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Essays on strategic trade policy : market uncertainty, incomplete information, and credit rationing Qiu, Dongxiao 1993

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ESSAYS ON STRATEGIC TRADE POLICY:MARKET UNCERTAINTY,INCOMPLETE INFORMATION,ANDCREDIT RATIONINGbyDONGXIAO QIUB.Sc., Zhongshan University, China, 1983M.A., The University of British Columbia, 1989A THESIS SUBMITTED IN PARTIAL FULFILMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIES( Department of Economics )We accept this thesis as conformingto the required standard THE UNIVERSITY OF BRITISH COLUMBIAMay, 1993© Dongxiao Qiu, 1993In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature) Department of tr:C-00 0 rili't 6The University of British ColumbiaVancouver, CanadaDate Ju ly 14, 0413DE-6 (2/88)ABSTRACTThis dissertation is a collection of three essays on strategic trade policy. The mainpurpose of this research is to make contributions to the strategic trade literature bydealing with some of its interesting and important issues.The first essay extends the well-known Brander-Spencer (1985) model, by con-sidering market uncertainty, endogenizing firms' choice of strategic variables, andintroducing a quadratic export tax/subsidy scheme; and investigates the interrela-tionship between trade policies and market competition. It is shown that firms arenot indifferent between setting prices and setting quantities in an uncertain envi-ronment. The quadratic export tax/subsidy scheme is proved superior to the linearexport tax/subsidy scheme because the former has the unique ability to influencethe domestic firm's choice of strategic variables and therefore to affect the marketconduct in favour of the domestic country.The second essay explores an incomplete information version of the Brander-Spencer (1985) model, in which the domestic firm's production cost is private in-formation. This model has the distinguishing feature that it contains a mixture ofscreening and signalling problems. Because of this, policy makers are confronted bytwin conflicting policy objectives: choosing between an information revealing policymenu and an information concealing uniform policy. We prove that the policy menuis preferred to the uniform policy in quantity competition while the opposite is truein price competition.iiIn essay three, we examine the implications of credit rationing for internationaltrade. Development and production of new products often involves uncertainty (e.g.R&D uncertainty and demand uncertainty), which could lead to credit rationing.We find that the presence of credit rationing may give partial explanation for theindeterminacy of the pattern of trade between two similar countries. When credit isrationed, two-way trade is less likely to occur.iiiTABLE OF CONTENTSpageAbstract^ iiList of Figures viAcknowledgement^ viiOverview^ 11 Quadratic Export Subsidy Scheme and Market Conduct^61.1 Introduction  ^71.2 The Model  ^101.3 Analysis  ^121.3.1 Linear Scheme  ^141.3.2 Quadratic Scheme  ^171.3.3 Linear Scheme vs. Quadratic Scheme  ^251.3.4 Robustness  ^261.4 Conclusion  ^282 Optimal Strategic Trade Policy under AsymmetricInformation^ 302.1 Introduction  ^312.2 The Model  ^342.3 Analysis  ^362.3.1 Separation Inducing Menus  ^382.3.2 Optimal Separation Inducing Menu  ^422.3.3 Optimal Uniform Policy  ^442.3.4 Optimal Policy and Equilibrium  ^452.4 Bertrand Competition  ^512.5 Conclusion  ^573 New Products, Credit Rationing, and International Trade^603.1 Introduction  ^613.2 The Model  ^64iv3.3 Trade ^  663.3.1 Firm's Expected Profit ^  663.3.2 The Bank's Expected Return  703.3.3 Credit Rationing  713.3.4 Pattern of Trade ^  723.4 The Timing of Moves  733.6 Concluding Remarks and Future Research ^ 78References^ 81Appendix I 84Appendix II^ 89LIST OF FIGURESpageFigure 1^ 91Figure 2 91viACKNOWLEDGEMENTFor providing guidance, advice, comments, suggestions, and much other help overthe years taken to complete this dissertation, I would like to thank my supervisorycommittee, Brian Copeland (Chairman), Barbara Spencer, and Guofu Tan. I amthankful to Mick Devereux and Ken Hendricks for reading the entire dissertation andgiving me helpful comments in the departmental thesis defense. I am also gratefulto John Weymark who always gave me encouragement during my graduate study atU.B .0The second essay of this dissertation, which by now has been accepted for pub-lication in the Journal of International Economics, has benefitted a great deal fromthe very helpful comments of two anonymous referees. A referee's specific suggestionsand criticisms and Barbara Spencer's extremely valuable help have made significantimprovement in the quality of this paper.Finally, I want to thank my wife, Jinglian, for her unfailing support and belief inmy ability. She has shared my joys and sorrows, failure and successes. Naturally, thisdissertation is dedicated to her and our lovely daughter, Alice.viiOVERVIEWIt had been traditionally argued and widely accepted that under almost all sit-uations free trade was the best trade policy a country could have. In fact, we havewitnessed a gradual move of the world economy towards free trade since the intro-duction of the Bretton Wood system in 1944. This movement is mainly characterizedby tremendous tariff reductions around the world, especially in developed countries.However, the world is still far from free trade. Use of non-tariff barriers has beensignificantly increased and other types of government intervention in internationaltrade such as export subsidies are frequently found. It can hardly been denied thatthe rapid growth of the newly industrial countries (Korea, for example) can largelybe attributed to these nations' industrial and trade policies such as export promo-tion and import restriction. We can often hear complaints from American producersthat they are facing unfair competition from their Japanese counterparts since theJapanese producers are helped directly by their government. If free trade is optimal,however, what is the rationale for government interventions in those economicallysuccessful countries? In the attempt to answer questions of this sort, we in the 1980shave witnessed a revolution in international trade theory: the emergence and develop-ment of the so-called new trade theory. Among those theories, the theory of strategictrade policies, pioneered by Jim Brander and Barbara Spencer,' has received thegreatest attention both in academic circle and in business. This theory, which is built'They are now associated with U.B.C.. Naturally and fortunately, my work has benefit-ted a great deal from this local contact.1upon the theory of industrial organization (especially oligopoly theory), was initiallyinspired by the observation that international market competition in many indus-tries is indeed imperfect. 2 The general idea underlying the strategic trade literatureis that firms earn positive rents under imperfect competition and thus appropriatetrade policies adopted by a government may affect the behaviour of those competingfirms in such a way to shift some of the rents otherwise earned by the foreign firmto the domestic firm. Although it is elegant and powerful, the theory has been sub-ject to many criticisms. As Harris (1989, p753) points out, "the basic problem as itturns out is that there are many models of imperfect competition, and answers toparticular policy issues are quite sensitive to assumptions as to how markets work andthe manner in which government intervenes in these markets." To make the theoryuseful for policy prescriptions, further and rigorous studies are both desirable andvaluable. In addressing and solving some of the existing problems, this thesis makesnew contributions to this growing literature.This thesis consists of three essays. Appropriate strategic policy design in variouscircumstances is the main concern of the first two essays (Chapters 1 and 2). Thethird essay (Chapter 3) turns to a different but also important issue. It examines theimplications of credit market imperfection for the pattern of trade.In Chapter 1, which is entitled "Quadratic Export Subsidy Scheme and MarketConduct" , we extend the well known Brander-Spencer (1985) model by introducingmarket uncertainty, endogenizing firm's choice of strategic variables, and taking non-2In contrast, perfect competition is one of the basic assumptions in traditional tradetheory.2linear export policies into consideration. In the strategic trade literature, all studieswith only one exception (Laussel (1992)) have one thing in common: assuming thatthe type of market competition (or market conduct) is exogenously given. However,the equilibrium market conduct, which is jointly determined by both the domesticand the foreign firms' choice of strategic variables, could be affected by many factorsincluding trade policies per se. Therefore, if market conduct is changeable, there isan obvious logical flaw in the derivation of optimal policies in many studies sincethey all assume fixed market conduct. Thus, policies so obtained are not necessarilyoptimal. The study contained in the first essay (Chapter 1) allows the type of marketcompetition to change responding to different government policies. In particular, weshow that when demand is uncertain, firms have strict preferences for setting pricesor quantities, depending on their different cost structures. Thus, the equilibriummarket conduct is determined by firms' cost structures which is in turn affected bythe government's tax and subsidy policy. After defining a quadratic export subsidyscheme, we show that it is superior to the often-studied linear export subsidy schemebecause the former has the ability to influence the domestic firm's choice of strate-gic variables and therefore affects the type of market competition in favour of thedomestic country.In Chapter 2. we analyze strategic trade policies taking into account. the incen-tive compatibility constraints arising from information asymmetry. Optimal strategictrade policies depend upon competition in export market, production costs, and mar-ket demands. among others. However, policy makers generally lack such information3required for policy design. Because producers are in the frontier of an economy, they,in contrast, have this information or at least know more than their governments. Thiscreates an information asymmetry between governments (regulating bodies, princi-pals) and producers (regulated bodies, agents). Chapter 2 deals with one of theseinformation problems, which is perhaps the most common one: asymmetric cost in-formation.Specifically, we consider an asymmetric information version of the Brander-Spencermodel by assuming that neither the domestic government nor the foreign firm knowsabout the domestic firm's production cost. This model is of particular interest sinceit is a mixture of screening and signalling problems, which has not been studied in theinformation economics literature or in the strategic trade literature. The screeningproblem is present when the domestic government attempts to overcome the incentiveproblem by offering a menu of policies to the domestic firm. The signalling problem isinvolved in the stage in which the domestic firm chooses a policy from the menu andthen competes with the foreign firm. Although use of policy menus can accomplishthe screening task, incentive compatible menus inevitably reveal the domestic firm'scost information to the foreign firm. This information revelation might or might notbe desirable from the point of view of the domestic country. If it is undesirable, thedomestic government could instead adopt a uniform policy to conceal the information.Due to these conflicting informational consequences of different policies, therefore, thegovernment is confronted by the following problem: choosing between a policy menuand a uniform policy. We find that policy menu is preferred to uniform policy in4Cournot competition while the opposite occurs in Bertrand competition.Chapters 1 and 2 have respectively investigated issues in strategic trade policyin the presence of demand uncertainty and asymmetric cost information. In Chap-ter 3, we focus on another important situation when uncertainty and informationasymmetry together affect international trade. In particular, we examine the patternof trade between two similar countries in the presence of financial market credit ra-tioning, which is caused by the coexistence of uncertain product market return andasymmetric information about borrowers' riskiness.We consider the case in which two countries face the same opportunities to producea series of new and risky products. Development of new products requires R&D anddemand for these new products is generally uncertain. Because of this, investmentin new product development is risky. If lenders and borrowers have asymmetricinformation about the riskiness of these investments, borrowers may be subject tocredit rationing when these projects have to be (at least partly) financed externally.In these circumstances, whether one country would eventually produce a certain newproduct and export to the other partly depends on whether the producers in thiscountry could borrow from a bank. This makes the pattern of trade indeterminate.5Chapter 1QUADRATIC EXPORT SUBSIDY SCHEMEANDMARKET CONDUCT61.1 IntroductionThe literature on strategic trade policy has been flourishing since early 1980s. Thereare at least two reasons for this. First, government intervention in international tradeis commonly found in the world. Second, international markets in many industriesare indeed imperfect due to entry barriers and/or product differentiation. The gen-eral idea underlying the studies in this literature is that firms earn positive rentsunder imperfect competition and appropriate trade policies adopted by the domesticgovernment may affect the competing firms behaviour in the export market in sucha way to shift some of the rents otherwise earned by the foreigners to the domesticproducers. This is the familiar "rent-shifting" argument. Following this idea, vari-ous optimal trade policies are derived under different assumptions about the type ofcompetition (market conduct), the nature of competing products, and the number offirms. 