  l i b r i u m a n u m b e r of differentiated p r o d u c t s are p r o d u c e d by firms which possess m o n o p o l y power b u t earn no m o n o p o l y profits. A s p o i n t e d o u t by E a t o n a n d K i e r z k o w s k i (1984), using a zero-profit c o n d i t i o n to det e r m i n e e q u i l i b r i u m requires two a s s u m p t i o n s about the nature of the process whereby entry is d e t e r m i n e d : first, firms enter t a k i n g the prices of existing firms as g i v e n ; second, any fixed cost of entry is not a that is i n c u r r e d sequentially a n d irreversibly  before  sunk  cost  t h e p r i c i n g decision takes p l a c e . E a t o n a n d K i e r z k o w s k i  (1984) develop a m o d e l of i n d u s t r i a l structure where entry a n d price decisions are taken sequentially. T h i s sequential d e c i s i o n - m a k i n g is considered p a r t i c u l a r l y a p p r o p r i a t e in the i n t e r n a t i o n a l context a n d it follows in the t r a d i t i o n of L i n d e r (1961) a n d V e r n o n (1966).  P u r e profits can now exist in full e q u i l i b r i u m .  Since  firms select p r o d u c t s at the first stage a n d take price decision at the second stage, free entry no longer leads to average-cost p r i c i n g . F i r m s use p r o d u c t selection as a means of entry deterrence a n d an artificial m o n o p o l y m a y be established by an a p p r o p r i a t e p r o d u c t choice. O p e n i n g of trade may have an impact on the structure of an e c o n o m y even if actual trade does not m a t e r i a l i z e .  It is n o t e d , however, that in their m o d e l , once a  f i r m has chosen a p r o d u c t , there is no later chance to exit that p r o d u c t . F i n a l l y , B r a n d e r (1981)  58  constructs  a m o d e l in which there are two firms, each located in a different country.  H e shows that when the firms  choose separately their deliveries for each country, a C o u r n o t d u o p o l y can give rise to two-way trade even in i d e n t i c a l p r o d u c t s . B u t there is n o attempt to explain the firms' choice of p r o d u c t in B r a n d e r (1981).  B y c o n s i d e r i n g exit cost as a variable a n d allowing firms to exit in response to entry, we examine in this p a p e r  firms'  strategic  behavior in i n t e r n a t i o n a l market share rivalry a n d its effects on trade  and variety of c o n s u m p t i o n . firms'  T h r e e basic results of the p a p e r are as follows.  pattern  T h e first of t h e m is that  strategic b e h a v i o r can give rise to two-way trade in i d e n t i c a l p r o d u c t s w h i c h are, p e r h a p s surprisingly,  p r o d u c e d only for t r a d i n g to each other's countries. T h i s result is m o r e likely to hold as exit costs are low, as t r a n s p o r t costs are s m a l l , as the p r o d u c t s are better substitutes, a n d as c o m p e t i t i o n in identical p r o d u c t s is intense. T h e n o n - c o o p e r a t i v e solution to the p r o f i t - m a x m i z i n g p r o b l e m involves such a two-way trade, b u t each firm m a y be better off if they c o u l d agree not to invade each other's home m a r k e t s . T h e second issue a n a l y s e d concerns w h e t h e r trade, t h r o u g h i n t r a - i n d u s t r y trade, makes a greater variety of p r o d u c t s available to c o n s u m e r s .  O u r m o d e l gives mixed results on this issue.  W h e t h e r trade increases or decreases variety  d e p e n d s on the firms' payoffs of various final m a r k e t structures as well as the level of entry a n d exit  costs.  A change in p r o d u c t variety c a n be brought about by either an actual flow of trade or a p o t e n t i a l for trade. For a specific case, o p e n i n g of trade would u n a m b i g u o u s l y either increase or decrease variety. F i n a l l y , when one of the firms has t h e advantage of m o v i n g first, it may only enter more profitable p r o d u c t s a n d specialize in t h e m for b o t h d o m e s t i c a n d foreign markets, leaving other substitutable p r o d u c t s to the foreign entrant. T h u s specialization c a n be i n d e p e n d e n t l y caused by oligopolistic interaction between  firms.  T h e p a p e r is o r g a n i z e d as follows. Section 2 presents the basic m o d e l which is a four-stage game between a domestic i n c u m b e n t a n d a foreign entrant. play in the m o d e l is addressed.  T h e game is modified f r o m J u d d (1985).  T h e role exit costs  T h e unique subgame-perfect N a s h e q u i l i b r i u m of the game is d e t e r m i n e d  u n d e r a set of a s s u m p t i o n s on firms' payoffs, entry costs, a n d exit costs.  Section 3 then extends the basic  m o d e l into a t w o - c o u n t r y international e n v i r o n m e n t where the firms are.assumed to have equal o p p o r t u n i t y . T h e rivalry of firms m a y give rise to two-way t r a d e . B y changing the a s s u m p t i o n s on firms' payoffs, section  59  4 moves to the discussion of the issue c o n c e r n i n g whether trade will b r i n g about greater p r o d u c t Section 5 e x a m i n e s the implications of the m o d e l when one firm is able to move first.  variety.  T h e specialization  issue is addressed there. F i n a l l y , section 6 provides c o n c l u d i n g r e m a r k s .  It is n o t e d concerning  t h a t the results of the p a p e r depends crucially on several different sets of  firms'  assumptions  payoffs under various market structures as well as the level of entry and exit costs.  n a t u r e of p o s t - e n t r y  rivalry, whether it is in quantity, price, or s o m e t h i n g else, is not essential.  The  We show in  A p p e n d i x , however, that these sets of a s s u m p t i o n s are consistent with two c o m m o n d u o p o l y models, namely C o u r n o t and B e r t r a n d rivalry with linear d e m a n d .  2. A D O M E S T I C I N C U M B E N T A N D A F O R E I G N E N T R A N T  We first e x a m i n e the case of a domestic i n c u m b e n t and a foreign entrant in the home m a r k e t . can p o t e n t i a l l y p r o d u c e two imperfectly substitutable  Both  firms  goods, b e a r i n g the same fixed and u n i t p r o d u c t i o n  costs. Since the foreign firm bears e x t r a unit t r a n s p o r t costs, its m a r g i n a l costs are higher than those of the domestic  firm  p r o d u c i n g i d e n d i c a l p r o d u c t s by the positive a m o u n t of unit t r a n s p o r t costs.  Consequently,  the foreign firm is in a disadvantaged position in terms of payoffs. For instance, if b o t h firms end up selling the same p r o d u c t in the home market, then the home firm would earn higher profit than its foreign rival.  In such an e n v i r o n m e n t , it seems that entry could be effectively d e t e r r e d , as argued by several previous studies. If p o s t - e n t r y c o m p e t i t i o n is in price and there are no l i m i t a t i o n s on firms' p r o d u c t i o n capacity, the B e r t r a n d  e q u i l i b r i u m would yield a price which is equal to or slightly less than the foreign  m a r g i n a l cost, namely equal to m + c ,  unit p r o d u c t i o n cost (m)  plus unit t r a n s p o r t cost (t).  then  entrant's  If the e q u i l i b r i u m price is  the two firms will divide the market evenly and the foreign entrant earns zero profit; if the  e q u i l i b r i u m price is less than m + c  but greater t h a n m , the domestic i n c u m b e n t captures the whole market  whereas its foreign rival sells n o t h i n g . In the presence of fixed p r o d u c t i o n costs, the foreign firm would even suffer losses. O n the other h a n d , the home firm earns positive profit in either case because price exceeds its 60  m a r g i n a l cost m , and it would have no incentive to leave. Foreign entry would be irrational since post-entry profit c o u l d not at least cover the fixed entry cost. T h e i n c u m b e n t c o u l d therefore c o m m i t itself to stay by t h r e a t e n i n g the entrant w i t h intense post-entry c o m p e t i t i o n a n d deter potential entry by b e i n g first to enter both products.  H o w e v e r , it c o u l d be argued that in the case of a differentiated p r o d u c t m a r k e t , it m a y not be credible for a m u l t i p r o d u c t i n c u m b e n t to threaten an entrant with intense post-entry c o m p e t i t i o n .  In other words,  foreign entry would actually h a p p e n u n d e r suitable c o n d i t i o n s . We still take the B e r t r a n d price c o m p e t i t i o n as an e x a m p l e to illustrate the basic a r g u m e n t .  B u t here we make an a s s u m p t i o n of zero fixed p r o d u t i o n  costs. O u r previous discussion suggests t h a t post-entry profits would be zero for the foreign firm and positive for the h o m e  firm.  S u p p o s e that the h o m e firm initially is a t w o - p r o d u c t m o n o p o l i s t .  the foreign firm does then enter one of p r o d u c t s , say p r o d u c t 1.  T h e n the post-entry  S u p p o s e also that price c o m p e t i t i o n  would y i e l d smaller, t h o u g h p o s i t i v e , profit from p r o d u c t 1 for the i n c u m b e n t and zero profit for the entrant. F u r t h e r m o r e , the lower d u o p o l y price of p r o d u c t 1 would depress d e m a n d for its s u b s t i t u t e , p r o d u c t 2. T h e depressed d e m a n d for p r o d u c t 2 would result in a smaller profit from p r o d u c t 2 for the i n c u m b e n t .  A t this stage, the two firms are not in a s y m m e t r i c position in terms of the likelihood of exiting p r o d u c t 1.  T h e foreign entrant has no reason to exit since it earns nonnegative profit and exiting is not  costless,  while the d o m e s t i c i n c u m b e n t might exit. T h i s is because after the i n c u m b e n t exits p r o d u c t 1, the higher m o n o p o l i s t i c price of p r o d u c t  1 charged  p r o d u c t 2, p r o v i d e d that the entrant  by the foreign entrant  would not further enter p r o d u c t 2.  "stay in b o t h p r o d u c t s " a n d "exit p r o d u c t 1", head-to-head  would b r i n g about  therefore,  a higher demand for  T h e i n c u m b e n t ' s choice between  is actually between m u l t i p r o d u c t profits facing  c o m p e t i t i o n on p r o d u c t 1 w i t h the entrant and p r o d u c t 2-only profit i n differentiated duopoly  s u b t r a c t i n g costs of exiting p r o d u c t 1. T h e fact that the h o m e firm earns positive profit of p r o d u c t 1 whereas the foreign firm earns zero profit is not essential to f i r m s ' exit decisions. M o r e o v e r , sunk entry costs at this stage are irrelevant to firms' choices.  61  It is thus conceivable that the domestic incumbent may exit product 1 when the exit cost is small, when the transport cost is sufficiently low, and when products in question are better substitutes. If this is the case, foreign entry is very likely to occur. In anticipating that the incumbent would exit product 1 in response to its entry, the foreign entrant would enter that product if the entry cost could be covered by the rent that accrues to a differentiated rather than an undifferentiated duopolist. Therefore, crowding the product spectrum may not credibly deter foreign entry if the level of exit costs is low and the level of transport costs is small. It is found in the foregoing argument that when entry costs are not so high as to blockade entry, it could be exit costs (as well as transport costs), not sunk entry costs, that deter foreign entry against a multiproduct domestic incumbent. Therefore, when transport costs are sufficiently small, the argument makes a critical distinction between exit costs on the one hand and irretrievable entry costs on the other. It is also noted that the nature of post-entry rivalry, whether it is Bertrand, Cournot, or others, is not essential to the foregoing argument for possible foreign entry. The crucial elements are firms' profits under various domestic market structures (e.g. the assumption offirms'nonnegative post-entry profits made in the argument, etc.), and the level of entry and exit costs, as well as the level of transport costs. We set the following notation. N, I, II, and I&II represent the state of the domestic incumbent's being in no market, being in product 1 only, in product 2 only, and in both products, respectively. N*, I*, I I * , and I k . I I *  represent the foreign entrant's being in no market (no invasion), being in product 1 only, in product  2 only, and in both products, respectively. The market structure in the home market is given by the states of the two firms. A firm in any of the four states must have made entry, exit, and production (quantity, price, etc.) decisions. In this paper these decisions are assumed to be made sequentially. Further, the homefirmis assumed to make entry decisions before the foreign firm does. The basic model is a four-stage game:  62  Stage  1.  T h e home firm decides how m a n y p r o d u c t s to p r o d u c e and which p a r t i c u l a r p r o d u c t s  to  p r o d u c e , a n d c o r r e s p o n d i n g l y pays entry costs, (the entry decision)  Stage  2.  T h e foreign firm decides how m a n y p r o d u c t s to p r o d u c e and which p a r t i c u l a r p r o d u c t s to  p r o d u c e , a n d c o r r e s p o n d i n g l y pays entry costs, (the entry decision)  Stage  S.  B o t h firms simultaneously decide how m a n y p r o d u c t s to exit and which p a r t i c u l a r p r o d u c t s  to exit, and c o r r e s p o n d i n g l y pay exit costs, (the exit decision)  Stage  4-  F i r m s play the d u o p o l y game of the final market structure, a n d c o r r e s p o n d i n g l y bear p r o d u c t i o n  costs (fixed p r o d u c t i o n costs and m a r g i n a l costs) as well as earn sales revenue.  T h i s basic m o d e l is very s i m i l a r to the m o d e l in J u d d ( 1 9 8 5 ) except one feature. In J u d d , as b o t h the i n c u m b e n t and the entrant are in one c o u n t r y , they can be assumed to be perfectly s y m m e t r i c in costs. Since the entrant f r o m the foreign c o u n t r y now bears e x t r a unit transport costs, we must make the assumptions on f i r m s ' payoffs for b o t h firms rather t h a n for just one firm as J u d d does.  T h e e q u i l i b r i u m is subgame perfect in the four-stage game where each firm anticipates the other  firm  will act in its own best interests when it chooses its strategy variables. T o find the e q u i l i b r i u m , we solve each subgame.  We start with the last stage, t a k i n g firms' entry and exit decisions as given. T h e n we analyse, one  stage by a n o t h e r , how a firm makes exit as well as entry decisions in the previous stages, correctly t a k i n g into account subsequent decisions and their i m p a c t on profits.  1) T h e f o u r t h - s t a g e subgame In the last stage, firms play the d u o p o l y game of the final market structure.  T h e r e are 16 possible  m a r k e t s t r u c t u r e s of entry and exit decisions with which firms enter the final stage. In this paper, the stage is not m o d e l e d as a specific form of rivalry such as a C o u r n o t or a B e r t r a n d game.  final  Instead, we give  a n u m b e r of a s s u m p t i o n s c o n c e r n i n g firms' payoffs u n d e r various market structures as well as the level of entry and exit costs. O n c e these assumptions are given, some duopoly models can be found to be consistent  63  with these a s s u m p t i o n s .  