CERGE-EI GOVERNMENT S (IN)ABILITY TO PRECOMMIT, AND STRATEGIC TRADE POLICY: THE THIRD MARKET VERSUS THE HOME MARKET SETUP.

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1 GOVERNMENT S (IN)ABILITY TO PRECOMMIT, AND STRATEGIC TRADE POLICY: THE THIRD MARKET VERSUS THE HOME MARKET SETUP Krešimir Žigić CERGE-EI Charles University Center for Eonomi Researh and Graduate Eduation Aademy of Sienes of the Czeh Republi Eonomis Institute WORKING PAPER SERIES (ISSN ) Eletroni Version 319

2 Working Paper Series 319 (ISSN ) Government s (In)ability to Preommit, and Strategi Trade Poliy: The Third Market versus the Home Market Setup Krešimir Žigić CERGE-EI Prague, Marh 007

3 ISBN (Univerzita Karlova. Centrum pro ekonomiký výzkum a doktorské studium) ISBN (Národohospodářský ústav AV ČR, v. v. i.)

4 Government s (In)ability to Preommit, and Strategi Trade Poliy: The Third Market versus the Home Market Setup Krešimir Žigić CERGE-EI Abstrat We shift the usual perspetive of strategi trade poliy the third market setup to the home market framework in order to reonsider the onsequenes of government (in)ability to preommit to its poliy and ompare these findings with those analogous from the third market setup. In addition, we also analyze how robust the sign is of partiular poliy instruments (R&D subsidies) within the home market setup, as opposed to the third market setup, when there is a shift from seond best to the first best poliy. For that purpose, we apply a standard dynami Cournot duopoly where the firm s strategi variable is investment in ost redution whereas poliy instruments are import tariffs and R&D subsidies. Abstrakt Posouváme obvyklé vnímání strategiké obhodní politiky od modelu třetího trhu k domáímu trhu ve snaze zvážit důsledky (ne)shopnosti vlády zavázat se ke své politie a porovnat tato zjištění s těmi analogikými z modelu třetího trhu. Rovněž analyzujeme, jak robustní je znaménko jednotlivýh nástrojů politik (dotae na R&D výzkum a rozvoj) v modelu domáího trhu jako protějšku modelu třetího trhu, kdy dohází k přesunu od druhé nejlepší k první nejlepší politie. Za tím účelem aplikujeme standardní dynamiký Cournotův duopol, kde jsou strategikou proměnnou firmy investie do reduke nákladů, zatímo politiké nástroje jsou dovozní tarify a dotae na výzkumu a rozvoj (R&D). JEL: F13; L11; L13; O31 Keywords: government ommitment, optimal tariffs and R&D subsides, first best versus seond best strategi poliy. I am very grateful to anonymous referees and Robert Staiger, o-editor of JIE as well as to Elie Appelbaum, Alan Deardorff, Avner Shaked, and Anu Kovarikova Arro for invaluable omments on this paper. The extraordinary researh assistane of Jan Mysilve ek, Mihael Kúnin, Eugen Kováč, and Boryana Madzharova was most appreiated. Address: CERGE EI, Politikýh vĕzňů 7, Prague 1 Kresimir.Zigi@erge-ei.z CERGE-EI is a joint workplae of the Center for Eonomi Researh and Graduate Eduation, Charles University, and the Eonomis Institute of the ASCR, v. v. i. 1

5 1. Introdution An intriguing but under appreiated aspet of strategi trade poliy is the ruial importane of timing in deision, noted J.Brander (1995) in his famous survey on strategi trade poliy. Related to the subjet of timing, but oneptually different, is the issue of a government s ability to ommit to its ation. More preisely, this (in)ability determines the timing in deisions. The government is usually assumed to set redibly its poliy instrument before the firm sets its respetive variables. However, the pratial appliation of the trade poliy might go the other way around; the poliy makers may either lak the ability to preommit, or they set the onrete poliy instruments after the relevant ation of the firm took plae. Notably, the importane of timing and government s ability to ommit to its ation have been studied mostly in the third market setup in whih domesti and foreign firms ompete in some third market thus ignoring onsumer surplus and (possible) tariff revenue. To paraphrase Brander, it is intriguing that the home market framework is under appreiated (or better to say, not appreiated at all!) in this kind of analysis. Using a third market setup, Carmihael (1987) was one of the first authors who turned attention to the issue of government ommitment and the onsequent timing in a deision pointing to the example of the Export Import bank of the United States that sets redit export subsides only after firms set their pries. A firm that antiipates a subsidy has an inentive to inflate a prie sine the size of the subsidy is usually positively related to the prie. In these irumstanes, trade poliy loses its strategi dimension, and it is a rather responsive devie in that governments try to offset an exessive inrease in the domesti prie 1. Thus, there is a pure transfer of 1 In fat, in Carmihael (1987), domesti firms have an inentive to inflate pries to infinity, and so equilibrium pries are obtained as a orner solution determined by the prie ap set by the poliy

6 rents from the government to the domesti firm without any strategi impat and so without any hange in effetive export pries and domesti soial welfare. Consequently, the government will lose nothing if it an preommit to free trade. Carmihael s (1987) analysis sparked a disussion and researh about the modus and timing of trade poliy. One of the ruial features of this disussion is the distintion between the very announement of a poliy program and its atual implementation. Thus, government s deision about the design of a poliy program may preede the seletion of the atual level of suh seleted poliy, splitting a single stage of the game into two stages. Moreover, different timings of the poliy hoie (and different poliies themselves) usually result in various degrees of poliy flexibility pointing to a trade off between flexibility and ommitment (see for instane, Cooper and Riezman; 1989, Arvan, 1991; and Shivakumar, 1993). Thus, for instane, Hwang and Shulman (1993) allow a government to expliitly ommit to non intervention (that is, to free trade, in our terminology) and investigate when the ommitment to free trade yields larger soial welfare. It is important to reall that the above issue of strategi intervention versus ommitment to free trade is an example of rules versus disretion in the sense desribed first by Kydland and Presott, Sine trade poliy is, by its nature, of seond (or even third best) harater, it is plagued with the time onsisteny problem and so the above dilemma of rules versus disretion is likely to be relevant here (see, for instane, Staiger and Tabellini, 1987 and 1989; and Stagier, 1995 for a survey of the literature that deals with rules versus disretion issues in the ontext of trade poliy). Inquiry into the impat of timing in subsequent strategi trade poliy literature is onduted in a somewhat riher and (for the purpose of our upoming analysis) more makers. However, this problem disappears if, as assumed by Gruenspeht (1988), the opportunity 3

7 important ontext, yet still within the third market framework. In this setup, domesti firms undertake some kind of strategi investment prior to market ompetition (see for instane, Goldberg, 1995; Karp and Perloff, 1995; Neary and O Sullivan, 1997; Grossman and Maggi, 1998; Neary and Leahy, 000; and Ionaşu and Žigić, 005). The reason why the strategi investment of the firm an preede the government s ation is the fat that the poliy makers may lak redibility with the firms whose behavior they try to influene (see Neary and Leahy, 000) or there may be an already noted time lag between the announement of a trade poliy program and the implementation of trade poliy instrument at the onrete level. Both these reasons give a strategi motive to the domesti firm to influene (or manipulate) the government's poliy response. In these irumstanes, preommitment to free trade looks even more attrative than in Carmihael s (1987) simple setting in whih trade poliy and free trade are equivalent in terms of soial welfare. The point is now that domesti firms are inlined to overinvest in a strategi variable (e.g. in R&D apital) that may be soially ostly and ineffiient. In turn, it an lead to lower soial welfare ompared to the orresponding soial welfare under free trade (see for instane, Karp and Perloff, 1995; Neary and O Sullivan; 1997, Grossman and Maggi, 1998; Neary and Leahy 000; and Ionaşu and Žigić, 005). This soially undesirable overinvestment ours, among other things, when the ost of apital is not exessively large sine high osts of apital neutralize the inentives for overinvesting. ost of raising a unit of government revenue is bigger than one. See also Neary (1991) and (1994). Surveying the empirial evidene on international omparison of the osts of apital, Karp and Perloff, 1995 informed us that the U.S. has substantially higher osts of apital than other developed ountries (double that of Japan, 89 perent more than in Germany, and 9 perent more than in the United Kingdom in 1988). Yet... aording to some empirial studies, even in the United States, real apital osts are low enough so that strategi U.S. subsides may ause exessive U.S investment (Karp and Perloff, 1995). 4