3 All these studies have one thing in common: they take the type of marketcompetition as exogenously given and confine themselves to linear policies.' However,a firm's choice of strategic variables (price or quantity) could be affected by manyfactors including trade policies per se. Therefore, the equilibrium type of market3For a survey of this literature, see Helpman and Krugman (1989) or Pomfret(1991).4Laussel (1992) is the only exception. The discussion paper version of Laussel (1992)came to my attention after the first version of this chapter had been finished in April 1991.The reader should find that these two studies are very similar in their motivations, ideas,and results. However. I focus on price setting and quantity setting behaviour of the firmsrather than using a more general approach  - the supply-function equilibrium approach,which is used by Laussel. Moreover, the analysis of the present study emphasizes on thedependence of the optimal quadratic export subsidy scheme on the firms' cost structures,given a fixed degree of demand uncertainty. Laussel (1992). on the other hand. stressesthe link between the optimal linear-quadratic schedule and the degree of uncertainty, underconstant marginal cost.competition should be endogenously determined given a particular trade policy. Wealso realize that there are many other possible forms of policies which are as easilyimplemented as the linear policy, for example, a quadratic export subsidy schemewhich will be defined later. The purpose of this study is to explore nonlinear policiesand compare them with the linear policy when firms' choice of strategic variables hasbeen endogenized.It has been well known in the strategic trade literature that the type of optimalstrategic trade policies depends on the type of market competition. In their seminalpaper, Brander and Spencer (1985) argue that certain policies precommitted by thehome government could have strategic effects on the international market competition.In particular, they find that if firms compete in quantities, export subsidization willshift the market share in favour of the home firm and therefore increase the nationalwelfare. However, as shown by Eaton and Grossman (1986), if firms compete inprices, the optimal policy involves export tax, which increases firms' profits at theexpense of consumers. Nevertheless, the central point is that government interventionputs the home firm in a Stackelberg leader's position vis-a-vis the foreign firm.Almost all studies in strategic trade policies focus on export tax-subsidy policiesin a certainty environment with the exception of Cooper and Riezman (1989) andAryan (1991). They consider export quota policies and compare them with exporttax-subsidy policies in the presence of demand and cost uncertainties. They findthat subsidization is preferred to quotas if demand uncertainty is high but a quotapolicy is better than subsidization if demand uncertainty is low. What is most im-8portant in their work is that they point out the importance of using different modesof intervention in different circumstances.In a duopoly model with demand uncertainty but without government interven-tion, Klemperer and Meyer (1986) show that firms are not indifferent between choos-ing a quantity and a price as their strategic variables. In particular, they prove thatthe dominant strategy is to choose quantities (prices) if the cost curve is convex(concave). Therefore, depending on the firms' cost structures, the equilibrium mar-ket conduct could be Cournot, Bertrand, or asymmetric competition (i.e., one sets aquantity and the other sets a price).In this chapter, I extend the Brander-Spencer (1985) model by introducing mar-ket uncertainty, endogenizing firms' choice of strategic variables, and consideringnonlinear export subsidy policies. In particular, I propose a quadratic export subsidyscheme in which subsidy rates vary with export volumes and find that it is superiorto the often-studied linear export subsidy scheme in which there is a uniform subsidyrate. Both the quadratic and linear subsidy schemes can shift the domestic firm tothe Stackelberg leader's position given a particular market conduct; but, in additionto that, the quadratic scheme has the ability to influence the domestic firm's choiceof strategic variable and therefore to affect the market conduct in favour of the do-mestic firm. Note that the practical two-step tax-subsidy policy is a special case ofthe quadratic subsidy scheme and implementing the quadratic scheme should not bemore difficult than the linear scheme.The remainder of this chapter is organized as follows. In Section 1.2, we develop9a model for analysis. In Section 1.3, the optimal linear scheme and the optimalquadratic scheme are derived and through a comparison we reach the conclusion thatthe quadratic scheme is superior to the linear scheme. The last section of this chapter,Section 1.4, summarizes the results and outlines future research. Most of the proofsare contained in Appendix I.1.2 The ModelAs in Brander and Spencer (1985), there are one domestic firm and one foreign firmand the domestic government assists its firm in export competition. Firms producedifferentiated products, all of which are exported to a third country. 5 There aredemand uncertainties due to many unknown factors such as consumer preferencesand income of the importing country. The domestic government is free to adopt anonlinear policy or a linear policy.The model can be viewed as a two-stage game. In the first stage, the domesticgovernment designs its trade policy. We confine ourselves in this study to the followingtwo types of policy schemes:1. linear scheme, in which the domestic firm receives s 1 q amount of subsidy fromthe government if it exports q units of goods (if s 1 < 0, it pays an export tax);and2. quadratic scheme, in which the domestic firm receives s 2 q2 amount of subsidy5This is to isolate producer's surplus and so to simplify welfare analysis.10from the government if it exports q units of goods (if s 2 < 0, it pays an exporttax).To determine the level of the chosen policy scheme, one needs to specify s 1 or s 2 . Thegovernment chooses a policy by taking into account its impacts on the second stagegame.In the second stage, firms make their decisions simultaneously. A firm may seta price and then produce the amount demanded for its products or it may set anoutput level and then sells its products at the price which clears the market. In thefirst case, the firm chooses price as its strategic variable while in the last case, itsstrategic variable is quantity. 6Let demand be characterized by the linear system proposed by Dixit (1979) witha slight modification. More specifically,p i = a — bqi — dqj^= 1, 2, i j, a > 0, b > d > 0^(1 )where qi and q2 denote the quantities of supply of (or demand for) the domestic firm'sand the foreign firm's products, respectively; p i and p2 are the prices of correspondingproducts; and e stands for a random variable with E(€) = 0 and E(e2 ) = a2 > 0.Assume that firms have the same cost functions:1^2C(q) elq + c2qwhere 0 < c 1 < a and c2 can be positive or negative. The restriction on c 1 is obviousbecause c 1 > a implies that firms will not engage in production without government6 This is the same as in Klemperer and Meyer (1986). In contrast, Singh and Vives (1984)assume that firms first commit to setting a price or quantity. then each firm determines thelevel of its strategic variable after observing its rival's choice of strategic variables.11subsidization. Although our analysis is based on the linearity assumption aboutdemand and the linear-quadratic specification about cost, the qualitative results holdin a more general case (see the discussion in Subsection 1.3.4).Thus, given an export subsidy S (S = s i qi in the linear scheme and S = s 2 q1 inthe quadratic scheme), the domestic firm's profit is71= pigi — C(qi) + S^ (2)and the foreign firm's profit is712 = P2q2 C(q2).The domestic government's objective function is the domestic country's expectedwelfare which is the expected domestic firm's profit net subsidy:W = E(7 1 — = E1.3 AnalysisOur setting is similar to Klemperer and Meyer (1986) except the presence of govern-ment intervention. In this section, we first derive a useful result similar to Lemma 1in Klemperer and Meyer (1986). We then analyze the linear scheme (in Subsection1.3.1) and the quadratic scheme (in Subsection 1.3.2). Finally, we compare the twoschemes and thus obtain the optimal export policy for the domestic government.Before we explore the linear and quadratic schemes individually, let us first exam-ine a general export subsidy function which contains the linear and quadratic schemesas its special cases:121S(q) = siq + 2s2q (3)where S i and s 2 can be positive, negative, or zero.According to the Nash equilibrium concept, each firm maximizes its profit bychoosing a strategic variable and a value for the chosen variable, having the conjecturethat its rival's action (i.e., the type of strategic variable and its value) is held constant.Thus, given any action chosen by the foreign firm, according to the demand system(1), the domestic firm faces a general residual demand:P 1 = A^Blql E^(4)where the values of A l and B 1 depend upon the foreign firm's choice and value ofstrategic variables. ? Similarly, the foreign firm faces the following residual demand:P2 = A2 — B2q2 E•Lemma 1 is helpful in finding the equilibrium market conduct. The proof iscontained in Appendix I.Lemma 1 : Given export policy S(q) as defined in (3),1. the domestic firm will choose to set a quantity (price) if c 2 — s 2 > (<0;2. the foreign firm will choose to set a quantity (price) if c 2 > (<0; and3. the expected welfare of the domestic country isT4' —[(A 1 —^— 4^x(2BI + c2 — s2 ) — s9(A i — c 1 + si)2^0'2 c292(2B1 c2 — s9) 2^2Br7This will become clear as the analysis goes on.(5)13where x is a dummy variable defined as x = 0 for c2 > s 2 and x = 1 for c9 < s 2 .A straight forward implication which is also the most important one is that a firm'soptimal choice of strategic variables depends on the slope of its marginal cost curve(and s 2 for the domestic firm) but not on its rival's choice. The intuition behind thisresult, as given by Klemperer and Meyer (1986), is that for convex (concave) costsor concave (convex) profits, a fixed level of output is more (less) attractive than arandom level with the same mean.It is worth emphasizing here that with the nonlinear policy the domestic govern-ment can influence the domestic firm's choice of strategic variables but not the foreignfirm's. However, if the government is confined to the linear scheme, i.e., s 2 = 0 in(3), it will no longer be able to manipulate the domestic firm's choice of strategicvariables.1.3.1 Linear SchemeThe linear scheme is a special case of (3) with s 2 = 0. Although the domesticgovernment can not control any firm's choice of strategic variables via the linearscheme, it is able to anticipate the prevailing type of market conduct. We now derivethe equilibria under all possible types of market competition in turn.(i): c2 > 0.By Lemma 1, both firms set quantities. Thus, the market competition is repre-sented by a Cournot game.Suppose the domestic government adopts the linear export policy S(q1 ) =14In the Cournot game, the domestic firm chooses q 1 to maximize its expected profitEir1 , where 7 1 is defined in (2), taking q2 as constant. Given the demand system (1),we can easily obtain the firm's reaction function q i = (a — c1 + s 1 — dq2 )/(2b + c2 ).Similarly, the foreign firm's reaction function is q 2 = (q — c i — dq i )/(2b + c2 ). Thus,given s 1 , the market equilibrium quantities are, letting k 2b + c2 ,(k — d)(a c i ) + ks i=^k2 — d2and*^(k d)(a — c i ) — ds iq2 .k2 — d2(6)Moreover, by comparing (1) and (4) and remembering that the foreign firm'schoice is quantity, we have A l = a — dq2 and B1 = b. Substituting these into (5)yieldsW_ (a—dq2—c i ) 2 — si2k (7)where q2* is given in (6).The domestic government chooses s 1 to maximize the welfare W. This optimalsubsidy rate is8d2 (k — d)(a — c 1 )^01 — k(k 2 — 2d2) >where superscript c indicates Cournot competition. The positive sign of 4 impliesthat the optimal policy is export subsidization. In addition, the optimal exportsubsidy rate increases with the substitutability of the two competing products since04^d(a — c i )[(2k — 3d)(k 2 — 2d2 ) + 4d2 (k — cl)]> 0.ad k(k2 — 2d2 ) 2(ii): c2 < 0.(8)15According to Lemma 1, firms will engage in Bertrand competition if c2 < 0.From the demand system (1), we can derive the respective residual demands for thedomestic and the foreign firms given that each firm's rival's choice is price. Theseresidual demands arepi = a + -YR; — f3T + (1 — -y)E, i,j = 1,2, i j^ (9)^where a = a(b — d) I b,^(b2 — d2 )/b,=^and y = d/b.Analogously (as in the Cournot game), we can derive the market equilibriumprices, given S i :^a(h — 3) + ci^3h,=s^h, — (h — )3)-y^h2 — (h — 3) 2 -y 2^P2 — h — (h — ,3)-y^h2 — (h — /3)2y2 s1^a(h — 3) + 3 ci^3'y(h — 3)where h 2,3 c2 . Note the second order condition for profit maximization requiresh > 0. Moreover, we assume h —13 > 0 to preclude the possibility of having downwardsloping reaction curves in Bertrand competition. 8 Comparing (9) to (4), we haveA l = a + yp2 and B 1 = /3. Thus, by Lemma 1, the government's objective functionbecomesW = (a + -yp'2" — c i ) 2 — s? U2 C2^2h^2h2where p; is given in (10). Hence, the optimal export subsidy rate issb^372(a — )(1 — 7)(h — ,3){11 + (h — 3) y]=[h — (h — 3)-y 2}[h2 — (h — 3)-y 2 c2]^< 0 (12)8 0ne can derive the reaction functions and check Op/app = -y(h— /3)/h < 0 if h— < 0and h > 0.(10)16where superscript b stands for Bertrand competition and the negative sign implies anexport tax.1.3.2 Quadratic SchemeA quadratic scheme can be obtained by setting 8 1 = 0 in (2). Before we can makea comparison between the linear and the quadratic policies, we should first derivethe optimal quadratic scheme by following the same procedure as in the precedingsubsection.