M o r e o v e r , these a s s u m p t i o n s have s u m m a r i z e d the possible outcomes at the  final  stage.  In what follows, we present a set of a s s u m p t i o n s , namely A s s u m p t i o n s 1-10, the u n i q u e e q u i l i b r i u m of the game under these assumptions. and  A s s u m p t i o n s 1-10  interesting for the discussions of credible m u l t i p r o d u c t p r e e m p t i o n .  and t h e n detailly derive  are regarded as a p p r o p r i a t e  M o r e o v e r , by using these basic  assumptions, we can analyse p r o d u c t i o n line rivalry, specialization, and two-way trade in later sections.  By  c h a n g i n g some of t h e m , we can also examine the effects of trade on p r o d u c t variety of c o n s u m p t i o n s . T h e s e fairly i n t u i t i v e a s s u m p t i o n s are checked in A p p e n d i x 9 and 10 to be consistent w i t h C o u r n o t and B e r t r a n d d u o p o l y m o d e l , respectively.  Before presenting assumptions, we state the following n o t a t i o n :  P ( S 1 , S 2 ) is the profit (the revenue net of p r o d u c t i o n costs) to a firm in state S i if the other firm in state S2, Si =  I, II, I&II, or N for the h o m e f i r m ; Si =  A . i stands for A s s u m p t i o n i , i = l , 2 , 3 ,  / * , / / * , / & / / * , or N*  for the foreign f i r m , i = l , 2 ;  ;  F ( E , i ) is the n o n n e g a t i v e fixed cost of entering p r o d u c t i , i = l , 2 ;  F ( X , i ) is the n o n n e g a t i v e fixed cost of exiting p r o d u c t i , i = l , 2 ; and  F(E,1&2)  and F ( X , 1 & 2 )  are the nonnegative fixed costs of entering and exiting b o t h p r o d u c t s , respec-  tively.  A s s u m p t i o n  1.  F ( E ,  1&2)  F [ X , l k 2 )  =  F  =  F { X ,  ( E ,  1)  +  F ( E , 2 )  1)  +  F ( X , 2 )  T h i s a s s u m p t i o n is not stated in J u d d (1985), b u t has been i m p l i c i t l y used. T h e assumption says that the two p r o d u c t s , t h o u g h i m p e r f e c t l y substitutable, are independent in i n c u r i n g entry and exit costs. So there are no economies of scope in terms of entry and exit costs. It may not be met in reality. For instance, it m a y 64  well be F(E,l) + F(E,2) > F{E, 1 & 2 ) . Nevertheless, a sight deviation from it would not affect the results of this paper. A s s u m p t i o n  2.  P  >  P(I&II*,I&II)>0.  Assumption 2 says that post-entry profits are always nonnegative. This holds as long as post-entry economies of scale are not so severe that competition forces profits to be negative. In the Bertrand example, our earlier discussion has indicated that the foreign firm would earn nonnegative profit facing head-to-head competition with the home firm if and only if the fixed production costs are zero. If post-entry competition is not so intense, such as in a Cournot industry where low-cost firms do not drive out high-cost firms, we may expect A.2 more likely to hold. Moreover, the smaller the transport costs, the more likely the post-entry profits of foreign firms to be positive. This assumption is necessary in order to avoid inessential complications.  A s s u m p t i o n  S.  F(E,I)  F(E,2)  >  p{i,r),p[i,ikir)  >  />(//,//*),/>(//,/&//*)  Because of the relations:  P(J,F)>  P(I*,I)  P(II,  and  IF)  > P(IF,  II),  the parallel assumptions for the foreign firm automatically hold if the above inequalities hold for the domestic firm.  65  A . 3 says that entry costs are sufficiently high that it does not pay a f i r m to enter a p r o d u c t if it will not eventually become a m o n o p o l i s t in that p r o d u c t . T h i s assumption is made in order to focus on preemption issues and it is not essential for the results.  Assumption  4-  p(ikii,r)  > p(i,r)  p(ikii,ir)  >  > p{ii,ir)  p{i&ir,i)  >  > p{r,i)  p(ikir,ii)  p(i,ikir)  p(ii.ikir)  >  > p{ir,ii)  p(r,ikii)  >  p(ir,mii)  A . 4 states that a s i n g l e - p r o d u c t firm facing c o m p e t i t i o n in that p r o d u c t will receive more post-entry profits by i n t r o d u c i n g the other p r o d u c t (Note 4), and may lose post-entry profits if its rival expands into the other p r o d u c t . T h i s a s s u m p t i o n reflects that the p r o d u c t s are imperfect  A s s u m p t i o n  substitutes.  5.  P ( I ,  I V )  P { I , N * )  P ( V  -  -  F ( E ,  F ( E ,  1)  1)  >  >  , 1 1 ) - F { E , \ )  P [ 1 * , N )  -  F ( E ,  1)  P { I I , I * )  P { 1 J , N * )  >  >  -  -  P ( I I * , I )  P  (  H  \  N  )  F ( E , 2 ) , 0  -  -  F ( E , 2 )  F ( E , 2 )  F ( E ,  2),0  A c c o r d i n g to A . 5 , p r o d u c t 1 is chosen to be more profitable than p r o d u c t 2 even taking into account costs.  66  entry  A s s u m p t i o n  6.  P { F , I I )  -  F ( E , 1 )  >  0  P(ir,I)  -  F { E , 2 )  > 0  and  A s s u m p t i o n  Because  7.  P ( I , I F )  >  P ( F , I I )  and  P ( I I , F )  >  P ( I F , I ) ,  the parallel assumptions for the domestic  a u t o m a t i c a l l y hold as long as the above inequalities hold for the foreign  firm  firm.  A . 6 a n d A . 7 say that if one firm is selling one p r o d u c t , the other can profitably enter the other p r o d u c t .  A s s u m p t i o n  8.  P(I,ir)  -  F ( X , 2 )  >  P ( I & i I I , I F )  P ( F , I I )  -  F ( X , 2 )  >  P [ I & I I * , I I )  and  A s s u m p t i o n  9.  P { I I , F )  -  P { i r , I ) -  A.8  >  P ( I & i I I , F )  F ( X , 1 ) >  P(Ibir,I)  and A . 9 state that it is better to be a differentiated duopolist t h a n a m u l t i p r o d u c t firm c o m p e t i n g  head-to-head A.9  F { X , l )  in one of the p r o d u c t s even if costs of exiting that c o m p e t i n g p r o d u c t are i n c l u d e d . A . 8 and  are c r u c i a l for the p u r p o s e of d e m o n s t r a t i n g the i m p o r t a n c e of considering exit costs on entry issue.  T h e y have i m p l i c i t l y assumed that exit costs are s m a l l , the p r o d u c t s are good substitutes, competition is intense, and t r a n s p o r t costs are s m a l l .  67  We our  shall see t h a t under A s s u m p t i o n s 1-9, we can solve for the unique subgame perfect equilibrium in  four-stage g a m e .  B u t , to focus on the spatial p r e e m p t i o n issue, we a d d one more a s s u m p t i o n on the  d o m e s t i c firm's payoff,  A s s u m p t i o n  10.  P [ I b I I , N * )  -  F [ E , l )  -  F { E , 2 )  >  P { I , N * }  -  F [ E , \),P(II,  N * )  -  F { E , 2 )  U n d e r A . 1 0 , the domestic i n c u m b e n t will enter b o t h p r o d u c t s if there is no threat of foreign entry because it is m o r e profitable to be a m o n o p o l i s t in b o t h p r o d u c t s t h a n in either one alone.  T h u s , t h e possible outcomes and associated  payoffs at the f o u r t h stage have been s u m m a r i z e d in the  P ( S l , S 2 ) ' s defined above (Note 5).  2) T h e third-stage  subgame  T a b l e 12 lists the possible states in the domestic c o u n t r y just before Stage 3 a n d the resulting states in e q u i l i b r i u m at the e n d of the third-stage  game.  In cases 1,2,3,4,5,9 a n d 13, there is only one m o n o p o l y firm in the market. In cases 6 a n d 11, b o t h firms enter t h e same p r o d u c t . In cases 7 and 10, each enters one different p r o d u c t . In all these cases, firms have no incentive t o exit their p r o d u c t s because A s s u m p t i o n 2 implies nonnegative profits for b o t h firms a n d e x i t i n g is not costless, given that entry costs are sunk.  The  more interesting situations arise when at least one firm has entered two p r o d u c t s and the two firms  c o m p e t e at least in one p r o d u c t . T h e s e are case 8,12,14,15 a n d 16. In case 14, the domestic  firm  entered  b o t h p r o d u c t s at the first stage a n d then the foreign firm entered one of p r o d u c t s , p r o d u c t 1, in the domestic m a r k e t at t h e second stage. In case 8, home firm entered p r o d u c t 1 domestically and then foreign newcomer  68  Table 12 Stage 3 equilibria under Assumptions 1-9 in the domestic country Initial domestic f i r m N N N N I I  Case  ;  i  i  ;  1 2 3 4 5 6 7 8 9 10 11 12 1  I I II II II  1  I  H I+II I+II I+II I+II  3  14 15 16  !  States  Final  foreign firm N* I* II* I+ II* N* I* II* I+II* N* I* II* I+ II* N* I* II* I+II*  States  domestic f i r m N N N N I I I I II II II II I+II II I (I+II,I,II)  foreign firm N* I* II* I+II* N* I* II* II* N* I* II* I* N* I* II* (I+II*,II*,I*)  ! | j  | !  Table 13 Stage 3 in the domestic country. Case 14 foreign --^^ firm Exit I domestic firm Exit  Stay i n I  --  I  P(II,N*)-F(X,1),  -F(x,l)  P(II,I*)-F(x l), P(I*,II) >  •  Stay i n I+II Exit  II  Exit  I+II  P(I+II,N*),  -F(x,l)  P(I+II,I*), P(I*,I+II)  P(I,N*)-F(x,2),  -F(x,l)  P(I,I*)-F(x,2), P(I*,I)  -F(x,l)-F(x,2),  -F(x,l)  -F(x,l)-F(x,2),  69  P(I*,N)  ;  Table 14 Stage 3 i n the domestic country, case 8 foreign ^-^^ firm Exit I  Stay i n I  domestic firm 'I' ^  Exit I  P(II* N)-F(X,1),  Stay i n I+II  P(I+II*,N),  E x i t II  P(I*,N)-F(x,2),  -F(x,l)  Exit  -F(x,l)-F(x,2),  -F(x,l)  I+II  >  -F(x,l)  -F(x,l)  P(II*,I)-F(x,l), P(I,II*) P(I+II*,I),  P(I,I+II*)  P(I*,I)-F(x,2), P(I,I*) -F(x,l)-F(x,2),  P(I,N*)  Table 15 Stage 3 in the domestic country, Case 16 foreign ^^-^^ firm Stay i n I + I I *  E x i t I*  Exit I I *  Exit  I+II*  domestic firm Stay i n I+ II  P(I+II,I+II*), P(I+II*,I+II)  Exit I  P(II,I+II*)F(x,l), P(I+II*,II)  Exit II  Exit  P(I+II,I*), P(I*,I+II)F(x,2)  P(I+II,N*), -F(x,l) -F(x,2)  P(I,II*)F(x,l), P(II*,II) -F(x,l)  P(II,I*) -F(x,l), P(I*,H) -F(x,2)  P(II,N*) -F(X,1), -F(x,l) -F(x,2)  P(I,I+II*)F(x,2), P(I+II*,I)  : P(I,II*)F(x,2), P(II*,I) -F(x,l)  P(I,I*) -F(x,2), P(IM) -F(x,2)  P(I,N*) -F(x,2), -F(x,l) -F(x,2)  -F(x,1) -F(x,2), P ( I + II*,N).  F(x.l)F(x,2), P(II*,N) -F(x,l)  F(x,l) -F(x,2), P(I*,N) : -F(x,2)  -F(x,l) -F(X,2), -F(x,l) -F(x,2)  -  I+II  . P(I+II,II*), P(II*,I+II)F(x,l)  70  entered b o t h p r o d u c t s . T h e payoff matrixes of the stage-three game for case 14 and case 8 are displayed in T a b l e 13 and T a b l e 14 respectively.  F r o m T a b l e 13, the foreign firm will not exit p r o d u c t 1 since strategy "stay in I" d o m i n a t e s "exit I" (A.2).  In response to this credible threat to stay by the foreign f i r m , the domestic firm has four choices.  won't w i t h d r a w b o t h p r o d u c t s since staying in b o t h is better t h a n exiting both ( A . 2 ) .  It  A s the p r o d u c t s are  i m p e r f e c t substitutes, s t a y i n g in b o t h is better t h a n exiting n o n - c o m p e t i n g g o o d , p r o d u c t 2 ( A . 4 ) . However, s t a y i n g in b o t h is inferior to exiting the c o m p e t i n g g o o d , p r o d u c t 1, according to our c r u c i a l A s s u m p t i o n 9.  T h e r e f o r e , "exit I" is the best strategy for the domestic f i r m .  T h u s we find that the N a s h e q u i l i b r i u m  in case 14 is "exit I" for h o m e firm and "stay in I" for foreign h o m e . It is noted t h a t large exit costs could m a k e it less likely for the i n c u m b e n t to exit. S i m i l a r analysis can be applied to case 8, and case 12,15.  The  last case, case 16, is one where b o t h firms are in b o t h p r o d u c t s at the b e g i n n i n g of Stage 3.  The  payoffs of this stage-three subgame is displayed in T a b l e 15.  F i r s t of a l l , A s s u m p t i o n 2 implies that  "stay in b o t h " d o m i n a t e s  "exit b o t h " for b o t h  firms.  After  strategies "exit b o t h " are d r o p p e d from the payoff m a t r i x , the same reasoning as we d i d in case 14 will give two p u r e strategy N a s h e q u i l i b r i a , namely each firm e x i t i n g one different p r o d u c t at the same time ( A . 4 , A.8, (A.2,  A . 9 ) . F u r t h e r , there is a t h i r d possible e q u i l i b r i u m , "stay in b o t h " for b o t h firms. B u t our assumptions A . 8 , A . 9 ) ensure that this potential e q u i l i b r i u m is worse in terms of payoffs t h a n the first two eqilibria.  T h u s the first two e q u i l i b r i a provide an u p p e r b o u n d for firms' payoffs.  3) T h e s e c o n d - s t a g e s u b g a m e In this stage the foreign entrant is faced with only four possible situations (see T a b l e 16).  S u p p o s e that the domestic i n c u m b e n t has entered one of the p r o d u c t s , say p r o d u c t  1.  T h e entrant  won't enter that p r o d u c t again because its postentry profit can not cover its entry cost ( A . 3 ) , while it m a y enter p r o d u c t 2 ( A . 7 ) .  B u t it won't enter b o t h p r o d u c t s because it anticipates that it will be forced to exit  .71  T a b l e 16 S t a g e 2 Subgaae under Domestic  X  J  ;  f l r m  \  A s s u a p t i o n s 1-9  (  11  choices  Foreign  -  1  j  firm c h o l c e s N ^  1*  II*  i  ; P(IM)-F(E,1), : P(I,I«)-F(E,I)  P(II,I*)-F(E,2)  j  P(II*.I)-F(E,2),  P(II*,II)-F(E.2),  P(II*,I)-F(E,2),  j  P(I,II*)-F(E,1)  P(II,II*)-F(E,2)  P(I,II«)-F(E,1)  P(l*,ll)-F(E.1),i. i  P(I*.N)-F(E,1),  P(I*,II)-F(E,1),  0  P(II,I*)-F(E,1)  [ -F(E,2)-F(X,2)  -F(E,2)-F(X.2)  j P(II*,N)-F(E,2). !  0  j  •  I+II*  P(IIM)-F(E,1),  P(I*,II)-F(E,1),  -F(E,2)-F(X,1),  -F(E.2)-F(X,2),  <P(IMI)-F(E.l), -F(E,2)-F(X.2),  P(I,II*)-F(E,1)  P(II,I*)-F(E,2)  <P(I,II*)-F(E,2)  P(l+Il*,N)-F(E,1)  -F(E,2). 0  -F(E,2)-F(X.2) N*  P(I,N*)-F(E,1)  0,  0,  0,  P(II,N*)-F(E,2)  0, 0  P(I+II,N*)-F(E,1) -F(E,2)  T a b l e 17 S t a g e 1 S u b g a i e under A s s u n p t l o n s 1-9  Domestic firm choices I P(I,II*)-F(E,1)  , 4- i |  ii P(II,I*)-F(E,2)  P(I,II*)-F(E,1) -F(E,2)-F(X,2)  72  M 0  p r o d u c t 1 at the t h i r d stage a n d hence bear extra entry and exit costs. T h e r e f o r e after t a k i n g into account the o u t c o m e s of later stages, the foreign firm will decide to enter p r o d u c t 2.  S u p p o s e that the domestic i n c u m b e n t has entered b o t h p r o d u c t s .  A s shown in T a b l e 16, the foreign  entrant will enter one and only one p r o d u c t in a n t i c i p a t i n g that any m u l t i p r o d u c t p r o d u c e r will eventually be forced to exit one of the p r o d u c t s . T h a t it enters which p a r t i c u l a r p r o d u c t will d e p e n d only on the relative p r o f i t a b i l i t y of the p r o d u c t s i n q u e s t i o n .  4) The first-stage subgame It is easily seen f r o m T a b l e 17 that the domestic firm should enter one a n d only one p r o d u c t ( A . 6 , A.7)  after t a k i n g into account all the outcomes in later stages. Since A s s u m p t i o n 5 has chosen p r o d u c t 1 to be  m o r e profitable, the domestic i n c u m b e n t will enter p r o d u c t 1 at the first stage.  U n d e r A s s u m p t i o n 1-9, we have d e t e r m i n e d a unique s u b g a m e perfect N a s h e q u i l i b r i u m for the case of one d o m e s t i c i n c u m b e n t and one foreign entrant in the domestic country. A d d i n g A s s u m p t i o n 10, we obtain the following result:  Result  1.  U n d e r A s s u m p t i o n s 1-10,  in domestic e q u i l i b r i u m ,  p r o d u c t 1 a n d the foreign entrant p r o d u c e s p r o d u c t 2.  