8 It is worth stressing one again that all of the above onlusions are obtained in the third market setup. Thus, the aim of this paper is to shift the fous from the third market setup 3 to the home market. One reason for this is to test robustness of the above third market setup propositions, and the other is the poliy relevane of the home market framework. To illustrate as lear as possible the analogous effets of trade poliy on the home market, we stik to the very simple dynami Cournot duopoly. Like in most of the above ited papers, the strategi variable is investment in ost redution 4 (see, for instane, Karp and Perloff, 1995; or Grossman and Maggi, 1998). We start by analyzing three stage games in whih either the firm or the government moves first depending on whether the government an ommit or not to its ation before the firm hooses its strategi variable. Sine the ation takes plae on the domesti market, the natural trade poliy instrument to onsider is an import tariff. In addition to the above issue of government s (in)ability to ommit, we also study how robust the sign is of partiular poliy instruments (R&D subsidies) within the home market setup (as opposed to the third market setup) when there is a shift from the seond best to the first best poliy. In a series of papers, Leahy and Neary (1996, 1997, and 1999) and Neary and Leahy (000) stress the distintion between the first best and seond best poliy. The first best versus seond best poliy issue arises in the ontext of dynami games where domesti firms have more than a one hoie variable (e.g. level of R&D and level of output). In this setup, the first best poliy in priniple inludes more than one poliy instrument in order to 3 As Helpman and Krugman (1989) point out the third market approah is useful for isolating strategi interations but is aterrible guide to poliy... 4 Investing in market-expanding investment or produt innovation where the investments shift the demand funtion is effetively idential with ost-reduing investment (see, for instane, Leahy and Neary, 001). 5

9 indue soially desirable levels of all hoie variables. However, in many irumstanes the government may be onstrained to a smaller number of instruments or even only one instrument (say, an R&D subsidy). Suh onstrained poliies are usually termed seond best (or even third best ). One of the interesting results of this literature is that, in the ase of a Cournot ompetition and a third market setup, the R&D subsidy, whih is generally positive in the seond best poliy setup, turns out to be negative (an R&D tax) when the first best poliy is implemented. The home market setup yields several strikingly different results in omparison to the third market setup that has routinely been onsidered in the literature. These are indiated in Table 1 and an be summarized as follows: a) There is likely overinvestment in the strategi variable from a soial point of view; b) The soial welfare in free trade an be higher than the soial welfare under a strategi trade poliy; ) The poliy in whih the government an ommit to at upon prior to the strategi ation of the domesti firm always generates higher welfare than its non ommitted ounterpart; and d) The seond best poliy instrument hanges sign when the first best poliy is employed. In ontrast, with the home market setup of this paper: a) There is underinvestment rather than overinvestment in strategi variables (i.e. R&D investment) from a soial point of view ; b) Free trade is never superior to strategi trade poliy; ) A government that is able to ommit to its poliy generates larger soial welfare, but this finding is not robust and generally eases to hold one we extend our basi model by allowing for a small amount of R&D spillovers; and d) Finally, the R&D subsidy is always positive in both the first best and the seond best poliy. 6

10 a) Investment in a strategi variable from a soial point of view Table 1 Third market Likely overinvestment b) Free Trade Can be superior to strategi trade poliy ) Soial welfare Always lower when the government annot ommit to its poliy instrument d) Robustness of the investment subsides when moving from the first to the seond best poliy Non robust (hange of the sign of the poliy instrument) Home market Underinvestment Never superior to strategi trade poliy Higher when the government annot ommit to its poliy instrument, provided that there are at least a small, ritial amount of R&D spillovers Robust (no hange of the sign of the poliy instrument). The basi model.1. ASSUMPTIONS The key differene of our approah is that the stage of ation is now domesti or home market. In order to fous exlusively on the home market, the easiest but the strongest assumption that we adopt here is that domesti firms produe the goods in question exlusively for the home market. Invoking the standard assumption of the segmented market hypothesis whereby foreign and domesti firms onsider their respetive home and foreign markets as separated, might be problemati here sine the inentive to invest in R&D is likely to be affeted by the existene of the foreign market for domesti goods. Moreover, Ben-Zvi and Helpman noted that market segmentation may not our in equilibrium even under the standard assumptions of onstant unit osts and no strategi investment 5 (and, espeially in a 5 I am grateful to both referees for pointing this out. 7

11 plausible ase when the quantity produed is determined after the market prie is set; see Ben-Zvi and Helpman, 1988). Muh like in the above desribed third market setup, we rely on the already standard and simple dynami setup in whih the domesti firm invests in a strategi variable prior to the market ompetition stage in whih the domesti and foreign firms set their respetive output levels simultaneously. As for the home government, we assume that for the time being it is onstrained to only one poliy instrument an import tariff, denoted as t. We onsider three government regimes: (1) the "ommitment regime" in whih the government is apable of ommitting to both a tariff program and an atual optimal tariff prior to the domesti firm s hoie of its strategi variable (so the assoiated variables arry the subsript ""); () the "non ommitment" regime in whih the government announes a tariff program or even the level of the tariff in the first stage but (say, due to the lag in the announement and implementation of the poliy, or due to lak of redibility) imposes the atual tariff only after it observes the domesti firm s hoie of its strategi variable (the assoiated variables have the attahed subsript "n"). The third regime, free trade, is a situation in whih the government is assumed to be able to ommit to non intervention, that is, no tariff program. In our setup this is equivalent to setting the tariff to zero. 6 Note that free trade and both "non ommitment" and "ommitment" regimes an be onsidered as seond best poliies sine there is only one poliy instrument and two hoie variables (strategi variable and quantities). 7 6 In a more omplex setup, setting an instrument to zero may not be equivalent to ommitting to free trade due to the different strategi impliations of these two situations (see for instane, Gruenspeht,1988 or Arvan, 1991) 7 For the whole spetrum of possibilities of ommitment patterns between the firms and the government in a dynami games setting under third market assumption, see Leahy and Neary,

12 As for the tehnial details of the basi model, muh like in the related third market literature (see for instane, Grossman and Maggi; 1998, Neary and Leahy; 000 and Ionaşu and Žigić, 005), we make use of the linear quadrati example. More speifially, we assume the inverse demand funtion in the domesti market to be linear (with units hosen suh that the slope is one). That is, P A Q whereq q d + q. The parameter A aptures the size of the market, whereas q d and f q f denote the hoie variables, that is, the orresponding quantities produed by the domesti and the foreign firms. The strategi variable, that we label y, an assume various interpretations, like upfront investment in apital or knowledge as in Grossman and Maggi (1998), or a variable related to R&D investment ( R&D ost funtion as in Žigić, 004 or Ionaşu and Žigić, 005). The point is that in eah of these interpretations, these investments are assumed to redue the marginal osts of the domesti firm by y. We assume that the R&D ost funtion has a quadrati form, h ( y) y / g, where g is a parameter apturing the effiieny of marginal ost redution (the parameter g is diretly related to the parameter k used in Grossman and Maggi,(1998) or Karp and Perloff (1995) who interpreted it as the ost of apital or investment, with g 1/ k ). We stik to the speifi funtional form of h (y) to state our results as sharply as possible. However, it is important to note that all our results hold for a general R&D funtion, h (y), under some plausible restritions on it. 8 The domesti firm is assumed to have initial onstant unit variable osts of prodution α, with A > α, where parameter α an be thought of as pre innovative onstant unit osts desribing an old tehnology initially aessible to both the 9

13 domesti and the foreign firms. We assume that " is always big enough so that y α holds in equilibrium. Consequently the post innovative unit 9 ost of the domesti firm is now expressed as C α y and the orresponding unit osts of the foreign firm are α. Soial welfare (W ) is defined as the sum of onsumer surplus ( S ), the domesti firm's profit ( Π ), and the revenue from tariffs ( R ). The onsumer surplus is defined as d q S( q) P( z) dz qp( q) 0 that, in the ase of a linear demand, redues to S +, the tariff revenue d ( 1 )( q f qd ) is given as R tq f and, finally, the domesti and foreign firms profits are respetively given as 10 : Π d ( A Q) qd Cqd h( y) and Π f ( A Q) q f q f tq f. As for the other model assumptions and restritions, they are primarily onerned with the issue of the existene and viability of a duopoly and the well defined maximization problems that in turn require onstraints on the R&D ost funtion, h (y). For a duopoly to be a viable market struture in both ommitment and non ommitment regimes, it is neessary that a strategy leading to the elimination of the foreign ompetitor strategi predation would be too expensive and is never 8 More speifially, it is suffiient to assume that h (0) h(0) 0 and that the h(y) is suffiiently onvex, that is, the marginal ost of the unit ost redution, h (y), has to be steep enough so that the resulting equilibrium market struture is always a duopoly (see Žigić, 003). osts. 9 In the rest of the artile, we use the term unit osts instead of the more orret unit variable variable. 10 Subsript d will be omitted further on sine we will onentrate only on the domesti 10

