(1) Negative values of t are subsidies, lower bound being -1

Transcription

1 MAKET STUCTUE AND TADE POLICY Standad esult is that in pesence of pefect competition, whee county is small, fist-best outcome is fee tade, i.e., taiffs ae not optimal Counties may be lage enough, howeve, to influence thei tems of tade, i.e., even if makets ae pefectly competitive, county may have monopsony/monopoly powe Taiffs may be used to exploit such maket powe Johnson (1954/54), Maye (1981), and Dixit (1987) Assume a home (foeign) county, with 2 goods x and y, whee home (foeign) impots x (y), t (t*) is home (foeign) ad valoem taiff ate (1) (p x, p y ) and (p x *, p y *) ae pices in the two counties, whee p x = p x *(1+t), and p y *=p y (1+t*) Let π = p x */p y be pices on the wold maket, i.e., intenational tems of tade, such that a decease in π impoves (wosens) the home (foeign) county s tems of tade Home (foeign) county impot demand is M(π,t) [M*( π, t*)], and home (foeign) county welfae is U(π, t) [(U*(π, t*)] (1) Negative values of t ae subsidies, lowe bound being -1

2 Given tade balance condition, πm(π, t) = M*(π, t*), π can be expessed as a function of t, t* Substituting into welfae expessions, these can also be expessed in tems of t, t*, W (t, t*) = U(π(t, t*), t) and W*(t, t*) = U*(π(t, t*), t*) Assuming Mashall-Lene stability condition (2) holds, each county s taiff impoves its tems of tade, i.e., δπ/δt <0 and δπ/δt*>0, while othe county s taiff huts a county s welfae, i.e., δw/δt* < 0 and δw*/δt < 0 Taiff equilibium can be illustated in (t, t*) space, as in Figue 1, whee W and W* ae home and foeign county welfae contous espectively Hoizontally (vetically) lowe contous coespond to highe home (foeign)-county welfae, and assumed that: (i) W (W*) has unique maximum with espect to t fo a given t*, locus of these maxima (**), whee δw/δt = 0 (δw*/δt* = 0), is home (foeign) county s eaction function (ii) and ** have a unique intesection at N, the Nash equilibium of a non-coopeative taiff game, the fee tade point F being pefeed (2) Sum of elasticities of impot demands exceeds 1

3 Locus EE* taces out Paeto-efficient combinations of taiff policies equies elative pice of x to stay the same in both counties, so that π(1+t)= π/(1+t*), o (1+t)(1+t*)=1 Fee tade point is on EE*, but thee is a continuum of policies whee one county o the othe subsidizes thei impots Points on CC* pefeed by both counties to N, feetade point lying in ange CC* AA* is locus of taiff combinations eliminating tade define p a, the autakic elative pice of x, as value of π(1+t) educing M to zeo, and p a * = π/(1+t*) when M*=0, then (1+t)(1+t*)=p a /p a * p a /p a * exceeds 1, as home county impots x, i.e., pinciple of compaative advantage, so autaky locus AA* lies above Paeto-efficient locus EE*, and eveywhee along AA*, each county s welfae is constant If AA* meets axes at Q = (t a,0) and Q* = (0,t a *), thee ae two othe cuves, QB and Q*B* meeting EE* at L and L* espectively in egion A*Q*B* (AQB) home (foeign) county is wose off than it would be in autaky it is subsidizing impots too heavily

4 Conside taiff ates (t, t*), whee t t a, and t* t a *, this is also a Nash equilibium of taiff game Each county s taiff is so high, no tade occus even if othe county sets a zeo taiff, so counties ae locked into autaky Implies non-uniqueness of taiff equilibium although Dixit (1987) claims in a one-shot game, point N will emege with positive tade, i.e., it is pefeed by both counties, and it is a stable equilibium in a noncoopeative game In a epeated-game context, existence of autaky equilibium implies a costly outcome if eithe county deviates fom coopeative outcome along CC*, i.e., evesion to A is a stonge theat than N N is not efficient, thee being joint policy choices, with lowe taiffs, that will leave both counties bette off, fee tade F being one such point Howeve, in a one-shot game, each county pusues its own self-inteest, leading to N, i.e., a Pisones Dilemma esolution of this inefficiency will equie coopeation, e.g., the GATT/WTO (Bagwell and Staige, 1999) esults also hold if each county has maket powe in tems of expots (Lene symmety theoem)