(i): c2 > 0.According to Lemma 1, the foreign firm will set a quantity. However, the domesticfirm's choice depends on the policy level 8 2 relative to c2 . Since the induced marketconduct varies with the policy level, we should first divide all possible policy levels intotwo regions such that in each region, we have the same type of market conduct. Wethen study the firms' behaviour in each region. Finally, we make a welfare comparisonbetween these two regions. Through the comparison, we would be able to know whichtype of market conduct is better for the domestic country and so obtain the optimalpolicy which induces the preferred type of market conduct.First, suppose the government is restricted to setting s2 such that 89 < c2 . Thispolicy might be an export tax or subsidy, depending on the sign of s 2 . By Lemma 1,the resulting market competition is Cournot.A simple calculation (which is similar to the corresponding case in Subsection1.3.1) produces the market equilibrium quantities, given 89:17(a — ci )(k —(k — s 2 )k — d2(a — ci)(k — s2 — d) .and q2 =^(k — s2)k — d2(13)Again, using (5), we obtainW— (a — — dg;) 2 (k — 2s 2 )2(k — s2) 2(1 4)where q; is given in (13). Then the government's objective is to maximize W, which isdefined above, subject to s 2 < c2 . By solving this constrained maximization problem,we obtain the sub-optimal export subsidy rate:4 = d2/k if d2 kc2C2^otherwise^ (1 5)where the superscript c stands for Cournot competition.Second, suppose the government's policy level is confined to s 2 > c2. Then themarket competition is characterized by an asymmetric game, with the domestic firmsetting a price and the foreign firm setting a quantity. We refer to this as (p,q)competition, where and hereafter the first element in a parenthesis stands for thedomestic firm's strategy and the second for the foreign firm's strategy.Similar to the derivation of Cournot-Nash and Bertrand-Nash equilibria, we obtainthe market equilibrium in the (p,q) competition, given s 2 :[oh — (a — ci)d](b c2 —s 2 )-I- bhcipl =^(k — s2 )(k — d-y) — d2q2 = (k — s 2 )(k — d-y) — d2.(a — c i )(k — s2 — d)^(1 6)Since the foreign firm sets a quantity, the domestic firm's residual demand in (4) isspecified by Al = a — 49 and B1 = b. Therefore, by Lemma 1, the domestic welfare,given s 2 , is18W = (a — —^(k — 2s 2) a2 c22(k — 82) 2 2b2where q; is given in (16). The domestic government's problem is to maximize W,which is defined above, subject to c2 < s 2 < k, where the upper bound for s 2 isrequired to satisfy the second order condition for the firms' profit optimization. Wehere skip the long and tedious computation for the sub-optimal export subsidy level,which is obtained as82q —^C12 (k (17) if 72 > bkC2/(b + C2)C2^otherwisewhere the superscript pq denotes the (p,q) competition.We now can start comparing the two sub-optimal policies in order to select theoptimal one. To make the comparison relevant and interesting, we should focus onthe interior solutions of the two sub-optimal policy levels. Substituting (15) into (14)yields the sub-optimal welfare in Cournot competition:(a — ci ) 2 (k — d) 2 .W? = ^2k(k 2 — 2d2) •Replacing s2 in (17) by sr given in (18) gives the sub-optimal welfare in the (p,q)competition:wpq = (a — ci ) 2 (k — d — d-y)2^a-9 C2 2(k — d-y)[k(k — d-y) — 2d2}^2b2 • (20)By comparing N with W/p, we obtain the following important result:Lemma 2 : Suppose c2 > 0. Then 1 ,17Qc > H'7' if d < N/kc;. Thus. the optimalquadratic policy is 4 which is defined in (15) and therefore firms engage in Cournotcompetition.(17)(18)(19)19Proof: See Appendix I.We now explain this result. The key to understand this result is to know why it isbetter to induce the domestic firm to set a quantity rather than a price. As it is wellknown in the strategic trade literature, the optimal strategic trade policy places thedomestic firm in a Stackelberg leader's position vis-b-vis the foreign firm. 9 Thus, wecould proceed with the following discussion as if the domestic firm was a Stackelbergleader, absent government intervention. In quantity competition, after the domesticfirm has chosen a quantity, say qi , the foreign firm chooses its quantity facing thefollowing residual demand: p 2 = a — dqi — bq2 . However, in (p,q) competition, theforeign firm sets its output level facing a different residual demand: p 2 = a+ -y/3 1 — /3q2if the domestic firm has chosen p l . Note the foreign firm has a flatter residual demandcurve in (p,q) competition than in quantity competition since = b — d-y < b. Thus,the adverse effect of increasing output by the foreign firm on its price is smaller in thecase of (p,q) competition and therefore it will set a higher output level in the (p,q)competition than in the quantity competition. Of course, the domestic firm is worseoff if the foreign firm has a higher quantity. Hence, the domestic firm will be betteroff by setting a quantity.Let us now briefly discuss the constraint (d < Vkc2 ) in Lemma 2. Like the linearscheme, the optimal export subsidy rate in the quadratic scheme 4 (given in (15)) isalso increasing with the goods' substitutability since04 2d °ad^•9This was first pointed out by Brander and Spencer (1985).20Therefore, when the two products are close substitutes, i.e., when d is big, the desiredsubsidy rate is very high and it may become too high (i.e., s 2 > c2 ) to prevent thedomestic firm from switching to setting a price. As a result, the restricted welfare forCournot competition will not reach its optimum and thus the advantage of setting aquantity is undermined. Because of this, the welfare in Cournot competition (IQ maybe lower than the welfare in (p,q) competition ■CM .(ii): c2 < 0.By Lemma 1, the foreign firm will set a price but the domestic firm's choicedepends on the government's export policy. As in the previous case, we will examinethe two possible choices by the domestic firm separately.If s 2 > c2 , then the domestic firm will also set a price and so the market compe-tition is characterized by a Bertrand game. Given s 2 , the market equilibrium pricesarePI = H f[a(0 + C2 — s2) OCl][h 'T(13 /3')/C1`921P; = —H { [a(i3 + c2) + ci][11 — s 2 + (13 + — orip + c2),92} (21)where H h(h — s2 ) — y 2 (3 + c2 )(3 + c2 — s2 ). Since A l = cti + -yp 2 and B1 = 3 whichare obtained by comparing (4) with the residual demand function (9), the expectedwelfare is= (a — c1 + -7'14) 2 (h — 2 s 9)^o-2 c22 (h — s2)2^2 32(22)where p2 is given in (21). The government maximizes W under the constraintc2 < s 2 < 23 + c2 , where the second inequality is to satisfy the second order con-21dition. Routine calculation gives the sub-optimal export subsidy rate in Bertrandcompetition:s2 =b^{—d')/(k b — (17)1(k — (17) if 7 2 ( 1 — 72 ) < —kc2 /b2C2^ otherwise^ (23)where the superscript b stands for Bertrand competition. Since —d'y (k — b — d-y)I(k —d-y) = —,3-y 2 (h — ,3)I[h — -y 2 (h — 13)] > 0, this policy is an export tax.We now turn to consider the case in which s 2 < c2 . From Lemma 1, we knowthat there will be a (q,p) competition, i.e., the domestic firm sets a quantity whilethe foreign firm sets a price. The market equilibrium, given s 2 , isqi = — ci )(k — d)/M19; = Rh — s2)(ab + ac2 + be i ) — d(b c2)(a — ci)]/M^ (24)where M k(h — s 2) d7(b c2 ). Furthermore, the expected welfare is(a — c l + 7/4) 2 (h — 28 2) 2(h — s2) 2where p2 is given in (24). Under the constraintW (25)82 < C2, we obtain the sub-optimalexport subsidy rate in the (q,p) competition:s2qp —^d2 (b + C9) I bk if d2 > —kbc2 /(b + c2 )C2^otherwise(26)where the superscript qp denotes the (q,p) competition.Substituting (23) into (22) gives the sub-optimal welfare in the case of Bertrandcompetition, denoted by W ic;, and substituting (26) into (25) yields the sub-optimalwelfare for (q,p) competition, denoted by W,3P. Let us leave the complicated welfarecomparison to Appendix I and report the result here.22v-r C20. 2^,kbcLemma 3 : Suppose c 2 < 0. Then 147v > Wb if d > V ---2,,^and ' -' is not tooQ ^ 202large. Thus, the optimal policy is an export tax s,q,P as defined in (26), which inducesthe domestic firm to choose quantity as its strategic variable. The resulting marketconduct is a (quantity, price) competition.Proof: See Appendix I.The rationale for inducing the domestic firm to set a quantity has been discussedbefore (right after Lemma 2). We now discuss the constraints for the result to hold.If the first constraint in Lemma 3 is not met (i.e., d < bk+b cc9 ), goods are close toindependent and so the benefit from setting a quantity is very small. As we knowfrom Klemperer and Meyer (1986), there is a benefit from setting a price when themarginal cost curve is downward sloping. When products are close to independent,the benefit from setting a price will dominate that from setting a quantity. The(-c2second restriction that 0- 2^) is not too large is also important. Let us concentrate2,32on discussing the size of a 2 . It has been stressed by Klemperer and Meyer (1986) thatuncertainty makes setting a quantity and setting a price nonequivalent. The higherthe uncertainty is, (i.e., greater a2 ), the larger the difference will be. Thus, whena2 •- is very big and c2 < 0, the domestic firm benefits more from setting a price thansetting a quantity. In any one of the above two circumstances, it might not be worthaltering the domestic firm's choice by imposing a very high tax.(iii): SummaryWe conclude the analyses in (i) and (ii), especially Lemma 2 and Lemma 3, in thefollowing proposition.23Proposition 1 Under all restrictions in Lemma 2 and Lemma 3, the optimal quadraticscheme always induces the domestic firm to choose quantity as its strategic variable.More specifically, the scheme is defined as S(q) = 2s2g2 whered2 I k > 0 if c2 > 0s2 = —d2 (b c2 )/bk < 0 if c2 < O.The equilibrium market conducts are (quantity, quantity) competition when c 2 > 0 and(quantity, price) competition when c2 < 0. The domestic country's optimal expectedwelfare under this scheme is(a — c i )2 (k — d) 2T/17 ;;; =2k(k 2 — 2d2 )(28)Proof: See Appendix I.Some remarks should be made on this proposition. First, the optimal quadraticscheme given in (27) is subject to some conditions, which limit the applications ofthe result. For example, it fails when the goods produced by two firms are closesubstitutes. Second, (28) should not be interpreted as that the optimal expectedwelfare are equal in the two cases, i.e., c 2 > 0 and c2 < 0. Although the expressionsare identical. k has different values in different cases, recalling that k 2b + c2 .Finally and more importantly, while Lemma 1 shows that the government has theability to manipulate the domestic firm's choice of strategic variables, Proposition 1emphasizes the desirability of doing this.(27)241.3.3 Linear Scheme vs. Quadratic Scheme(28) gives the maximum welfare under the quadratic scheme. In order to make awelfare comparison, we should also calculate the maximum welfare under the linearscheme.By substituting q; defined in (6) and 4, defined in (8) into (7), we obtain themaximum welfare under the linear scheme in the case of c2 > 0:— (a — c i )2 (k — d) 22k(k2 — 2d2 )which is identical to WQ*. Despite their differences, the two policies generate the samewelfare for the domestic country.When c2 < 0, it is difficult to make a direct comparison between N and W i,",where VII stands for the maximum welfare under the linear scheme in the case ofc2 < 0 and can be derived by substituting p2 defined in (10) and sb defined in (12)into (11). However, we can show (see Appendix I) thatWb = Wb^ (29)Note, when c2 < 0, WQ = NP. By Lemma 3 and Proposition 1, we immediatelyhave vvz > w,b. That is, the quadratic scheme generates higher welfare for the do-mestic country than the linear scheme does. We now summarize the above discussionin Proposition 2. Let TV;" denote the maximum welfare under the linear scheme.Proposition 2 : Under all restrictions in Lemma 2 and Lemma 3, the quadraticscheme is superior to the linear scheme. In particular, TVZ > (=)U/7 when c2 < (>)025It has been argued by Singh and Vives (1984) that from the point of view ofstrategic interaction between firms, a firm's dominant strategy is to set a quantityin order to discourage price cut from its rival. However, as shown in Klemperer andMeyer (1986), when demand is uncertain and its marginal cost is decreasing, the firmshould choose a price to avoid price fluctuation. Therefore, in the case of uncertaindemand and downward sloping marginal cost curve, there is a trade off between settinga quantity and setting a price. This trade off is resolved for the domestic country ifthe government uses the quadratic export subsidy scheme since the quadratic schemecan change the domestic firm's cost structure in such a way that the firm will face anupward sloping marginal cost curve. Consequently, the domestic firm will optimallyset a quantity, which gives the domestic country higher welfare. The linear scheme,however, cannot alter the curvature of the firm's marginal costs and so cannot inducethe firm to adopt a quantity strategy which is in the best interest of the domesticcountry. Therefore, the quadratic scheme is better than the linear scheme.When c2 > 0, the domestic firm's optimal choice of strategic variables is alreadyquantity. Hence the quadratic scheme loses its strict superiority over the linear schemesince there is no need to change the curvature of the firm's marginal costs and so thesetwo schemes are equivalent.1.3.4 RobustnessThe analysis in the preceding subsection is based on a model with many strongassumptions. To examine usefulness of these results, we discuss their robustness in26this subsection.A. General Cost StructureFirms have strict preferences on strategic variables whenever demand is uncertainand their marginal costs are not constant. As explained by Klemperer and Meyer(1986), when the slope of marginal cost curve is positive (negative), firms wouldset a quantity (price) to avoid output (price) fluctuation. Thus, in a more generalsetting (i.e., with a general cost function), the domestic firm might set a quantity orprice, depending on the curvature of the cost function at the relevant (or potentialequilibrium) output level. Note