14 optimal for either the domesti firm or the domesti government. Thus, the marginal ost of the unit ost redution, h '( y) > 0, has to be steep enough so that its intersetion with the aompanied marginal benefit ours at a level of y suh that p 0 < y < y α where y is the optimal unit ost redution in a duopoly and p y is the level of unit ost redution that leads to the zero output of the foreign firm in equilibrium. More speifially, it means that the size of the parameter, g, should not be too large implying an upper bound on g suh that for all values of g below this upper bound all problems under onsiderations would be well defined (that is, the duopoly is both feasible and soially an optimal market struture and all seond order onditions in our analysis are automatially satisfied). 11 The interval of g (or onisely, the feasibility region ) that satisfies the above restritions, is defined as 1 : (i) g 0(0, g r ) with g r We assume further on that g takes values from this interval... THE "NON COMMITMENT" REGIME Given our urrent framework in whih the government relies on trade poliy, it ould be argued that the assumption of the non ommitted government is a natural one and the one that is easier to justify than its ommitted ounterpart. As noted by Kydland and Presott, 1977, the neessary ondition for a government to lak ommitment ability is that it finds itself in a seond or even third best situation. This is a typial situation with trade poliy indeed sine reliane on trade poliy in general implies that the government for some reason does not have other, less distortionary 11 Following an alternative interpretation (e.g. Grossman and Maggi, 1998 or Karp and Perloff, 1995) the upper bound on g is equivalent to the lower bound on the ost of apital, k. The reason is that low osts of apital may lead to high investment in R&D that in turn results in drasti innovation and the exit of the foreign firm. 11

15 instruments at its disposal (see Staiger, 1995). In suh irumstanes the government has an inentive to surprise firms by unexpeted poliies. For instane, in our setup the poliy makers are tempted to announe a high tariff to enhane the domesti firm s inentive to invest in soially insuffiient R&D investment (or unit ost redution), and then if the domesti firm believed this announement and did the orresponding R&D investment, it beomes optimal for the government to renege ex post on its promise and set a lower, less distortionary tariff. Finally, the fat that the government in our setup relies on strategi trade poliy whose suessful appliation requires a high degree of flexibility and disretion, reinfores the ase of the non ommitted government. 13 The above setup implies strategi interation between the domesti government, the domesti firm, and the foreign firm, and it an be depited by means of a sequential, three stage game. So when, for instane, the domesti firm does not onsider the government s poliy announement to be redible, the first stage of the game is the one in whih the domesti firm strategially hooses its innovation effort and onsequent unit ost redution. In the seond stage, the non ommitted government sets the tariff on imports after it observes the firm s hoie of y. Finally, in the last stage, the firms selet quantities, and onsequently, profits and welfare are realized. As is already lear, the ation is on the domesti market, in whih the duopoly is assumed to be a viable market form both before and after the tariff is set. In order to asertain the subgame perfet equilibrium, we proeed by solving the game 1 It turns out that the strongest restrition on g is imposed by the requirement of the existene of a duopoly in the ommitment regime, that is, by the onditions that q f (y(t),t) >0. 13 Ultimately, the (in)ability of the government to ommit to its poliy depends on the strength of the ountry s institutional and politial setup. 1

16 bakwards. In the last (third) stage, the firms hoose the equilibrium quantities. The domesti firm maximizes Max[ Π ] ( A Q) q C( y) q h( y) (1.a) q d d d d given q and f Q q d + q. The first order ondition for an interior maximum is f Π d / q d 0 and yields A q q f C 0 d. The maximization problem for the foreign firm yields: Max[ Π ] ( A Q) q q tq (1.b) q ff f f f f given q d and t. The first order ondition is: A q f qd t 0. Solving the reation funtions yields the Cournot outputs as a funtion of y and t : ( A + C( y) + t) q d ( y, t) (.a) 3 q f ( A + C( y) t) ( y, t) (.b) 3 Substituting (.a) and (.b) into (1.a) yields the domesti firm s profit funtion expressed in terms of y, R&D investment osts, h (y), and the tariff: ( A + C( y) + t) Π d ( y, t) h( y). (3) 9 In the seond stage of the game, the domesti government selets the optimal tariff given the unit ost redution of the domesti firm. Its objetive funtion is given by the expression W ( t) Π( t) + S( t) + R( t) (4) where onsumer surplus, S (t) and tariff revenue R(t) are respetively given by 13

17 S( t) 1 ( q ( A α t + 9 y d + q f ) ) (5) and R( t) tq t( A α t 3 y f ). (6) Note that domesti profit monotonially inreases in tariff (the higher the tariff the larger the effetive unit ost differene and, onsequently, the higher the domesti firm s profit) while onsumer surplus monotonially delines in the tariff. Finally, the funtion R (t) initially inreases in t as t goes above zero, reahes its maximum at 1 t ( A α y), but eventually falls to zero as t reahes the prohibitive tariff, t p, a 4 tariff that auses the exit of the foreign firm. Thus, the funtion W (t) is stritly onave in t with d W ( t) / dt 1 < 0 while the whole tariff domain on whih a duopoly is defined is given by the interval t [0, t p ]. The assumption (i) ensures an interior maximum suh that optimal tariff, t n is obtained by solving W / t 0, yielding: t < t n p and the α t A n. (7) 3 There are several interesting observations to be made about the above optimal tariff t n. First, note that the expression for t n is a pure profit shifting tariff 14 (see Bhattaharjea, 1995), and it is quite general sine it is independent of the funtional form of the R&D ost funtion. Seond, it does not depend either on the domesti unit ost [α in (7) represents foreign firm unit osts], or on the domesti strategi 14 More preisely, it is equivalent to the standard strategi tariff that leads to improvement in terms of trade and to prodution effiieny gains (see Helpman and Krugman, 1989). 14

18 variable, y. The latter is rather important for us beause it indiates that the manipulation of the government by the domesti firm (in the form of overinvesting in y ) is not possible here. Finally, given the fat that in a "non ommitment" regime, the government laks the ability to preommit to the tariff before the firm hooses y, the tariff t n then is time onsistent. 15 In the first stage of the game, the domesti firm selets the optimal level of marginal osts redution, y, taking into aount its subsequent impat on its foreign rival s behavior. By substituting t into (3) and realling that h ( y) y / g, we obtain n Π 4(( A ) + 3y) ( y, tn ( y)) Π d ( y) 81 α d y g. (8) Maximizing (8) with respet to y gives the first order ondition 16 and the optimal y n : 4 (( A α) + 3yn ) h ( y 81 n ) (9) that given the funtional form of h(y) results in y n 8( A α) g 3(9 4g) (10) Finally, by substituting (10) into (5), (6), and (8) and summing these three items, we obtain the optimal soial welfare in the non ommitment" regime: 15 A suffiient and standard proedure that we apply to solve for a time onsistent tariff is the onept of subgame perfet equilibrium (see Fesrthman,1989). 16 The seond order ondition requires g <6.75, and (i) is suffiient for this seond order ondition to hold. 15

19 W n ( A α) (567 8(43 6g) g) 18(9 4g). (11).3. THE "COMMITMENT" REGIME, FREE TRADE, AND SOCIAL PLANNER Let us now assume that the government somehow possesses the ability to ommit to its poliy prior of any strategi move (investment) by the domesti firm. Similarly to the above ase, this an be again aptured by the appropriate three stage game. In the ase of the ommitment regime, the only formal differene with the non ommitment regime is that the first two stages are reversed. Thus, the government now redibly ommits to the tariff level in the first stage of the game; in the seond stage, the domesti firm strategially hooses its innovation effort and the onsequent unit ost redution. Finally in the last stage, the firms hoose their equilibrium quantities. In the ase of free trade, the government is assumed to be able to ommit to non intervention, and in our setup this is equivalent to preommitment to zero tariff (see footnote 6). The soial planner setup refers here to the situation in whih the government, besides a tariff, also sets R&D investment, y. We now briefly haraterize the optimal tariff, unit osts redution and soial welfare in the ommitment regime, free trade, and the onstrained soial planner and then make the relevant omparisons aross the regimes. a) The "ommitment" regime Maximization of (3) with respet to y, gives the first order ondition that determines the optimal y (but now as a funtion of the tariff): 4 ( A α + t + y) h ( y ). (1) 9 Label it as y ( t ) and the expliit value of unit ost redution is now: 16