the domestic i n c u m b e n t produces only  H e n c e , if (1)  the domestic market is sufficient for  differentiated d u o p o l y to be profitable net of entry costs, (2) exit costs are s m a l l , (3) t r a n s p o r t costs are low, (4)  the p r o d u c t s are better substitutes, (5) c o m p e t i t i o n in homogeneous p r o d u c t s is intense, and (6)  post-  entry economies of scale are not so severe that c o m p e t i t i o n forces f i r m s ' post-entry profits to be negative, then at the e q u i l i b r i u m of the domestic m a r k e t , the home i n c u m b e n t only p r o d u c e s more profitable goods even t h o u g h it would have earned more profit by p r o d u c i n g all available goods if there were no threat of foreign entry, and allows the foreign entrant to enter less profitable goods.  73  We  offer two examples in the Appendix in which Assumptions 1-10 are consistent with each other.  Consequently, Result 1 holds for a certain range of parameters (demand, the level of entry and exit costs, fixed production costs, transport costs, etc.).  3 . TWO COUNTRIES  Suppose now there are two countries, A and B, and each country has only one firm, called firm A and firm B respectively. We assume that country A and B have the same pattern of factor endowments and identical technology. Consumers in the two countries have identical tastes and have the same preference to the two products under consideration. Further, firms can potentially produce and export two imperfectly substitutable products. A firm which exports a product will bear extra unit transport cost. A firm needs to make entry, exit and production decisions for both home and foreign markets. We assume that firms make these decisions sequentially and a firm has the advantage of entering its home market before its foreign rival. This seems an appropriate assumption to make in models dealing with international trade, as Eaton and Kierzkowski (1984) point out. A number of authors, most notably Linder and Vernon, have argued that production is typically first developed for a domestic market. Trade takes place at a later stage of the product cycle, long after firms selected their products and incurred fixed costs. What is new in our model is that there is an exit stage. Firms may exit in response to entry. More formally, our model is a four-stage game:  Stage  1.  Both firms simultaneously decide how many products to produce and which particular products  to produce in their domestic markets, and correspondingly pay entry costs, (the home entry decision)  Stage  2.  Both firms simultaneously decide how many products to produce and which particular products  to produce for the foreign markets, and correspondingly pay entry costs, (the foreign invasion decision)  74  5.  Stage  B o t h firms simultaneously decide how m a n y p r o d u c t s to exit and which p a r t i c u l a r  products  to exit in b o t h home and foreign m a r k e t s , and c o r r e s p o n d i n g l y pay exit costs, (the exit decision)  4- F i r m s  Stage  play the d u o p o l y game of the  final market  s t r u c t u r e in a two-country  world, and  c o r r e s p o n d i n g l y bear p r o d u c t i o n and transport costs as well as earn sales revenue.  It is noted that the two firms play this four-stage game with equal o p p o r t u n i t y in a two-country w o r l d . Each  firm  is an i n c u m b e n t at home and a p o t e n t i a l entrant a b r o a d .  A s an i n c u m b e n t , it would be faced  with the threat of foreign entry by trade; as an entrant, it would p o t e n t i a l l y invade foreign c o u n t r y  through  trade.  B r a n d e r and Spencer (1984) point out that in considering a two-country eration  is whether  markets are u n i t e d or segmented.  Segmented  world one i m p o r t a n t consid-  m a r k e t s arise when firms treat different  countries as different markets in that they choose their strategy variables for each market separately. T h u s , if the rivalry of firms is along the C o u r n o t ( B e r t r a n d ) line, the segmented-markets perception will lead  firms  to choose separately their o u t p u t quantities (prices) for each country. T h e assumption of segmented markets i m p l i e s that oligopolistic firms w o u l d face distinct country-specific  d o w n w a r d sloping d e m a n d curves.  So  there are no cross-effects between the p r o d u c t s p r o d u c e d for one c o u n t r y and the p r o d u c t s p r o d u c e d for the other c o u n t r y even if the p r o d u c t s may be identical.  We shall adopt the segmented-markets assumption in  our t w o - c o u n t r y w o r l d . In p a r t i c u l a r , we make the following a s s u m p t i o n :  A s s u m p t i o n  11.  A p r o d u c t i o n line for domestic country a n d a p r o d u c t i o n line for foreign country  are  considered by b o t h firms as two independent lines even though they may p r o d u c e identical p r o d u c t s .  U n d e r A s s u m p t i o n 11, each firm chooses its strategy variables, namely entry and exit decisions, postentry  production  (output level, price, particular  forms of advertising,  etc.)  decisions,  not only for each  p r o d u c t separately, but also for each market separately, and also assumes the other firm acts in the same way.  R e c a l l that in A s s u m p t i o n 1, the two p r o d u c t s are unrelated in i n c u r i n g entry as well as exit costs.  75  W i t h o u t c h a n g i n g any result of the m o d e l , we can also make s i m i l a r assumptions c o n c e r n i n g p r o d u c t i o n costs.  A p p a r e n t l y , A s s u m p t i o n 11 is consistent  with these a s s u m p t i o n s .  M o r e o v e r , A.11  rules out b o t h  economies of scope and economies of scale in our m o d e l , and t h u s allows us to examine trade u n d e r neither economies of scope nor economies of scale.  We show in A p p e n d i x 11 that in C o u r n o t m o d e l with constant m a r g i n a l costs, f i r m s ' m a x i m i z i n g overall profits for b o t h countries is equivalent to f i r m s ' separately m a x i m i z i n g profits for each country, p r o v i d e d that final e q u i l i b r i u m market structures are s y m m e t r i c for b o t h firms and countries. T h e s y m m e t r y of our m o d e l has i m p l i e d s y m m e t r i c a l e q u i l i b r i a . So as long as m a r g i n a l costs are constant a n d the e q u i l i b r i a exist, the two countries can be separated.  G e n e r a l l y , A.11 i m p l i e s that our four-stage  be s e p a r a t e d i n t o two parts c o r r e s p o n d i n g to two countries.  game in a t w o - c o u n t r y world m a y  Since the two parts are perfectly s y m m e t r i c ,  the e q u i l i b r i a for one are also the e q u i l i b r i a to the other. T h e r e f o r e , we only need solve one part in which a h o m e i n c u m b e n t and a foreign entrant strategicly interact in the h o m e m a r k e t . T h i s is exactly the game we have discussed in the last section.  B a s e d on the o b t a i n e d results for one country, we m a y c o r r e s p o n d i n g l y  derive the results for two countries. T h i s section and next section are concerned w i t h cases where the two countries can be separated.  Result 1 of section 2 says that at the e q u i l i b r i u m of each country, the home i n c u m b e n t only produces the m o r e profitable g o o d even t h o u g h it would have earned more profit by p r o d u c i n g b o t h goods if there were no threat of foreign entry, and the foreign entrant produces the other g o o d . W i t h segmented markets, we have  Result 2.  Under Assumptions  1-11,  at the e q u i l i b i u m of our two-country world, each f i r m produces b o t h  p r o d u c t s , the m o r e profitable p r o d u c t for the domestic market and the less profitable one for the foreign market.  H e n c e , two-way trade arises in the less profitable p r o d u c t w h i c h is p r o d u c e d only for t r a d i n g .  In a d d i t i o n to the segmented-markets  assumptions, the following conditions are either necessary  suitable for the emergence of the kind of two-way trade:  76  or  (1) post-entry economies of scale are not so severe  that c o m p e t i t i o n (3)  forces  firms'  post-entry  profits to be negative,  c o m p e t i t i o n in identical p r o d u c t s is intense, (4)  d u o p o l y to be profitable net of entry costs, (5)  (2)  the p r o d u c t s  are b e t t e r  substitutes,  d e m a n d in each c o u n t r y is sufficient for differentiated  exit costs are s m a l l , and (6) t r a n s p o r t costs are sufficiently  low.  T h e cause of this type of two-way trade need investigating. which  firms'  For this purpose, we consider the game in  choices are to invade or not to invade foreign m a r k e t .  T h e firms' choices are reflcted in the  second stage of our four-stage game. If b o t h firms invade foreign markets, b o t h choose / * , / / * Satge 2. If b o t h firms do not invade foreign markets, b o t h choose N* does not invade the foreign m a r k e t , F r o m the d e t e r m i n a t i o n final  or  lk.II*  in  i n Stage 2. If either firm u n i l a t e r a l l y  it chooses JV* whereas its rival chooses  I*,  11*,  or  Ik.II*  in Stage 2.  of e q u i l i b r i u m in the last section, we can o b t a i n T a b l e 18 which summerizes  the  e q u i l i b r i u m market structures c o r r e s p o n d i n g to firms' choices in our two-country w o r l d .  S u p p o s e i n i t i a l l y there were no trade (in b o t h p r o d u c t s ) .  Each  firm  would produce both  products  d o m e s t i c a l l y a n d act as a m o n o p o l i s t . Nevertheless, each would then have an incentive to invade the foreign market.  A s is a s s u m e d , it is better for each firm in each c o u n t r y to be a differentiated duopolist t h a n to be  a m u l t i p r o d u c t d u o p o l i s t c o m p e t i n g h e a d - t o - h e a d in one of the p r o d u c t s even after taking into a c c o u n t exit costs. W h e n facing foreign entry into one of the products, the home i n c u m b e n t would thus be b e t t e r off by exiting t h a t p r o d u c t .  A n t i c i p a t i n g this, the entrant would take an invasion position as long as its  post-entry  profit, w h i c h w o u l d be the rent that accrues to a differentiated rather than an undifferentiated d u o p o l i s t in the foreign m a r k e t , can cover the entry cost. If either firm, say firm A , unilaterally d i d not invade its rival's c o u n t r y , it would p r o d u c e only one p r o d u c t in country A after foreign invasion, while its rival, firm B , would p r o d u c e b o t h p r o d u c t s in its home market and invade the other p r o d u c t in c o u n t r y A . C o n s e q u e n t l y ,  firm  A w o u l d lose m a r k e t shares while firm B would expand market shares. It is the firms' incentive to m a i n t a i n a n d increase m a r k e t shares as well as to protect their positions in more profitable p r o d u c t s that causes and sustains  our two-way  trade.  T h e two m u l t i p r o d u c t m o n o p o l i s t s , each in a different country, invade each  77  T a b l e 18  Not  Invade  Invade  Firm B^s.  Not Invade  Invade  Each f i r m i s a two-product monopolist i n i t s home market.  F i r m B produces only product 1 f o r B; f i r m A produces b o t h p r o d u c t s f o r A as w e l l as p r o d u c t 2 f o r B.  F i r m B produces both products f o r B as w e l l as product 2 f o r A; f i r m A produces only p r o d u c t 1 f o r A.  Each f i r m produces both p r o d u c t s , product 1 f o r i t s home market and product 2 f o r the f o r e i g n market.  T a b l e 19 Firm A Not  Invade  Invade  Firm B  Not Invade  Invade  R,R  T,S  78  S,T  other's home markets and become a b i n a t i o n a l duopolists p r o d u c i n g two i m p e r f e c t l y substitutable p r o d u c t s , one for each country.  M o r e f o r m a l l y , we can show that strategy "Invade" dominates strategy " N o t I n v a d e " . T h e payoff m a t r i x of the game is shown in T a b l e 19. Since the players are in a s y m m e t r i c p o s i t i o n , we observe a s y m m e t r i c payoff s t r u c t u r e .  B y referring to T a b l e 18, we can calculate R , T , P, and S. F o r e x a m p l e , suppose firm A chooses " N o t Invade" and firm B " I n v a d e " .  T h e n a c c o r d i n g to T a b l e 18, firm A ends up selling p r o d u c t 1 in A and its  payoff S is  S  =  P ( I , I I * ) - F ( E , l )  F i r m B ends up with selling b o t h p r o d u c t s in B and p r o d u c t 2 in A and its payoff T is  T  =  ( P ( I k I I , N * )  -  F ( E , 1 )  -  F { E , 2 ) )  +  ( P { I 1 , I )  -  F [ E , 2 ) )  S i m i l a r l y , we have  R  P  =  =  P { I k I I , N * )  [ P { I , I J * )  -  F ( E ,  =  -  F { E , \ )  1))  +  -  F { E , 2 )  { P ( I F ,  /)  -  F ( E ,  2))  F r o m R , T , P, and S, we calculate  P  A c c o r d i n g to A s s u m p t i o n  T  7, one  -  P{ir,J)  T  -  R  S  =  P { I I *  ,1)  -  -  F ( E , 2 )  F ( E , 2 )  =  of assumptions made in Result  T  -  2, P  R  ( I I * , I )  —  F ( E , 2 )  >  - R > 0 and P - S > 0, that is, strategy "Invade" d o m i n a t e s " N o t Invade" for b o t h firms.  79  0.  Therefore,  T h e level of exit costs plays an i m p o r t a n t role in the rise of o u r two-way t r a d e . Lower exit costs make the i n c u m b e n t s more likely to exit in response  to foreign entry  and thus give the foreign entrants  more  incentives to increase market shares by i n v a d i n g a n d d r i v i n g out the i n c u m b e n t s .  T h e two-way t r a d e d p r o d u c t is less profitable than the n o n - t r a d e d p r o d u c t . B e i n g a domestic i n c u m b e n t , each c o u l d not enter b o t h p r o d u c t s when facing potential foreign entry but would enter the more profitable p r o d u c t . B y s t a y i n g out of the m o r e profitable p r o d u c t , the foreign entrant gives the i n c u m b e n t an acceptable retreat.  W e have seen in this m o d e l that i n t r a - i n d u s t r y trade m a y arise due to firms' strategic  interactions  t h r o u g h trade. O u r analysis follows B r a n d e r (1981) where the possibility of i n t r a - i n d u s t r y trade in identical g o o d s d u e to f i r m s ' strategic interactions  is first examined  in the trade literature.  T h e m o d e l proposed  by B r a n d e r considers a s i n g l e - p r o d u c t i n d u s t r y consisting of two firms, each in a different country. segmented  markets  a n d a C o u r n o t setting,  With  B r a n d e r shows t h a t i n t r a - i n d u s t r y trade m a y take place even  in i d e n t i c a l goods despite the existence of t r a n s p o r t  costs. A s transport  costs fall, goods p r o d u c e d abroad  m a k e u p a greater a n d greater share of domestic c o n s u m p t i o n , with the share a p p r o a c h i n g a fifty percent as t r a n s p o r t  costs a p p r o a c h to zero.  T h e cause of this two-way trade comes from the f i r m s ' m o t i v a t i o n of  price d i s c r i m i n a t i n g , o r " d u m p i n g " , into each other's m a r k e t s , so called " r e c i p r o c a l d u m p i n g " by B r a n d e r a n d K r u g m a n (1983).  