that given a cost function, theoretically, as long as thepolicy parameter 8 2 is set at a sufficiently low level, the resulting cost function (i.e.,production cost plus subsidy) would have a positive second order derivative at therelevant output level and the domestic firm would be induced to choose a quantitystrategy. Thus, under a general cost structure, the quadratic scheme still has theability to influence the domestic firm's choice of strategic variables.However, inducing the domestic firm to adopt a quantity strategy is not the solepurpose of ally export policy. It is well known in the strategic trade literature thatan optimal strategic trade policy should place the domestic firm in a Stackelbergleader's position. Therefore, if the subsidy rate 8 2 required to induce a quantitystrategy is too distant from the optimal rate for the Stackelberg leader's position, thegovernment may find it better to let the domestic firm choose a price strategy. Inthis case, adopting a quadratic scheme will not give more benefits than using a linearscheme since altering the domestic firm's strategic variable is no longer desirable.27Conceivably, so long as the marginal cost curve is not very steep, the quadraticscheme continuously dominates the linear scheme.B. General Demand StructureIn their model with general demand and cost functions, Klemperer and Meyer(1986) show that the equilibrium market conduct is jointly determined by the cur-vature of demand and the slopes of marginal costs. They also point out that if themarginal cost is sufficiently steeper, with either positive or negative slope, the impactof cost structure dominates the demand. Since a quadratic scheme changes the slopeof marginal cost, we can always get such a domination by setting the policy at a highlevel. Thus, quadratic scheme does not lose its power of affecting the domestic firm'schoice of strategic variables. The question then is whether altering the firm's strategyis still desirable, as discussed above.1.4 ConclusionIf demand uncertainty and nonconstant marginal costs are present in a model ofinternational duopoly, firms have strict preferences on the choice of strategic variables,namely quantity and price. A quadratic export subsidy scheme can influence thedomestic firm's preference and therefore shift the equilibrium market conduct to theone which is in the best interest of the domestic country. The often-studied linearexport subsidy scheme lacks such ability. As a result, the quadratic scheme dominatesthe linear scheme.Ironically, the design of the optimal quadratic scheme is much simpler than the28optimal linear scheme in terms of the expression of the optimal subsidy rates. More-over, the implementation of the quadratic scheme should not be more difficult thanthe linear scheme. In fact, the linear scheme is not the only policy form observed inreality. Two-step tax-subsidies are found in use, which could be viewed as a specialcase of the quadratic scheme.The present study can be extended to include incomplete information problems.For example, if firms have private information about their costs, then the govern-ment's optimal strategic policies are subject to incentive compatibility constraints.The study can also be extended in a different direction. Consider that the govern-ment of the product importing country is to protect its consumers by using importpolicies. Although there are a lot of studies on optimal tariffs, our approach couldbe very different. We are interested in finding an import policy which has the abilityto influence the exporters' strategic variable selections. This is important becauseconsumers in the importing country are affected differently by quantity competitionand price competition between the two exporting firms.29Chapter 2OPTIMAL STRATEGIC TRADE POLICYUNDERASYMMETRIC INFORMATION302.1 IntroductionAs Stegemann (1989, p.89) has put in a survey article, "the evidence around us —increasing international economic interdependence, rekindled protectionism, and theincrease in policy actions with real or perceived strategic intent — will continuallyforce the economics profession to address the issues that authors of models of strategictrade policy have tried to address." One of the most influential models of strategicexport policy is the well known Brander – Spencer model (1985), in which it is shownthat the home government has a unilateral interest in adopting an export subsidypolicy if the home firm competes with a foreign firm in quantities. The central motivefor these types of strategic policies is to "shift profits" from foreign firms to the homecountry. Subsequently, Eaton and Grossman (1986) demonstrated that the optimalpolicy is an export tax when the home firm competes with a foreign firm in prices.One important implication of these two studies is that the type of optimal strategicexport policy is sensitive to many industrial-specific factors such as market conduct.It then becomes clear that lacking the relevant information, the government couldvery likely adopt a wrong type of policy. Moreover, it is reasonable to be expect thatpolicy makers have less information than firms concerning production and markets.Information is also crucial in determining the appropriate policy. Wong (1990) hasshown that if policymakers do not have complete information about the home firm'scosts, some export policies could be welfare worsening. In particular, Wong (1990)demonstrated that in the Brander – Spencer model with asymmetric information(about cost), the optimal export subsidy scheme derived from the full information31case is no longer incentive compatible in general and may even be detrimental to thehome country. The reason is simple. The home firm has an incentive to misreportits cost in order to maximize its subsidy-cum-profit. The production decision is thusdistorted (compared to the equilibrium outcome without government intervention)and the distortion could be sufficiently large such that national welfare is reducedto a level lower than that under free trade. However, Wong (1990) did not go anyfurther to explore incentive compatible policies.The present study develops strategic trade policies taking into account the con-straints arising from incentive compatibility. We assume that the home firm's marginalcost is private information. Being uninformed, the home government faces two policyoptions. It can offer a menu of policies or simply a uniform policy. In the case of apolicy menu, the home firm makes a selection from the menu, after which anotheruninformed party, the foreign firm, observes the policy selection. The two firms thencompete in a third market for their exports.The distinguishing feature of this model is that it is a mixture of screening andsignalling problems. We can divide the game into two stages: the policy stage andthe market stage. The former is a screening sub-model in which the uninformedparty (government) offers a menu to the informed party (home firm). The latter is asignalling sub-model in which the informed party (home firm) takes an action (policyselection) before it meets another uninformed party (foreign firm). 1° Moreover, thetwo tasks, screening and signalling, are accomplished in one action — when the home10 See Kreps (1990, p.651) for the conceptual difference between screening and signallingmodels.32firm makes a selection from the given menu. The home government faces a dilemmabecause of this. On the one hand, it wants to discern the home firm's type in orderto provide proper export subsides or taxes for the purpose of profit shifting. On theother hand, it wishes to have the high cost firm sending out a low cost signal underCournot competition in order to reduce the foreign firm's production, or the low costfirm signalling a high cost under Bertrand competition to raise the foreign firm'sprice. In this study we find that under Cournot competition it is optimal for thehome government to offer a menu of policies which leads to a separating equilibrium,but under Bertrand competition it is optimal to adopt a uniform policy which resultsin a pooling equilibrium.As is well known in the strategic trade literature, the role played by the governmentis to make the home firm's output expansion credible. In the model with private costinformation, we find that there is a second role for which the government can play.By offering a separation inducing menu, the government enables the home firm tocredibly reveal its true type to its rival.Recently Brainard and Martimort (1992) and Maggi (1992) also examine the im-pacts of asymmetric information in the Brander- Spencer mode1. 11 However, the focusof their papers is somewhat different. Brainard and Martimort (1992) incorporate acost of raising government funds and Maggi (1992) considers non- linear policies.Neither paper is concerned with the signalling aspect of the design of governmentpolicy.11 These papers came to my attention after the initial submission of this paper to theJournal of International Economics.33The remainder of this chapter is organized as follows. In the next section, wepresent a model with screening and signalling characteristics when firms competein a Cournot fashion. A complete analysis of the model is contained in Section2.3. Section 2.4 discusses Bertrand competition and gives results contrary to thoseobtained under Cournot competition. Section 2.5 concludes this chapter.2.2 The ModelConsider the following situation. Two firms, 1 and 2, who respectively locate incountries 1 and 2, produce homogenous goods for a third market. Both firms areassumed to produce strictly positive outputs and, unless stated otherwise, competein a Cournot fashion. The inverse demand function takes the form: p = a — b(qi + q2 ),where a > 0, b > 0, p is the price of the product, and qi the output of firm i, i 1, 2.Only the government in country 1 is involved in policy intervention.'The information structure is as follows. Firm l's marginal cost, c, is constant andprivate but it is common knowledge that firm 1 is of either high cost, cH , or low cost,c,, with Prob(c=c,)=-Ft. 13 Firm 2's marginal cost is assumed known to all partiesand equal to zero for simplicity. The reason for this assumption is that in the presentsetting, even if there were some uncertainties associated with firm 2's marginal cost,there is no way for firm 2 to signal it. Hence both government 1 and firm 1 wouldbase their decisions on the expected value. Consequently, this will only complicate12This supposition is common in the literature of trade policies and is made for simplicity.It can be justified, for instance, if government 2 unilaterally adopts a free trade policy.13 Allowing government 1 and firm 2 to have different priors will not change our resultsas long as these priors are common knowledge.34the model without changing the qualitative aspect of the results. In contrast, firm 1is able to signal its cost through its policy selection.In the environment described above, we consider the following two-stage one-shotgame. At the beginning of the first stage, called the policy stage, government 1 designs(and commits to) its policy. 14 The government has two options: it can use a uniformpolicy or a menu of policies. 15 Under the uniform policy regime, the governmentsets a specific (per unit) export subsidy rate for firm 1 regardless of its type. Thealternative possibility, a menu of policies, gives firm 1 a choice as to the policies thatwill be applied. After the government has announced its menu of policies, firm 1makes its policy choice. When information revealing is desirable, a policy menu playsa role in inducing this revelation. However, without such policy menus, a simpleannouncement by firm 1 about its cost is not credible.The menu approach allows the policy to be conditional on the firm's type. As istypical in asymmetric information models, at least two policy instruments are requiredfor the underlying type of an agent to be revealed through self selection. In our setting,each choice on the menu consists of two policies: a specific export subsidy rate anda level of lump sum tax. 16 If the subsidy rate were the only instrument available to14The government's ability to commit is commonly assumed in the literature. If thisis not assumed, precommitment effects should be carefully investigated as in Caillaud etal.(1990).15 Policy menus have been explored extensively in the regulation literature. The studiesof incentive compatible policies can also be found in the literature of trade policy. See, forexample, Feenstra (1987) and Prusa (1990).16In a real world context, one could perhaps view the lump sum tax as a tax on profit.However, it is hard to find a case in which an industry- specific profit tax is tied to an exportsubsidy. As suggested by a referee, another possibility is that the fixed cost represents acost of lobbying. To be viewed as a low cost firm, the firm must incur a lobbying cost thatexceeds some threshold set by the government.35the government, firm 1 would have chosen the highest subsidy rate independently ofits type and no information would be revealed.We confine policy options to linear subsidies, i.e., the subsidy rate does not varywith other informative variables such as output and price. This has the advantageof simplicity. Some possible implications of non-linear policies are discussed in theconcluding remarks.In the second stage, referred to as market stage, two firms compete in quantitieson the basis of their respective information sets. Between the two stages, there is atransition period, in which firm 2 observes the policy choices made in the first stageand then updates its belief concerning firm l's true marginal cost. This belief iscorrectly inferred by firm 1 and government I. In particular, if government 1 designsa menu of policies inducing firm 1 to reveal its true type, then firm 2 observes this andthe outputs of both firms are determined on the basis of full information. Otherwiseboth firm 2 and government 1 estimate the marginal cost of firm 1 at its expectedvalue.2.3 AnalysisWe analyze the model by solving the game backwards. When we look at the secondstage game, we know that its nature depends on the results of the first stage which areinfluenced by the types of policies used by government I. Under all policies, however,there are only two different first stage results as far as the second stage information isconcerned: the policy selection is either pooling or separating. The analysis proceeds36as follows. We first determine the optimal policy among the class of policies that leadto separating equilibria (in Subsections 2.3.1 and 2.3.2). We then consider poolingequilibria (in Subsection 2.3.3). Finally, we derive the optimal policy (in Subsection2.3.4) by comparing the maximum social welfare achieved under these two types ofpolicies. In considering pooling equilibria, we assume, without loss of generality, thatthe government sets a uniform policy. A uniform policy causes pooling (involuntarily)but a policy menu approach could also lead to pooling if both types of firms choosethe same option.For the purpose of comparison, we briefly illustrate the optimal policy in the caseof full information. Obviously, neither a policy menu nor a lump sum tax is necessary.We denote variables in the full information case with a superscript f . Then, givenany export subsidy rate, s, the second stage game yieldsqi— a — 2c + 2s and q2 = a + c — s3b 3b •Government 1 chooses sf to maximize its objective function, denoted Wf (s), which issimply the profit the home firm earns from exports less any subsidy payments. Withlinear demand, this can be expressed as:Wf (s) = [a — b(gf(s) + qr.