5 A t Figue 1: Taiff Equilibium E Q L * W egion of autaky B C N W* Q* -1 F -1 C* B* L* * E* A* t*

6 OLIGOPOLY AND TADE POLICY Once thee is oligopoly in tade models, what happens if tade policies ae intoduced? A liteatue has gown up aound this, often descibed as stategic tade theoy, poducing some non-taditional esults, e.g., an expot subsidy may impove national welfae The liteatue tends to be full of a lot of special cases, changes in basic assumptions often evesing esults, making it difficult to genealize As Dixit (1987) notes, a citical featue of the theoy is the emphasis on inteactions between ational agents such as fims and policymakes Stategic tade theoy can be chaacteized in tems of non-coopeative, static and simultaneous- move games in the sense that agents do not coodinate thei actions, the game is played once, and agents make thei moves at the same time A citical featue of the analysis is that one agent, the policymake, can make a move befoe othe agents, which intoduces the notion of pe-commitments

7 Conside a situation whee an intenational maket is chaacteized as a duopoly, fims i =1, 2. Equilibium concept is Nash equilibium, whee each fim simultaneously sets its elevant stategy vaiable s i(output o pice) in ode to maximize pofits, given action of the ival fim, s j Given pofits aeπ i, a set of stategic actions is a Nash equilibium, if, fo all i and any feasible action s i : * π = (, * ) (, * i si s j si s j ) * i.e., the set of actions, s i, is an equilibium if neithe fim can change its action to incease pofits, given its ival s action In the absence of govenment intevention, this equilibium is consistent with fee tade, neithe fim being able to unilateally impove its payoff If govenment i announces it will pay fim i an expot subsidy befoe fim i selects its optimal stategy, this altes the level of potential pofits π i and hence the behavio of fim i in equilibium

8 This captues essence of stategic tade theoy: in impefectly competitive makets, fims act stategically, and govenment cedibly pecommits to tade policies that change the final maket equilibium Govenment i has to have some eason fo wanting to povide fim i with a subsidy at the fist stage of the game The standad agument is that thee ae positive economic pofits to be eaned by fim i, and if these ente govenment i s objective function, it has an incentive to pe-commit to policies that incease fim i s pofits Assuming govenment j is not active with espect to fim j, then the incease in fim i s pofits can be thought of in tems of pofit-shifting OPTIMAL TADE POLICY AND OLIGOPOLY Following Eaton and Gossman (1986), fomally chaacteize optimal tade policy in the pesence of oligopolistic competition among domestic and foeign fims in intenational maket

9 Fims poduce single poduct, competition being specified in tems of quantities with abitay conjectual vaiations Single home fim competes with single foeign fim in the intenational maket, with no domestic consumption Home govenment can tax o subsidize expots of home fim, assuming absence of policy by foeign govenment, objective being to maximize national poduct, equal weight being placed on fim pofits and tax evenue Output of home (foeign) fim is x (X), c(x) [C(X)] is home (foeign) poduction cost, with c'(x)>0 [C'(X)>0]. Pe-tax evenue of home and foeign fims given by (x,x) and (x,x) espectively, satisfying these conditions: ( x, X ) 2 ( x, X ) = 0 X ( x, X ) 1 ( x, X ) = 0 x i.e., incease in output of competing poduct lowes evenue of each fim

10 Afte-tax pofits of home and foeign fims ae: = (1- t) ( x, X) - c( x ) Π = ( x, X) - C( X ) whee t is an ad valoem tax The home (foeign) fim s conjectue about the foeign (home) fim s output esponse to changes in its own output given by paamete γ (Γ) Nash equilibium, given home policy, detemined by the fist-ode conditions: (1) (1- t)[ 1( x, X ) + γ 2( x, X )]- c ( x ) = 0 (2) 2( x, X ) + Γ 1( x, X ) - C ( X ) = 0 Theoem 1: A positive (negative) expot tax can yield highe national welfae than laissez-faie (t=0) if home fim conjectues a change in foeign output in esponse to an incease in its own output that is lage (smalle) than the actual esponse Poof: National poduct w is given as: (3) (1- t) ( x, X) - c( x) + t( x, X) = ( x, X) - c( x)

11 Change in w fom a small change in tax ate t is: (4) dw x X = [ 1( x, X ) - c ( x)] + 2( x, X ) dt t t Substituting in fom fist-ode condition (1): (5) dw = - tc x 2 + X 2 dt 1-t t t whee aguments of evenue and cost functions dopped fo bevity (2) implicitly defines X as a function of x, denote this as ψ(x). As t is not an agument of this function, then we can wite, dx / dt ψ ( x)( dx/ dt), and then define a tem g that measues the slope of the foeign fims eaction function, g ( dx/ dt)/( dx/ dt) ψ ( x), i.e., its actual eaction to changes in x. Incopoating g into (5) and finding maximum dw/dt=0: (6) ( g γ) tc /(1 ) 2 t As 2 < 0, both sides of (6) have same sign if 1 > t > 0 and g > γ, o t < 0 and g < γ. The tem (g γ) is diffeence between actual esponse of X to change in x, ψ ( x ), and home fims conjectual vaiation, γ. When g > γ, an expot tax yields moe than laissez-faie, convesely when g < γ

