Discussion Paper No The Effects of Quotas on Vertical Intra-Industry Trade. Stefan H. Lutz

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1 Discussion Paper No Te Effects of Quotas on Vertical Intra-Industry Trade Stefan H. Lutz ZEW Zentrum für Europäisce Wirtscaftsforscung GmbH Centre for European Economic Researc

2 Discussion Paper No Te Effects of Quotas on Vertical Intra-Industry Trade Stefan H. Lutz Download tis ZEW Discussion Paper from our ftp server: ftp://ftp.zew.de/pub/zew-docs/dp/dp0261.pdf Die Discussion Papers dienen einer möglicst scnellen Verbreitung von neueren Forscungsarbeiten des ZEW. Die Beiträge liegen in alleiniger Verantwortung der Autoren und stellen nict notwendigerweise die Meinung des ZEW dar. Discussion Papers are intended to make results of ZEW researc promptly available to oter economists in order to encourage discussion and suggestions for revisions. Te autors are solely responsible for te contents wic do not necessarily represent te opinion of te ZEW.

3 Te Effects of Quotas on Vertical Intra-Industry Trade Non-Tecnical Summary According to recent teoretical studies of imperfect markets, quotas on foreign competition will increase product qualities, prices and profits of bot domestic and foreign firms under fairly general assumptions. Tis view also enjoys widespread empirical support, for example, for te automobile industry. Te above mentioned results old, since a quota imposes a degree of collusion on firms tat tey could not obtain oterwise. In doing tat, te quota raises te marginal profitability of product quality for bot firms at te former free-trade qualities; and it does so even if te quota is not binding. One notable exception to te validity of te results mentioned above can arise wit vertically differentiated but still substitutable products, were one product may be of iger quality tan te competing product. Previous researc so far analyzed tis case wile treating product qualities as uncanged. But to te best of my knowledge, te preceding competitive stage of quality coice as never been presented in te literature. Product quality, owever, is a strategic variable for te firm significantly affecting resulting profits. Te coice of product qualities witin an industry can also be influenced by trade policies suc as quotas or Voluntary Export Restraints. In tis paper, I specifically analyze te endogenous coice of product qualities witin te framework of vertical product differentiation. I sow tat a quota on foreign competition will generally lead to quality-upgrading (downgrading) of te low-quality (ig-quality) firm, an increase in average product quality, and a reduction of domestic consumer surplus, irrespective of weter te foreign firm produces te iger or lower quality. Te effects of a quota on industry profits and domestic welfare depend crucially on te direction of international vertical differentiation. If te foreign firm produces low quality, bot firms' prices and profits will rise but domestic welfare will fall. Tis describes well some major effects of a Japanese Voluntary Export Restraint in te US auto market and relevant empirical findings. If te foreign firm produces ig quality, foreign profits will fall. Since domestic consumer surplus falls only unsubstantially, domestic profit gains will lead to an overall increase of domestic welfare.

4 Te Effects of Quotas on Vertical Intra-Industry Trade 27 September 2002 Stefan H Lutz * ZEW, Manneim and ZEI, Bonn Abstract A quota on foreign competition will generally lead to quality-upgrading (downgrading) of te low-quality (ig-quality) firm, an increase in average quality, a reduction of quality differentiation, and a reduction of domestic consumer surplus, irrespective of weter te foreign firm produces iger or lower quality. Effects of a quota on industry profits and domestic welfare depend crucially on te direction of international vertical differentiation. If te foreign firm produces low quality, bot firms' prices and profits rise but domestic welfare falls. Tis describes well some major effects of a Japanese VER in te US auto market and relevant empirical findings. If te foreign firm produces ig quality, foreign profits will fall. Since domestic consumer surplus falls only unsubstantially, domestic profit gains lead to an increase of domestic welfare. JEL classification: F12, F13, L13 Keywords: trade, quotas, vertical product differentiation, quality-dependent costs * Correspondence: Stefan H Lutz, Centre for European Economic Researc (ZEW), Department of Industrial Economics and International Management, L7, 1, D Manneim, Germany, T (F. 170), E. lutz@zew.de.