A m o n g m a n y similarities between o u r m o d e l and B r a n d e r ' s m o d e l , several differences are worth n o t i n g . F i r s t , o u r m o d e l is c o n c e r n e d with a m u l t i p r o d u c t industry where firms' entry and exit decisions are made prior to firms' p r o d u c t i o n decisions. T h u s firms m a y use the entry a n d exit decisions for strategic purposes. In o t h e r words,  firms  understand,  before a n y t h i n g is a c t u a l l y p r o d u c e d , how the noncooperative  output  g a m e will work o u t . Secondly, the role of exit costs has been i n t r o d u c e d in o u r m o d e l , a n d lower exit costs may m a k e it possible for an i n c u m b e n t to exit in response to foreign entry.  C o n s e q u e n t l y , lower exit costs  m a y give a firm an o p p o t u n i t y to e x p a n d market shares by entering the foreign m a r k e t . firms'  n o n c o o p e r a t i v e foreign invasions, i n t r a - i n d u s t r y t r a d e might arise. 80  A s the result of  T h i r d l y , since the exit stage is  added in o u r m o d e l , a different type of two-way trade is d e r i v e d . In B r a n d e r ' s m o d e l , two-way traded good p r o d u c e d a b r o a d makes u p a smaller share of domestic c o n s u m p t i o n of that g o o d than the g o o d p r o d u c e d at h o m e .  In o u r m o d e l , t h e two-way t r a d e d good p r o d u c e d abroad c a p t u r e s the whole domestic market of  that g o o d , while the g o o d p r o d u c e d by the domestic firm is entirely delivered to the foreign market  despite  the existence of t r a n s p o r t costs. So a c o u n t r y entirely exports a good a n d simultaneously entirely imports it. T h i s e q u i l i b r i u m o u t c o m e m a y be viewed as an extreme case of i n t r a - i n d u s t r y trade, a n d seems not realistic.  T h i s o u t c o m e could arise in o u r m o d e l due to firms' n o n c o o p e r a t i v e profit m a x i m i z a t i o n .  In the home  m a r k e t , a firm is a m u l t i p r o d u c t i n c u m b e n t a n d it would be better off by exiting a p r o d u c t when the foreign firm invades that p r o d u c t ; in the foreign m a r k e t , the firm becomes a p o t e n t i a l i n v a d e r a n d it w o u l d pay the firm  to invade a p r o d u c t in the foreign m a r k e t .  W i t h segmented  markets,  firms'  m a x i m i z i n g overall profits  can be equivalent to firms' separately m a x i m i z i n g each c o u n t r y ' s profits. It is the n o n c o o p e r a t i v e solution to this p r o f i t - m a x i m i z i n g p r o b l e m faced by firms in a sequential e n t r y - e x i t - p r o d u c t i o n  game that gives rise to  o u r two-way t r a d e . We shall show in the next section that our two-way trade can introduce p r o d u c t s which will otherwise not be p r o d u c e d i n autarky, a n d thus b r i n g about greater variety of c o n s u m p t i o n .  W h a t o u r m o d e l has a d d e d to B r a n d e r (1981) is that i n t r a - i n d u s t r y trade m a y be caused by the firms' m o t i v a t i o n to d r i v e the foreign firms out of some p r o d u c t s in which their positions are v u l n e r a b l e . W h a t is m o r e , the n a t u r e of post-entry rivalry, whether it is C o u r n o t , or B e r t r a n d , or s o m e t h i n g else, is not essetianl in o u r m o d e l . T h e c r u c i a l elements here, in a d d t i o n to segmented m a r k e t s , are firms' payoffs under various market s t r u c t u r e s as well as the level of entry, exit and transport costs. B o t h C o u r n o t a n d B e r t r a n d rivalry with linear d e m a n d can be consistent with the assumptions made, suggesting that two-way trade due to firms' strategic b e h a v i o r m a y arise not only in C o u r n o t d u o p o l y m o d e l but in others as well. In p a r t i c u l a r ,  two-way  trade in i d e n t i c a l p r o d u c t s discussed by B r a n d e r (1981) would not arise in B e r t r a n d m o d e l . T h i s is because in a h o m o g e n e o u s p r o d u c t i n d u s t r y , only one firm with lower m a r g i n a l cost can survive if c o m p e t i t i o n is in price.  In the presence of unit t r a n s p o r t cost, the foreign firm's m a r g i n a l cost is higher than the domestic  81  firm's.  H o w e v e r , two-way  trade in identical p r o d u c t s  may still arise in o u r m o d e l with B e r t r a n d  rivalry  where a m u l t i p r o d u c t i n d u s t r y is u n d e r consideration.  F i n a l l y , we show t h a t the two firms m a y be engaged in a P r i s o n e r ' s D i l e m m a game. A s defined previously, each f i r m ' s choices are to invade or not to invade the foreign m a r k e t .  A s s u m p t i o n  We shall m a k e the following a s s u m p t i o n :  12.  P ( I k I l , N ' )  >  P ( I , I I " )  +  P { i r , I ) .  A . 1 2 i m p l i e s t h a t it is better to be a m u l t i p r o d u c t m o n o p o l i s t in the domestic market t h a n to be a singlep r o d u c t d u o p o l i s t in b o t h domestic and foreign markets. and  Bertrand  The  T h i s a s s u m p t i o n can be checked in b o t h C o u r n o t  m o d e l s to be consistent with A s s u m p t i o n s 1 - 1 0 ( A p p e n d i x 1 2 , 1 3 ) .  d e f i n i t i o n of the P r i s o n e r ' s D i l e m m a requires that two relationships h o l d a m o n g the four different  p o t e n t i a l o u t c o m e s . T h e first r e l a t i o n s h i p specifies the order of the four payoffs: T > R > P > S. Because  T  -  R  =  P  -  S  >  0  ( A . 7 ) and  R  -  P  =  P ( I k I I , N ' ) -  P { I , 1 I * ) -  P ( I I ' , 1 )  >  0 (A.12),  T  >  R  >  P  >  S  is  satisfied.  The  second p a r t of the d e f i n i t i o n of the Prisoner's D i l e m m a is 2 R > R + S. T h a t is, the players cannot  get out of their d i l e m m a by t a k i n g t u r n s e x p l o i t i n g each other. T h i s condition holds in this game because 2 R -  ( T + S ) = ( R - P ) + ( P - S ) - ( T - R ) = R - P > 0 (since P - S = T - R and A . 1 2 ) . T h u s , we have  s h o w n t h a t the g a m e in question is a P r i s o n e r ' s D i l e m m a game.  A s the result, if the game is played only once, b o t h firms would invade foreign markets and trade w o u l d take place in the same good which is p r o d u c e d only for t r a d i n g . particular to  two-way  Since foreign entry  into a  p r o d u c t u s u a l l y lasts for several years, the s h o r t - r u n gains from such entry seem very attractive  firms.  82  4. T R A D E A N D P R O D U C T  VARIETY  An important aspect of international trade is that there is a substantial intra-industry tarde: trade with similar products. The greater variety of consumption brought about by trade becomes an important source of gains from trade. Therefore, the issue concerning whether trade, through intra-industry trade, will make a greater variety of consumption is important in the analysis of gains from trade. Jacquemin (1982) notes that both theory and empirical evidence give mixed results on this issue. First, there is a strong presumption that the diversity of products will be larger after trade than before. When there are economies of scale, there will always be products for which demand is not sufficient to make production profitable. By expanding the market, trade will lessen the importance of scale economies and hence leads to an increase in product variety. Krugman (1979, 1980, 1981), Dixit and Norman (1980), and Helpman (1981), among others, prove that trade can, in addition to improving resouce allocation, bring about greater variety. They use a Chamberlinian monopolistic competition model which incorporates an increasing returns-to-scale technology. In their equilibrium, each firm in different countries ends up producing a single variety of a differentiated product but earns no monopoly profits. Nonetheless, with different assumptions, different results could be derived. Dixit and Norman (1980) demonstrate through an example that with imperfect competition, some products, although produced with increasing returns to scale, could also disappear and product selection could be altered by a larger economy made possible by trade.  It is noted that their example arises in a framework in which there is a single  monopolistic firm before as well as after trade.  Eaton and Kierzkowski (1984) develop a model in which  firms make entry and price decisions sequentially and firms can credibly threaten entrants with intense postentry competition. Eaton and Kierzkowski show an example where trade reduces the variety of products in the world economy. It does so by eliminating firms serving a small market with idiosyncratic tastes. In the new equilibrium the consumers in this market do not necessarily buy a less desirable product but may cease consuming altogether.  83  In this section we examine the effects of trade on p r o d u c t variety using the m o d e l developed in the previous sections.  In our m o d e l neither economies of scope nor economies of scale is assumed.  Consumers  in different countries have identical tastes and consumers have the same preference to the p r o d u c t s . F i r m s , each in a different country, strategically  interact w i t h each other t h r o u g h trade and may exit a p r o d u t in  response to an entry. T h e r e f o r e , our a p p r o a c h is different from the previous studies just cited. It seems that the m o d e l p r o v i d e s a flexible t o o l of analysis for the variety issue in our two-country world. B y c h a n g i n g the firms'  payoffs u n d e r various market s t r u c t u r e s as well as the levels of entry and exit costs, we can c o m p u t e  c o r r e s p o n d i n g m a r k e t equilibria. Since the e q u i l i b r i u m analysis is s i m i l a r to that in section 2 and 3, we shall not go into details.  a)  T r a d e increases  product  variety  S u p p o s e t h a t A s s u m p t i o n 10 fails to h o l d . T h e following A s s u m p t i o n 13 is the opposite of A . 1 0 :  A s s u m p t i o n  18.  P { I , N * )  >  P ( I k I l , N * )  -  F [ E , 2 )  C o n s e q u e n t l y w h e n facing no threat of foreign entry, the domestic i n c u m b e n t which produces the  more  profitable g o o d , p r o d u c t 1, will not e x p a n d to p r o d u c t 2 since a m u l t i p r o d u c t m o n o p o l y is not as valuable as a s i n g l e - p r o d u c t m o n o p o l y . In this case, each firm will only p r o d u c e p r o d u c t 1 in a u t a r k y .  We want to  show t h a t o p e n i n g of trade will b r i n g about p r o d u c t 2 into the markets.  F i r s t , assume that the other assumptions r e m a i n true. A s was noted earlier, whether A . 1 0 holds or not will have no i m p a c t on the d e t e r m i n a t i o n of the unique e q u i l i b r i u m in section 2 as long as A s s u m p t i o n s 1-9 h o l d . T h u s we have  Result  3.  U n d e r A s s u m p t i o n s 1-9,  13 and 11, at the equilibrium of our two-country world, each  p r o d u c e s b o t h p r o d u c t s : p r o d u c t 1 for the home market and p r o d u c t 2 for the foreign m a r k e t .  firm  H e n c e the  a c t u a l flow of trade introduces p r o d u c t 2 into the markets that will otherwise not be p r o d u c e d in autarky.  84  Result 3 is interesting in that our seemingly pointless two-way trade, where trade takes place in identical p r o d u c t s which is p r o d u c e d only for t r a d i n g , can involve the p r o d u c t s w h i c h w o u l d otherwise disappear from c o n s u m p t i o n w i t h o u t trade a n d c a n thus bring about greater variety available to consumers.  N e x t , consider the case where exit costs are so large that b o t h A.8 a n d A . 9 fail to h o l d . T h i s is reflected in the f o l l o w i n g A a s s u m p t i o n 14:  A s s u m p t i o n  14-  F ( / & / / , / / * ) > P(I,ir)  -  > P[II,r)  -  P(Ikll,I*)  F(X,2)  F{X,l)  In this s i t u a t i o n , t h e n , the threat to stay in both p r o d u c t s by the i n c u m b e n t is credible a n d deterrence is possible.  However, whether t h e i n c u m b e n t will actually deter foreign entry into p r o d u c t 2 will depend on  the relative profitability in the home market between its b e i n g a m u l t i p r o d u c t m o n o p o l i s t and its b e i n g a s i n g l e - p r o d u c t d u o p o l i s t . T h i s is reflected in the following A s s u m p t i o n 15:  A s s u m p t i o n  15.  P(IkII,N*)  - F(E,2)  >  P{I,W)  if A.15 holds, then being a m u l t i p r o d u c t monopolist is more valuable t h a n b e i n g a s i n g l e - p r o d u c t duopolist in the home m a r k e t ; otherwise, less. T h u s , if A.15 holds, it pays for the i n c u m b e n t to deter foreign entry into p r o d u c t 2 by i n t r o d u c i n g p r o d u c t 2 itself; otherwise, it is not a n d the i n c u m b e n t will allow foreign entry. We therefore o b t a i n the following result:  R e s u l t 4.  U n d e r A s s u m p t i o n s 1-7,  14, 15, 13, a n d 11, at the e q u i l i b r i u m of our two-country world, each  firm p r o d u c e s b o t h p r o d u c t s only for its home market if A s s u m p t i o n 15 holds; a n d each firm produces b o t h p r o d u c t s , p r o d u c t 1 for the h o m e market and p r o d u c t 2 for the foreign market, if A s s u m p t i o n 15 does not hold.  H e n c e , o p e n i n g of trade i n t r o d u c e s p r o d u c t 2 into the markets and thus increases p r o d u c t variety.  85  W h e n A . 1 5 does not h o l d , the actual flow of trade makes greater variety possible; when A . 1 5 holds, the p o t e n t i a l for t r a d e does the j o b .  T h e new feature arising from Result 4 is that the ability to trade, even if no trade actually occurs, can affect the final m a r k e t s t r u c t u r e in an i n t e r n a t i o n a l e n v i r o n m e n t . A greater variety made possible by trade could be associated w i t h either actual trade or p o t e n t i a l trade.  b) T r a d e reduces p r o d u c t v a r i e t y N o m a t t e r what the level of exit costs is, b o t h R e s u l t 3 and Result 4 suggest that trade, either actual or p o t e n t i a l , c a n increase p r o d u c t variety available to consumers.  B u t they are not conclusive. Suppose that  A s s u m p t i o n 10 holds now, that is, each firm will p r o d u c e b o t h p r o d u c t s in a u t a r k y . Here, we want to show that o p e n i n g of t r a d e m a y lead p r o d u c t 2 to d i s a p p e a r f r o m the markets.  S u p p o s e also that A s s u m p t i o n s 1-9 hold except A s s u m p t i o n 7.  T h e opposite of A . 7 is the following  A.16:  A s s u m p t i o n  16.  0 >  P(H*,I)  -  F[E,2)  E i t h e r lower post-entry profit of p r o d u c t 2 (due to the high t r a n s p o r t entry into p r o d u c t 2 will make A . 1 6 more likely h o l d .  cost, for instance) or higher cost of  A.16 implies that from a domestic point of view, it  does not pay the foreign firm to invade p r o d u c t 2 when the home firm has entered p r o d u c t 1. A s A . 1 0 holds now, the domestic firm p r o d u c i n g p r o d u c t 1 would be profitable for its expansion to p r o d u c t 2 if there were no t h r e a t of foreign invasion. In the presence of p o t e n t i a l entry, however, if it did such an expansion, then A . 6 a n d A . 9 i m p l y that the foreign firm would invade p r o d u c t 1 in the domestic market and force the home firm  to exit p r o d u c t 1.  