12 Pe-commitment to policy by home govenment allows home fim to set output as if it wee a Stackelbeg leade with espect to foeign fim. If g > γ, without pe-commitment, equilibium involves moe home output than at Stackelbeg as home fim does not fully account fo foeign fim s eaction to an incease in its output when choosing its own output. Convesely if g < γ. Counot Conjectues Unde Counot, each fim conjectues that when it changes its output, othe fim holds output fixed, so γ = Γ = 0, and (6) becomes: (7) g tc /(1 ) 2 t Totally diffeentiating (1) and (2) to solve fo g, (7) can be witten as: (8) 21/( C ) tc /(1 t) 2 22 Second-ode condition of foeign fims pofit maximization ensues left-hand side of (8) has sign of 21 Poposition 1: In a Counot duopoly with no domestic consumption, optimal expot tax t*=sgn 21

13 Poposition 1 is Bande-Spence (1985) agument fo an expot subsidy: policy aises home welfae by shifting pofits to home fim (Figues 2-5) Figue 2, isopofit loci fo home fim given by π, lowe cuves coesponding to highe pofits, Counot eaction function connecting maxima of isopofit loci, slope of being given by sign of 12 found similaly in Figue 3, its slope being detemined by 21. Linea demand necessaily implies 12 < 0 and 21 < 0, and most othe demand specifications Nash-Counot equilibium at N-C in Figue 4, home fim eaning pofit of π C. Along, highest level of pofit would be at π S, equilibium level of pofit if home fim could cedibly pe-commit to being a Stackelbeg leade howeve, unable to do this (see Table 1) Home govenment can achieve this in a Nash equilibium (Figue 5), if it can shift home fim s eaction function tangent to at S Optimal policy will be an expot subsidy unde Counot assumption, povided is downwad-sloping, i.e., 21 < 0 - downwad-sloping foeign eaction function implies output level in Counot equilibium less than Stackelbeg

14 Figue 2: Output Choices fo Home Fim X Home fim s eaction function π 1 Inceasing pofits fo home fim X 2 π 2 x 2 π 3 Monopoly output home fim x

15 Figue 3: Output Choices fo Foeign Fim X Foeign fim s eaction function Monopoly output foeign fim Π 3 Π 2 Inceasing pofits fo foeign fim Π 1 X 2 x 2 x

16 Figue 4: Nash-Counot Equilibium X Π c π c Nash-Counot Paeto-supeio π s Stackelbeg x

17 Table 1: Nash-Counot Stategies Home Fim s f s h Low output High output Foeign Fim Low output 15, 15 C 20, 5 S h High output 5, 20 S f 10, 10 N-C N-C = Nash-Counot equilibium S h = Home fim is Stackelbeg leade S f = Foeign fim is Stackelbeg leade C = Collusive outcome

18 Figue 5: Expot Subsidy to Home Fim X π c N-C Π c π s S x

19 Optimal expot subsidy unde Counot, benefits home fim and county, at expense of foeign fim pofitshifting outweighs any losses fom decline in tems of tade, and wold welfae inceases as pices fall Betand Conjectues Eaton and Gossman (1986) show Bande and Spence esult is sensitive to game played by fims what happens if fims play Betand? Unde Betand, each fim conjectues ival will hold pice fixed in esponse to any changes in its own pice Define diect demand functions fo output of home and foeign fims as d(p,p) and D(p,P) espectively, total pofits of two fims being: π( p, P) (1 t) pd( p, P) c( d( p, P)) Π( p, P) PD( p, P) C( D( p, P)) Each fim sets pice to maximize pofit, taking othe pice as constant, fist-ode conditions being: (9) (1 t )( d pd ) c 0 π d (10) D ( P C ) 0 Π D 2 2 Actual and conjectued pice esponses can be tanslated into output esponses by totally diffeentiating demand functions:

20 dx dx d 1 D 1 d 2 D 2. dp dp Betand conjectue on pat of home fim implies esponse given by: (11) γ dx dp dx dp dp 0 D d 1 1 Actual esponse being: g dx dp dx dp D d 1 1 D Π 2 d Π 2 21 /Π /Π It can be shown that tem (g- γ) is positive only if Π 21 > 0, i.e., foeign fim esponds to a pice cut by cutting its pice. Applying Theoem 1, Poposition 2: In a Betand duopoly with no home consumption, t* = sgn Π 21 If poducts ae substitutes, d 2 > 0 and D 1 > 0, and etuns to scale ae deceasing, c 0, C 0, then Π 21 > 0 necessaily holds with eithe pefect substitutes o linea demands Consequently, sign of optimal tade intevention unde Betand is opposite to Counot case an expot tax is equied