5 1 Te Effects of Quotas on Vertical Intra-Industry Trade 1. Introduction According to recent teoretical studies of imperfect markets, quotas on foreign competition will increase qualities, prices and profits of bot domestic and foreign firms under fairly general assumptions (Falvey 1979, Rodriguez 1979, Das and Donnenfeld 1987, Harris 1985, Krisna 1989 and 1990) 1. Tis view as also found widespread empirical support, for example, for te automobile industry (Feenstra 1984, 1985, 1988, 1993; Goldberg 1992, 1994). 2 Te above mentioned results obtain, since a quota imposes on firms a degree of collusion tat tey could not obtain oterwise. In doing tat, it raises te marginal profitability of quality for bot firms at te former free-trade qualities; and it does so even if te quota is not binding. Terefore, te quota also canges te nature of oligopolistic competition. Tis is te oligopolistic analogue to te case of a domestic monopoly (Bagwati 1965). However, teoretical researc by Krisna (1987), Das and Donnenfeld (1989), and Herguera, Kujal, Petrakis (1994) suggest tat a quota could also lead to quality downgrading of te domestic or te foreign quality. Krisna analyzes a monopoly, wile bot te latter approaces assume a duopoly wit Cournot competition in te last stage of te industry-game. However, te duopoly studies differ in te exact timing of te games analyzed. Krisna (1989) empasizes te importance of te form of last stage game for te resulting payoff functions of te firms. Important attributes are te cosen strategic variables (prices, quantities), te form of te restrictions or policy variables (quotas, tariffs), te sequencing of te game (simultaneous, Leader-Follower, quality first or quality jointly wit price, etc.). Se sows tat a quota will still lead to increased prices and profits for bot firms for te case of differentiated substitute products and simultaneous price competition. But te 1 Falvey (1987), Rodriguez (1987), Das/Donnenfeld (1987) and Krisna (1987) deal wit cases of perfect competition or monopoly. Oter studies take oligopolistic competition into account but assume exogenously fixed product qualities (Leland 1979, Sapiro 1983). Harris (1985) and Krisna (1989) model in effect orizontal product differentiation and do not analyze effects on te quality stage. 2 Similar findings ave been forwarded by Boorstein and Feenstra (1991) for te steel industry, by Aw and Roberts (1986, 1988) for te footwear industry, and by Anderson (1985, 1991) for te ceese industry. Mintz (1973) found tat U.S. quotas on meat, dairy products, textiles, and sugur lead to increased import qualities.

6 2 price equilibrium will now involve mixed-strategies on te part of te domestic firm. However, se does not analyze te previous stage of quality coice, treating quality in effect as uncanged. But given te researc received so far, effects on quality are just wat we are interested in. 3 Product quality is a strategic variable for te firm tat can be influenced by trade policy 4 and especially by quotas or Voluntary Export Restraints (VERs). Te conceptual economic framework tat explicitly includes tese vertical quality aspects into te analysis is provided by models of vertical product differentiation. Using tis approac, I sow tat a quota (near te free-trade level) on foreign competition will generally lead to quality-upgrading (downgrading) of te low-quality (ig-quality) firm, an increase in average product quality, a reduction of quality differentiation, and a reduction of domestic consumer surplus, irrespective of weter te foreign firm produces te iger or lower quality. Te effects of a quota on industry profits and domestic welfare depend crucially on te direction of international vertical differentiation. If te foreign firm produces low quality, bot firms' prices and profits will rise but domestic welfare will fall. Tis describes well some major effects of a Japanese VER in te US auto market and relevant empirical findings. 5 If te foreign firm produces ig quality, foreign profits will fall. Since domestic consumer surplus falls only unsubstantially, domestic profit gains will lead to an overall increase of domestic welfare. For our model 6, analytical solutions for all equilibrium variables are available for te unregulated case 7 and te case of a quota at te free-trade level. As for te unregulated case, solutions for te free-trade-quota case are linear functions of te ratio of a market-size parameter (raised to some integer power) and a cost parameter. 8 Te effects of canging te 3 Vertical quality differentiation ("ig" vs. "low" product quality) between substitutable products is, of course, an important dimension in international trade, since trade in differentiated but substitutable products (intraindustry trade) as grown most in te last decades. 4 See also Levinson (1988), Feenstra (1993), Menzler-Hokkanen (1994). 5 Empirical studies of te U.S. car market find quality upgrading also for U.S. cars. However, tere are some conceptual problems wit tese studies tat will be discussed at te end of te paper. Tis migt indicate, tat tis empirical researc at least supports te notion of reduced quality differentiation as a quota effect. Furtermore, a igly binding quota will still lead to quality upgrading of all products witin te verticaldifferentiation framework. 6 Te model setup used ere is based on an earlier, unpublised paper presented at te ZEI, Bonn (Lutz 1997). 7 Tese solutions and teir derivation for te unregulated case are well-known (e.g. Ronnen 1991, Motta 1993, Lutz 1996). 8 All solutions were obtained using Matematica.