(s)) — dgf(s).Thus, we obtainsf = a — 2c4(30)372.3.1 Separation Inducing MenusWe now consider separating equilibria. Note that only policy menus could lead toseparating equilibria. Let t = (t,; tH ) denote a policy menu, where t, is a policyintended for the low cost firm and tH is a policy intended for the high cost firm. Eachpolicy t i = (s i , Ti ) for i L, H consists of two elements, a specific export subsidy rates i and a lump sum tax Ti.Letting 7 i (ti) denote firm 1's profit when it is of type i and chooses policy ti fori,j = L, H. A menu t is called a separation inducing menu if for i j(1) 7r 2 (t i )^7 2 (ti ),^and^(ii) 7f 2 (t i ) _> 0,^= L, H.Condition (i) is the separation constraint while condition (ii) is the participationconstraint. As mentioned above, if a separation inducing menu is used by government1, firm 2 will be able to discern firm l's type and it then follows that all parties havecomplete information at the second stage Cournot game.Given a separation inducing menu t, the market stage game can be described bythe following maximization problems, i L, H,7r i (ti)^maxfia — b(qs i + q2i) — + si]q8i — Ti}q.imax[a — b(q,i + q2i)]q2iq2iwhere qsi is firm l's output and q2i firm 2's output under the policy menu regime andwhen firm 1 is type i. If t, ( tH ) is adopted, then i = L (H) in both (31) and (32),which constitute a Cournot game between firm 2 and a low (high) cost firm 1 withfirm 2 knowing firm l's true type. Thus, the respective reaction functions are(31)(32)38qs za —^si — bg2i i = L,H^ (33)2b a — bqs ,z = L,H.q2i = 2bGiven s, the market stage equilibrium outputs areq.92a — 2ci + 2s i^a + ci — s iand q2i =  ^= L,H.^(34)3b 3bAs mentioned in the introduction, the model incorporates both screening andsignalling. Use of a menu of policies allows the government to screen for the type offirm so as to better design its export policy, but at the same time, firm l's policyselection signals the same information to firm 2. To understand the implications ofthis, it is helpful to first consider a pure screening version of the model in which firm2 knows firm l's marginal cost. In this case, firm 2's output level will be affectedby the policy imposed by the government, but the means by which the policy ischosen conveys no information and consequently has no effect on firm 2's output. Inparticular, if firm 1 chooses a policy that is not consistent with its type i, thenfirm 2 will produce q2, = (a + c, — sj )/3b, the Cournot output based on firm l's truemarginal cost c, and subsidy sj . Therefore, we haveT 2 (t.)^9b (a — 2ci + 2sj ) 2 — rj , i,j = L,H.^ (35)If the firm selects policy t i corresponding to its type i. its profit 7r 2 (t i ) is given bysetting j^i in (35).If menu t is separation inducing, condition (i) must be satisfied. Comparing 7r i (t i )with -K i (ti ) (j i), we obtain Lemma 4.39Lemma 4 : In the pure screening model, if t is a separation inducing menu, thenSL > SH and r,, > TH .Proof: See Appendix II.Next, we provide some intuitions for Lemma 4. First and foremost, the twoinstruments in a separation inducing menu have to go hand in hand, with a highsubsidy associated with a high tax and vice versa. Otherwise both types would pickthe policy with higher subsidy and lower tax. Secondly, a separation inducing menumust have s L > s ig . To see this, suppose t is separation inducing with 8,, < sH (soTr, < TO. Given that the high cost firm chooses tH rather than tL , the firm's benefitfrom the high subsidy rate s i, must be sufficient (relative to s,) to more than offsetthe loss from the higher lump sum tax TH (relative to TL ). The problem is that in thiscase the low cost firm will also prefer t H . Since the low cost firm produces more thanthe high cost firm, it benefits more than the high cost firm from any increase in thespecific export subsidy rate. Thus by choosing tH , the low cost firm enjoys a greaterincrease in the total subsidy payment than would the high cost firm yet suffers thesame penalty as would the high cost firm from the higher lump sum tax associatedwith tH . This contradiction implies that t cannot be separation inducing. It followsthat in a pure screening model, s L > 8,, is a necessary condition for separation oftypes.We now return to our original model incorporating both signalling and screening.Since firm 2 does not know firm l's marginal cost, its output level will depend onits updated belief which is influenced by firm l's policy selection. Suppose that40the government offers a separation inducing menu, firm 2 will believe firm l's typeas signalled by the adopted policy. More precisely, if firm 1 chooses ti , then firm 2believes that firm 1 is of type j and correspondingly sets q2j = (a +ci — s i )/3b. Takingthis into account, firm 1 with type i will optimally set qsi (2a — 3c i — + 4si )/6b.Consequently,1^ 1(t j)^36b (2a — 3c i — + 4si )2 — ri and 'x i (t i )^— ( a — 2c i + 2s i ) 2 — . (36)9bLemma 5 gives a necessary condition for the separation of types (the proof issimilar to that of Lemma 4).Lemma 5 : In the model with screening and signalling, if t is a separation inducingmenu, then s, — 8, > —(c, — c,)14.Lemma 5 differs from Lemma 4 in several aspects. First, in Lemma 5, there isno monotonicity property imposed on the two policy instruments. Monotonicity is acommon requirement in the optimal contract and mechanism design literature becausesuch models contain only a screening problem. Thus, the inclusion of signallingweakens the constraint required for the separation of types. Secondly and morespecifically, when signalling is taken into account, the separation constraint does notrule out the possibility that s, < s H . These results follow because there are now twobasic forces influencing firm 1's decision on policy selection. On the one hand, as inthe case of the pure screening model, the low cost firm benefits more than the highcost firm from an increase in the export subsidy rate because the former producesmore than the latter. On the other hand, the low cost firm loses more than the41high cost firm when firm 2's belief about firm l's type changes from low to high. Tosee this, note that if firm 2 believes that firm 1 is a high cost firm, it will increaseits output. Consequently, the price drops. The decrease in price hurts the low costfirm more than the high cost firm since the former has a greater output than thelatter. Now suppose s L < s, (letting TL, = TH for ease of analysis). We argue that itis quite possible that such a menu is separation inducing for particular levels of 8„and 8 L . The high cost firm might prefer tH to tL because the benefit from a highersubsidy rate at least covers the loss from being identified. Moreover, the low cost firmmight choose tL . Although the low cost firm's benefit from the higher subsidy rateassociated with tH is greater than the high cost firm's, it might not be sufficientlygreat to offset the larger loss that arises when a low cost firm is identified as a highcost firm by firm 2.2.3.2 Optimal Separation Inducing MenuIn designing its optimal profit shifting policy in stage 1, the objective of the govern-ment is to maximise the expected social welfare in country 1. This is simply the profitof each type of firm 1 less any net subsidy weighted by the probability of that type.When menus induce separation, the expected social welfare is given byW(t) it(R-L (tL) — sLgsL + TL) + (1 — p)(7 11 (tH) — sHqsH + TH)where outputs qsi, and q„ are given by (34) and 7 -L (t L ) and R-H(t H ) are given by (36).To derive the optimal menu, we first maximize W(t) by ignoring the separationconstraints. The first order condition yields the optimal subsidy rates sl and s*H :42s* = —1(a — ^and s* = —1(a — 2cH ).L^4 4from which and (34), we obtain the equilibrium outputs of each type of firm 1 andfirm 2:qsz =a —2ci^a + 2c i2b^ and q2i =  4b^i = L, H. (38)As expected, the optimal subsidy rates (37) are just the full information subsidyrates corresponding to the firm's particular type. Since the optimal menu imposesno restrictions on the lump sum tax instrument, we are free to use lump sum taxesto ensure separation. For convenience , we first normalize the lump sum tax bysetting 7-;., = 0. When s*, and s*„ are set at their optimal levels as in (37), wedemonstrate in Appendix II that the menu t* induces separation (i.e., 7r- L (q) > 7rL(t*, )and 7 11 (tH* > 7 11 (q)) if1= 2b (c, — cL )(a — c, — cL ). (39)These results are summarized in Proposition 3.Proposition 3 : t* as defined in (37) and (39) is the optimal separation inducingmenu.The intuition behind Proposition 3 is clear. It is well known in the literature ofstrategic trade policy that when demand is linear, the optimal profit shifting policyrequires that a higher export subsidy rate s i,* (relative to s*H ) be granted to the lowcost firm.' A lump sum tax is levied on the low cost firm in order to prevent the17This can be seen from the formula for the optimal subsidy in Brander and Spencer(1985).(37)43high cost firm from pooling so as to obtain the higher subsidy rate. The tax Ts; ischosen so that the low cost firm still selects t*L but the high cost firm chooses t*H .2.3.3 Optimal Uniform PolicyWe now consider uniform policies. Whenever a uniform policy is adopted by thegovernment, firm 2 receives no information from the policy stage, so it remains unin-formed. It follows that the market stage game is a quantity competition with asym-metric information (firm 2 has incomplete information about firm l's cost). Lettings denote the common subsidy rates, qpi denote firm l's output under the uniformpolicy regime when it is type i (i = L, H), and q-2 denote firm 2's output. Then themarket stage game is characterized by the following maximization problems:i i (8)^max[a — b(qpi^-42) — ci + s]qpi,qpimax[a — b(qi. + q2 )]q2q2i L, Hwhere^+ (1 — ,u)q". Firm l's reaction function is the same as (33) exceptq2i^q2 , but firm 2 now reacts to firm l's expected output q l , giving rise to thereaction function,a — 141q2 = 2b •^ (40)Hence, given s, the market stage equilibrium outputs are_ ^_qpi = a(20 — 3ci — --e+ 4s) and q2 5 (a + c —^i = L, H,^(41)where c stands for the expected value of firm l's marginal cost. i.e., -e = pc,,+ (1— ,u)c,Thus, the resulting firm 1's profit given s is (using (41))44a — 2F,^=4a — c i — c^a +^ and 4-2 =  ^ (42)2b 4bS* =36—lb(2a — 3e i + 4s — -e) 2 , i = L, H.Under the uniform policy regime, the expected social welfare in country 1 is theweighted sum of each type's profit net of subsidy, which is given byW(s) µ0-L(8) — sqpd + ( 1 —^— sqpH).From the first order condition for the maximization of W(s), we can easily derive theoptimal subsidy rate sp* and the equilibrium outputs:As expected, asymmetric information creates some distortions if the optimal uni-form policy sp* is adopted. By comparing sp* in (42) with sf in (30), we realize thats* can never shift profit from firm 2 optimally since there exists no type of firm 1with marginal cost equal to F. It oversubsidizes (undersubsidizes) firm 1 and causesoverproduction (underproduction) when firm 1 is a high (low) cost firm.2.3.4 Optimal Policy and EquilibriumIn this subsection, we derive the overall optimal policy by comparing the social welfareunder the optimal separation inducing menu with the welfare under the optimaluniform policy.We first illustrate the equilibria under the two different optimal policies usingFigure 1. Note that the level of per unit subsidy rate affects the position of firm 1'sreaction curve. Since s*, > sp*, the low cost firm's reaction curve in the separatingcase R„ is to the right of RPL , its reaction curve in the pooling case. Similarly, the45high cost firm's reaction curve in the separating case R„ is to the left of R,, itsreaction curve in the pooling case because s*„ < sp. However, firm 2's reaction curvein the separating case, as shown by R2, is unaffected by the subsidy level in country1. Thus, in Figure 1, SSL and SSH are the equilibria in the separating case.In the pooling case, firm 2's output q 2 is a function of firm l's expected outputqi (see (40)). If firm 1 is actually a low cost firm, then the equilibrium is at S"where the horizontal line at q2 intersects firm l's reaction function R,. Similarly,the equilibrium is at S" if firm 1 is a high cost firm. The expected value of thesetwo equilibria is shown by SP, the intersection of q-2 and firm l's expected reactioncurve P i (which is derived as if firm 1 had marginal cost -e)Figure 1 is hereIt is well-known in the strategic trade literature that the optimal subsidies placethe home firm (firm 1) in a Stackelberg leader position vis-a-vis the foreign firm(firm 2). Thus, SSL and SSH are the respective