20 ( A α + t ) g y ( t) 9 4g (13) Straightforward substitution of ( t ) into the soial welfare funtion yields the y government objetive funtion, W ( y ( t ), t ) to be maximized in the first stage. Setting dw / dt 0 yields: t ( A α)(7 g(10 g)) 81 g(3 6g). (14) Again, the restrition (i) makes sure that the tariff, t, lies between zero and the orresponding predatory tariff, t p. Finally, soial welfare in the ommitment regime is given by (15): b) Free Trade W ( A α ) (7 g)(9 g). (15) (81 4(16 3g) g) As for the free trade regime, it is equivalent to preommitting to the zero tariffs, so obtaining the respetive omparable equilibrium values (that we label with subsript ft ) is straightforward: ( A α) g y ft 9 4g (16) and W ft ( A α) (7 (8 g) g) 18(9 4g). (17) ) Soial planner 17

21 W s ( y s If the government an selet both tariffs and R&D, it would maximize, t) with respet to both y and t, and that in turn yields: y s ( A α) g 3( g) (18) and α t A s. (19) 3 Finally, the soial welfare is given by W s ( A α) (14 3g) 18( g). (0) Note that t s is idential to the non ommitment tariff that should not ome as a surprise sine the tariff now has only a profit shifting funtion beause R&D is hosen diretly by the government..4. COMPARISON ACROSS THE REGIMES We start with a omparison of unit ost redutions. The diret omparison reveals that the soial planner undertakes the largest unit osts redution, followed by ommitment, non ommitment, and free trade regimes, respetively. LEMMA 1 Unit osts redution and onsequent R&D investment in any of the regimes are below the orresponding soial planner s hoie. The optimal unit osts redution and onsequent R&D investment are the biggest in the ommitment regime and the lowest in the regime of free trade, that is y > y > y > y. [Lemma 1 holds for s n ft general h (y) ; see Appendix 1] 18

22 Note that the government ould have ahieved the level of soially optimal unit ost redution, y s, if it had at its disposal an instrument that diretly targets the soially insuffiient unit ost redution like, for instane, an R&D subsidy 17. A tariff, on the other hand, is not apable of ahieving that goal due to its high distortionary effet. Unlike the R&D subsidy, a tariff has an adverse effet on the market prie and onsequently, on the onsumer surplus, and the government takes this into aount when seleting the optimal tariff. Sine a tariff ensures a larger market share for the domesti firm ompared to free trade, and thus enhanes the firm s inentive to invest in R&D, the respetive value in free trade, y ft, assumes the lowest value. As for tariffs in the two tariff regimes, they are generally different due to the somewhat different funtions that they perform. Namely, a distintive harateristi of the tariff in the ommitment regime is its "tehnologial funtion". The ommitted government that sets the tariff, t, takes into aount the tariff's impat on the subsequent hoie of a domesti firm s R&D (note that dy / dt > 0 ). Thus, t, besides its profit shifting role, also has the funtion of stimulating R&D investment and more so the larger the effiieny of the R&D investment, sine t inreases in g. In the absene of a R&D subsidy, the tariff t assumes part of the R&D subsidy s role and ats not only as a trade poliy but also as an industrial or tehnologial poliy instrument. This additional role of the tariffs in the ommitment regime indiates that their optimal values may exeed the optimal values of their ounterparts in the non ommitment regime given that in the non ommitment regime R&D investment is 17 For the related analysis of R&D subsidy see, for instane, Spener and Brander, 1983; Bagwell and Staiger, 1994; Maggi, 1996; Leahy and Neary, 1997, 001; Hinloopen, 1997; and Žigić,

23 already in plae when the tariff t n is set. So t n has no diret impat on the firm s hoie of R&D. LEMMA The optimal tariff in the ommitment regime always exeeds the optimal tariff in the non ommitment regime and, onsequently, the first best tariff. Proof: A straightforward omparison between (7) and (14) reveals that t < for all n t permissible values of g > 0. [Note that t ( g 0) tn ts and that dt / dg > 0. Lemma 1 holds also for general R&D ost funtion, h (y) ; see Appendix 1]. As already made lear, the underlying intuition is that the ommitted government enjoys the redibility of the domesti firm. This, in turn, implies that the tariff has a diret benefiial effet on the firm s R&D, and the government exploits this fat in order to boost soially insuffiient R&D at the expense of the inreased distortion aused by the tariff larger than the first best. Lemma gives also a lue for a omparison between y and y n. The larger unit ost redution in the ommitment regime is a onsequene of the higher tariff that the domesti firm enjoys that in turn stimulates higher R&D investment. Finally the soial welfare omparison reveals that muh like in the ase of R&D investment, we have W > W > W > W. Again this ranking holds for the s n ft general R&D ost funtion, h (y) ; see Appendix. Proposition 1 In the home market setup, free trade never generates larger soial welfare than the non ommitment" regime. Moreover, there is underinvestment rather than overinvestment in the strategi variable. However, the ommitment regime still yields the highest soial welfare. 0

24 A loser look, however, reveals that the relative differene between W and W n is rather small. As the simple simulations aross the feasible range of g (0, g r ) show, the ratio of W / W always exeeds 99% while both tariff regimes generate n signifiantly higher soial welfare than in free trade (16-0%). 3. Extending the basi model: R&D spillovers 3.1. WHY R&D SPILLOVERS? Although soial welfare in the ommitment regime is still the largest among the three regimes, the striking issue is that the result is not robust if we slightly enrih our basi model. Given our setup in whih the domesti firm exhibits innovative ativity before the market ompetition takes plae, we argue that a natural extension of the basi models is to allow for R&D spillovers from the domesti to the foreign firm. The rationale for introduing R&D spillovers stems from the fat that innovations, in general, are subjet to R&D spillovers. In partiular, our extended setup fits well into an already standard North South trade setup in whih the domesti Northern firms innovate, and the Southern firms imitate or in jargon, benefit from R&D spillovers through trade 18. (Our analysis and the forthoming onlusions would be idential if, instead, we onsider market expanding investments that, for instane, our due to produt innovation, and we also allow for demand spillovers; see footnote 19). Moreover, from the point of view of the omparison to the third market models, one possibly unsatisfatory feature of our basi setup is the absene of the manipulation effet. One there is a lak of government preommitment, the domesti firm typially manipulates the size of the poliy instruments in the third 18 The importane of R&D spillovers, imitations and its eonomi impliations in both North- South trade and in general seems to be well and broadly doumented in both theoretial and empirial literature (see, for instane, Chin and Grossman, 1990; Grilihes,199; Deardorff, 199; Žigić,

25 market setup through overinvesting in the strategi variable (see for instane, Grossman and Maggi, 1998; Karp and Perloff, 1995; or Ionaşu and Žigić, 005). As seen from expression (7), the optimal tariff in our basi setup does not depend on the strategi variable, y. However, the introdution of R&D spillovers, as we will see soon, brings bak this broken link and the investment in R&D and, onsequently unit ost redution, do affet the optimal tariff in the non ommitment regime. Tehnially, allowing for R&D spillovers leads to the hange in the profit of the foreign firm whih is now expressed as Π ( A Q) q ( β y) q tq where f f f f β [0,1] stands for the R&D spillovers parameter 19. In other words, the foreign firm is now assumed to apture a part of the domesti firm s R&D output. However, to be as lose as possible to the basi model, we will onstrain ourselves to the ase of small spillovers (onsequently, we evaluate and ompare the relevant derivatives at β 0) TARIFFS AND R&D COMPARISON ACROSS THE REGIMES a) Tariffs In what follows we briefly repliate our omparison aross the regimes in this extended setup. First, we note that now the optimal tariff (see expression 1) does and 000; Coe and Helpman, 1995; Lai and Qui, 003; Qui and Lai, 004; Grossman and Lai, 004; among many others). 19 The respetive profit funtions in the ase of market-expanding investment and demand spillovers would be A d (A + x - Q)q d - q d - x /g and A f (A + γx - Q)q f - q f - t q f where the demand spillovers parameter, γ [0,1] and x stands for the market-expanding investment. 0 Note that the introdution of spillovers alls for the modifiation of the feasibility region defined by (i). The upper border, g r (β), is now an inreasing funtion in β sine inreasing spillovers softens ompetition for the given g and enables the foreign firm to survive in the market for values of g(β) > g r (0) (see Žigić, 003). However, sine we onstrain ourselves to the region around zero spillovers, we do not have to bother with this.