7 3 quota marginally starting at te free-trade level are investigated using simulations for bencmark values of market-size and cost parameters. Tese results are presented grapically. 9 Canging tese bencmark values does not suggest any qualitative canges in te results. Interpretation of tese results also makes use of oter analytical results presented so far in te literature. Te remainder of te paper is organized as follows. Section 2 describes te basic analytical framework, te price and quality stages of te industry game, and te simulation procedure. Section 3 reviews te analytical results and te simulations. Section 4 presents discussions of te empirical significance as well as te robustness of te results. Section 5 concludes. 2. Vertical Product Differentiation Te standard model of duopolistic competition wit endogenous product qualities as been developed since te beginning of te 80s (Mussa/Rosen 1978, Gabszewicz/Tisse 1979, Saked/Sutton 1982, Ronnen 1991). Consumers ave identical preferences and different incomes. Te income differences lead to differences in te willingness to pay for a particular product quality. Two firms (domestic and foreign) offer products of different qualities in one (domestic) market. Te firms bear quality-dependent costs and compete in qualities and prices in a two-stage industry game. Since iger product differentiation reduces substitutability and price competition, even identical firms will offer distinct qualities in te resulting market equilibrium. Trade will take place since te foreign firm operates in te domestic market. (In te two-market extension, bot firms operate in bot markets.) National governments can use trade policy to improve te strategic position of domestic industries. 10 Tere is also te possibility of strategic noncooperative interaction between two national governments. 9 Te procedure is te same as in Lutz (1998), were te effects of tariffs were investigated. 10 See e.g. Brander/Spencer 1984, Krisna 1989.

8 Te Model Tere are two firms, te domestic firm d and te foreign firm f, bot competing in te domestic market. If bot firms remain in te market, ten tey produce distinct goods, sold at prices pd and pf, respectively. Te two products carry a single quality attribute denoted by sd and sf, respectively. Eiter firm faces production costs tat are increasing, convex (quadratic) functions of quality, te exact level of wic depending on quality cosen and a quality cost parameter b. Marginal costs are equal to zero for bot firms. Total costs of firm i are ten: ci = bi si 2 (1) In te domestic market, tere is a continuum of consumers (indexed by t) distributed uniformly over te interval [0, T] wit unit density. 11 Eac consumer purcases at most one unit of eiter firm d's product or firm f's product. Te iger a consumer's income parameter t, te iger is er (is) reservation price. Consumer t's utility is given by equation (2) if good i is purcased. 12 Consumers wo do not purcase receive zero utility. u t = s i t - p i (2) Te domestic government and firms d and f play a tree-stage game 13. In te first stage, te government sets an ad-valorem tariff on foreign imports. In te second stage, firms determine qualities to be produced and incur costs ci (i = d, f). In te tird stage, firms coose prices simultaneously (Bertrand competition). Since te derivation of market equilibria witout quotas is generally known and straigtforward, it is relegated to te Appendix Price Competition and Mixed Strategies Te introduction of a quota substantially alters te price game between firms, leading to mixed-strategy pricing by te domestic firm (but not te foreign firm). Te domestic firm randomizes between a price tat makes te quota binding on te foreign firm and a price tat does not (leading to foreign quantity below te quota). If te quota is binding, we assume te 11 Te parameter t represents willingness to pay and increases wit income. Let U[0,T] be te Uniform probability distribution. Ten tis distribution of consumers corresponds to T*U[0,T] wit density T*1/(T-0)=1 for all t, regardless of te upper bound T. Te total mass of consumers representing population size is equal to T, wile te average income parameter T/2 represents per-capita income. 12 Consumers wo do not purcase receive zero utility. 13 In tis formulation, firm i not entering te market is equivalent to firm i coosing s i = 0. Te entry decision by firms is made simultaneously wen coosing quality.

9 5 rationing rule is given by costless arbitrage. Tis implies tat te domestic firm faces a demand wen making te quota binding tat is identical to its demand if te foreign firm cooses a price to equate foreign demand wit te quota (even toug te foreign firm actually carges a lower price). 14 Te actual derivation of te price strategies and equilibria is identical to Krisna (1989, pp ) and is illustrated in Figure Quality Coice Te derivation of quality best responses and equilibrium qualities is, in principle, almost identical to te derivation of te results witout regulation sown in te appendix. Te only difference is, tat revenue und consumer surplus functions are now convex combinations of te respective functions given one of two domestic price realizations. Te relative weigts are given by te probability tat te domestic firm cooses te iger price wic makes te quota binding. As for te unregulated case, solutions for te free-trade-quota case are linear functions of te ratio of a market-size parameter (raised to some integer power) and a cost parameter. 16 Tese solutions are reported in Table 1. Some canges in te properties of quality best responses are indicated by te simulation results indicated below. Te existence of a quota flattens bot quality best responses. A quota-constrained firm faces a lower resulting revenue increase from a quality increase, because its quantity is constrained. If it increases quality, it will also strongly increase price since it cannot gain muc troug quantity increases Te unconstrained firm will react wit a (costless) price increase rater tan a (costly) quality increase. For te case of a quota on te foreign low-quality firm, tis even leads to a sligtly negative slope of te ig-quality best response. 14 Boccard/Wauty (1998) discuss te te existence of a case were tis rationing rule is violated. Suc a case may arise wen te foreign firm offers low quality and due to te fundamental asymmetry given by vertical product differentiation. Given tat a foreign low-quality firm is restricted by a quota, a domestic ig-quality firm now as an alternative coice of capturing foreign customers at te lower end of te income distribution by price (and quality) decreases. However, since in our model setup, cost of quality development are assumed to be independent of quantity produced and ig quality is not fixed, te resulting ig-quality profits and marginal profits are so ig as to prevent tis case. 15 For te case of costless production and a fixed iger quality, te derivation of price strategy and equilibria is also developed in Boccard/Wauty (1998). Consequently teir free-trade setup is based on Coi/Sin (1992). 16 All solutions were obtained using Matematica. Tey are available upon request.