Stackelberg quantity equilibria inthe separating case when firm 1 is respectively the low cost firm and the high costfirm. In the pooling case, SP could be viewed as a modified Stackelberg equilibriumin which a Stackelberg leader reveals only its average output qi (and firm 2 respondsby committing to q2 ) but the leader's actual output subsequently varies with its type.Due to the linear reaction function (R 2 ), it is not difficult to see that firm l's averageoutputs are the same under both cases and that firm 2's output in the pooling case isequal to its average output in the separating case. Our previous results in Subsections2.3.2 and 2.3.3 also prove this. By (38) and (42).46a — 2 -ePqpr, + (1 — µ)q„ = =^+ ( 1 — ii )qs„2b (43)a — 2O— 4b = Pq2L + ( 1 — [I)q2H.Moreover, the total outputs in the market are unchanged in the two cases since using(38) and (42)3b — 2ci4bgsi + q2i = ^ = qpi q2 i = L,H.Thus, the optimal separation inducing menu and the optimal uniform policy give riseto the same equilibrium price for the product, i.e.,PSL = PPL^and^PSH = PPH•^ (44)Although firms 1 and 2's expected outputs and the equilibrium price do not vary inthe separating and pooling cases, Lemma 6 below shows that the optimal separationinducing menu dominates the optimal uniform policy. If we denote the expectedsocial welfare under these two optimal policies as W* and W*, respectively, whereW * =^cL)gsL + (1 — 1-1 )(PsH — ca)gsu^ (45)T/i7* = p(p, — cL)gpL, + ( 1 — 1,t)(Ppx — cH)qpH,^ (46)then we have Lemma 6.Lemma 6 : The optimal separation inducing menu gives country 1 higher welfarethan the optimal uniform policy: W* >Proof: Using (43)-(44) in (45)-(46), the welfare difference can be expressed by47W* — W* µ(p„ — cL)(gsi, — gpL) + (1 — 1-1 )(PsH — cH)(qsH qPH)^(47)= ti (gsL — qpL )Rpsi, — CL) — (psi' — cif)]• (48)Because the low cost firm produces more in the separating case than in the poolingcase, i.e., qsL, > qPL , and the low cost firm's price-cost margin is higher than the highcost firm's sincea — 2cL,^a — 2c,Psc^= 4 4^  PSH CH,(49)(48) shows W* —^> 0. Q.E.D.Note that the first term in (47) is positive (since qsL > gp L ) but the second term isnegative (since )0SH < PPH)• This implies that use of the optimal separation inducingmenu instead of the optimal uniform policy results in a welfare gain if firm 1 turnsout to be a low cost firm but a welfare loss if it is in fact a high cost firm. Thus, thereis an ex ante trade off using the optimal separation inducing menu.To understand how the trade off can be resolved, let us make use of Figure 1.Since points S" and SPH entail the same total output and the same price, all pointson the segment (which is not depicted in the figure) between these two points alsoentail the same total output and the same price. Similarly, all points on the segmentbetween points S' and SPL (including these two points) entail the same total outputand the same price. It follows that firm 1 has equal price-cost margin (psH — cH )at all points on the segment between S" and SPH and equal price- cost margin(PsL — C L ) at all points on the segment between S' and SPL. Note that at both thepooling equilibrium (shown by (SP', SPL)) and the separating equilibrium (shown by48ssL )) firm 1 has the same expected output (di ) but a higher variance in itsoutput at the separating equilibrium. Thus, the issue is whether country l's welfareis increasing or decreasing in the variance of firm l's output. To answer this, let usconsider a continuum of "outcomes" between the pooling and separating equilibria.An "outcome" here is represented by a pair of points with one on the segment betweenSPL and Ss', the other on the segment between SPH and S", and the expectationat SP. Then an increase in the variance in firm l's output is achieved by an increasein the low cost firm's output (a point on the segment between SPL and SsL) and adecrease in the high cost firm's output (a point on the segment between SPH andS") keeping expected output unchanged at ql . Since the low cost firm's price-costmargin is higher than the high cost firm's (see (49)), welfare in country 1 must riseas the variance in firm l's output increases. Hence, the optimal separation inducingmenu is preferred to the optimal uniform policy.With Lemma 6 we are now ready to analyze the entire game described in Section2.2. To do this, we must consider all policy options, both menu and uniform, at thesame time.Since government 1 is a Stackelberg leader vis-a-vis the firms, it will choose apolicy which results in the highest social welfare in country 1. This, together withLemma 6, rules out the uniform policies. Moreover Lemma 6 and Proposition 3indicate that t" is the optimal one among all policies. Once the government adoptst", we have all results obtained in Subsection 2.3.2. We now conclude the aboveanalysis in Proposition 4.49Proposition 4 : In the two-stage sequential game with asymmetric information andCournot competition, there exists a separating equilibrium with t* as the optimal sep-aration inducing menu. The full information equilibrium allocation is achieved. Pool-ing is never an equilibrium.The result that the full information allocation is attained is not surprising. Onthe one hand, the export subsidy rate which firm 1 receives in the optimal separationinducing menu is identical to that in the full information case corresponding to thefirm's type. 18 On the other hand, the additional policy instrument used in our modelhas no impact on the export market, i.e., the introduction of a lump sum tax per sedoes not cause the firms' outputs and price to differ from those in the full informationmode1. 19Lemma 6 and Proposition 4 seem to suggest that it is always preferable for thegovernment to set a policy so as to induce firm 1 to reveal its information. Thisresult, however, is sensitive to the nature of market competition. We will see this inthe next section.18Because of this, the government's commitment is not a problem in the Cournot model.Although the government knows the firm's type after the firm has chosen a policy from thisoptimal menu, there is no need to revise the level of that policy because it is already equalto the optimal level in the full information case.19This result of course depends upon a common assumption that monetary transfer eitherfrom the government to firm 1 (i.e., subsidy) or from firm 1 to the government (i.e., tax)is costless. The government is never reluctant to introduce an additional instrument whenit is necessary, for example, a lump sum tax in this model, as it can be implemented at noexpense. For the possible effects of relaxing this assumption, see Caillaud et al.(1988) andBrainard and Martimort (1992).502.4 Bertrand CompetitionThe government always wants to learn firm l's true cost in order to design a precisepolicy. However, if firm 1 tries to inform the government or if the government usessome rules to induce firm 1 to reveal its cost, in our setting, the information is alsoreleased to firm l's rival (firm 2), which may not be desirable. Earlier results indicatethat information revelation is desirable in a Cournot game. The question is whetherrevelation is always optimal. To answer this, we now consider another model whichdiffers from the earlier one in two respects: the firms produce imperfect substitutesand compete in prices.Suppose the demand system is given byqi = a —^+ ypi, where i , j = 1, 2, i j, o > 0, and ,3 > -y > O.^(50)We adopt the same notations defined before but interpret them in the context ofa Bertrand game. For brevity, we only present results related to Lemma 6 andProposition 4. In doing so, we first derive the optimal uniform policy. We thencharacterize the optimal separation inducing menu. Finally, we compare the socialwelfare under these two optimal policies. Results are summarized in Proposition 6.Given s under the uniform policy regime, the market stage game is characterizedby the following two maximization problems:max(ppi — e• + s)(a^+ 7P2),^= L, H, and max/52(a — 0/32 + 7151)Ppi^ P2where Ppi is firm l's price when it is type i in the pooling case, pi [tp„ + (1 — u)pp His the expected price charged by firm 1. and P-2 is firm 2's price in the pooling case.51By solving these problems simultaneously, we obtain the market stage equilibriumprices (i^L, H):1P2 = ^ ia( 2 ,3 + -Y) +137("e s)]4,32 _ -y 21PIA 7-- 2(40 2 — ,y2) [20(20 +^+ 72 (e — c2 ) + 4,32 ( — s)} .Maximizing the expected social welfare, which isW(s) /t(Ppi, — CL)(cv — 3Ppr, + 7P2) + ( 1 — P)(PpH CH)(a — OPpli^ P2)gives the optimal uniform policy s;:*Y2 sP*^432(2/32 — 72) [a(23 -y) — (23 2 —Therefore, the equilibrium prices are11 [^a(2/3 + 7) ]^— L H and^/32 =^[ce-Py-f- 2a3G3 +](51)Ppi = 2 -cz + 2/32 — 40 202 -y2and analogously to (46), country l's expected welfare at the pooling equilibrium isT/i/* = it(pp L — cL)qpi, + ( 1 +11)(PpH — cH)qpir,^ (52)whereQPL = a — 35pL + 2152 and qp„ = — Op, + -y132 .To avoid repetition, we omit the derivation of the optimal separation inducingmenu and the resulting market equilibrium. The optimal separation inducing menuhas the per unit subsidy rates'2°The levels of lump sum tax are chosen to make the policy satisfying the separationconstraints.524/32(2/32 -^ 72) [a(2,3 + -y) — (2/3 2 — 7 2 )ci J^i = L, Hand the market equilibrium prices are1^a(213 + -y),Psi =^+ 202 — ,y2 11and p2i = 4b [a +^+ 20(13 + 7) ] i = H.(53)2/3 2 —Moreover, analogously to (45), the separating equilibrium welfare of country 1 isW * = 1-1 (Psi, — cL)gsL + ( 1 1-1 )(PsH — cH)qsx^ (54)wheregsL, = — OPsi, + 7P2L and gsH = a — IPsx + 7P2H•Figure 2 is hereWe illustrate the above equilibria in Figure 2. Note that the position of firm l'sreaction curve (shown as R„, R-SH 7 RPL, and R, in Figure 2) depends on its type andthe tax rate. When changing from the optimal uniform policy to the menu, the lowcost firm's reaction curve is shifted downward (because s*,, < s;) , i.e., the firm faces ahigher tax); and the high cost's reaction curve is shifted upward (since s*H > sp*, i.e.,the firm faces a lower tax). Also in Figure 2, S' and S" represent the Stackelbergprice equilibria in the separating case. 5' would be the Stackelberg price equilibriumif firm had marginal cost e sPL and SPH are the actual equilibria in the pooling case.Similar to the Cournot case. linearity of the reaction function implies that theprice /59 charged by firm 2 in the pooling case is equal to the average price in theseparating case: i.e., by (51) and (53)531_ 2c0(/3 + 7),^_+ (1 -^+ 7c + 2,32 ,2 = P2. (55)Also by (51) and (53), we havePSL = PPL and JOSH PPH^ (56)meaning that each type of firm 1 sets the same price under these two cases, butP2L < P2 and P2H > P2.^ (57)Due to the strategic complementarity of Bertrand competition, firm 2 sets a lowerprice if it knows that its rival is a low cost firm than if it does not know. Similarly,firm 2 sets a higher price when it knows that it is competing with a high cost firm.We now make welfare comparison between the pooling and separating equilibria.From (52) and (54), the welfare difference can be expressed in the same form as (47)for the Cournot case:W* 17(7* = lt(PSL^CL)(gSL gPL) + ( 1 - I1 )(PSH CH)(gSH qPII)^(58)Note from the demand system (50) and (57)gsL — QPL = 'T(P2L — P2) < 0 and gsH — qPH "Y(P2F1 — P2) > O.^(59)Thus, the first term of (58) is negative, implying a loss from using the separationinducing menu when firm 1 is a low cost firm. However, the second term is positive,which captures the gain from adopting the menu when firm 1 is a high cost firm.Moreover, the gain and loss are proportional to firm l's price-cost margin. It followsthat to show that welfare is lower at the separating equilibrium than the pooling54equilibrium, we need only to show that firm 1 earns a higher price-cost margin whenit is low cost than when it is high cost. To do this, we use (55) and (59) to rewritethe welfare difference (58) asW* — fi%* = —1 it(gsL ch-L)RPsi, — CL) — (Psi/ — cH)l•^ (60)By (53),1 r a(2/3^-y)PSL CL = 2 [ 2)2 — _y 22^f5'CL] > 1 [a2(223— ')/2)CH] psH — CH .^(61)Using (59) and (61) in (60), we immediately obtain W* < W*. This establishesProposition 5.Proposition 5 : In the two-stage sequential game with asymmetric information andBertrand competition, W* > W*, i.e., the optimal uniform policy achieves highersocial welfare than a separation inducing menu. The equilibrium is pooling.The welfare difference (58) for the Bertrand case is identical in form to (47) forthe Cournot case. Moreover, since firm 1 has the same expected output (4 -0 at theseparating and pooling equilibriums, 21 it is again true that the difference between theseparating and pooling equilibriums could be explained on the basis of the differencein the variance of output. However, in the Bertrand case, it is more convenient touse Figure 2 to express the explanation in terms of the difference in the variance offirm 2's price. As can be seen from (59), when firm 2's price is high, then firm l'soutput is high (and vice versa) and an increase in the variance of firm 2's price causesa proportional increase in the variance of firm l's output.21 Following (55) and (56), one can easily check this by calculating the two expectedoutputs.55In Figure 2 and from (56) , firm 1 has the same price and price-cost margin at allpoints on the segment between SPL and SSL and likewise on the segment between SPHand SSH. However, firm 2's price varies as an "outcome" moves from the separatingequilibrium (shown by (S",S")) to the pooling equilibrium (shown by (SPL, SPH)).The variance in firm 2's price is higher at the separating equilibrium than at thepooling equilibrium. In fact, a reduction in firm 2's price variance is achieved by arise in firm 2's price when firm 1 is a low cost firm (a point moving upwards from SSLtowards SPL) and a drop in firm 2's price when firm 1 is a high cost firm (a pointmoving downwards from SSH towards SPH) keeping the expected price unchanged atp2 . Thus, to select between these two equilibria, we must know whether country l'swelfare is increasing or decreasing in firm 2's price variance.Since the welfare difference (58) for the Bertrand case is identical in form to (47)for the