21 Figues 6-9 illustate Poposition 2. Isopofit loci in pice space in Figue 6 fo home fim ae π, highe cuves coesponding to highe pofits, the home fim eaction function being, and similaly fo foeign fim in Figue 7, slopes coesponding to π 12 and Π 21 espectively Without any policy intevention, Betand equilibium at intesection of eaction functions at B, home fim eaning pofit of π B, but along, a highe pofit could be eached at S whee home fim chages a highe pice (Figue 8) Unless home fim can pe-commit to being a Stackelbeg leade, S is unattainable (see Table 2) Home govenment can achieve this by setting an appopiate expot tax such that home fim eaction function is shifted to intesect at S (Figue 9) Betand equilibium whee Π 21 > 0, involves a lowe pice, and theefoe highe domestic output than at Stackelbeg equilibium in contast to Counot Also, implementation of optimal policy by home govenment also aises pofits of foeign fim by facilitating collusion, esulting in a decline in wold welfae

22 Figue 6: Pice Choices fo Home Fim P Home fim s eaction function π 3 P 2 π 2 π 1 Inceasing pofits fo home fim p 2 p

23 Figue 7: Pice Choices fo Foeign Fim P Inceasing pofits fo foeign fim Π 1 Π2 Π 3 Foeign fim s eaction function P 2 p 2 p

24 Figue 8: Nash-Betand Equilibium P π S Paeto-supeio π B Stackelbeg Nash-Betand Π B p

25 Table 2: Nash-Betand Stategies Home Fim s f s h High pice Low pice Foeign Fim High pice 15, 15 C 20, 5 Low pice 5, 20 10, 10 N-B N-B = Nash-Betand equilibium C = Collusive outcome

26 Figue 9: Expot Tax on Home Fim P π S π B S N-B Π B p

27 Foeign Policy esponse Assumed so fa that foeign govenment follows laissezfaie instead assume a 2-stage game whee both govenments pe-commit to policies befoe fims play out duopolistic game in intenational maket With a foeign ad valoem tax of T, foeign fim s fistode condition (2) becomes: (2') (1 T )[ ( x, X ) Γ ( x, X )] C ( X ) A Nash equilibium in policies is a pai of policies (t,t), such that t maximizes w given T, and T maximizes W ( x, X ) C ( X ), given t, whee (1) and (2') detemine x and X Fo T<1, pesence of foeign tax does not affect pevious esults fom Popositions 1 and 2. Fo example, unde Counot, (8) is eplaced by: (8') (1 T ) 2 21 (1 T ) C 22 tc 1 t t* emains sign of 21 i.e., sign of optimal policy unaffected by pesence of foeign expot subsidy o tax, and likewise fo level of T that maximizes W given t Unde Counot, with 12 < 0, and 21 < 0, pefect Nash equilibium is fo both govenments to subsidize expots (see Tables 3 and 4)

28 Table 3: Pisones Dilemma Fo Home and FoeignCounties Home County c f c h No expot subsidy Expot subsidy Foeign County No expot subsidy 10, 10 20, 5 C s S 1 Expot subsidy 5, 20 S 2 7, 7 N N = Nash equilibium C s = Coopeation ove no expot subsidies

29 Table 4: Pisones Dilemma Fo Home and Foeign Counties Home County c f c h Expot taiff No policy Expot subsidy Expot taiff 15, 15 C t 20, 8 25, 3 Foeign County No policy 8, 20 10, 10 20, 5 C s S 1 Expot Subsidy subsidy 3, 25 5, 20 S 2 7, 7 N N = Nash equilibium C s = Coopeation ove no expot subsidies C t = Coopeation ove expot taiffs

30 With Counot behavio, both eaction loci ae shifted outwad, maket becoming moe competitive, benefiting consumes in intenational maket (Figue 10) In the case of Betand competition, with π 12 > 0 and Π 21 > 0, pefect equilibium is fo both counties to tax expots, intevention moving fims towads pofitmaximizing (collusive) equilibium, expotes gaining, consumes losing in intenational maket Both eaction functions ae shifted outwad each county impoves its tems of tade, eplicating esult of optimal taiff unde county monopoly powe (Figue 11) Numbe of Fims If numbe of fims based in home county is inceased, and thei choice of stategic actions is quantity, Counot outcome asymptotically appoaches competitive equilibium, and optimal policy intevention is a tax on expots (Dixit, 1984)

31 Figue 10: Expot Subsidies to Home and Foeign Fims X S 2 π N-C π C C t N C s N-C Π C Paeto-supeio Π N-C S 1 x

32 Figue 11: Expot Taxes on Home and Foeign Fims P π π B B Π Π p