10 Simulations Te paper presents 2 simulations, making a distinction between te case of low quality produced domestically (A) and ig quality produced domestically (B). For te derivation of te simulations sown grapically, market size equals T=1 and cost parameter b=1. 17 Te quota is ten varied between 80% and 110% of te free-trade level of imports for eiter case. Te results are summarized in 18 figures per simulation, sowing te foreign quota quantity, te foreign lower quantity (wen te quota is not binding), te probability tat te quota binds, te equilibrium ratio of ig to low quality, te equilibrium qualities, (expected) profits, (expected) consumer surplus, (expected) domestic welfare, (expected) average prices, te domestic iger and lower prices, (expected) average quantities, and te domestic iger and lower quantities respectively. Te orizontal axis sows te ratio of te quota to te freetrade-level (1 represents te free-trade level). Hence te quota becomes more binding towards te left end of a particular grap. Alternative calculations suggest tat canges in parameters for eac simulation (oter tan cost differences between firms) would not alter te qualitative results. 3. Quotas on Foreign Competition Te results presented in tis section are grouped into analytical results of a quota introduced at te free-trade level and simulation results of canging tat quota level Effects of Introducing a Quota at te Free-Trade-Level A quota at te free-trade level on foreign competition will generally lead to qualityupgrading (downgrading) of te low-quality (ig-quality) firm, an increase in average product quality, a reduction of quality differentiation, and a reduction of domestic consumer surplus, irrespective of weter te foreign firm produces te iger or lower quality. But te effects of a quota on industry profits and domestic welfare depend crucially on te direction of international vertical differentiation. 17 Te results for a quota at te free-trade level only are generally valid for any positive values of T and b, since tese variables enter strictly in a multiplicative way, once te quota is fixed.

11 7 If te foreign firm produces low quality, bot firms' prices and profits will rise but domestic welfare will fall. Te fall in domestic welfare is due to tree effects: ig quality decreases, prices rise, total quantity bougt (of bot goods) falls. Te last effect reduces market participation (sare of consumers buying eiter good) to suc an extent, tat tis negative effect overcompensates for an increase in average quality. Te increase in average quality is te result of te reduced market sare of te low-quality product. If te foreign firm produces ig quality, foreign profits will fall. Te foreign firm is bound by te quota, but it cannot profitably increase its already ig and costly quality. Since its quantity must be reduced, it actually needs to decrease its quality. However, te domestic low-quality firm increases quality substantially. Tis leads to a decrease in quality-adjusted price of te low-quality good wile te ig quality good becomes relatively more expensive. For te consumers as a wole, tese two effects almost cancel out. Terefore, domestic consumer surplus falls only unsubstantially, and domestic profit gains will lead to an overall increase of domestic welfare Effects of Canging te Level of an Existing Quota As a function of te quota level, te quota-constrained equilibrium quality exibits a concave sape (wit te maximum near te free-trade level), wile te domestic equilibrium quality is decreasing in a quota increase (relaxing te constraint), irrespective of te ordering of qualities. Similarly, te profits of te quota-constrained firm exibit concave sapes, wile te profits of te domestic firm decrease wen te quota is relaxed. Domestic consumer surplus and domestic welfare increase generally wit a relaxing of te quota. Significant differences depending on te ordering of qualities arise wit respect to quality differentiation and canges in low-quality quantity. Wit a quota on ig quality, quality differentiation decreases wit a tigtening of te quota. Low-quality quantity rises wile ig-quality quantity falls wit a tigter quota, leading to only small canges in total quantity sold. Wit a quota on low quality, quality differentiation exibits a U-sape (wit te minimum near te free-trade level). Consequently, quality differentiation rises wit a