Cournot case and that the low cost firm has a higher price-cost margin thanthe high cost firm in both cases (see (49) and (61)), as discussed before (for Lemma6), we prefer a higher output from the low cost firm. Note that a higher outputfor the low cost firm is achieved by a lower variance in firm 2's price (and thus alow variance in firm l's output). Consequently. the optimal uniform policy whichresults in a smaller variance in firm 2's price is preferred to the menu in Bertrandcompetition.The sharp difference between Lemma 6 and Proposition 5 arises because the pool-ing and separating equilibria have significantly different consequences for outputs inthe Bertrand case than in the Cournot case. It is known from (59) that, in the56Bertrand case, the low cost firm produces less while the high cost firm producesmore in the separating equilibrium than in the pooling equilibrium. However, in theCournot case, the low cost firm produces more but the high cost firm produces lessin the separating equilibrium than in the pooling equilibrium, i.e., the expressions in(59) have opposite signs in the Cournot case. 22When government 1 adopts an optimal uniform policy, the equilibrium necessarilydiffers from the full information equilibrium. Interestingly enough, Proposition 5indicates that country 1 achieves higher social welfare in a world with incompleteinformation than in a world with full information. This is because firm l's costinformation has positive net effects on the social welfare if it is being kept private.One important implication of this finding is that in a " rivalrous agency " model, 23in some cases it is better not to induce the agent to reveal its information becausethe revelation has a signalling effect.2.5 ConclusionWhen information asymmetry problems are present in the Brander — Spencer model,the home government can design a menu of policies, by introducing an additionalpolicy instrument, to induce information revelation and achieve the full informationsocial welfare.22It can be easily verified that this is also true if we had differentiated products insteadof homogenous products in the Cournot case.23Our model differs from Ferstman and Judd's (1987) owner-manager model. In a "rival-rous agency" environment we consider a hidden information problem while they deal withissues of hidden action.57However, if the home firm's cost is private information, the model is characterizedby a mix of screening and signalling. In models of this kind, it is not always optimalfor the uninformed government to design a mechanism which induces the informedhome firm to reveal its information because this firm's rival (the foreign firm) alsobecomes informed. The information nature of the optimal policy is very sensitive tothe type of competition between home and foreign firms. Under Cournot competition,the government offers a menu of policies which induces the home firm to reveal itstype. Under Bertrand competition, however, the government chooses a uniform policywhich helps the home firm to conceal its information.As suggested by a referee, it would be of interest to investigate non-linear policiesthat do not reveal the home firm's cost information to the foreign firm and comparethem with linear polices. 24 Under the non-linear policy regime, the government firstoffers a subsidy scheme in which subsidy rates are contingent on output levels, thenfirms produce, and finally the home firm receives subsidy payments at the rate corre-sponding to its output. This has the advantage that different types of the home firmreceive different subsidy rates which are better designed for them. Also the typesare separated only after the foreign firm has produced and so the home firm's costinformation does not influence the foreign firm's output decision. Such non-linearpolicies might dominate linear policies, especially when information concealing is de-sirable, for the reason that the non- linear policies share the advantages which are241n a model in which the foreign firm knows the home firm's marginal cost (no signalling),Maggi (1992) shows that non-linear policies enhance the government's degree of freedom toimplement the Stackelberg outcome.58respectively attained by separation inducing menus and uniform polices.59Chapter 3NEW PRODUCTS, CREDIT RATIONING,ANDINTERNATIONAL TRADE603.1 IntroductionAccording to product cycle theory, 25 new products are first introduced and producedin developed countries (the North), then after a certain time period, these prod-ucts, which become old, are imitated and produced in less developed countries (theSouth), while newer products emerge in the North. This can explain the pattern ofNorth-South trade as a function of differences between the two regions in their R&Dcapabilities, capital availabilities, labour qualities, and market structures. However,it is less clear what shapes the North-North and South-South trade when countriesare very similar in every respect. 26 The purpose of this study is to explore the patternof North-North trade in those new and risky products.Development of new products involves the following two stages: scientific researchand product commercialization. In developing new products, especially hi-tech prod-ucts, there is a risk in the first stage, which is referred to as R&D (research anddevelopment) uncertainty. On the other hand, it is always difficult to predict de-mands for new products. This is the risk in the second stage, which will be referredto as market uncertainty. 27 In this chapter, we study trade in new products in asso-ciation with these two types of uncertainties. Since these uncertainties severely affect25 lnternational trade in product cycle was first studied by Vernon (1966). Krugman(1979) was the first to make formal modelling. More recent works can be found in thereferences of Grossman and Helpman (1991).26 lncreasing returns and product differentiation are two of the major explanations ofintra-industry trade in which each country simultaneously produces. exports. and importsproducts of the same industry (see Krugman (1980)).2 i These two important aspects of the development of new products have also been em-phasized by Ben-Zion (1981) who stated that a project is often subject to major uncertaintyabout both the probability of its scientific success and commercialization.61the profitability of potential products, risk neutral lenders may be reluctant to investin these risky projects. As a result, the demand for loans may exceed the supply offunds and credit could be rationed. 28To examine the pattern of trade in risky products, we develop a model in whichthere are two identical countries facing the possibility of innovating and producinga set of products. Potential producers must borrow to finance their R&D and pro-duction. Because these projects are risky, as in Stiglitz and Weiss (1981), credit isrationed, i.e., banks will only lend to some of the loan applicants. Those who re-ceive loans can then undertake R&D and if successful they start to produce. Thus,whether a new product can eventually be produced in one country and exported tothe other depends on whether the potential producer of the product is able to borrowand whether the R&D is successful. Although the pattern of trade may be somewhatindeterminate,29 we can calculate the probabilities of the following three possible out-comes for a product: (i) it is produced in both countries and sold in both markets(two-way trade); (ii) it is only produced in one country and exported to the other(one-way trade); and (iii) it is produced by none (no trade).28There are generally three types of credit rationing: (1) a limit on the number of loans,(2) a limit on the size of each loan, and (3) different interest rates on different loans. Asin Stiglitz and Weiss (1981), we consider the first type of credit rationing. For discussionsof the other two types, see Jaffee and Russell (1976) and Gale and Hellwig (1985). In thecredit rationing literature, it has been argued that contractual mechanism, such as loancommitments and collateral, may mitigate the rationing problem. For a brief review of thetheoretical debate on whether credit rationing may persist in equilibrium and the empiricaltests on whether credit rationing might be a significant macroeconomic phenomenon, seeBerger and Udell (1992).29In a different model. Grossman and Helpman (1990) found that even if two countriesdiffer in their initial stock of knowledge capital but which is globally accessible, the patternof trade would be completely indeterminate.62The Stiglitz and Weiss (1981) framework has been used previously in the studyof international trade. For example, Copeland (1990) and Flam and Staiger (1991)have developed models in which they reconsider the infant industry argument forprotection. In these models, capital market imperfections lead to insufficient entry ofthe domestic infant industry, but a tariff improves welfare in Flam and Staiger (1991)while it may or may not do so in Copeland (1990) due to their different assumptionsabout direct foreign investment. In contrast to these studies, the present study focuseson trade between two developed economies, without any one having any advantages,and examines the pattern of trade.Kletzer and Bardhan (1987) have also investigated the impact of credit rationingon the pattern of trade. However, they consider North-South trade under a differenttype of credit rationing in which borrowers face different interest rates. Unlike theirmodel, we study North-North trade in new and risky products under credit rationingin which the number of loans is constrained.The rest of this chapter is organized as follows. Section 3.2 presents a model inwhich information asymmetry between lenders and borrowers about the riskiness ofnew products leads to credit rationing. The pattern of trade is analyzed in Section3.3. In Section 3.4, we argue that the home and foreign banks could mutually benefitfrom making their decisions sequentially rather than simultaneously and we brieflydiscuss its implication for the pattern of trade. In Section 3.5, we conclude and outlinefuture research.633.2 The ModelThere are two countries: home and foreign. They are identical in all aspects and sowe shall just illustrate the situation at home.There are N potential and (for simplicity) independent products. Each product isto be developed and, if successful, produced by a single firm, the innovating firm. 3°Firms face two types of uncertainty. First, whether a new product emerges dependsupon whether the R&D is successful or not. For simplicity, we assume that all prod-ucts have equal probabilities of success in R&D, which is denoted by a E (0, 1). 31Second, even if R&D is successful, the demand for the new product is uncertain.We now specify market uncertainty. Let e i stand for an additive random variablein the inverse demand function of product i, i.e.,Pi (q) = P(q) + Ei^= 1 , • • • , N^ (62)where q is the demand of product i and P(q) is the inverse demand function whene i = 0 (i.e., without uncertainty). 32 P(q) < 0. c, E [E, E] withE(E i ) = 0 for all i.^ (63)As in Stiglitz and Weiss (1981), we adopt the definition of mean preserving spreads"This is the case if each producer has a national patent for her invention. Our analysisand results are still valid if we allow a number of producers to compete in each product(oligopoly).31 This assumption could be replaced by a less restrictive one. for example, assuming thatthe probabilities of succeeding in R&D are different but they are private information to thefirms. Alternatively, to characterize these products' risk differentials, we could emphasizeon R&D uncertainties by assuming different probabilities of successful R&D but identicalmarket uncertainties for these products.32The assumption that all products have identical non-random inverse demand functionP(q) can be relaxed. See Footnote 33 for a discussion.64to measure riskiness. In particular, we order the products increasingly by riskiness,i.e. if 1 < i < j < N and E < X < thenix J(0de JX Fi(0de^ (64)where P,(.) and Pj (.) are cumulative distribution functions (c.d.f.) of Ei and €3 , re-spectively.All firms have identical cost functions. 33 Each requires the same amount of funds,B, for R&D and the expense must be financed by borrowing from banks. There aremany banks which compete among themselves by choice of interest rate to maximizetheir profits. In this competitive banking system, we hereafter refer to a representativebank as "the bank". There is an information asymmetry between the bank and theborrowers. Firm i knows the distribution of c i ex ante and realizes the value of eiex post. The bank is aware that there is a firm with demand uncertainty ei but itcannot tell which one. Given an interest rate, the demand for loans is the number offirms which want to borrow and the supply of loans is the number of loans which thebank is willing to provide.The sequence of moves is as follows. At the very beginning, the bank announcesan interest rate r. Then, each firm decides whether to submit an application for aloan at the given interest rate. Upon receiving all applications, the bank makes aloan offer. In the case when supply exceeds or equals demand, all applicants receive33The assumptions of identical demands and identical costs are not essential. Our resultsstill hold so long as all firms have equal expected profits or more realistically the lenderslack information about demands and costs and so they can not discern the firms' differencesin their expected profits.65loans from the bank; otherwise (i.e., when demand exceeds supply) the bank onlyprovides loans to some of the applicants. Credit rationing occurs in the latter case.When credit is rationed, the bank makes a random offer. Those applicants whoare able to receive loans (the eventual borrowers) can then undertake their R&Dactivities and if successful, they start producing and selling to both the home andforeign markets. Market uncertainties are realized after firms have made their outputdecisions. Finally, the bank receives payments (principal plus interest) from theborrowers. There is limited liability and the minimum the bank can claim back fromeach loan is the prerequisite collateral K (> 0). 