26 depend on y that, in turn, enables the domesti firm to manipulate its own government t A α + βy ( y). (1) 3 n n In terms of the parameters of the model, the orresponding levels of optimal tariffs in the two tariff regimes are given now by: β ( A α)(7 4g(1 β )(3 β )) 81 4g(3 β ) t n ( ) () and ( A α)(7 g(10 g( β )(1 β ) 11β )( β )) t ( β ). (3) 81 g(3 g(3 β )( β ) 10β )( β ) Proof: The straightforward omparison between () and (3) reveals again that t ( β ) < t ( β ) for all permissible values of g > 0 and β. This extends the validity of n Lemma 1 to the ase of spillovers. [The relation t ( β ) < t ( β ) holds for a more general R&D ost funtion; proof available from author upon request]. Clearly, for β 0, both tariffs ollapse to their orresponding values in the basi model. In addition, (at least initially) both tariffs inrease in spillovers assuming n a new, R&D spillover ounterating role. That is, both dt n / dβ and dt / dβ are positive around β 0. However, the key distintion lies in the different sensitivity of the two tariffs to spillovers. LEMMA 3 The optimal tariff in the ommitment regime inreases more than its non ommitment ounterpart with the appearane of small spillovers, that is, dt / dβ > dt n / dβ at β 0. 3

27 Proof: See Appendix 3 (The relation holds for more general R&D ost funtion; proof available from author upon request). As a onsequene of Lemma 3, there is an inreasing gap between the two tariffs when spillovers appear. To understand this, note first that both t ( β ) and t ( β ) have a profit shifting funtion that alls for an inrease in the optimal tariff sine spillovers make, eteris paribus, the foreign firm s output and profit larger. However, t ( β ) performs in addition a distint tehnologial funtion. Sine the inreased spillovers lead to a disinentive for the domesti firm to invest in R&D, the aring ommitted government adjusts the tariff upwards to restore (at least partly) the firm s inentive for R&D investment (reall that dy / dt > 0 with or without spillovers). This mehanism is absent in the non ommitment regime leading to a lower sensitivity of t ( β ) to spillovers. n b) R&D Besides ausing an inreasing gap between the two tariffs, the appearane of spillovers has a onspiuous effet on R&D investment of the domesti firm. Muh n like the ase of the tariffs, the lue for this result lies in the different sensitivity of y n and y with respet to the hange in spillovers where now 8( A α)(3 β ) g 81 4g(3 β ) y n (4) and ( A α + t )( β ) g y. (5) 9 g( β ) LEMMA 4 4

28 The optimal unit ost redution in the ommitment regime is more sensitive to spillovers than its non ommitment ounterpart with the appearane of small spillovers, that is, dy / dβ > dy n / dβ at β 0 (note that dy / dβ dy / dt dt / dβ + / β ). y Proof: See Appendix 4. [The validity of Lemma 3 extends to a more general funtion, h (y) ; proof available from author upon request]. To understand the intuition behind the lesser sensitivity of unit ost redution on spillovers in the non ommitment regime, we briefly review the harateristis of the firm s strategi behavior in the ontext under onsideration. First, it is well known that in dynami Cournot duopoly models, where the domesti firm exhibits limited leadership, the domesti firm (inumbent) overinvests in its strategi variable in order to gain advantage over its ompetitor 1. The higher the spillovers, the more the foreign firm appropriates the innovative output of the domesti firm and onsequently the higher are the disinentives to invest in R&D. In other words, sine this strategi investment effet (present in both regimes) is aimed diretly at the ompetitor, it is very sensitive to spillovers. On the other hand, in the non ommitment regime, there is an additional, manipulating motive that the domesti firm faes on top of the standard strategi investment motive desribed above. Namely, the domesti firm has an inentive to manipulate the government deision on the tariff beause in the non ommitment regime, a higher unit ost redution indues a higher tariff that in turn benefits the domesti firm s profit. This additional motive for overinvestment is not present in the ommitment regime, and it is targeted towards the domesti government and not diretly towards the foreign firm. Thus the manipulating 1 The notion of over-investment is defined here with respet to the non-strategi benhmark, in whih the domesti firm selets its R&D investment by ignoring its impat on the subsequent stage 5

29 investment is therefore less vulnerable to spillovers. Consequently, the overall R&D investments in the non ommitment regime (that an oneptually be broken up into two parts: strategi and manipulating R&D investment) are less sensitive to spillovers than the orresponding R&D (and unit ost redution) in the ommitment regime leading to y > when spillovers exeed a ertain small threshold. n y SOCIAL WELFARE AND SMALL SPILLOVERS IN THE TWO REGIMES We start with an analysis of the marginal effets of small spillovers on soial welfare. Although we use a speifi funtional form of the R&D ost funtion, we proeed by ignoring this fat for a while by first trying to see what an be inferred assuming a more general form of h (y). From the previous setion, we know that t ( β ) < t ( β ), n W < at β 0 n W and y n < y at β 0. Also dti / dβ > 0, dyi / dβ < 0 with dt / dβ > dt n / dβ, and dy / dβ > dy n / dβ at β 0. Sine all these results hold for a more general R&D ost funtion, we now try to make some general inferene on the effet of small spillovers on soial welfare in the two regimes under onsideration. Differentiating W with respet to β yields: dw β 0) Wi dβ y dyi Wi + dβ t dti W + dβ β i ( i (6) where subsript i stands for either n or. By taking partial derivatives of respetive omponents of W (that is, S, R, and Π ; expressions 5, 6 and 7) with variable of the ompetitor. This onept should not be onfused with the notion of overivestemnt (or underinvestment) from the soial point of view! That is, around β 0. However, it is easy to show that none of the qualitative results and none of the signs of the marginal hanges of S, R, and A would hange if we allow β to be in the interval [0,1/] (at least). 6

30 respet to y, t and β evaluating them at β 0 and, at the optimal y i and t i, and substituting in (6), we obtain (7): dwi ( β 0) (( A α) + yi 4t dβ 9 i ) dyi ( A α 3t + dβ 3 i ) dti ( t + dβ i yi ) yi 3. (7) Note that the first part of the first term of (7) is positive 3 reminding us again that R&D is below the soially optimal level in both regimes and implying that the ombined marginal effet of R&D on the tariff revenue and the onsumer surplus is positive (that is, / y > 0 ). This, in turn, implies that the first term in (6) is learly W i negative (reall that there is no marginal profit effet in the first term due to the impliit funtion theorem). As for the respetive magnitudes of the first term in (7), in the two regimes, it is likely that the adverse effet is larger in the ommitment regime due to higher sensitivity of R&D to spillovers in this regime. The first part of the seond term in (6), / t, represents the net effet of W i (due to spillovers) the inreased tariff on onsumer surplus, the tariff revenue and domesti firm s profit. The first two effets of / t W i (that is, / t S i and / t ) are R i learly negative. As for onsumer surplus, the tariffs ause an inrease in the equilibrium prie and thus have a distortional effet on onsumer welfare. As for tariff revenue, the optimal tariffs in both regimes are larger than the orresponding tariffs that maximize R i implying that / t < 0. Finally, the last effet, Π / t, is learly R i positive on the domain t [ t i, t m ] sine an inrease in the tariff inreases the unit osts of the foreign firm and enables the domesti firm to apture a larger market share and realize larger a profit ( t m stands for the tariff level that enables the domesti firm to ahieve the unonstrained monopoly position). Clearly, in the non ommitment 7

31 regime, the whole seond term, / t, vanishes sine the non ommitment tariff W n oinides with the first best tariff that exatly balanes the negative marginal effet of tariff on onsumer surplus and tariff revenue with the marginal positive effet of the tariff on profit. Consequently, any higher tariff implies that the marginal effet of the tariff on soial welfare is negative and so the seond term in (6) is unambiguously negative in the ommitment regime, due to the fat that, W / t < 0. Finally, the third term in (6) is positive sine the two diret positive effets of spillovers on the onsumer surplus and tariff revenue more than offset the orresponding negative effet of spillovers on profit, but this effet is slightly larger in the ommitment regime. 4 Taking all of the above onsiderations into aount, we onjeture that allowing for a small dose of spillovers auses more adverse (or less favorable) welfare effets in the ommitment regime than in its non ommitment ounterpart. In other words, the larger adverse effets of spillovers on R&D and the larger optimal tariff in the ommitment regime translate to a larger adverse or, analogously, smaller positive impat on soial welfare (depending whether dw / dβ is positive or negative) than in the analogous non ommitment setup. That is, we expet that dw / dβ < dw n / dβ holds at β 0. Moreover, if the initial differene between W and W n is small enough, the reversal in the rank of these two soial welfares may our at the level of spillovers already lose to zero. The relation between dw / dβ and dw n / dβ in our 3 Substituting the upper bound of the tariff, t p 1/(A - α - y) into the first part of the first term in (7) yields y i /3 > 0. 4 Note that S i / β > 0 sine an inrease in spillovers inreases total output in equilibrium. Furthermore, R i / β > 0 sine, other things being equal, an inrease in spillovers inreases foreign firm output in equilibrium and onsequently tariff revenue. Finally, Π/ β < 0 sine, other things being equal, inrease in β enables a foreign firm to derease its units ost and apture a larger market share in equilibrium at the expense of the domesti firm. 8