12 8 tigtening of te quota away from te free-trade level. Tis tigtening of te quota also leads to decreases of bot quantities. Tis difference explains te relatively weaker negative effect on consumer surplus for a quota on te ig-quality firm. It also explains wy a foreign ig-quality firm is armed more by te tigtening of a quota (away from te free-trade level). 4. Discussion In tis section, I first review empirical findings about te U.S. auto market in ligt of te presented teory. Tis is followed by a discussion of robustness issues Empirical Results Te standard empirical case cited is te development of te US car market during te 1980s, were Japanese imports were subjected to bot quantity constraints and tariffs. To my knowledge, tere is no closure yet on te debate weter quality upgrading was induced by tariffs, VERs, or a combination of bot. However, te general notion is tat te quality of Japanese cars was initially lower tan tat of U.S. cars, and tat it was upgraded. Feenstra (1993) reports a quality increase of Japanese cars. Goldberg (1992, 1994) performed tradepolicy simulations using an econometric model of US car demand, coming to te conclusion tat quotas lead to quality upgrading, wile tariffs migt lead to downgrading. Goldberg also reports quality-upgrading for U.S. cars, wile Feenstra does not analyze te effects on U.S. cars. I want to argue tat te case of a quota on a low-quality foreign firm in my model describes te U.S-Japan auto case well. On first glance, Goldberg's results seem to contradict two of my teoretical results. Tese are decreased quality differentiation and a decrease in ig quality. However, Goldberg infers an increase of quality for U.S. products from a demand sift towards iger-quality car models. Se does not actually analyze any quality cange of tese car models. Tis result is arguably better comparable to my teoretical result of average quality increases. From anectodal evidence (for example comparisons of reliability of Japanese and U.S. cars in te

13 9 1980s), I would also argue tat te first reaction of U.S. car firms te quotas was to not put as muc effort into quality improvement of teir own models as tey would ave done oterwise. It is also noteworty, tat tis teoretical model predicts te same tariff effects as sown in Goldberg's work, namely a quality decrease (see also Lutz 1998). Noting tat te tariff affects low-quality Japanese cars, tis would also relieve te pressure on U.S. firms to increase te quality of teir cars to some extent Robustness of te Model Wit Cournot competition instead of Bertrand competition, many of te results presented above remain valid. Analyzing te case of Cournot competition, Herguera/Kujal/Petrakis (2000) ave sown tat a quota on a foreign low-quality firm will lead to upgrading of te foreign product, downgrading of te domestic product, decrease in differentiation and increase of average (quantity-weigted) quality. 5. Conclusions Tis paper as demonstrated tat te direction of international vertical differentiation can be a major factor in determining te results of trade policies suc as quotas or VERs. Furtermore, empirical observations suc as for te U.S. auto market can be more fully explained taking te direction of quality differentiation into account. Literature Anderson, J. E. (1991). "Te Coefficient of Trade Utilization: Te Ceese Case," in: R. E. Baldwin (ed.) Empirical Studies of Commercial Policy (University of Cicago Press, Cicago). Anderson, J. E. (1985). "Te Relative Inefficiency of Quotas: Te Ceese Case, American Economic Review, Vol. 75(1), pp

14 10 Aw, B. Y. and M. J. and Roberts (1988). Price and Quality Level Comparisons for U.S. Footware Imports: An Application of Multilateral Index Numbers," in: R. C. Feenstra (ed.) Empirical Metods for International Trade (MIT Press, Cambridge, MA). Aw, B. Y. and M. J. and Roberts (1986). "Measuring Quality in Quota-Constrained Import Markets: Te Case of U.S. Footware," Journal of International Economics, Vol. 21(1/2), pp Bagwati, J. (1965). "On te Equivalence of Tariffs and Quotas," in: R. E. Baldwin et.al. (eds.) Trade, Growt and te Balance of Payments: Essays in Honor of Gottfried Haberler (Rand McNally, Cicago). Boccard, N. and X. Wauty (1998). Import restraints and Quality Coice under Vertical Differentiation, CORE Discussion Paper Boom, A. (1995). "Asymmetric International Minimum Quality Standards and Vertical Differentiation," Journal of Industrial Economics, Vol. 43(1), pp Boorstein, R. and R. C. Feenstra (1991). "Quality Upgrading and its Welfare Cost in U.S. Steel Imports," in: Helpman, E. and A. Razin (eds.) International Trade and Trade Policy (MIT Press, Cambridge, MA). Brander, J. A. and P. R. Krugman (1983). "A Reciprocal Dumping Model of International Trade," Journal of International Economics, Vol. 15, pp Brander, J. A. and B. J. Spencer (1984). "Tariff Protection and Imperfect Competition," in: H. Kierzkowski (ed.) Monopolistic Competition and International Trade (Clarendon Press, Oxford). Coi, C. J. and H. S. Sin (1992). A Comment on a Model of Vertical Product Differentiation, Journal of Inndustrial Economics, Vol. 40(2), pp