A s the home firm relizes this consequence, it stays out of p r o d u c t 2 to protect its  86  position in the more profitable good, product 1. On the other side, the foreign firm does not invade product 2 either since A.16 implies that the invasion is not worthwhile. Therefore, we obtain the following Result 5: R e s u l t 5.  Under Assumptions 1-11  except Assumption 7, at the equilibrium of our two-country world,  each firm produces only product 1 for only the home market. Each firm would also produce product 2 for the home market in autarky but would not do so because of potential foreign invasion through trade. Each firm does not introduce product 2 by invasion either because doing so is not profitable. Therefore, opening of trade, although no actual trade occurs, leads product 2 to disappear from the markets and thus reduces product variety available to consumers.  As has been demonstrated, our model gives mixed answers to the question of whether trade, through intra-industry trade, makes a greater product variety available to consumers.  However, we can show that  for a specific case, the answer to the variety question will be unambiguous. We prove this by showing that for a specific case, Result 3 (Result 4) and Result 5 can not hold at the same time. Note that in deriving both Result 3 and Result 4 we made the assumtions, among others, that A.10 fails (i.e. A.13 holds) and A.7 holds, 4.13 :  P [ I , N * )  A.7  >  P ( I t z I I , N * )  P(II,r)  :  -  -  F ( E , 2 )  >  F [ E , 2 )  0  That A.13 and A.7 hold simultaneously means that there is a range for F(E,2) such that  P { I I , F )  >  F { E , 2 )  >  P ( I k I I , N * )  -  P ( I , N * )  leading to  P ( I I , I " )  >  P ( I k I I , N * )  87  -  P ( I , N * )  (1)  (1) is necessary for Result 3 and Result 4.  N o t e also t h a t i n d e r i v i n g Result 5, we assumed that A . 1 0 holds and A . 7 fails (i.e. A . 1 6 holds). Similarly, the following (2) is necessary for Result 5:  P{IbII,N*)  - P(I,N*) >  P(II,r)  (2)  O b v i o u s l y , (1) a n d (2) can not hold simultaneously. T h e r e f o r e , Result 3 (Result 4) and Result 5 can not be true at the same t i m e . In other words, we have the following result:  Result  6.  O p e n i n g of trade may increase or reduce p r o d u c t variety available to consumers,  but for a  specific case trade w o u l d u n a m b i g u o u s l y either increase or reduce p r o d u c t variety.  We show in A p p e n d i x 14, 15 that inequality (1) and all assumptions m a d e either in Result 3 or in the first p a r t of R e s u l t 4 are consistent w i t h b o t h C o u r n o t and B e r t r a n d models with linear d e m a n d functions. C o n s e q u e n t l y , b o t h Result 3 and Result 4 (the first part) will hold for a certain range of p a r a m e t e r s in these two e x a m p l e s . T h i s is contained in the following result:  R e s u l t 7.  In the case of either C o u r n o t or B e r t r a n d rivalry with linear d e m a n d , trade, either potential or  actual, would increase p r o d u c t variety available to consumers.  We have seen that f i r m s ' strategic interaction t h r o u g h trade in order to m a x i m i z e their profits can increase or decrease p r o d u c t variety. O p e n i n g of trade can have an impact on the final market structure in which firms play oligopolistic games even if there is no actual flow of trade.  F u r t h e r m o r e , whether  trade,  t h r o u g h i n t r a - i n d u s t r y trade, increases or reduces variety, can d e p e n d on, a m o n g others, the level of entry costs as well as the level of exit costs.  88  5. SPECIALIZATION A n alternative extension of the basic m o d e l of section 2 is that one of the firms, say firm A , is able to act not only in the h o m e market b u t also in the foreign market prior to firm B. T h i s could arise when firm A is a t e c h n o l o g y i n n o v a t i n g firm, while the new technology can be accessed by firm B at a later stage using the sunk n a t u r e of investment costs ( b u y i n g patent, s p e n d i n g R & D , etc.). T h i s m a y h a p p e n in cases where the legal p r o t e c t i o n for innovations will be ended soon, or i m i t a t i o n is possible. In this section we examine s p e c i a l i z a t i o n a n d trade by using this sequential game in o u r t w o - c o u n t r y w o r l d .  T h e game to be analysed is very similar to the game of section 3 where firms have equal o p p o r t u n i t y to first enter their home m a r k e t s and then enter the foreign m a r k e t s .  A t the first stage,  firm A makes  entry decision in b o t h h o m e and foreign markets. A t the second stage, firm B makes entry decision in b o t h h o m e a n d foreign markets. foreign m a r k e t s .  A t the t h i r d stage, firms s i m u l t a n e o u s l y make exit decisions in b o t h home and  A t the f o u r t h stage, firms engage in a d u o p o l y game of the final market structure in an  i n t e r n a t i o n a l e n v i r o n m e n t . D e n o t e 1 and 2 to be respectively p r o d u c t 1 and 2 firm A (firm B) p r o d u c e s for its h o m e (foreign) m a r k e t , and 1* and 2* to be respectively p r o d u c t 1 and 2 firm A (firm B) p r o d u c e s for its foreign (home)  market.  T h e A s s u m p t i o n s 1-11 remain to hold in this game. T h e segmented-markets a s s u m p t i o n , A . 1 1 , implies that there are no cross-effects  between p r o d u c t s in one c o u n t r y and p r o d u c t s in the other country even  t h o u g h the p r o d u c t s are i d e n t i c a l or imperfectly substitutable w i t h i n one country. So c o m m o d i t y pairs (1,  2) a n d (1*,2*) are imperfectly s u b s t i t u t a b l e while pairs (1,1*), (1,2*), (2,1*), and (2,2*) are unrelated. We for s i m p l i c i t y assume that there are no transport costs in e x p o r t i n g . T h u s w i t h i n a country, the two firms i n c u r the same costs in all aspects.  F u r t h e r , since consumers in the two countries have identical tastes, 1 (2)  and 1*(2*) will be equally profitable for a f i r m .  F i n a l l y , as has been assumed, p r o d u c t 1 is more profitable  t h a n p r o d u c t 2, so 1 (1*) is more profitable t h a n 2 (2*) for a  89  firm.  T h e above m o d e l specification may be viewed as a direct extention of the basic m o d e l of section 2 (from t w o - p r o d u c t case to f o u r - p r o d u c t case), b u t is concerned w i t h the case of two segmented markets r a t h e r t h a n just one u n i t e d m a r k e t .  T h e unique e q u i l i b r i u m of the basic m o d e l of section 2 involves the i n c u m b e n t ' s  p r o d u c i n g p r o d u c t 1 a n d the entrant's p r o d u c i n g p r o d u c t 2. B y using the e q u i l i b r i u m analysis there, we can easily find the u n i q u e e q u i l i b r i u m for the current game played in o u r t w o - c o u n t r y w o r l d . O b v i o u s l y , firm A would enter all the available p r o d u c t m a r k e t s if there were no p o t e n t i a l invasion. B u t firm A won't enter more t h a n one p r o d u c t in each country, a n t i c i p a t i n g that if entering b o t h in any of the countries, it will w i t h d r a w one of the two s u b s t i t u t a b l e p r o d u c t s in response to an invasion in that p r o d u c t . T h u s , firm A will enter one a n d only one p r o d u c t in each c o u n t r y a n d let firm B enter the other p r o d u c t . Because p r o d u c t 1 is m o r e profitable t h a n p r o d u c t 2, firm A will choose p r o d u c t 1 to enter.  W e therefore reach the following  Result 8:  Result  8.  U n d e r the a s s u m p t i o n that firm A is an i n c u m b e n t in b o t h h o m e a n d foreign markets a n d  A s s u m p t i o n s 1-11, at the e q u i l i b r i u m of our two-country world, firm A p r o d u c e s p r o d u c t 1 for b o t h countries, and firm B p r o d u c e s p r o d u c t 2 for b o t h countries. H e n c e , countries specialize in p r o d u c t i o n a n d trade w i t h each other.  E a t o n a n d L i p s e y (1979), a m o n g others, have the idea that a foresighted m o n o p o l i s t would i n t r o d u c e a new p r o d u c t in a g r o w i n g market before a rival. p r o d u c t s in b o t h countries.  A c c o r d i n g to their m o d e l , firm A would crowd into b o t h  T h i s is contrast to our result in which firm A would not crowd the p r o d u c t  s p e c t r u m a n d allow the entrant to p r o d u c e the substitutable p r o d u c t s in b o t h countries. B r a n d e r and E a t o n (1984) develop a m o d e l t o examine p r o d u c t i o n line rivalry. In B r a n d e r a n d E a t o n ' s m o d e l , firms make three decisions (scope, line, a n d output quantity) sequentially.  They  find  that this sequential d e c i s i o n - m a k i n g  can n a t u r a l l y give rise to e q u i l i b r i u m in which a single firm m o n o p o l i z e s close substitutable p r o d u c t s , called market segmentation by t h e m . Suppose that firm A , a first mover, can now only choose two out of 1, 2, 1*, and 2*. T h i s constraint has no impact on the e q u i l i b r i u m outcome of o u r m o d e l : firm A produces (1,1*) a n d  :  90  firm B ( 2 , 2 * ) . A p p l y i n g B r a n d e r and E a t o n ' s m o d e l to the game, however, firm A in e q u i l i b r i u m produces (1, 2) a n d firm B ( 1 * , 2 * ) .  So firms m o n o p o l i z e their home markets a n d a m a r k e t segmentation  based on  different countries can be expected. T r a d e does not actually o c c u r even t h o u g h it has o p e n e d .  It is noted that in b o t h E a t o n a n d L i p s e y (1979) a n d B r a n d e r a n d E a t o n (1984), there is no possibility for firms to exit i n response to entry. If exit is allowed, we have found that firms would specialize in p r o d u c t s a n d trade to each other. trade.  T h u s a "market s e g m e n t a t i o n " based on s u b s t i t u t a b l e p r o d u c t s can emerge with  In some real cases the story may go like this. F i r m s initially p r o d u c e all p r o d u c t s for their domestic  markets.  A t later stage of the p r o d u c t cycle w h e n , for instance, the p r o d u c t s become better substitutes as  the p r o d u c t s are more finely differentiated, they invade each other's home m a r k e t s in order to e x p a n d their m a r k e t shares. M e a n w h i l e , a n t i c i p a t i n g p o t e n t i a l foreign invasion, they w i t h d r a w some p r o d u c t s in order to protect their positions in the other p r o d u c t s . U n f o r t u n i t e l y , by i n v a d i n g one another, they m a y achieve an inefficient o u t c o m e , while b o t h might have been better off by agreeing not to do so.  T r a d e can be e x p l a i n e d as being due to the c o m b i n e d effects of two motives for s p e c i a l i z a t i o n : differences between countries (as conventional trade theory shows), a n d economies of scale (as K r u g m a n (1979, 1980, 1981), L a n c a s t e r (1980), a m o n g others, analyse). B r a n d e r (1981) a n d B r a n d e r a n d K r u g m a n (1983) show in a s i n g l e - p r o d u c t i n d u s t r y that the rivalry of oligopolistic firms can serve an i n d e p e n d e n t cause of trade. O u r m o d e l is in a s i m i l a r spirit, b u t is concerned with a m u l t i p r o d u c t i n d u s t r y where the issue of specialization is e x p l i c i t l y a d d r e s s e d .  6. CONCLUDING REMARKS T h i s p a p e r has shown that the type of trade p a t t e r n which will emerge is closely related to t h e cost conditions (entry a n d exit costs, fixed a n d m a r g i n a l p r o d u c t i o n costs, t r a n s p o r t cost). costs as a variable seems largely ignored in the trade literature. in this p a p e r several interesting a n d significant results. 91  In particular, the level of exit  B y considering exit costs, we have shown  T w o - w a y trade might arise in identical p r o d u c t s  which are p r o d u c e d only for t r a d i n g in the presence of t r a n s p o r t costs. T h i s might h a p p a n purely because oligopolistic firms have an incentive to t r y to gain market d r i v i n g the foreign firms out of some p r o d u c t s .  shares by i n v a d i n g the foreign markets a n d  F u r t h e r , this kind of two-way trade c a n i n t r o d u c e p r o d u c t s  which would otherwise not be p r o d u c e d in a u t a r k y  and t h u s b r i n g about greater variety of c o n s u m p t i o n .  F u r t h e r m o r e , o p e n i n g of trade m a y also reduce p r o d u c t variety available to consumers.  M o r e o v e r , instead  of p r o d u c i n g all s u b s t i t u t a b l e p r o d u c t s a n d m o n o p o l i z i n g the h o m e markets, firms m a y specialize in some of the p r o d u c t s a n d invade each other's home m a r k e t s .  Since the costs of w i t h d r a w i n g a p r o d u c t can be s m a l l  and the f i r m s ' strategy of raising exit costs is often not viable, the analysis of considering exit costs m a y have some suggestive power.  T h e kind of two-way trade where trade takes place in identical p r o d u c t s which are p r o d u c e d only for t r a d i n g is h a r d l y found in reality.  It is possible to construct  this p a p e r to explain this e m p i r i c a l aspect.  alternative  models based on the m o d e l of  A m o n g t h e m , we briefly discuss the following two which use  r e p e t i t i o n a n d i n c o m p l e t e i n f o r m a t i o n . F i r s t , a p p l y i n g K r e p s et al. (1982) to the P r i s o n e r s ' D i l e m m a game of section 3 w h i c h is now played finite times, we expect that each firm would take a " N o t Invade" p o s i t i o n u n t i l the last few stages, provided that each firm initially assigns a positive p r o b a b i l i t y that the other will not i n v a d e . S e c o n d , the basic game of section 2 can be varied as an e x a m p l e of the chain-store game. are two possible e q u i l i b r i a in the chain-store  There  game (see Selten (1978) o r K r e p s a n d W i l s o n (1982)). O n e of  t h e m is a perfect e q u i l i b r i u m i n v o l v i n g the entrant's.entry, the one discussed in this paper. T h e second is an i m p e r f e c t e q u i l i b r i u m i n v o l v i n g the entrant's s t a y i n g out. In an environment of perfect i n f o r m a t i o n , the first e q u i l i b r i u m will prevail even if the game is played several times. S u p p o s e , however, that the entrant initially assesses some positive p r o b a b i l i t y , p , that the i n c u m b e n t will " i r r a t i o n a l l y " fight, rather t h a n exit, in response to entry. Since h a v i n g a reputation for being t o u g h is advantegeous t o t h e i n c u m b e n t , the i n c u m b e n t would try to develop this reputation early in the game even though by doing so it would suffer s h o r t - r u n losses. K r e p s a n d W i l s o n (1982) show that even for very s m a l l p , the r e p u t a t i o n effect soon predominates a n d it can give rise to credible threat even in a finitely repeated game.  92  U n d e r this m o d e l , therefore, foreign entry  m a y be effectively deterred, especially in earlier stages of the game, and the kind of two-way trade m a y not occur.  T h e p a p e r is an a t t e m p t to c o n d u c t an e x p l o r a t i o n of the trade models, if not any a t t e m p t to prescribe the reality of trade.  T h e kind of two-way trade may be viewed as non-realistic.  