32 speifi setup onfirms the above intuition. 5 Moreover, as we noted before, the ratio between W and W n is in our basi setup lose to one, indiating that the above mentioned reversal in the rank between W and W n ours at a low level of spillovers. We summarize the above disussion in Proposition. Proposition Soial welfare in the non ommitment regime exeeds the soial welfare in the ommitment regime within the home market setup as soon as spillovers exeed a w threshold level of β (g) whereby its maximum value is given by β w g ) for h ( y) y / g. See Appendix 5 for the proof. As for the underlying intuition of the proposition, reall that (a) the non ommitment tariff oinides with the first best tariff, at β 0, and b) that a higher tariff than the first best one in the ommitment regime has its rationale in the fat that it leads to an inrease in soially insuffiient R&D. In terms of soial welfare, that inrease in R&D more than ompensates for the inreased distortion aused by a tariff higher than the first best one. However, R&D spillovers ause disinentive for investing in R&D that in turn leads to a faster rise in the ommitment tariff reating further divergene between the ommitment and non ommitment tariff (see subsetion 3.. a). This leads to a larger distortion ompared to the initial situation without spillovers. At the same time, the higher sensitivity of R&D to spillovers in the ommitment regime leads to the omparably faster derease in R&D implying that the gap between R&D levels in the two regimes shrinks as spillovers appear (see subsetion 3.. b). Consequently, the inreased soial osts due to the rising tariff ( r 5 As it an be easily shown, the above onlusion is valid for any arbitrary value of β when h(y) 9

33 distortion and dereased soial gain from the tehnologial role of tariff aused by spillovers, imply that there is a ritial level of spillovers beyond whih soial welfare in the non ommitment regime starts to dominate its ommitment ounterpart. To the extent that the differene between diret effets of spillovers on welfare in the two regimes, W / β / β, is negligible 6 at β 0, the suffiient ondition W n for the soial welfare in the non ommitment regime to dominate its ommitment analog is that y sine t ( β ) < t ( β ). By ontinuity, of ourse, the ritial point n y n of β at whih W is already at the point where n W y <. n y Also note that Proposition is in stark ontrast with the third market models outome. Just a small dose of spillovers would be suffiient to reverse the key result of the third market model in whih the value of ommitment was unquestionable The first best versus seond best poliy Another topi that we now fous on is the first best versus the seond best poliy within the home market setup and its impliation on the robustness of the sign of poliy instrument when passing from the first to the seond best poliy (or vie versa). Namely, it is well established that in the third market framework (in the benhmark ase of Cournot ompetition) the R&D subsidy is generally positive in the seond best poliy setup, but then turns out to be negative (R&D tax) when the first best poliy is implemented. To illustrate this issue within the home market framework, we again extend a little bit our basi model but now by allowing the domesti government to have an y /g. 6 More preisely, this differene has to be small enough relative to the orresponding between- the- regimes differenes for the first and the seond terms in (6). As an be easily shown, this is the ase when h(y) y /g. 30

34 additional poliy instrument at its disposal. As in the above third market literature, an R&D subsidy is an obvious hoie in the onsidered setup. The relevant framework is now a four stage game whereby the government sets an R&D subsidy in the first stage, domesti firms selet R&D in the third stage, then again the government sets a tariff in the seond stage and finally, the foreign and domesti firm ompete in quantities on the home market in the last stage. This timing reflets the stylized fat that it is easier for government to ommit to an R&D subsidy than to an output subsidy or tariff (see Carmihael, 1987; and Leahy and Neary, 001). Before we proeed, it should be made lear at the outset that the term first best is not ompletely appropriate in this setup (a more orret name would be onstrained first best poliy ). The true first best poliy would involve three poliy instruments: an import tariff, an output subsidy, and an R&D subsidy or tax. However, the optimal output subsidy would in our setup indue the domesti firm to produe at the point where marginal osts equal prie, whih in turn would imply that the domesti firm serves the whole domesti market. That is, the optimal market struture would be a domesti monopoly. Moreover, the optimal tariff would be zero. Sine the duopoly interation between the domesti and foreign firms and the strategi tariff are at the ore of our analysis, the issue of an optimal output subsidy naturally has to be disregarded. More generally, the output subsidy is onsidered to be an unrealisti (Dixit, 1988) and due to its heavy informational ontent often an infeasible and impratial instrument (Bhattaharjea, 1995). Despite the above autions, we nonetheless stik to the term first best poliy to distinguish it from the one instrument, seond best poliy (whih, by the above logi would be the third best poliy ) and also to be in line with Neary and Leahy s 7 Moreover, Grilihes (199) finds in his summary of the empirial work on spillovers that typial values of β range between 0. and 0.4, and this is far above the highest possible value of 31

35 (000) terminology who (although in their setup fully orretly) alled the ombination of two instruments like output and R&D subsidies the first best poliy. Sine the rest of the game is already solved in the first part of the paper (see setion..), we turn immediately to the first stage and the government s hoie of the optimal subsidy. The objetive funtion of the government that implements the first best poliy is now given by expression (8): W fb [ y ( s), t ( y ( s), s), s] Π ( ) + S ( ) + R ( ) sh( y ) (8) where "fb" stands for the first best and " s " denotes the subsidy. The domesti firm s profit now has an additional term stemming from its subsidy inome, sh (y). The soial marginal ost of raising a unit of subsidy is assumed to be one, and so the ost of subsidy payment for the government is sh (y). Differentiating (8) with respet to the subsidy and equating it to zero while using the domesti firm's first order ondition, (envelope theorem) and noting that Π / s h( y ) yields (impliitly) the optimal first best subsidy: s 1 S R S R t ( + + ( + ) ). (9) h ( y ) y y t t y Note that in our first best setup the optimal tariff is the same as the tariff that a soial planner sets (that is, t s ( A α) / 3 ) implying that t / y 0. Thus, expression (9) further simplifies to: s 1 S ( h ( y ) y R 1 W + ) y h ( y ) y. (30) A positive optimal subsidy requires that W / y > 0, and this is learly the ase in our setup. Moreover, note that the optimal first best subsidy is β w (g r ). 3

36 proportional to the size of the externality, W / y, where the fator of proportionality is aptured by the value of marginal R&D effiieny, 1/ h ( y ). Substituting the relevant values obtained by the differentiation of expressions (5) and (6) into (30) gives s ( A α) + 3y 7h ( y ) s s > 0. (31) Finally, using our speifi funtional form h ( y) y / g, we obtain (( A α) + 3ys ) g s 54y s (3) where the domesti firm selets now the soially effiient level of R&D, y s [note that y s is the same as (18) ]. The optimal first best R&D subsidy stimulates investments in R&D, removing the distortion between the privately and soially desirable R&D investment levels and ensuring the unit ost redution to be at the soially optimal level, y s. We will now turn to an R&D subsidy only or the seond best poliy. Our look at this poliy will be very brief sine this issue is disussed at length elsewhere (see for instane, Spener and Brander, 1983; Bagwell and Staiger, 1994; Maggi, 1996; Leahy and Neary, 1997, 001; and Hinloopen, 1997). In the absene of a tariff, expression (9) haraterizing the optimal subsidy redues to: s sb 1 h ( y sb S ) y ( A α) + y 9h ( y sb ) sb > 0 (33) 33