15 11 Crampes, C. and A. Hollander (1995). "Duopoly and Quality Standards," European Economic Review, Vol. 39, pp Cremer, H. and J.-F. Tisse (1994). "Commodity Taxation in a Differentiated Oligopoly," International Economic Review, Vol. 35(3), pp Cremer, H. and J.-F. Tisse (1991). "Location Models of Horizontal Differentiation: A Special Case of Vertical Differentiation Models," Journal of Industrial Economics, Vol. 39(4), pp Das, S. P. and S. Donnenfeld (1989). "Oligopolistic Competition and International Trade: Quantity and Quality Restrictions," Journal of International Economics, Vol. 27(3-4), pp Das, S. P. and S. Donnenfeld (1987). "Trade Policy and its Impact on Quality of Imports: A Welfare Analysis," Journal of International Economics, Vol. 23, pp Falvey, R. E. (1979). "Te Composition of Trade Witin Import-Restricted Categories," Journal of Political Economy, Vol. 87, pp Feenstra, R. C. (1993). "Measuring te Welfare Effect of Quality Cange: Teory and Application to Japanese Autos," NBER Discussion Paper No Feenstra, R. C. (1988). "Quality Cange under Trade Restraints in Japanese Autos," Quarterly Journal of Economics, pp Feenstra, R. C. (1985). "Automobile Prices and Protection: Te U.S.-Japan Trade Restraint," Journal of Policy Modelling, Vol. 7, pp Feenstra, R. C. (1984). "Voluntary Export Restraint in U.S. Autos, : Quality, Employment and Welfare Effects," in: R. E. Baldwin and A. Krueger (eds.) Te Structure and Evolution of Recent U.S. Trade Policy.

16 12 Gabszewicz, J. J. and J.-F. Tisse (1979). "Price Competition, Quality and Income Disparities," Journal of Economic Teory, Vol. 20, pp Goldberg, P. K. (1994). "Trade Policies in te U.S. Automobile Industry," Japan and te World Economy, Vol. 6(2), pp Goldberg, P. K. (1992). "Product Differentiation and Oligopoly in International Markets: Te Case of te U.S. Automobile Industry," mimeo., Princeton University. Harris, R. (1985). "Wy Voluntary Export Restraints are Voluntary?" Canadian Journal of Economics Vol. 18. Herguera, I., Kujal, P. and E. Petrakis (2000). "Quantity Restrictions and Endogenous Quality Coice," International Journal of Industrial Organization, Vol. 18(8), pp Herguera, I. and S. Lutz (1998). Oligopoly and Quality Leapfrogging, Te World Economy, Vol. 21(1), pp Irmen, A. and J.-F. Tisse (1998). Competition in Multi-Caracteristics Spaces: Hotelling was Almost Rigt, Journal of Economic Teory, Vol. 78(1), pp Krisna, K. (1990). "Export Restrictions wit Imperfect Competition: A Selective Survey," NBER Working Paper No Krisna, K. (1989). "Trade Restrictions as Facilitating Practices," Journal of International Economics, Vol. 26, pp Krisna, K. (1987). "Tariffs vs. Quotas wit Endogenous Quality," Journal of International Economics, Vol. 23, pp Leland, H. E. (1979). Quacks, Lemons, and Licensing: A Teory of Minimum Quality Standards, Journal of Political Economy, Vol. 87, pp

17 Levinson, J. (1988). "Empirics of Taxes on Differentiated Products: Te Case of Tariffs in te U.S. Automobile Industry," in: R. Baldwin (ed.) Trade Policy Issues and Empirical Analysis (NBER, Cicago). 13 Lutz, S. (1998). "Can Taxing Foreign Competition Harm te Domestic Industry?" ZEI Policy Paper B Lutz, S. (1997). Quotas wit Vertical Differentiation and Price Competition, ZEI, Bonn, mimeo. Lutz, S. (1996). "Vertical Product Differentiation, Quality Standards, And International Trade Policy," CEPR Discussion Paper No Menzler-Hokkanen, I. (1994). "Empirical Comparisons of Quality Measures in International Trade," in: Quality Cange and Competitiveness in International Trade (Helsinki Scool of Business Administration, Helsinki). Mintz, I. (1973). "U.S. Import Quotas: Cost and Consequences," American Enterprise Institute for Public Policy Researc. Motta, M. (1993). "Endogenous Quality Coice: Price vs. Quantity Competition," Journal of Industrial Economics, Vol. 41, pp Mussa, M. and S. Rosen (1978). "Monopoly and Product Quality," Journal of Economic Teory, Vol. 18, pp Rodriguez, C. A. (1979). "Te Quality of Imports and te Differential Welfare Effects of Tariffs, Quotas and Quality Controls on Protective Devices, Canadian Journal of Economics, Vol. 12, pp Ronnen, U. (1991). "Minimum Quality Standards, Fixed Costs, and Competition," Rand Journal of Economics, Vol. 22(4), pp