analysis for the effects of trade on variety, we have not doen a systematic  F u r t h e r m o r e , except the  welfare analysis i n c o r p o r a t i n g  the c o n s u m e r s u r p l u s . Nevertheless, we do show a n u m b e r of interesting theoretical possibilities concerning i n t r a - i n d u s t r y t r a d e , specialization, and p r o d u c t variety.  F i n a l l y , the m o d e l in this p a p e r has been described and interpreted as a m o d e l of trade.  Instead of  e x p o r t i n g , invasion m a y also take the form of foreign direct invesment (establishing p r o d u c t i o n facilities in the foreign countries, for instance).  We note t h a t the basic results o b t a i n e d w i t h trade in this p a p e r would  continue to h o l d in the presence of foreign direct investment.  93  NOTES  1.  T h e case of c h a n g i n g c  2  given c can be s i m i l a r l y analysed, a n d most results r e p o r t e d in the paper are t  s i m p l y reversed in this case.  2. 2fi  If the d e m a n d p a r a m e t e r s are estimated u s i n g eqs. (10)—(14) in the paper, then bi > k as long as  U  > P  2 U  ; b > fc as long as Q 2  i  0  > Q . 2U  Q , and P u  l 0  are respectively the a c t u a l quantities a n d prices for  a year.  3.  T h e r e are s m a l l errors in T a b l e 4 a n d 5 of D i x i t (1985).  In T a b l e 4, the J a p a n e s e profit under the  M F N - t a r i f f should be $.7730 billion rather t h a n $.928 billion which is given in D i x i t ' s p a p e r . T h i s is because the tariff revenue 100 x Q  2  = $100 x .001546 = $.1546 billion must be s u b t r a c t e d f r o m the total Japanese  profits of $.928 b i l l i o n . T h e same error is also f o u n d in T a b l e 5. A n o t h e r error in T a b l e 4 is in the c a l c u l a t i o n of the J a p a n e s e profit u n d e r the o p t i m a l subsidy. In this case the Japanese profit should be $.7192 billion r a t h e r t h a n $.574 b i l l i o n .  T h e latter is the difference between $.7192 billion a n d $.1491 =  100 x Q  2  which  m a y be considered as the U . S . tariff revenue. B u t in the o p t i m a l subsidy case, the tariff is set at zero, a n d hence there are no tariff revenues to be considered.  4.  A s i m i l a r a s s u m p t i o n is m a d e in J u d d (1985) w h i c h says that a s i n g l e - p r o d u c t firm will receive more  profits (gross of entry costs) by i n t r o d u c i n g the other p r o d u c t . We find the c o n d i t i o n of "gross of entry costs" is not necessary for the d e t e r m i n a t i o n of equilibria. So we exclude this c o n d i t i o n from our a s s u m p t i o n .  94  5.  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B r a n d e r , 1983, International  R & D rivalry and i n d u s t r i a l strategy, Review of  E c o n o m i c s Studies 50, pp.707-722.  26.  V e r n o n , R . , 1966, International  investment  and i n t e r n a t i o n a l trade in the p r o d u c t cycle,  J o u r n a l of E c o n o m i c s , 80, pp.190-207.  99  Quaterly  Appendix 1 C o n s i d e r the linear d e m a n d functions:  Q i = a  Q  2  T o find the p a r a m e t e r s or,, a ,  = a  2  +  7  l  P  l  +  P  1  (1)  2  F , - pP 2  (2)  2  /3 , and 7 , three seperate sets of conditions are used.  p  2  - / 3  L  2  lt  (i) T h e s y s t e m s h o u l d be compatible w i t h the actual prices F  1 U )  P  2 U  a n d quantities Q\u, Q20 for the  year u n d e r c o n s i d e r a t i o n :  Qio = a - 0 P l  Q20 = a  2  l  l o  + P 1  - PP  + iPiu  2  (3)  2 u  (4)  20  (ii) T h e overall price elasticity of d e m a n d for automobiles in the U . S . is to be e . Since U . S . and Japanese cars 1  are b e i n g treated as imperfect substitutes, this elasticity is interpreted as the effect of an e q u i p r o p o r t i o n a t e rise in the price of the two on the c o r r e s p o n d i n g (dual) quantity aggregate.  Pi — f i P,  and change P while h o l d i n g JT , JT X  2  P  2  =  fixed. T h e d u a l quantity is  100  *P 2  Let  Use ( 1 ) and  (2),  Q =  (ft* -  (7r,a, + 7r a ) 2  2  2  2 n-ijr 7  + /? )P  (5)  2  2  Then  —  B  e  = -(ft*? -  277^2  + /? TT ) 2  2  dP Q - ' >  l  e  (/g.TT -  2 7rnr  2  7  (jTia, + 7r a ) 2  2  2  M u l t i p l y P on b o t h sides and note ^ P  e,(F,a,  =  2  2  2 7 ^ ! ^ + ^ 2 T  (e! +  2  (  ei  2  2  2  Pi,w P  + P a ) -  + )g 7r )F  (/9!jr -  2  «i(Tiai + T a ) -  2  7rJ -  2  )  F  277TiJr + / ? T T ) F = 2  0  2  2  = P , we get 2  + IK/?,/*,  2  -  27P P  -  2  1  + / 3 F ) = 0.  2  2  (6)  2  E q . ( 6 ) holds at the observed p o i n t , i.e.,  e,(F  1 0  a,  + F  2 0  a ) 2  (e, + 1)(/9,F  2  0  7  F  1  0  F  2  0  + /3 F 2  2  2  0  ) = 0.  (iii) T h e elasticity of s u b s t i t u t i o n between U . S . and Japanese cars is to be e . 2  (7)  T h a t is, at the observed  point, <*Iog(Qi/Qa) _  rflog(F,/F ) 3  101  6 2  1  J  T o have Q1/Q2  as a f u n c t i o n of P i / P  2  and thus the substitution elasticity defined, the parameters must  be at least at the observerd point satisfied an a d d i t i o n a l c o n d i t i o n ,  P,o ( a , 7 + a / ? i ) = P 2  2 0  (a  2 7  + (X1P2)  W e can show eqs. (8) and (9) are equivalent to the following two  ft<?20  TfQlO +  art  ,  =  (9)  equations,  ~  r\  e  (10)  2 3iuQ20 l  "20  T h i s is because f r o m (9), a n d (3), (4),  P i o ( « i 7 + «2/3i) = P  =>  (a  2 7  + (X1P2)  Pl0{PlQ2U + 7 Q l o ) = P2i>{lQ20  ^20  _  Pit)  From  2 0  P1Q2U  +  + PiQio)  iQw  (12)  lQ20+P2Qli>  _  (12),  dlo&iQi/Qi)  =  dlog(P,/P2) =  cilogQi -  dlogQ  2  dlog F , - dlog F  2  dQJQ  lu  -  2 0  /Q  dP /P  dPJP -  2  10  =  dQ  2 u  (i/Qi»+p2/Q2u)dP 2  dPi/Pio =  2 u  7Q2U  +^2Ql  U f >  QluQ2U  102  {Pl/Qw + l/Q20)dP  - dP /P 2  2 u  l  F r o m (8),  we have  P2Q1V =  7<?2l) +  „  •  S i m i l a r l y , we have  + 7<3iu =  T h u s , eqs.  (3),  (4),  (7),  (10)  a n d (11)  ~  •  are five i n d e p e n d e n t and linear equations.  We can solve for oti, 012,  Pi, ft? and 7 u s i n g C r a m m e r ' s rule, y i e l d i n g  Qfl = (ei + l ) 9 i o a  2  =  (ei +  1)<?20  Qio(eif iuQi J  Pi =  02 = 7 =  The  +  P2o(PloQlO  +  (e  F20  2  1(  fr  2  2  -  e P 2  2  0  Q  2  u  )  eifiiu<?2o) ^20^20)  ei )QIQQ U 2  •fioQio +  c o r r e s p o n d i n g inverse d e m a n d functions  parameters a i , a , 6  +  + P20Q20)  Q2o(e2^ioQio  Pit)  The  0  Pio{PiuQio  P20Q20  are  = <*i -  =  a  2  +  b i Q i o + *<?20  ^ Q l O  —  a n d k can be easily estimated  to be those given in section 2.  103  6  2  Q  2  U  using a , a , Pi, ft? and 7, a n d they t u r n out x  2  APPENDIX 2 SENSITIVITY ANALYSIS FOR ELASTICITIES E1 AND E2, 1979 (PERCENT CHANGE FROM BASE)  MFN-TARI OPT-TARI OPT-SUBS  O  E1 T S P1 P2 01 02 JAPAN PROFIT US PROFIT US CONS SURPL TARI REV SUBS COST US WELFARE  -5 0  -5 1.412  O 0 0 0 0 o 5 . 263 0  .0064 . 1547 .0689 -.3123 -.6237 . 1378 5 . 331 1 .095  4.498  4.494  -5 .4761 -.0993 -.0578 -.3450 -.4656 -.9290 - .6888 4.510 . 1294 4.441  MFN-TARI OPT-TARI OPT-SUBS E1 T S P1 P2 01 02 JAPAN PROFIT US PROFIT US CONS SURPL TARI REV SUBS COST US WELFARE  -2.500 0  -2.500 .7031  0 0 0 0 0 0 2.564 0  .0032 .0770 .0341 -.1557 -.3112 .0683 2.597 .5462  2.191  2 . 190  -2.500 .2303 -.0487 -.0287 -.1724 - . 2312 - .4619 -.3445 2 . 197 .0576 2. 163  OPT-TS -5 - . 3182 - . 3511 0 -.0616 - .351 1 -.3182 -.6353 -.7010 4.511 -.6353 -.7010 4.431 OPT-TS -2.500 -.1590 -.1755 0 -.0308 -.1755 -.1590 -.3178 -.3506 2 . 198 -.3178 -.3506 2 . 158  MFN-TARI OPT-TARI OPT-SUBS E1 T S P1 P2 Q1 02 JAPAN PROFIT US PROFIT US CONS SURPL TARI REV SUBS COST US WELFARE  E1 T S P1 P2 01 02 JAPAN PROFIT US PROFIT US CONS SURPL TARI REV SUBS COST US WELFARE  E2 T S P1 P2 01 02 JAPAN PROFIT US PROFIT US CONS SURPL TARI REV SUBS COST US WELFARE  2.500 0  2.500 -.6973  0 0 0 0 0 0 -2.439 0  -.0031 -.0763 -.0335 . 1548 . 3099 -.0670 -2.469 -.5435  -2.084  -2.083  -.0441 -2.057  2.500 . 1589 . 1753 0 .0307 . 1753 . 1589 .3180 . 3509 -2.090 .3180 . 3509 -2.053  MFN-TARI OPT-TARI OPT-SUBS  OPT-TS  5 0  5 -1.389  0 0 0 0 0 0 -4.762 0  -.0062 -.1520 -.0664 . 3088 .6185 -.1328 -4.820 -1.084  -4.069  -4.067  2.500  OPT-TS  -.2159 .0468 .0284 . 1721 .2283 .4570 . 3446 - 2 .091  5  -.0756 -4.016  5 .3176 .3505 0 .0615 .3505 .3176 .6362 . 7022 -4.080 .6362 . 7022 -4.007  MFN-TARI OPT-TARI OPT-SUBS  OPT-TS  -5  -5 1 . 101 -.1262 0 .2131 -.1262 1 . 101 2.215 -.2522 -.0536 2.215 -.2522 -.0182  -5 0  -5 -.8303  0 0 0 0 0 0 0 0  -.0089 -.0108 -.0951 1 .040 2.090 -.1900 .0095 . 2008  0  -.0148  - .4182 .0919 .0564 . 3441 .4537 .9095 .6893 -4.082  -.8154 .0860 .0747 - . 1427 .6014 1 .206 -.2852 - . 1444 -.9570 -.0154  MFN-TARI OPT-TARI OPT-SUBS E2 T S P1 P2 01 02 JAPAN PROFIT US PROFIT US CONS SURPL TARI REV SUBS COST US WELFARE  E2 T S P1 P2 01 02 JAPAN PROFIT US PROFIT US CONS SURPL TARI REV SUBS COST US WELFARE  E2 T S P1 P2 01 02 JAPAN PROFIT US PROFIT US CONS SURPL TARI REV SUBS COST US WELFARE US WELFARE  - 2 . 500 0  -2.500 -.3995  0 0 0 0 0 0 0 0  -.0044 -.0037 -.0474 .5159 1.034 -.0947 . .0044 .1143  O  -.0074  -2.500  OPT-TS  -.4736 -.0077  -2.500 .5466 -.0626 0 .1058 -.0626 .5466 1.096 -.1252 -.0265 1.096 -.1252 -.0090  MFN-TARI OPT-TARI OPT-SUBS  OPT-TS  -.4030 .0424 .0373 -.0709 .3005 .6018 -.1417 -.0714  . 4640 .0076  2.500 -.5384 .0617 O -.1042 .0617 -.5384 -1.074 . 1234 .0260 -1.074 . 1234 .0089  MFN- TARI OPT-TARI OPT-SUBS  OPT-TS  2.500 0  2.500 . 3707  0 0 0 0 0 0 0 0  .0044 .0007 .0470 - .5081 -1.014 .0940 -.0037 -.1392  0  .0073  5 0  5 .7148  0 0 0 0 0 0 0 O  .0087 -.0014 .0937 -1.008 -2.007 .1874 -.0068 -.3009  0 0  .0145 -.0148  2.500 .3938 -.0414 -.0373 .0700 -.2999 -.5988 . 1400 .0699  5 .7786 -.0818 -.0744 .1390 -.5991 -1.195 .2783 .1383 .9188 .0151 -.0154  5 -1.069 .1224 0 -.2068 .1224 -1.069 -2.126 .2450 .0516 -2.126 .2450 .0176 -.0182  Appendix 3  The  Let  4 K  X  A  K  3  =  -  b  K  x  b  2  ~  2  k  >  2  =  [ b  A  =  I  =  b  =  b {2(V  >  V  2  A  1  of  4 K  K  X  -  3  K  >  2  0  0,  +  b  +  I  2  Proof  V  x  2  { 2 b  2  A  +  V ))((f>, +  +  2  I  2 V  2  ) A  1  +  V  2 l  b  +  2  2 V  2  ( b  +  l  V  )  x  2  )  -  k  2  ( A  +  (2b  +  x  3  where h  I  2  ( 2 V  2  2  b  +  x  { 2 b  2  +  x  { V  2  )  x  b  -  x  +  x  )  2  b  k  V  2  )  x  2  > K (26 (26iVi + 2  -  = V2(4MM2  /  3  >  0,  =  b  >  V  =  V  V  x  2  { 2 b  { 2 b  2  2  { 4 b  b  x  b  x  +  2  2 V  2  2  ( b  V  ( b  2  2  2  2  2  2  Therefore,  4 K  X  K  3  k  +  V  +  b  )  + 2fc & -  )  2  +  x  2 b  k  2  x  2  x  )  2  +  { 2 V  +  x  2  +  2  b  (2V, +  +  2  ) ( V  2  = V (4b (f>!() >  b  2  0,  >  2  2 b  b  2  V  x  V  x  )  +  +  )  2  +  4 b  b  x  b  V  2 V  +  x  { b  2  ) { V  4 k  2  2  x  b  2  2 V  +  x  x  V  b  2  2 b  -  2k 2Vx)  { b  )  K  2  >  0.  b  x  )  2  2  2  )  -  -  +  2  4 k  2  b  2 b  2  x  -  k  k  2  2  - 2fc (2b + V , ) ^ 3  )  ( V  -  2  ( V  1  2 k  2  X  , V  2  X  )  V  V  x  >  )  ( V  o)  ) )  ( 2 b  +  x  V  2  2  - Ar(26, + V i ) K ) 2  V  x  2  V  )  x  { b  -  x  k  b  2  2  ( 4 b  -  k  2  )  Q.E.D.  107  2  4bxVx  +  2  0.  -  V  x  +  x  x  ) b  x  +  V  2  +V 2))  ( 4 b  x  b  2  -  k  2  )  +  4b 6 V,) 2  2  2 x  b  2  >  o)  V  l  ) V  2  )  2  Appendix 4  The  A"  4  =  If a , ,  fc(6 V,  6,-,  (P u - c ) / Q 2  2  K  *  -  2  fciV )(a, 2  a n d k are  2 U  -  Proof  of  c i ) + ((6, + V , ) V 2  estimated  K  2  >  4  -  k  2  0  and  K  V , ) { a  using eqs.(10)-(14)  2  it  pn2 (AF2Q1(2P  -  c , ) ^ ^ ,  A r t n  +  ( ( F i ( 2 P , Q , + P <? ) + 2 ( F , Q , + P Q ) ( P i 2  2  1  2  0  c,)  and V j  2  2  C l  ))  2  =  (Pi  U  — C i J / Q j o , Vj,  we have  - c.KP.Q, + 2P Q ) - P,(P  =  V  >  in the p a p e r ,  , by s u b s i t u t i n g t h e m into the expression of K  4viV2-« V  -  b  -FfP  2  2  2  Q,(Pi -  2  - c )(2P,Q, + P Q )) 3  2  c,))Q (2P 2  2  -  2  c )) 2  1 * Q \ Q  where P i , P  2  2  P Q  2  and (?i,C?2 are the actual prices and quantities, i.e., P , =  108  P, , Q, = u  Q^,  and PC? = P i Q i  +  + P20Q20  P2 Q2 = PioQn)  Q  = PxP.QiiPi  + [P - c ))P {P x  - P P Qi(2P Q 2 l  2  = PQu-  l  i  2  2  + PQ) 2  + 2(PiQi  2  + 2P Q ){Pi  - Pi P Qi(2PiQi  + P Q )(Pi  2  2  2  2  + 4PMPiQi  2  +  +  + P2Q2HP1  2  2  + [Pi - Ci)(P > 0  if  2  - Ci)(P  PMtfPxQi  = P P Qi{PiQi  2  2  2  2  -  2  2  2  - c ) + P{Qi(2PiQi  2  2  F <3 )(F, 2  2  2  Ci)(P  -  ~ Ci)  + P (2P Qi 2  2  -  2  c,)(2P  2  - c )  2  2  + P Q ) (P 2  2  2  2  2  2  + P Q ){P  2  + P Q ){PiQi(4Q  2  2  2  2  - F ) + 2  P >0 2  2  b  2  2  2  - c )  2  2  - c ) - P iPlQiQ (Pi  2  T h e r e f o r e , K4 > 0 as long as 2 Q u > F u -  That K  P P QiQ {Pi  c ) -  -  2  2  2  2  2  - c )  - c )2Pi(PiQi 2Q -  2  - Ci)) Q (2P  2  3  2  - Ci)(P  2  l  - c)  2  + P Q )(Pi 2  l  - a) - Pi P Qi(2PiQi+P Q )(P  2  - Pi P QiQ (Pi 2  + (Pi - Ci))(P  2  > Pi P Qi{PiQi 2  l  + P Q ){Pi  l  + (Pi{2PiQi 2  -c )(P Q +2P,Q )  i  > 0 as long as 2 Q i o > F  2  i y  can be similarly  Q.E.D  109  shown.  - c )(PiQi(2Q 2  2P Q ) 2  2  2  - P) + 2  PQ ) 2  2  2  -  c ) 2  Appendix 5  The  ^ ±  = A  o f d K  / d c  b  <  l  0  (((b + K ) K, - fc V )(a, - ) + fc(6,V - fc V,)(a - c ) ) 2  2  =  ^-((62  =  ^  =  ^ - b  L  Proof  b  ac!  ( ( b  2  2  { [ b  2  2  2  Cl  2  2  2  2  + V ) (a! - c,) - fc *(a - c )) - ((6 + K ) K, 2  2  + V  2  2  2  ) ( a  2  + V  2  2  2  k  2  V  2  2  )  - c,) - fc(* - c )) + ^-V (&2 + V )(a, - c,) - (f> + K ) V, + fc V acj 2  2  l  ) ( a  2  2  2  2  2  2  2  C l  2  2  2  3  2  3  2  3  Using (19) in the paper and the fact that  dV  d V x / d c  <  x  0,  ,  = - — ( M ( f c + ^2)(ai - ci) - k{a - c )J  h  x  2  d c  2  2  x  dV, =  ~  h  ac,  Q  u  <  D  <  0,  / = (f> + V ) V! > 0, 2  2  h  2  - ) - f c ( 0 3 - c )) - (fc +V ) V, - ((_^-)K (r> + V )(a, - c,) - fc  x  = /1 - / - i . 2  2  2  2  > ( - ^ 7 ) 2 f c ( a - c ) - fc V L  2  V/  2  2  2  ((^) - - )  =  fcK2  , /  2P  2U  — c  (02  ^  2  2(PioQlU + P uQ2u) 2  "" ° + kV ( ^ " Qn, W,0 2  >2U  2  = * V  fc  Fn)F u  2  <3lU _  C2)  2  2  2  a  ^ i  +  { P  l  u  ^ ^ ^ _ _ ( F  > 0. 110  Q  w  Piu^u \ + P Q u)/  1  2 U  0  Q  2  I  0  +  2P Q ) 2 0  2 U  2  Therefore,  d K  b  / d c i  0.  <  Q.E.D.  Appendix 6  The  Since  V i / V  2  >  Proof  of  2  k ( b  2  V i  -  (b  2  +  V  2  dci  dci  + K ) V, 2  2  2  2K  k  2  V  fc(6 V,  2K  2  k ' V ^ i i b r  2  V  2  +  (fc,6 -  k  2  +  ( ( ( &  2  +  V  2  )  2  ) ( { ( b  2  2  V  2  k  2V ){b b l  x  l  2  2  V  2  2  k  2  2  )  +  V ? b  2V (b  +  2  2  l  +V,) ) 2  + V )) > 0  2  2  2  2  2  2  2  2  " fc ^2)(V, b + 2V2(f' + V,) ) - fc(6 V, -fc,V )6,V (2b 2  t  -  V- ) V, - fc V )(6, +2Vi) - *(6 K, - fc,K )6 )  +  2  i  t  2  3  )  3  fc(6 Vi - 6 , V ) ( 6 ( 6 i f c - k ) + b V {2b 2  2  - f.,^)  2  2  3  => ((& + V2) Vi "  )  2K  dci  (b  h V  2fc,  dci ds*  dt*  7  using Result 6,  bi/b ,  dt*  ds*  Result  2  2  2  1  2  2  2  ( M 2 - it )/, + 7 > 0 2  2  where  7 = ( ( 6 + V ) K, - * K )(V, 6 + 2V (6, + V,) ) - *(6 V, - 6,V )6,K (2b + K ). a  3  2  2  2  2  2  2  2  2  2  Ill  2  2  2  2  2  +  V  2  ) ^  >0  By  a d d i n g the t e r m t> fc V (bi 4- 2 V , ) into 7, while at the same time s u b t r a c t i n g it f r o m J , , we have, 1  h  2  2  =  {(h + V ) V , ( f > , + 2 V , ) -  -  fc(6 V,  >  (<>2 'i( 'i + 2 V , ) -  -  2  -  2  V  6 , ^ 2 ( 6 , + 2 V , ) ) + (fc, W  2  2  > 0  + 2V,) -  fc V (6, 2  2  +  2V,))  6^2)63  (  b  i  b  2  V  2  { b  Jfc(b2V, - 6 , V 2 ) f c 2  = 6 (6,  i  + 2V,)(6 V, 2  if  ((b  fc,V )  2V,)) + V (6, + 2V,)(6,6  +  l  2  2  + V ) 2  2  > b  2 2  a  -  A; ) 2  )  + V (6, + 2V,)(6,6  2  3  2  - A: ) 2  *(fc V, 2  b , V  2  ) b  2  6, > fc.  