37 By visual inspetion of (31) and (33), it is lear that s sb > s. 8 This is in line with the findings emphasizing the robustness of the seond best R&D subsidy that has to boost ineffiient R&D investment and at as a surrogate for the unavailable tariff (see for instane, Brander,1995; Bagwell and Staiger,1994; and Leahy and Neary, 1997; Hinloopen,1997; and Neary and Leahy, 000). We summarize the above observations in Proposition 3. Proposition 3 Both the first best and the seond best R&D subsidies are always positive with s sb > s. The differene from the standard results in Cournot ompetition where the first best subsidy is negative (i.e., a R&D tax is optimal) stems primarily from the different speifiation of the welfare funtion. If we neglet the onsumer surplus and tariff revenue, then it is lear from (30) that the optimal subsidy will be zero. 9 The reason for this is that in suh a situation both the firm and the government have the same ability to ommit, so the firm an ahieve the most advantageous strategi position on its own (see also Neary and Leahy, 000). 8 Allowing for spillovers would have no impat on the sign of the optimal R&D subsidy in either the first or seond best setup nor on their relative size (see Žigić, 003). However, the optimal subsides would be the funtion of the level of spillovers in both first or seond best setup, so the role of the optimal subsidy in the first best setup would be somewhat blurred due to R&D spillovers. Beause of its primary role of orreting for soially insuffiient R&D, the firstbest subsidy would also affet the optimal tariffs and thus, at least indiretly, assume a profit shifting role (see Žigić, 003). 9 However, this is no longer the ase if the foreign firm also invests in R&D. 34

38 5. Conlusion The aim of this paper was to hange the usual perspetive of the strategi trade approah from the third market setup to the home market framework in order to reonsider several propositions stemming from the third market setup. In the first part of the paper, we analyze the value of poliy preommitment in the home market framework. We show that the trade poliy of the ommitted government generates lower soial welfare than its non ommitted ounterpart one we slightly and realistially extend our basi model by allowing for only a small dose of R&D or demand spillovers. In addition, unlike in the third market models, there is underinvestment rather than overinvestment in strategi variables (i.e. R&D investments) from the soial point of view, irrespetively whether the government an make a ommitment or not. Finally, ommitment to free trade is never optimal. However, it is important to note at this point that the message here was not to disredit the virtue of ommitment in general, but rather to stress that there are irumstanes in whih the signifiane of government ommitment is not ruial. This seems to be the ase when poliy makers do not deal only with strategi onsiderations and government s expenditures but also with issues like onsumer benefits and government revenue. In the seond part of the paper, we show that, unlike in the third market models, the R&D subsidy in the home market setup is always positive in both the first best and the seond best poliy setup, and this finding is robust to whether or not we allow for any degree of spillovers. The reason for this is the soially ineffiient level of private R&D due to the appropriability problem that a subsidy aims to orret and due to the sale eonomies that larger R&D investment brings about. 35

39 Our framework may allow us to address some further interesting issues and omparisons between the third market setup and the home market framework. Thus, analogous to that of tariff omparison, the omparison of ommitted to non ommitment R&D subsidies may be of some interest. Moreover, permitting for a large, full fledged R&D or demand spillovers would, for instane, lead to interplay and a more omplex relation between the R&D subsidies and tariffs while the domesti firm s strategy would turn from top dog to lean and hungry look after a ertain spillover threshold is surpassed (see Žigić, 003). Also, allowing for large spillovers seems to be suffiient to eliminate the overinvestment result even in the third market set up. 36

40 R E F E R E N C E S Arvan, L., Flexibility versus ommitment in strategi trade poliy under unertainty: A model of endogenous poliy leadership, Journal of International Eonomis 31, Bagwell, K. and R.W. Staiger, The Sensitivity of Strategi and Corretive R&D Poliy in Oligopolisti Industries, Journal of International Eonomis 36: Ben-Zvi, S, and E.Helpman, Oligopoly in segmented markets, NBER, No 665 Bhattaharjea, A "Strategi tariffs and endogenous market strutures: Trade and industrial polies under imperfet ompetition", Journal of Development Eonomis, Vol.47, Brander, J "Strategi Trade Poliy", in G.M. Grosman and K.Rogoff editors, The Handbook of International Eonomis, vol. 3. North-Holland. Carmihael, C "The Control of Export Credit Subsidies and Its Welfare Consequenes," Journal of International Eonomis 3:1-9. Chin J. C. and G. M. Grossman "Intelletual Property Rights and North-South Trade." In R. W. Jones and A. O. Krueger, eds. The Politial Eonomy of International Trade: Essays in Honor of Robert E. Baldwin. Cambridge, MA: Basil Blakwell. Coe, D. and E. Helpman, "International R&D Spillovers." NBER Working Paper No Cooper, R., and Riezman, R., Unertainty and the hoie of trade poliy in oligopolisti industries, Review of Eonomi Studies, 56, Deardorff, A.V., 199. "Welfare Effets of Global Patent Protetion." Eonomia 59, Dixit, A Role of Investment in Entry Deterrene, The Eonomi Journal, 90,

41 Dixit, A "Anti dumping and Countervailing Duties under Oligopoly," European Eonomi Review 3: Fersthman, C "Fixed Rules and Deision Rules, Time Consisteny and Subgame Perfetion," Eonomi Letters 30: Goldberg, P.K Strategi export promotion in the absene of government preommitment, International Eonomi Review, 36, Grilihes, Z.,199. "The searh for R&D spillovers," Sandinavian Journal of Eonomis 94, S9-S47. Grossman, G., Lai, E. (004). International Protetion of Intelletual Property. Amerian Eonomi Review, 94(5), Grossman, G. M. and G. Maggi "Free Trade versus Strategi Trade: A Peek into Pandora's box." CEPR Disussion paper No Gruenspeht, H.,K Export Subsides for Differentiated Produts, Journal of International Eonomis 4, pp Helpman, E. and P.R. Krugman, Trade Poliy and Market Struture, Cambridge, Mass. and London: MIT Press, pages xii, 191. Hinloopen, J "Subsidizing Cooperative and Nonooperative R&D in Duopoly with Spillovers", Journal of Eonomis, Vol. 66, No.. pp Hwang, H., and Shulman, C. T., Strategi non intervention and the hoie of trade poliy for international oligopoly, Journal of International Eonomis, 34, Ionaşu, D. and Žigić, K Free Trade versus Strategi Trade as a Choie between Two Seond Best Polies: A Symmetri versus Asymmetri Information Analysis, International Eonomi Journal, Vol. 19, No. 3, Karp, L.S. and J.M. Perloff, "The failure of strategi industrial poliies due to manipulation by firms," International Review of Eonomis and Finane 4,

42 Kydland, F.E and E.C Presott, (1977). Rules rather than disretion: The inonsisteny of optimal plans, The Journal of Politial Eonomy, Vol. 85, No.3, Lai, E.L.-C., Qiu, L.D., 003. The North s intelletual property rights standard for the South? Journal of International Eonomis, 59, Leahy, D. and J.P. Neary "Publi Poliy Towards R&D in Oligopolisti Industries." Amerian Eonomi Review 87: Leahy, D., and J.P. Neary "R&D Spillovers and the Case for Industrial Poliy in an Open Eonomy," Oxford Eonomi Papers, 51, Leahy, D. and J.P. Neary "International R&D rivalry and industrial strategy without government ommitment," Review of International Eonomis, 4, Leahy, D. and J.P. Neary "Robust rules for industrial poliy in open eonomies," Journal of International Trade and Eonomi Development, 10:4, Maggi, G Strategi Trade Poliies with Endogenous Mode of Competition, The Amerian Eonomi Review 86(1): Neary, J.P Export Subsidies and Prie Competition in E. Helpman and A.Razin (eds.): International Trade and Trade Poliy, Cambridge, Mass., MIT Press, Neary, J.P "Cost Asymmetries in International Subsidy Games: Should government help winners or losers", Journal of International Eonomis, 37, Neary, J.P. and D. Leahy, 000. "Strategi trade and industrial poliy towards dynami oligopolies," Eonomi Journal,100,

43 Neary, J.P. and P. O'Sullivan, "Beat 'em or join 'em?: Export subsidies versus international researh joint ventures in oligopolisti markets," Disussion Paper No.1916, London, CEPR. Qiu, L. D., and E.L.-C. Lai, 004. "Protetion of Trade for Innovation: The Roles of Northern and Southern Tariffs." Journal of Japan and World Eonomy, 16, Shivakumar, R., Strategi trade poliy: Choosing Between export subsidies and export quotas under unertainty, Journal of International Eonomis, 35, Spener, B.J. and J.A. Brander, "International R&D rivalry and industrial strategy," Review of Eonomi Studies, 50, Staiger, R. W, "International Rules and Institutions for Trade Poliy," in Gene M. Grossman and Kenneth Rogoff (eds.), The Handbook of International Eonomis, vol 3, North Holland. Staiger, R. W & G. Tabellini, "Disretionary Trade Poliy and Exessive Protetion," Amerian Eonomi Review, Amerian Eonomi Assoiation, vol. 77(5), pages Staiger, W.R. and Tabellini, G "Rules and Disretion in Trade Poliy", European Eonomi Review, 33: Žigić, K "Intelletual Property Rights Violations and Spillovers in North South Trade," European Eonomi Review,Vol.4, "Strategi trade poliy, intelletual property rights protetion, and North South trade, Journal of Development Eonomis, Vol. 61: "Does "Non Committed" Government always generate lower soial welfare than its ommitted ounterpart? CEPR Disussion Paper, No