18 Scarpa, C. (1996). "Quality Standards in a Vertically Differentiated Oligopoly," International Journal of Industrial Organization, fortcoming. 14 Saked, A. and J. Sutton (1982). "Relaxing Price Competition Troug Product Differentiation," Review of Economic Studies, Vol. 49, pp Sapiro, C. (1983). Premiums for Hig Quality Products as Returns to Reputations, Quarterly Journal of Economics, Vol. 98, pp

19 15 Appendix (All calculations are available upon request.) Te Model Witout Quotas Tis appendix demonstrates te derivation of te unconstrained market equilibria for te model presented in Section 2. Firms d and f play a two-stage game 18. In te first stage, firms determine qualities to be produced and incur costs ci (i = d, f). In te second stage, firms coose prices simultaneously. 19 Price Competition To solve te game, consider first te demand faced by te ig-quality and low-quality firm, respectively. Let and o stand for ig and low quality, respectively. Tese demands are ten given by: 20 q T ( p p o s s ) p po po, q o (A.3.1) o s so so Let i =, o; let j i. Te profit function for firm i is given by i = p i q i (p i,p j,s i,s j ) - c i (s i ). Taken bot qualities as given, te price reaction functions in eac market are given as te solutions to te first order conditions. Solving te resulting equations for bot prices, equilibrium prices are ten given as: p 2Ts (s s o) T(s s )s, p o = 4s s 4s s o 0 o o (A.4.1) Note tat for all s > s o, T > t > t o > 0 will old, i.e., equation (A.4.1) is in fact an unconstrained price equilibrium. Given te price equilibrium depicted above, demands and tus profits can be expressed in terms of qualities. For positive qualities s i (i =, o), tese profit functions are: T s (s s 0) 2 Ts(s s)s o o 2 bs 2, o bs 2 o o (4s s 0) (4s s o) Similarly, consumer surplus 21 can be expressed in te following way: (A.5.1) 18 In tis formulation, firm i not entering te market is equivalent to firm i coosing s i = 0. Te entry decision by firms is made simultaneously wen coosing quality. 19 To derive solutions, we will use te concept of subgame-perfect equilibrium, computing te solutions for eac stage in reverse order. Bot firms coose teir respective product quality from te same interval [0, ). Te resulting market equilibria will include some consumers in te lower segment of te interval [0, T] not valuing quality enoug to buy any product. Tis guarantees an interior solution of te price game. 20 Let t = (p - p o )/(s - s o ) and t o = p o /s o. Consumers wit t = p o /s o will be indifferent between buying te low-quality product and not buying at all. Consumers wit t = (p - p o )/(s - s o) will be indifferent between buying eiter te ig-quality or te low-quality product. Consumers wit T ### t > t will buy ig quality, consumers wit t > t > t o will buy low quality, and consumers wit t < p o /s o will not buy at all. 21 Consumer surplus is defined as { (t*s - p )dt + (t*s o - p o )dt} were te first integral goes from t to T and te second goes from t o to t.

20 T s 4s 5s CS 2 2 4s s o o (A.6.1) Properties of te Revenue and Consumer Surplus Functions Let R i denote firm i's revenue function. Let and o denote ig and low quality, respectively. R 0; R 4s R 0 0 for s o ; 0, Ro 0; (A.7.1) s so 7 so s 2 R ; R R o Ro 2 0; > 0; > 0. 2 s s s s o o s o s Let CS I (I = D, F) denote region I's consumer surplus function. Firms' qualities are denoted by s and s o for ig and low quality, respectively. CS s I 0 for s < 4s ; o 5 CS s o I 0 ; 2 CSI 0 2 ; s 2 CSI 0 2 ; s o 2 CSI s s o 0. Quality Competition To derive te firms' quality best responses, we investigate eac firm's profit function, given te oter firm's quality coice, and taking into account te beavior in te price-setting subgame. Given te order of qualities, te profit functions in equations (A.5.1) are concave in te respective firm s own quality. Te profit-maximizing coices form a Nas-equilibrium in qualities, were bot marginal profit functions evaluate to zero. Te first order conditions for te ig and low quality firm, respectively, are ten given as: T s (4s 3sso 2s o ) / (4s s o) 2bs (A.9.1) T s (4s 7s o) / (4s s o) 2boso Te slopes of te ig and low quality firms' quality best responses can be calculated (using te implicit function teorem) as ds i /ds j = -( ( i / s i )/ s j )/( ( i / s i )/ s i ), were i is eiter ig or low quality and j is te oter quality. Bot slopes are positive, but less tan one. From te properties of te revenue functions and te slopes of te quality best responses, it can be derived tat te two qualities are strategic complements. Furtermore, a forced increase of te low quality will reduce product differentiation and increase price competition. Divide te first order conditions given in (A.9), rearrange and write s = r s o and b o = a b to obtain: 2 4(2 3r 4r ) r 2 4r 7r a For a=1 ( i.e. b o = b = b) r = wile for a=2 ( i.e. b o = 2 b = 2 b) r = Using r to express s in terms of s o and substituting for s in te first equation of (A.9.1) allows for