O n c e again, b y a d d i n g the t e r m 6, b V ( V , b + (6, + V , ) 2 V ) into I 2  2  2  2  2  2  112  2  while at the same time s u b t r a c t i n g  it from / ,we have, 2  h  =  +  { ( h  V  2  )  2  V i ( V  b  2  +  2  2V {b 2  +  l  Vi) ) 2  -  bib  V  2  (V  2  b  2  + 2V (6, + K , ) )  + ( M a W , ^ + a ( i + ' ) ) ~ ^ ^ ( V ' h + 2V (6, + 3  2 V  V  f t  2  2  2  2  Vi) )) 2  2  - fc(6 V, - 6 , V ) 6 , l / ( 2 6 -|-V ) 2  2  2  2  2  = (K, 6 + 2V (6, + K,) )((6 2  2  2  2  - *(6 Vi -  biV )biV {2b  >  {V b  2V {bi  -  k(b Vi  2  2  +  2  -  2  2  2  +  2  +  2  2  2  2  (b Vi  +  V  -  2  6,V ) + V ( K 6  -  2  +  2  ( V  2  b  biV ){V bi 2  2  2  +  2V (b 2  1  +  +  2  V)  2  2  2  2  ) { b i b  -  2  - k  = (6 V, - 6,V )(26 + K )V 6,(6, 2  > 0  2  if  6, >  2  2  2  +  2  2  2  2  V ) 2  2  +  2  2  -  k) 2  2  2  +  V {V b 2  2  2  +  V  2  {V  2  b  2  +  2V (6, + V , ) ) ( 6 , 6  >  > (K 6,) ,(6, + K , )  2  2  2  + 2V (6, + V , ) ) ( 6 , 6 2  k.  9c,  V ))  2  2  2  2  2  2  6)  {(Vib )  +  k )  2  V ))  )  k)  >  2  2  2  Therefore,  Q.E.D.  2  + 2V (6, + V , ) ) ( 6 , 6 -  2  fc6,V (26  kbiV (2b 2  2  2  ((6  1  2V b b  V i )  2  2  2  = (62V, - 6 , K 2 ) ( V 2 6 2 + 2V 2 (6, + V , ) 2 6 2 -  >  2  V)  2  2  2  2  Vi) )b {b Vi  biV )biV (2b 2  + K ) K , - 6,6 K ) + K ( V , 6 + 2V (6, + K , ) ) ( 6 , 6  2  dt* dci  2  2  > 6)  2  2  k ) 2  2  Appendix 7  The  Proof  of  K  >  7  0  F r o m (19) a n d (20) in the p a p e r , we have  tf  7  = (rj,6  -  fcV,(26  = (6,6  -  -  2  fcK,(6  = (f> + V ) ( o , -  Q  =  fc )((6,  2  t  + K )(a, -  2  2  k  ) Q  2  2  )  2  D  + K,)(o  2  -  2  Q i o D  D  U  C l  2  (6, + V , ) ( o  - c  2  2  - c - 100) 2  - 100) - fc(a, -  2  C l  )  k  2  ) { a  -  2  fc )(a 2  c  2  -  - c  2  2  - 100) -  fcV b (o, 1  2  2  + V,6 ((6,  + K,)(a  k  - fcV^,((6  + V ) ( o , - ci) - k ( a  2  -  2  )  Q  D  w  2  2  k  2  ) Q  2  t  >  D  - c  2  - 100) - * ( a , -  2  2  + V,6 (5 2 I J Z? -  k V i Q i u D  2  +  100(6, +  U s i n g eqs. (10)-(14),  (6,6  2  -  fc )Q 2  2u  +  V i b  P,(P,<?  2  2  +  Q  -  w  2 P  2  Q  k V x Q i u  2  )  Pi  Z Q i P Q  2(?,FQ  P i P Q  +  2  -  Q i  2F Q (F, 2  c,))  - c - 100)) + 100(6, + K,)Z?  2  ci))  >0  114  c,  - c  2  100) + 100(f), + V , ) D  + K ) ( a , - c,) + 100(1), + V , ) D  2  3  -  2  + V,) +  = (Mz -  = (6i6  - c  2  k ( a  2  ) - K,(6,6  2  ,) -  - 100) - fc(o, - c,)) + 6 V , ( 2 6 , + V , ) ( a  2  + V,(6 (6,  C  V i ) D  -  c,)  2  -  100)  where P , = P , Q i = Q , o , P Q = P Q u i0  W i Q i o ) # + 100(6!  +  V  i  )  D  >  = f i u Q i u + FauQau. Therefore,  0.  115  K  7  = ((6,6  2  -  fc )C? 2  20  + VjfcaQau -  Appendix 8  The  H i  =  [bi  H  2  =  k b  H  3  =  k  V  x  G i  =  k ( b  2  H  t  =  k b  x  #  5  =  k  b  2  2  +  V  { b  x  V  x  ( b  2  =  k [ b  G  2  =  k ( b  x  H  7  =  (bi  + V  H^  =  k{b  H  =  2 ( b  3  V  2  x  b  x  V  V  2  )  (b  V  -  2  X  + V  = ((&, +  b  b  2  X  x  V  V  x  ) ( a  )  b  -  2  k  )  X  2  )  +  x  V  )  X  -  k  2  -  k  -  k  2  V  x  ) ( a  2  ) ( a  x  -  3  x  X  -  c )  -  2  b  2  V  c  2  -  2  ) +  x  ) b  )  +  3  ) ( V  +  x  2  ) V  X  2 V  2  { b  2  2  ) { a  -  2  V  +  x  G i  )  + V  x  ) { ( b  2  2  +  ( b  2  and  - c.) + ((6, + V i ) V  x  k V  V  ) ( V  x  +  k  x  V  2  -  H i  2  ) { a  2  V  )  1  Parameters  )  2  k{{b  + V  x  ) { { b  2 V  +  +  2  -  x  + V  x  1  -  -  2  )  2  of  +  2  ( b  +  6  G  V  -  H  9  f ( b  x  +  2  List  k  2  -  ((6  b  2  ) +  2  +  k  V  2  2  )  2  V  X  2  V  2  -  )  3  k  2  )  - fc(o, - c , ) ) ( ( 6 , +  116  V  X  ) ( V  2  -  b  2  )  +  #iu  =  if,, =  H\2 =  (fri  +  V  1  )  2  b  k (b,  -  3  k(bib - k 2  +  2  2  -  V  X  V  2  2V,)  )  #n  #13 = (ba + V a ) ; ) ! -fc ((, 2 + 2 V ) 2  2  G  4  =  fc(6,V  G  5  =  ((fc + 3  2  2  + b V, + 2  V  2  )  2  V  t  +  2 V  l  V  2  ) { a  fc V )(a, 3  2  l  - c,) -  - c,) -  117  ((6, +  fc(6,V  2  V0 V + 2  2  fc V",)(a 2  2  + 6 V, + 2V V )(a 2  1  2  2  -  c )  -  c)  2  2  Appendix 9  Assumptions  1 - 1 0  Are  Consistent  With  E a c h  Other  in  a  C o u r n o t  Duopoly  M o d e l  Suppose that there are two countries, A and B; each country has only one firm. The firm located in country A is called Firm A and the firm in B is called Firm B. In this Appendix, we examine the case of country A . The inverse demand functions are linear,  P  P  l  =  d  =  2  d  where all parameters are positive, and b > a. Q and P  2  b  -  Q  1  a Q  t  and Q  t  2 in country A . P i  -  -  a  -  Q  (1)  2  b Q  (2)  2  are respectively the total output of product 1 and  2  are corresponding prices.  The cost functions are,  f o r F i r m A  f o r F i r m B  :  :  C{ =  c,  =  F(p,i)  F(p,i)  +  +  mj,  (m  +  (3)  t)q,  (4)  where F(p,i) is the fixed production cost of product i, i = 1,2; m and t are respectively the unit production cost and the unit transport cost, which are assumed as constants; and F(E,i) and F ( X , i ) are respectively denoted as entry and exit costs of product i, i=l,2. 118  1) F i r s t , we check A s s u m p t i o n 2:  p > p{ikir  , / & / / ) > o.  T h e inverse d e m a n d functions are,  P  P  where q f  =  x  ^  2  d  d - b { q f  + q  -  + q ? ) - b l q  a  {  q  A  B 1  ) -  a ( q  +  A  )  + q % )  A  is the o u t p u t level of p r o d u c t i p r o d u c e d by F i r m A , a n d q f by F i r m B , i = l , 2 . T h e f i r m s ' profit  functions are,  F i r m A  F i r m B  :  :  = (F, - m)q* +  P(JkII,/&//*)  Ikll)  P(IkII*,  =  -  m  -  t)qf  ( P  +  ( P  2  2  -  m ) q  -  m  A  -  F(p,l)  -  F[p,2),  - t ) g f - F ( p , 1) - F ( p , 2).  T h e first-order c o n d i t i o n s are ,  d P  A  d P  0,  —T-= 6»crf  d P  A  — r = 0 ; dq*  d P  B  B  — ~ = 0, — ^ = 0. d q f d q *  that is, + 2ag  2bqf  2 a q  A  +  2 b q  4  2  A  + 6gf +  a q %  -  d-  +  bqf  =  d  aqf  +  tyf + a<l + 2f>?f + 2 a g A  a q  A  +  b q  A  +  2bqf  +  119  2  3  2 a q %  -  m  (5)  m  (6)  = d- m - t  =  d  -  m  -  t  (7)  (8)  In eqs. (5)-(8), we assume d > m + t, that is, the m a r g i n a l cost ( i n c l u d i n g t r a n s p o r t cost) is lower t h a n the demand.  S o l v i n g these simultaneous equastions, we obtain the e q u i l i b r i u m o u t p u t levels,  H  R  -  3(6 + a)  d  B  -  m  -  V  It  '  „  3 D + a)  It c a n be seen f r o m (9) a n d (10) that as the transport  cost rises, the d o m e s t i c f i r m , F i r m A , increses its  o u t p u t level whereas the foreign f i r m , F i r m B , reduces its output level. F u r t h e r m o r e , F i r m A p r o d u c e s more o u t p u t s in e q u i l i b r i u m t h a n F i r m B . S u b s t i t u t i n g the e q u i l i b r i u m o u t p u t levels into P(I&II*,  I&iII), we  have  2(d P(/fe/r,/fcfJ) = - ^ -  2t)--F(p,l)-F(p,2) 9(b -I- a) m  -  (11)  )  So A s s u m p t i o n 2 imposes an u p p e r b o u n d on t h e fixed p r o d u c t i o n costs.  A . 2 is more likely to hold as  t r a n s p o r t costs are s m a l l , as d e m a n d is high, a n d as the fixed p r o d u c t i o n costs are low.  2) C h e c k A s s u m p t i o n 8:  P(J,ir)  P(F  - F{X,2) > P(lkII,ir)  , II) - F(X, 2) > P(Ik.IF  120  for F i r m A ,  , //)  for F i r m B .  Using the similar procedure in 1), we obtain,  - m) (136 - 5a)  Id  Pi  I {  '  —  11\ '  2  (d-m) 6 2  -  —A  ( 2 b + a )  2 l d ~ m ) t  t  2  2ab(d-m)t  a  b t  2  2  I(26+a) (26 - a) (26 + a) (26 - a ) 2  2  2  x  F ( v 2  K  V  I) ,  )  Thus, for Firm A ,  Id - m) (6 - a)(166 + 12a6 + 5a ) 2  i r ) + x, 2)  iv )-PU,  | +  F[  (6 + a)(6 - a)(46 + a)(46 - a ) 9^6(26+a) (26^  must be negative.  2  = i  %  2  ^  +  m  (6 - a)(86 + 3a6 + a )(d 2  4  There is only one item  2  (26 + a) (26 - a)  +  2  ( - F ( p , 2 ) )  2  1 b  +  a  )  ro)t F  (  P  . », '  2 )  +  v 2 )  in (12) which is possible to be negative.  (  1  2  )  Therefore,  when F(p,2) = 0, A.8 cannot hold and the domestic firm will stay in product 2 even if facing competition from the foreign entrant. For F ( p , 2) > 0, A.8 may hold. The following conditions are suitable for A.8: (1) smaller transport costs; (2) smaller (6 - a), i.e., the products are better substitutes; (3) smaller F(X,2), i.e., exit costs are small; and (4) larger F(p,2), i.e, the fixed production costs are larger. It is noted that smaller F(p,2) makes A.2 more likely hold while larger F(p,2) makes A.8 more likely hold. More specificly,  fromA.2:  F[p,  2) < V, (t) - F(p,  from A.8:  F{p,  2) > V [ t ) + F [ X , 2), 2  121  1),  where  9 { a + b )  (d - m ) ( b - a)(166 + \ 2 a b + 5 a )  (b + a)(b - a)(46 + a)(4b -  (26 + a) 366(6 + a)  96(26 + a ) ( 2 b -  2  MO  2  2  2  +  (ft -  2  a ) ( 8 6 + 3a6 + a ) ( d (26 + a ) ( 2 6 -  2  2  m)t  2  2  a)  a)t  a)  2  T h u s , F ( p , 2 ) must satisfy the following c o n d i t i o n ,  V (t) 2  + F(X,  1) < F(p,  2)  + F[p, 1) < V ,  (0  (13)  in o r d e r for A . 2 and A . 8 to be consistent with each other. S i m i l a r l y , f r o m A . 2 and A . 9 , we have,  V (t) 2  Because at t =  <  F(X,2)  F(p,2)  + F(p,l)  < V,(0  (14)  0, M<) MO  F u r t h e r , because V , ( 0 / M 0 Because M O  +  86(26 (6 -  o)(166  2  +  +a)  2  > 1  6 >  > 0  Vfe[0,t„),  a  >  0,  2  »s a continuous function of t, => 3 t  > °. => ^ i ( 0 > M O -  for any  12o6+5o )  0  3  => V (t)IV (t) x  2  > \.  T h e r e f o r e , when t, F ( X , 1 ) and F ( X , 2 ) are sufficiently s m a l l , there exist  a p p r o p r i a t e F ( p , l ) and F ( p , 2 ) such that conditions (13)  and (14)  hold s i m u l t a n e o u s l y . T h e similar analysis  can be done for F i r m B .  We have so far checked for A . 2 , A . 8 and A . 9 , and the consistency a m o n g t h e m . N e x t we examine the other a s s u m p t i o n s . In what follows, we shall assume that the t r a n s p o r t costs are zero. A s we have seen, an i n f i n i t e s i m a l increase in t will preserve the results obtained u n d e r t — 0.  3) C h e c k A s s u m p t i o n 4 :  P(IkII,r)  >  P ( I , F )  122  >  P{l,IkJF)  T e d i o u s calculations  show  [d-  m ) ( 1 3 b - 5o)  t  2  2(d - m ) t  2  „ .  .  „ .. o  T h e r e f o r e , at t = 0 , (d - m) (fc - o) 2  Hence, A . 4 ,  P [ I k I I ,  / * ) - / * ( / , / * ) > 0, sets an u p p e r b o u n d on F ( p , 2 ) .  R e c a l l that A . 8 sets a lower b o u n d  on F ( p , 2 ) . T h u s , if b o t h A . 4 a n d A . 8 h o l d , an appropriate F ( p , 2 ) must be f o u n d to satisfy  (d-m) (fc-a)(166 2  3  ^  ^  +  2  + 12afr+5  a  2  )  ^  (d - m ) ( b - a) 2  +  F ( X , 2 ) <  F ( p , 2 ) <  4  b  [  a  +  b  (15)  )  It c a n be s h o w n that (d -  m )  ( b  2  - a)(m2  +  12ab  +  5a )  36(26 + a ) ( 6 + o)fr 2  T h e r e f o r e , for s m a l l F ( X , 2 ) , such an F ( p , 2 ) exists.  2  (d - m ) ( 6 - a) 2  46(a + 6)  T h e other part of A . 4 ,  P [ I , I * )  >  P ( I , I k I I * )  can be  s i m i l a r l y checked.  4) C h e c k A . 3 , A . 6 , A . 7 , and A . 1 0  A . 3 imposes a lower b o u n d on entry costs, whereas A . 6 , A . 7 a n d A . 1 0 impose u p p e r b o u n d s .  More  specificly, for p r o d u c t 1, we have  p(i,ikir),  p{i,r)  < F(E,\)  < p(ikii,N*)  123  - P[II,N'),  p{i,ir).  (i6)  obviously exceeds b o t h  P[I,ir)  and  P ( I , F )  Here we only show  P ( l , l k W ) .  P ( I k I I , N " )  -  P ( J I , N * )  >  P{I,I*).  Because P { I k I I , N ' ) =  ^~^--F{ ,l)-F(p,2),  {  P  [d - m)  2  P [ I I , N ' ) =  =  A  h  46  '  - F [ p , 2 ) ,  Id — m)  ^ ,  P [ U %  [  u  =  L  -  ^  L r  2  -  F  {  p  ,  l  )  ,  id - m ) ( 5 6 2  = >  P { I k l I , N * ) - P ( I I , N * ) - P ( U  )  =  ~  ,  f  l i  13a)  , \  ^>0  if  56  >  13a,  366[a + 6)  a c o n d i t i o n consistent with other  5)  assumptions.  In the foregoing analysis, the two p r o d u c t s are assumed to be equally profitable, b u t an infinitesimal  decrease in t h e m a r g i n a l assumptions.  cost of p r o d u c t  1 will yield A s s u m p t i o n 5 without  F i n a l l y , A s s u m p t i o n 1 can be i n d e p e n d e n t l y made without  affecting  any of the other  affecting the other  assumptions.  T h u s , o u r exercises in this A p p e n d i x show that A s s u m p t i o n s 1-10 are consistent w i t h each other in C o u r n o t c o m p e t i t i o n with linear d e m a n d .  124  Appendix 10  Assumptions 1-10 Are Consistent With Each Other in a Bertrand Duopoly Model  In A p p e n d i x 1, the inverse d e m a n d functions are assumed to be linear,  d - bQi - aQ  P, =  2  P = d - aQi - bQ 2  2  where d > 0, b > a > 0.  The  c o r r e s p o n d i n g d e m a n d functions can be derived as,  Q =a-pP + l  Q =a  2  + P - &P  2  | .1_  iP  l  1  1  2  where  a  1)  N o t e first that the neccessary c o n d i t i o n for A s s u m p t i o n 2,  = ^  > 0,/? =  t+ t  t  u > > 0,  =  n  ,  f r + u  ,", „ b  > 0, a n d /? >  a )  7  .  P{Ik.lI*,  lk.Il)  >  0, is that the fixed  p r o d u c t i o n costs must be zero; otherwise, by setting the price below the m a r g i n a l cost of the foreign  firm  ( m + t ) , the d o m e s t i c firm can m a k e the foreign firm suffer losses. In price c o m p e t i t i o n , we thus assume that the fixed p r o d u c t i o n costs are zero.  2)  i)  W e now show that P(1,IP)  > P(IklI,IF)  In the case where the domesitc  > 0 in price c o m p e t i t i o n .  f i r m , F i r m A , produces both p r o d u c t s a n d the foreign f i r m , F i r m B ,  p r o d u c e s one of t h e p r o d u c t s , say, p r o d u c t 2. T h e firms' porfit functions are,  forFirmA  :  P (lkII,ir) A  = [P  A  125  - m)q + (P A  A  - m)q  A  f o r f i r m B  S u p p o s e that F i r m A chooses P  qf  — 0. T h e n , at given P  A  :  P  B  ( I l * , I k I I )  — ( m + t) -  A  (P  =  * - Q .  P  (m  +  t))gf  to m a x i m i z e its profit,  A  P  -  B  e, 0 < t < t, so as to force F i r m B out of the market . T h u s ,  — ( m + t) — t, F i r m A chooses P  d  2  A  a/Y  a + /?m+ m  =  + 2 7 ( 1 - e)  7  1  2/?  and the m a x i m a l profit is,  P t l k l l 1  '  11*)  '  =  [ a  ~P  m  +  i  m  A s t —* 0 , « -+ 0 since 0 < e < t, hence (t -  p ( /  T h e r e f o r e , for s m a l l t r a n s p o r t costs, t,  ii)  ]  2  +  4  (  <  8  +  7  )  (  t  ~  (  e)  ~  Q  4/3  (  <  g  "  7  )  (  m  +  f  ~  ))  e  e) —» 0 and  / 7 , / r ) - ^ ^ ^ ^ > o .  &  P ( l k I I ,  II*)  0.  >  In the case where F i r m A p r o d u c e s p r o d u c t 1 and F i r m B p r o d u c t 2, the firms' profit functions are,  f o r F i r m A :  f o r F i r m B  P (1,  :  P  B  =  11*)  A  ( I I * , I )  =  [ P  ( P  B 2  and d e m a n d functions are,  q  A  =  =  a  -  j 3 P  +  7/V - PP*  126  A  +  -,P*  A  -  -  (m  m ) q  +  A  t))q*  F i r m A a n d B choose, respectively, Pf  dP  D P  B  and P  2  to m a x i m i z e their profits. T h e first-order c o n d i t i o n s are,  B  = 0 :  A  N  .  0:  2/JF, -  -  _. A , 0  i  P  A  2(3P?  +  = a + /3m  7*7  a +  =  /3(m  +  t)  Solve for t h e e q u i l i b r i u m prices, A  P  (c» + /3m)(2/3 + 7) + 7/?<  =  (  1  )  (2/3 + )(2/3 - 7) 7  P  B  ( « + ^ m ) ( 2 0 + 7) + 2/? <  =  2  )  (  2  (2/3 + )(2/3 - 7) 7  T h u s , the e q u i l i b r i u m prices P  /3(a  PA(I,U)-  -  2  B  and P  /3m +  (2/3- ) 7  will rise as the transport cost rises, a n d P f > P .  