44 Appendix 1: Proof that y > y > y > y for a general R&D ost funtion, h (y) s n ft To prove that the ranking from Lemma 1 holds for a general R&D ost funtion h (y), we postulate the following assumptions onerning h (y) : (ia) h ( y) > 0 for y > 0 and h ( 0) h(0) 0 4 (iia) h ( y ) > (4 + 7) While the assumption (ia) is a rather standard one, the requirement (iia) guarantees that a duopoly is a viable market struture in both the ommitment ( C ) and non ommitment ( NC ) regimes. It ensures that a strategy leading to the elimination of the foreign ompetitor strategi predation would be too expensive and is never optimal for either the domesti firms or for the domesti government. Moreover, ondition (iia) is more restritive than any other seond order onditions in the optimization problems under onsiderations. So when (iia) holds, all seond order onditions in our analysis are automatially satisfied. Finally, note that g g is a speial ase of (iia) for h ( y) y / g. < r We first show that there is underinvestment in R&D from a soial point of view in the both C and NC regime. The marginal soial welfare is given by the expression (1A): W i y 1 (A 4t + yi 9 α ). (1A) To obtain W n y, we evaluate (1A ) at t tn ( A α) / 3 and y y n that yields: W n y 1 n (A + 3y 7 α ) > 0. 41

45 In the ase of W y, we find its lower border by evaluating it at y y and at the prohibitive tariff, t p > t where lb W y This yields > 0 y 3 t p 1 ( A y α). W implying that > 0 at y. Thus, given that y W < 0, it follows that y s > y i (where y s is determined by the equation y W y 0, and where i stands for either NC or C regime). Now, we show that y >. The orresponding first order onditions are y n 4 h ( y ) ( A α + t + y ) (A) 9 and 8 h ( yn ) (( A α ) + 3yn ) (3A) 7 If y y n, then the orresponding tariff rate would be exatly t n α t A n. (4A) 3 If the tariff t is greater than t n, then the right hand side of the first order ondition (A) is inreased, whih means that also h ( y ) is inreased. This would imply that y > y n, sine the other first order ondition remains unaltered. So, the proof that y > y n is equivalent to the proof that t > t n. The tariff rate t an be obtained from equation 4

46 dw ( y ( t ), t ) 0 dt whih gives t ( A α)(7h ( y ) 16) + 4y 81h ( y ) 56 (5A) Thus the differene between t and t n is given by t t n ( A α)(7h ( y ) 16) + 4y 81h ( y ) 56 ( A α) 3 4 (A + 3y α ) 3 (81h ( y ) 56) (6A) Sine both the numerator and the denominator (by iia) are positive, t > and t n thus y >. y n Finally, to omplete the ranking, it is enough to show that y >. Again, n y ft we start by omparing the first order onditions in NC and FT respetively: 8y 16( A α) h ( y) and 8y 4( A α) h ( y) Note that the left hand sides of the two first order onditions have the same slopes but the interept in the NC regime is larger than the one in FT, and given the properties of h (y), the intersetion of h (y) and the orresponding left hand side in NC regime ours at a larger y, than in the FT setup (See Fig 1A). Consequently, y >. n y ft 43

47 Fig. 1A Appendix : Proof that W > W > W > W for general h (y) s n ft Soial welfare is defined as the sum of the domesti firm s profit, onsumer surplus, and tariff revenue, that is, W Π + S + R. We start first with the omparison of soial welfare in the two regimes. Let W ( t, y) be the welfare funtion and Π ( t, y) be the innovating firm's profit funtion for given t and y. Let y (t) be the R&D hoie as a funtion of tariff in the ommitment regime, when the firm maximizes Π ( t, y) with respet to y taking t as given. Then it holds that ( y y t ), W W ( t, y ), and W W ( t, y ), (as usual, the asterisks denote n the optimal values). In addition, the optimality of t in the ommitment regime means that for all t, W n n W ( t, y ) W ( t, y ( t)). (A1) 44

48 The key fat for the proof is that the non ommitment tariff, ( A α) / 3 does not depend on y n sine the welfare funtion is additively separable in t and y, i.e., W / t y 0. Reall that in the non ommitment regime the firm hooses y n taking into aount that the government's subsequent hoie of t n t n in general depends on y n. However, given the above separability, the domesti firm de fato takes the hoie of t n ( A α) / 3 as given, whih implies that 30 y ( n y tn). Substitution of t n for t into (A1) ompletes the proof. As for Ì W s, it learly dominates both Ì W and W Ì n, sine Ì W s is maximized in both t and in y. To omplete the ranking among onsidered soial welfares, it suffies to show that Ì Ì n W ft W >. Realling that Ì Ì n y ft y > (see Appendix 1) and that both W ft y and W n y are positive at y Ì n and y Ì ft respetively, we an evaluate both expressions at y y ft, to find out that W n Ì ( y ) W ( y ) 1 ( A α) > 0 ft ft ft 18 implying that Ì Ì n W ft W >. Appendix 3: Proof that dt dt n dβ dβ > for h ( y ) y g Differentiating t with respet to β and evaluating at β 0 we obtain dt dβ (A -α) 4 g (97-8 g (45 - (17 - g) g)) (81-4(16-3g) g) Repeating the above proedure for t n yields:. 30 Note that in the absene of the above separability, this does not hold in general (for instane, when R&D spillovers are positives, β > 0, separability breaks away). 45

49 dt n d β (A -α) 8 g 9(9-4 g) dt dt n Define D. It is now straightforward to hek that D > 0 for dβ dβ g (0, g r ) (see Fig. A). D 0,08 0,07 0,06 0,05 0,04 0,03 0,0 0, ,1 0, 0,3 0,4 0,5 0,6 0,7 0,8 g Fig. A Appendix 4: Proof that dy dy n > for h( y) dβ dβ y g Differentiating y with respet to β and evaluating it at β 0, we obtain dy (A -α) 4 g (43 - g (13-4 g(1 - dβ (81-4(16-3g) g) + g))). Repeating the above proedure for Ì y n yields: dy n (A -α) 8 g (9 4 g) - + dβ 9(9-4 g) dy dy n Define B. It is now straightforward to hek that dβ dβ B > 0 for g (0, g r ) 46

50 (see Fig. 3A below). B 0,5 0, 0,15 0,1 0, ,1 0, 0,3 0,4 0,5 0,6 0,7 0,8 g Fig 3A Appendix 5: Comparison of soial welfare in the two regimes when h( y) y g To find ritial values of β and g beyond whih Ì Ì n W W >, we ould solve Ì Ì the equation W 0, (expressed in terms of parameters of the model), for, n W say, the ritial value of g w ( β) and then find the region of g and β for whih Ì Ì n W W > taking into aount the viability region of duopoly (see Žigić, 003). The ritial value of β w ( g) is obtained by inverting ( β) g w. However, this approah, although feasible, gives an extremely messy solution (see Žigić, 003). Sine surpasses Ì W n Ì W at a rather small level of spillovers, a more elegant approah would be to find an approximation of β w ( g) Let us label this approximation as β wa ( g) by linearizing Ì W n and that is found by solving Ì W at β 0. dw dw. dβ dβ n W n (β 0) + β β 0 W (β 0) + β β 0 Thus, β wa ( g) is given by: 47

51 wa 3(9 4g)g(81 4(16 3g)g) β (g) g(57591 g(383 g(9497 4(79 6g)g))) The funtion, β wa ( g), is depited in Figure 4A. For all values of β, suh that ( g) wa Ì Ì β > β, W > and this region is represented by the area above the urve n W β wa ( g). The ritial value of spillovers is inreasing in g. So the biggest value of β wa ( g) is obtained at the upper border of g r wa g r g β ( ) exat value is even lower sine β w ( g r ) Thus, β wa ( g) an upper border of β w ( g) while the an be viewed as Fig 4A 48