21 17 calculating te equilibrium qualities for any given value of T and b. (However, te ratio of cost parameters a must be fixed.) Te resulting equilibrium qualities for identical firms (i.e. b = bo = b) are ten: 22 s = T 2 / b and so = T 2 / b Te resulting equilibrium profits for identical firms (i.e. b = bo = b) are ten: = T 4 / b and o = T 4 / b Quota and Price Competition Figure 1 sows te actual calculated price best responses for te parameter set {T=1, b=1, s f = , s d = and quot= }, i.e. te domestic firm produces ig quality and te foreign firm is subjected to a quota equal to ist free-trade quantity coice. Te grap also includes iso-profit lines of te domestic firm, were domestic profits increase to te rigt and interior of a particular contour line, i.e. wit increases in foreign price. Figure 1 P d 0.1 pbr f 0.08 pqr f p d 0.06 pbr d p f* p f Te straigt lines pbr d and pbr f are te domestic and foreign free-trade price best responses, respectively. As usual tey are bot upward-sloping. Since te foreign firm produces low quality, its best response starts from te origin. Originally, te foreign firm is not quota-constrained wen moving upward along ist best response since ist optimal price coice is ig relative to domestic price. Te line pqr f denotes te ratio of domestic to foreign

22 price coice suc tat te quota would be exactly binding. It becomes te foreign firm s best response from te point of teir intersection. In equilibrium, te foreign, low-quality producer cooses p f* wile te domestic, igquality producer randomizes between p d and pbr d (p f* ).At p f*, te domestic firm is indiffernt between using te quota to coose te iger price and playing its free-trade best response. An equilibrium is obtained wen te domestic firm cooses te probability for te iger price suc tat te expected price induces te foreign firm to coose p f* as best response Note tat T 2 /b enters in a multiplicative way and terefore does not affect te calculations.

23 19 Table 1. Results Variable Unregulated Quota Firm 1 Quota Firm 2 s 1 1) s 2 1) s 1 /s Average s p 1 2) p 2 2) q 1 3) q 2 3) Total q PI 1 4) PI 2 4) CS 4) W 1 4) W 2 4) ) Multiply values wit T 2 /b; 2) Multiply values wit T 3 /b 3) Multiply values wit T; 4) Multiply values wit T 4 /b

24 20 Case A. Quota on te Foreign Hig-Quality Firm (Domestic Low-Quality Firm Randomizes Price) A.1. Quota A.2. Foreign Lower Quantity A.3. Probability Binding Quota A.4. Quality Ratio A.5. Foreign Quality A.6. Domestic Quality A.7. Foreign Profits A.8. Domestic Profits

25 A.9. Domestic Consumer Surplus A.10. Domestic Welfare A.11. Foreign Average Price A.12. Domestic Average Price A.13. Domestic Higer Price A.14. Domestic Lower Price A.15. Foreign Average Quantity 0.24 A.16. Domestic Average Quantity

26 A.17. Domestic Higer Quantity 0.24 A.18. Domestic Lower Quantity Case B. Quota on te Foreign Low-Quality Firm (Domestic Hig-Quality Firm Randomizes Price) B.1. Quota 0.18 B.2. Foreign Lower Quantity B.3. Probability Binding Quota 4.88 B.4. Quality Ratio B.5. Foreign Quality B.6. Domestic Quality

27 B.7. Foreign Profits B.8. Domestic Profits B.9. Domestic Consumer Surplus B.10. Domestic Welfare B.11. Foreign Average Price B.12. Domestic Average Price B.13. Domestic Higer Price B.14. Domestic Lower Price

28 B.15. Foreign Average Quantity B.16. Domestic Average Quantity B.17. Domestic Higer Quantity B.18. Domestic Lower Quantity