A  7m)  Further  A  P {3 -2P){a-  2  2  Pm  2  1  (2/3 + )(2/? -  +  7  7  +  )  1  2/3 ~,{p -  m)t  )<  3  7  2  7  (2/3 + ) ( 2 / 3 -  2  2  7  )  2  as ( - » 0, Z3(a - /3m + 7 m )  2  T h e r e f o r e , as < —» 0,  /3(a -  (/,//*) - PAikiUD  —  Pm + 7 m ) ( 2  ^  4/3(2/3-  W h e n the t r a n s p o r t cost , t, is sufficently s m a l l ,  P { I , 1 I * )  7  >  )  2  1  2  4/3  2  -7(4/3-7) > °  P { I t I I , I I * )  therefore holds for s m a l l exit cost F ( X , 2 ) , as does A s s u m p t i o n 9.  127  ( a - /3m + 7 m )  - —  7 7 ) 2  (a - /3m + 7 m )  2  >  0. T h e c r u c i a l A s s u m p t i o n  )  3)  In the absence of t r a n s p o r t  costs, if b o t h firms produce a c o m m o n p r o d u c t , its price will be driven to  m a r g i n a l cost in price c o m p e t i t i o n . T h i s implies that  f o r F i r m A  :  P { J , /*) = P { J , Ihir)  = P { J I , II') = P ( I I , / & / / * ) = 0  j o r F i r m B  :  p{i\i)  = p{ir,n)  = p{r,iiiii)  = p{ir,ikii)  if fixed p r o d u c t i o n costs are zero. T h u s , for a sufficiently small t r a n s p o r t  =o  cost, these profits will be close to  zero. T h i s p r o p e r t y assures other assumptions hold in price c o m p e t i t i o n .  4) F i n a l l y , in the foregoing analysis, the two p r o d u c t s are assumed to be equally profitable, b u t an infinitesi m a l decrese i n the m a r g i n a l cost of p r o d u c t 1 will yield A s s u m p t i o n 5 w i t h o u t affecting any of the other assumptions.  A s s u m p t i o n 1 can always be independently m a d e . T h e r e f o r e , A s s u m p t i o n s 1-10 are consistent  with each other in B e r t r a n d c o m p e t i t i o n with linear d e m a n d .  128  Appendix 11  The  T w o  Contries  C a n  B e  Seperated  S u p p o s e that there are two countries, A and B . E a c h contry has only one  firm.  T h e firm in country A is  called F i r m A ( F A ) , and the firm in B is called F i r m B ( F B ) . T h e inverse d e m a n d f u n c t i o n s are assumed to be linear,  where Q  x  and Q  P, =  d  -  bQi  F  d  -  a Q i  =  2  -  a Q  -  2  b Q  2  are respectively the total o u t p u t of p r o d u c t 1 and 2 in a country  2  , P  x  and F  2  are the  c o r r e s p o n d i n g prices. U n d e r A s s u m p t i o n 11, each firm perceives the distinct country-specific d e m a n d curve, and therefore the d e m a n d system is c o r r e s p o n d i n g to only one country, i.e., the prices in one c o u n t r y depend only on the quantities p r o d u c e d for that country.  M o e r o v e r , the two countries have the same structure of  demand functions.  T h e cost f u n c t i o n s are the same as those given in A p p e n d i x 1. T h e firms' profit f u n c t i o n s are,  for F i r m A : fyAB FA ~ =  n  rfA , r?B FA ~*~ FA {<I£FA{PI '  n  n  A  + {V?,FA(PI  B  -  M  m  + 1 .FA(P  )  -  A  t  )  +  q l  F  F ( P , 1) -  ~ r n ) ~  A 2  A  { P f  -  m  -  t  )  -  F(F,2))  1) -  F ( P ,  F ( P ,  2)),  for F i r m B : T>AB FB ~  n  -  ryA FB  n  | nB FB n  ( l u F B i P ?  + {<FB{PI  ~ m )  -  m  -  t  +  q l  )  +  F  B  q  { P  A  ,  B 2  F  B  ( P  129  -  m)  A 2  -  -  m  1)  F ( P ,  -  t  )  -  -  F ( P , 2 ) )  F ( P ,  1) -  F(F,2))  where R  represents the profit of F i r m A in contry A , qf'  FA  F  is the o u t p u t level of p r o d u c t 1 p r o d u c e d  A  for c o n t r y A b y F i r m A , a n d the other notations c a n be s i m i l a r l y i n t e r p r e t e d . not p r o d u c e p r o d u c t 1 for country A in t h e market e q u i l i b r i u m , qf  F  Note that if F i r m A does  is set to b e zero; otherwise, it is  A  chosen o p t i m a l l y by F i r m A . Since there are eight quantity variables, there are 256 possibilities of t h e final market structures i n o u r two-country world. Because both the countries a n d the firms come into the m o d e l of section 3 with perfect s y m m e t r y , it is neccessary  that the e q u i l i b r i a , if they exist, of the four-stage  game  of section 3 are s y m m e t r i c with respect t o b o t h firms and countries. W e t r y to show that i n t h e s y m m e t r i c market e q u i l i b r i a , t h e t w o countries can be separated if the m a r g i n a l costs are constant.  W e illustrate this by using one of the s y m m e t r i c cases in w h i c h b o t h firms p r o d u c e b o t h p r o d u c t s for b o t h countries. c o u n t r y , eight  Since the firms are assumed to be able to choose separately first-order  their o u t p u t levels for each  conditions are ensued ,  for F i r m A : d FA R  _ =  d  9l,FA A  „  0 >  d  R  F  _  B  CM- = l2,FA „A  _  0 n  CM- = U 1l.FA a„B '  d  U  A  dRtt  n Q  ?2 =„B  u  >  CM-  9  d  =  0  FA  fl\ (> L  for F i r m B : d  d  R  F B  1\.FB  _  - o n  d  d  R  F B  _  l " , F B  d  = 0 n  R  F B  _  ~= 0  L M  d  1?,FB  ft  d  R  F B r  d  1:  "  = 0  (21  2.FB  L o o k at  3 FA  _ <  lt.FA  d  RA  Because  the f o u r q u a n t i t y variables in country  dRf  +  1 FA  d  D  A  B are i n d e p e n d e n t of  constants, d R f  —  A  FA  0  Thus d R  A  ? ,FA  A  il  1?1A  =  dlf.FA  d  130  (  l t F A  q  A  F  A  a n d ( m + t ) are assumed as  T h e r e f o r e , c o n d i t i o n s (1) and (2) are equivalent to the following c o n d i t i o n s (3) a n d (4),  for F i r m A :  1 ^ — • d  f^-"-  f £ * — . d  1?,FA  l2.FA  0^">-  <> s  l2.FA  d  1I,FA  d  for F i r m B : _  **fs  »«tB  Q  _  ™£iL  0  =  r  j  ^  =  0  (4)  T h a t is, the f i r m s ' m a x i m i z i n g overall profit is equivalent to the firms's separately m a x i m i z i n g profit of each p r o d u c t in each country.  In p a r t i c u l a r , there are four first-order c o n d i t i o n s in each c o u n t r y , each firm t a k i n g  the other firm's o u t p u t levels t o each country as given. In c o u n t r y A :  - m  P  P  P  *  -  A  -  -  A  m  ro  m  -  +  q  A  +  q  A  t  -  +  F  A  ( - b )  +  F  A  ( ~ b )  + q  q £  t +  q  A  F  ,  [ - b )  B  F  B  q *  F  A  A F  A  { - a )  =  0  (5)  { - a )  =  0  (6)  +  q £  ( ~ b )  +  q f _  )  -  a [ q  F  B  F  [ - * )  =  [ - a )  =  B  (7)  0  0  (8)  where  The  P *  =  d-  b ( q  A  P  =  d-  a ( q  A  A  A  F  A  +  +  q  q  A F  B  A F  B  )  -  b ( q  A F  A  A F  A  +  q  A  +  q  A  F  B  )  (9)  F  B  )  (10)  c o n d i t i o n s (5)-(8) contain four unknowns which are the four quantity variables in c o u n t r y A . T h e s e four  u n k n o w n s can be determined by eqs. (5)-(8). B  F  w h i c h contains  S i m i l a r l y , we can write d o w m the four c o n d i t i o n s in country  the other four u n k n o w n s , and we can solve those four q u a n t i t y variables in country  131  B  w i t h o u t refering to eqs.(5)-(8). T h e r e f o r e , c o n d i t i o n s (3) and (4) in eight u n k n o w n s can be p a r t i t i o n e d into two separable  sets based on different countries.  M o r e o v e r , the two sets are perfect s y m m e t r i c .  In other  words, the two countries can be separated and only one country need c o n s i d e r i n g .  Appendix 12  A s s u m p t i o n  I S  and  A s s u m p t i o n s  1-10  Are  In A p p e n d i x 1, we have d e m o n s t r a t e d d u o p o l y m o d e l with linear d e m a n d . also consistent  Consistent  With  O n e  that A s s u m p t i o n s 1-10  A n o t h e r  in  are consistent  a  C o u r n o t  :  In this A p p e n d i x , we show that A s s u m p t i o n 12 m a d e in section 3 is  p(ikii,N')  p[i,ir)  >  +  p[ir,i).  A c c o r d i n g to the results o b t a i n e d in A p p e n d i x 1, as t —> 0,  P { I k , I I , N ' )  -  P(I,ir)  f(d -  M o d e l  with each o t h e r in a C o u r n o t  with the C o u r n o t m o d e l .  ,4.12  Duopoly  P{ir,I)  -  m f  -  ( P , l ) - F ( p , 2 ) V  2 { a + b )  a —  (d  -  m )  2{a  >  0.  T h e r e f o r e , for s m a l l t r a n s p o r t costs, t, A.12 holds.  132  2  2  +  b){2b  +  a)-  Appendix 13  A s s u m p t i o n  12  and  A s s u m p t i o n s  1-10  Are  Consistent  With  O n e  In A p p e n d i x 2, we have d e m o n s t r a t e d that A s s u m p t i o n s Bertrand  d u o p o l y m o d e l with linear d e m a n d .  consistent with the B e r t r a n d  Another  in  a  Bertrand  Duopoly  1-10 are consistent w i t h one another in a  Here we show that A s s u m p t i o n 12 m a d e in section 3 is also  model.  4.12 :  P { J k I l , N * )  >  P ( 1 , J I * )  +  P ( I T , 1 ) .  A c c o r d i n g to the results obtained in A p p e n d i x 2, as t —> 0,  (a - fim + 7 m ) P ( I k I I , N " )  -  P { I , I I * )  -  M o d e l  P ( I I ' , I )  —  *  2  2(0-7)  ( a - /3m + 7m) /? 2  (2/3 -  7  )  ( a - fim + 7m) /3 2  {W-T?  2  ~2  )3  1  2 ( / S - 7 ) ( 2 / ? - 7) > 0.  T h e r e f o r e , for s m a l l transport costs, t, A.12 holds.  133  Appendix 14  Result  S  and  Result  4  Hold  in  the  C o u r n o t  Duopoly  M o d e l  1. R e s u l t 3 holds  In A p p e n d i x 1, we have d e m o n s t r a t e d that A s s u m p t i o n s 1-10 linear d e m a n d . In Result 3 of section 4, A s s u m p t i o n s 1-9  are consistent with a C o u r n o t m o d e l with  h o l d , while A . 1 0 fails.  T h e opposite of A . 1 0 is  A.13,  P{I,N*) > P{lkII,N*) -  4.13 :  A . 1 3 p u t s a lower b o u n d on F ( E , 2 ) .  F{E,2)  Because only A . 3 and A . 7 a m o n g A s s u m p t i o n s 1-9 concern the level  of costs of entry into p r o d u c t 2, we need only e x a m i n i n g the consistency of A . 1 3 , A . 3 , and A . 7 . T h e other a s s u m p t i o n s w o n ' t be affected by A . 1 3 .  F i r s t , since A . 7 sets an u p p e r b o u n d on F ( E , 2 ) , A . 1 3 and A . 7 must be consistent with each other, that is,  P{IkII,N*) - P(I,N*) < F(E,2) < P(II,F)  (1)  T h u s the following c o n d i t i o n must h o l d ,  P(IkII,N*) - P[I,N*) < P(II,r)  which is c o n d i t i o n (1) in section 4.  134  (2)  B a s e d on the results in A p p e n d i x 1, as t —» 0,  P ( I I , F )  -  { P ( I k I I , N * )  -  P [ I , N * ) )  (d F ( P , 1 ) )  -  -  m ) 4b(b  2  =  4 a b  2  +  3 a  b  2  +  a  2  ( b  -  a)  ( +  a)  3  ( d - m ) (2b  +  a )  2  \ b ( a  +  b)  > 0  T h u s , for small t r a n s p o r t  costs, t, c o n d i t i o n (2) holds and the entry cost F ( E , 2 ) can be chosen to satisfy  S e c o n d , as A . 3 also puts a lower b n o u n d on F ( E , 2 ) ,  it won't be affected by A . 1 3 .  T h i s shows that  A s s u m p t i o n s m a d e in Result 3 are consistent with the C o u r n o t d u o p o l y m o d e l w i t h linear d e m a n d .  2. R e s u l t 4 holds  In  Result 4, besides A . 1 0 , b o t h A . 8 and A . 9 fail.  If the failure of A . 8 a n d A . 9 can be assumed to be  due to high exit costs, it won't affect other assumptions.  T h e new a s s u m p t i o n made in Result 4 is thus  A s s u m p t i o n 15 or its opposite. In the first part of Result 4, A . 1 5 holds,  A.15 :  P [ l t e I I , N * )  -  F [ E , 2 )  >  P ( I , I F ) .  So A . 1 5 imposes an u p p e r b o u n d on F ( E , 2 ) , and it will affect b o t h A . 3 and A . 1 3 w h i c h i m p o s e lower b o u n d s on  F(E,2).  F i r s t , we examine the consistency between A.15 and A . 3 , i.e.,  P(lljr)  <  F ( E , 2 )  <  P ( l k I I , N * )  135  ~  P { 1 , I F )  (3)  Because as t —» 0,  p[ii,ir)  -  = (d - m ) ^ '  7  p[ikii,N')  2o  2  K  '  + o b - 10b 2  2ab  3  2  9b(2b + o)2(o + 6)  „2b d- m)  <  3  p(i,r)  +  3  + ;  9b{2b  b -10b -2ab — — 3  +  3  a)2{a  +  2  (a  b)  <  b) '  1  < 0.  T h e r e f o r e , for s m a l l t r a n s p o r t costs, t, F ( E , 2 ) can be chosen to satisfy c o n d i t i o n (3).  N e x t , we e x a m i n e the consistency between A . 1 5 a n d A . 1 3 ,  P i l k l l . N " )  -  P ( I , N * )  <  F ( E , 2 )  <  P ( I k I I , N * )  -  P { I , I P )  (4)  Because as t —* 0, (d  -  m )  2  { - 4 a b  -  o ) 2  So  P ( I k I I , N * )  -  P ( I , N * )  <  P ( I k I I , N * )  -  P(I,ir)  H e n c e , for small t r a n s p o r t costs, t, F ( E , 2 ) can be chosen to satisfy c o n d i t i o n (4).  T h e r e f o r e , t h e first part of Result 4 in which A . 1 5 holds can be checked to be consistent with the C o u r n o t model.  It is n o t e d t h a t the second part of Result 4 in which A . 1 5 fails cannot be consistent with o u r C o u r n o t model.  T h i s is because when A . 1 5 fails, it imposes a lower b o u n d on F ( E , 2 ) , whereas A . 7 puts an u p p e r  136  b o u n d on F ( E , 2 ) , a n d the two must be consistent with each other, i.e.,  P{IkII,N*) {I,ir)  B u t as  t —•  (5)  < F(E,2) < P(II,r)  P  0,  p(iui,  N 1  - pui.n -  - Piun  >  0  T h e r e f o r e , for s m a l l t r a n s p o r t costs, t, no positive F ( E , 2 ) can be found to satisfy c o n d i t i o n (5).  Appendix IS  Result  S  and  Result  4  Hold  in  the  Bertrand  Duopoly  M o d e l  1. R e s u l t 3 holds  A s have been analysed in A p p e n d i x 6, we only need e x a m i n i n g whether the following inequality holds for s m a l l t r a n s p o r t costs,  P[IkII,N*)  - P(I,N*)  (1)  < P(II,F)  Since the profit of an m o n o p o l i s t will be the same in cases where either the q u a n t i t y or the price as the decision variable, f r o m A p p e n d i x 1,  (d-m) K  '  '  '  V  2 (a  +  b)  2  (d-m)  2  4b  F r o m A p p e n d i x 2, when t = 0 ,  P  [  1  J  '  1  ' -  (2/?- ) 7  137  2  [  2  )  Also from Appendix 2,  d  a  b  _ 6 +— a'  a  p _ ( 6 +— a)(6-a)'  )  (6+a)(6-a)'  7  Substituting into (2), and (2) becomes  b(b  -  a)(d  - m)  ,„  2  Hence as t —» 0, { P { I k I I , N * )  (d  -  m )  2  -  P { I , N * ) )  a ( b  -  P{ll,r)  -  o)(-4fc  46(6 + a)(26 - a)  +  o)  (6 > a)  < 0  2  that is, (1) holds for small t. Result 3, therefore, holds for a certain range of parameters in the Bertrand Model. 2. Result 4 holds As has been shown in Appendix 6, when A.15 holds, we only need examining the consistency between A.15 and A.3, and the consistency between A.15 and A.13. i) A.15 and A . 3 ;  P(II,ir)  As  t ->  0,  P ( I 1 , I I * )  ->  0  p(mn,N-)  < F(E,2)  <  P ( I k I I , N * )  -  (4)  P { 1 , 1 F )  and  -  pu,m — _  (  (a  '  a  -  P  m + ym)2  0m  +  1  m )  2  { 2 / 3  2  2(0- )(207  > 0  ~  p [ a  2(/3-if)  (0 > 7)  138  -  P m+ i  207 7  )  m  2(0 3  +  ?  )  7  7  2  )  2  T h e r e f o r e , for s m a l l t, F ( E , 2 ) can be chosen to satisfy  (4).  ii) A . 1 5 a n d A . 1 3 :  P(Jfc//,7V*) -  As  t  P ( I , N * )  <  F [ E , 2 )  <  P { l k l l , N * )  -  (5)  P ( I , I F )  -> 0,  [ P ( I k I l , N ' )  -  P ( I , I I ' ) )  -  { P ( I k I I , N * )  -  P ( I , N * ) )  =  - P ( I , I I " )  (d  ~~*  -  m )  +  2  P ( I , N * )  -  b { b  a)  ~ ( 2 6 - a) (f> + a) 2  (d  -  2  46  +  (d - m ) ( 4 a 6 ( 6 - a) + o 6 + 2  m)  2  a ) 3  (26 - a ) ( 6 + o)46  =  2  > 0  (6 > o)  for s m a l l t, F ( E , 2 ) can be chosen to satisfy (5). T h e r e f o r e , the first p a r t of Result 4 holds for a certain range  of p a r a m e t e r s in t h e B e r t r a n d m o d e l .  It is noted t h a t the second p a r t of Result 4, in which A . 1 5 does not h o l d , can not be consistent  with  our B e r t r a n d m o d e l . T h i s is because  P ( l k l I , N * )  ~  P ( I J I ' )  >  P ( U , 1 * )  holds for small t. C o n s e q u e n t l y , n o positive F ( E , 2 ) can be found to simultaneously satisfy b o t h A . 7 a n d the opposite of A . 1 5 for small t r a n s p o r t costs t:  P ( l k l I , N * )  -  <  P{J,ir)  139  F ( E , 2 )  <  P ( 1 I , I * )  

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