34 This happens when the loan receiverfails in R&D. The bank may receive the maximum (gross) return (1 + r)B from a loan,providing that the loan receiver earns a sufficient profit from the product market. 35Depending on the firm's profit from the markets, any partial return between K and(1 + r)B to the bank is possible.3.3 Trade3.3.1 Firm's Expected ProfitIn this and the next two subsections, the analysis is focused on the home country.Analogous arguments apply to the foreign country.We define market return as sales revenue minus production cost. A firm's profitthen is its market return net of R&D expenditure and payment to the bank. We con-34As shown by Stiglitz and Weiss (1981). credit rationing may still occur even if the bankuses collateral combined with interest rate in a contract. Here, for simplicity, we focus onthe case where only interest rate is used as a screening device.35 0bviously, (1 + r)B > K, otherwise the bank bears no risk.66sider the following hierarchy in each firm: the owner makes the borrowing decisionwhile the production and sales manager makes the output decision. More specifically,the manager chooses an output level to maximize the expected market return. Al-though it is true at least for many firms and in many cases that the production andsales manager has a goal different from the owner's, this separation assumption ismade only to simplify the following analysis. Our results (which are qualitative) holdwithout this assumption.A firm's market return varies with the market structure which is determined bythe R&D results of the firm and its foreign counterpart. If firm i succeeds in R&Dbut its foreign counterpart fails, firm i becomes a monopolist in both the home andforeign markets of product i. We denote the maximum expected market return as7r m and the optimal output as qm for this case. If, however, the foreign counterpartalso succeeds in R&D, then both the home and foreign markets are characterized byduopolistic competition. In this case, we use 7r d to denote firm i's maximum expectedmarket return and qd the optimal output level. 36 Thus, the actual returns to firm iin these two cases are 3 i11 175 =^Eiqk k = m, d,36 Under the specification of market uncertainty (62), property (63). and identical costfunction, these output levels and expected returns are the same for all industries. Hence, asubscript i is unnecessary.37The production and sales director faces market uncertainty only, but the owner facesboth R&D and market uncertainties. In the case of monopoly, the production and salesdirector chooses q to maximize E[2(P(q12)+f i )(q12) — C(q)] where C(•) is the cost function.At optimal output qm, the maximum expected return 7rm . = P(qm I2)qm — C(qm) and theactual return R7' = 2(P(qm 12) + c,)(e/2) — C(qm) = €2qm . The derivation of Ra issimilar.67and therefore the expected market returns over these two cases are38^R = (1 — a)R7 + cur(' = 71e^(65)where 71 e (1 — a)en + cy7rd and ge a- (1 — a)qm + aqdSince 7re and q€ are positive constants, (65) is an affine transformation from ei toRi. 39 This allows us to define riskiness directly on the random market return insteadof on the random market demand because any affine transformation preserves theproperty of mean preserving spread (64). 4° That is, for all 1 < i < j < N andR < x < R, where R = 7r e + Eqe and R = 7r e -eqe^Fi (R)dR > f x Fi (R)dR^(66)where Fj (.) and Fj (•) are the c.d.f. of R i and R. For simplicity and without loss ofgenerality, let € = —7r€1qe to normalize R = 0.Firm i's profit 71- (Ri, r) is a function of its market return and the interest rate.Note when R, + K < (1 + r)B, the firm's net loss is K, since, in addition to thecollateral (K), the earning from the market (Ri ) is totally used up to pay the bank;when (1 + r)B — K < R i < (1 + r)B, part of the collateral will be claimed by thebank because the market return is not sufficient to pay the bank; when and only whenR i > (1 + r)B, the firm earns a positive profit (R i — (1 + r)B). In sum,z(R i .r) = max{Ri — (1 + r)B,—K}.38Although the word "expected" is used here. Ri is still a random return because theexpectation is taken over all possible results of the foreign firm's R&D for a given marketuncertainty.39 An affine transformation from x to y is defined as y = a + bx, where a and b are anyconstants and b > 0."This result can be easily proved and so the proof is omitted here.68Therefore, the expected profit to firm i, given interest rate r, isR7i (r) = (1 — a)(—K) + a Jo^r)dFi(R)(1-Fr)B-K= - (1TR.a)K +^J(—K)dFi (R) + a10 + B-K— (1+ r)BldFi (R)=where—(1 —^)K + a.A i (r) + a[lre — (1 + r)B], (67)(1-f-r)B-KA i (r) [(1^r)B — K — R]dF(R) > 0. (68)Since 7r(R , r) is convex in R, 7ri (r ) must be increasing with the degree of riskiness (seeRothschild and Stiglitz (1970)). Thus, from (67), we know that .A i (r) increases in i.In the last expression of (67), the first term is the firm's loss when R&D fails; thelast term is the profit when R&D succeeds under unlimited liability; the second termis the benefit from limited liability.Firm i borrows if and only if its expected profit is nonnegative or equivalentlyAi(r) (1 — a)K + (1 + r)B — re.a(69)Since A i (r) increases in i and the right hand side of (69) is constant with respect toi but increases in r, we immediately obtain our first result.Result 1 (Theorems 1 and 2 in Stiglitz and Weiss (1981) ): For a given interestrate r, there exists i" such that firm i borrows from the bank if and only if i > Asthe interest rate increases, the critical value i* increases.69An important implication of this result is that if the bank raises the interestrate, the demand for loans drops and the average degree of risk from the set of theremaining applicants rises and hence the applicant pool becomes worse.3.3.2 The Bank's Expected ReturnWe now consider the (gross) return to the bank from a loan to firm i. If firm i's R&Dfails, the bank claims the collateral K. If the R&D succeeds, the return to the bankdenoted as p(R,, r) is a function of firm i's market return and interest rate. The hankgets the full return (1 + r)B only in the case that the firm has the ability to pay, i.e.Ri + K > (1 + r)B; otherwise the bank receives partial payment R, + K. Thus,p(Ri,r) = mintR i + K, (1 + r)B}.Hence, the expected return to the bank is— a)K + a f p(R, r)dFi (R)= ( — ct)18: +f (1-1-0B-K(R K)dFi (R)+ a I^(1+ r)BdFi(R)0^ (1-1-013-K=- (1 — a)K — aA i (r) + a(1 + r)B.^ (70)In the last expression of (70), the first term is the return to the bank from a loan whenR&D fails; the last term is the return to the hank when R&D succeeds but underunlimited liability; the second term adjusts the return to the bank due to limitedliability.Recall that NO increases in the riskiness of the products, (70) leads to Result 2.70Result 2 (Theorem 3 in Stiglitz and Weiss (1981)): The expected return to the bankfrom a loan decreases as the riskiness of the loan increases.3.3.3 Credit RationingLet p(r) denote the average return to the bank at interest rate r if the bank lends toall applicants. From Results 1 and 2 it should be clear that there exists an interestrate r* that maximizes p(r). 41 The bank's supply of loans can then be obtained fromthe supply function at interest rate r*, regardless of the demand. Similar to Theorem5 in Stiglitz and Weiss (1981), we know that there exist supply functions which giverise to credit rationing.Result 3 : At the equilibrium interest rate r*, there is credit rationing, i.e., thedemand for loans exceeds the supply of funds.For ease of later discussion, let i* be the critical value such that all firms withi > i* apply for loans at interest rate r*; I* = {firms with i > i*}, which is theset of all applicants at interest rate r'; /** be the set of applicants whose applica-tions are not denied, i.e., the eventual borrowers. From Result 3, /** C /*. Wedefine the degree of credit rationing x* as the fraction of the number of applicationsdenied over the total number of applications, i.e., f = (number of firms in /* —number of firms in /**)/(number of firms in /").41 To see this, note, as pointed out by Stiglitz and Weiss (1981). that an increase in interestrate has two conflicting effects: the positive effect which gives the bank a higher return dueto the interest payment; and the adverse-selection effect — the average riskiness of the loansgoes up (by Result 1) and so the return to the bank decreases (by Result 2). Initially, thepositive effect dominates the adverse-selection effect but the domination is altered after r*.713.3.4 Pattern of TradeSince the two countries are identical, the preceding analysis and results apply to theforeign country as well. In particular, these countries have the same equilibriuminterest rate r*, the same applicant pool ./*, and the same degree of credit rationing.27*. However, since the lucky applicants are determined randomly in each country, theset of the eventual borrowers at home 1$ may differ from that in the foreign countryIr . There are three possibilities: (i) = /7; (ii) th" fl I7 = 0, where 0 denotes theempty set; and (iii) neither (i) nor (ii) holds.In case (i), two countries support the same set of products. Although the finalentry to each product market in this set depends upon the success of R&D, we arelikely to see more duopoly markets in this case than in cases (ii) and (iii) becauseevery product in this set is financed at home and abroad. Thus the competition ishigh. However, the product variety is small since the number of different productsbeing financed in the world is small.Case (ii) becomes possible only if x. > .5, i.e., more than half of the applicants arenot able to borrow from the bank. This could happen when a large number of productsare highly risky so the demand for loans is high (by Result 1). For similar reasonsgiven above, we are likely to observe low market competition and large product varietyin this case. In fact, all markets which come to exist are supplied by monopolists.Observing case (iii) is most plausible. The resulting market competition andproduct variety will be between those in cases (i) and (ii).When both firm i at home and its foreign counterpart receive loans and succeed in72R&D, two-way trade occurs and both the home and foreign markets are characterizedby duopolistic competition. If, however, the foreign firm does not get a loan or itobtains a loan but fails in R&D, the home firm will be the sole producer of producti and becomes a monopolist in both the home and foreign markets. In the last case,we say that the home country is a pure exporter and the foreign country is a pureimporter of product i. 42We now establish Proposition 6.Proposition 6 : (i) Products with i < i* will not be produced in either country; allproducts with i > i* have equal chances (a(1 — x*)) to be produced in both countries.(ii) The home country may become a pure importer or a pure exporter of producti (i > i*), each with probability a(1 — x*)[1 — a(1 — x*)]; the probability of havingtwo-way trade in product i is equal to a 2 (1 — x*) 2 .By observing that 0,2 (1 — x*) 2 > 2a(1 — x*)[1 — a(1— x*)] if and only if a(1 x*) >2/3, we immediately obtain a corollary from Proposition 6.Corollary 1 : Two-way trade is more likely than one-way trade if the R&D successfulrate (a) is high and credit is not severely rationed (i.e., x* is small).3.4 The Timing of MovesIn the above analysis, the home and foreign banks are assumed to make their decisionssimultaneously. We now relax this restriction by allowing the banks to choose the time42We distinguish this from the case of two-way trade, in which the home country (andthe foreign country as well) produces, imports, and exports product i at the same time.73of moves, i.e., when to make offering decisions, and then briefly discuss its impact onthe pattern of trade. In particular, we ask whether a bank, say the home bank, hasan incentive to delay its loan offer. In other words, we want to know if the home bankcan benefit from making its offering decision after it has been aware of the foreignbank's offering decision.If the home and foreign banks move simultaneously, there are two possibilities:(i) fl 1-7 0 and (ii) ./7* n 0. In case (i), some firms at home and theirforeign counterparts receive loans from their respective banks, while in case (ii), thereexists no such a firm who and its foreign counterpart both receive loans. For ease ofanalysis, we first investigate a special case of (i) by supposing ir fl {x}, i.e.,only product x is financed in both countries. We then discuss the general case of (i)and finally case (ii).Suppose the home and foreign banks make their loan offer simultaneously andfl 1-7 {x}. We are going to show that the home bank will be better off if itredistributes loans by cancelling the one which was designated for x and giving it toanother firm, say y, which is not in the previously determined set of loan receivers,i.e., yAlthough the home bank cannot discern the riskiness of products x and y, it isaware that firm x's counterpart abroad gets a loan from the foreign bank but firm y'scounterpart does not. If it lends to firm y, firm y will be a monopolist. However, if itlends to firm x, firm x may become a duopolist. It is this difference that makes theloan for y more attractive than the loan for x. We now provide proof of this assertion.74Recall that the bank does not even know the probability distributions of marketuncertainty associated with products x and y. The bank then will take the twodistributions as the same when it calculates market returns to these firms. We useE to denote the representative distribution. Thus firm y's market return is R(€)+ eel because the firm faces no competition. However, firm x's market returnis R(E) = 7re Eqe as given by (65) in Section 3.3. Let m(E) denote the differencebetween these two market returns:M(e) -kW — R(E) = a [( 7rm — 7rd ) + E (g ni qd )] •^ (71)Then, we find Lemma 7 useful in deriving the main result of this section.Lemma 7 : Assume 7rmqd — qrdgm > 0. Then m(e) > 0 and so R(E) > R(e) for everyE.Proof:m(E) = ct (rm qd _ 7rdqm)>^and m'(€) = ce(qm — qd ) > 0.(1 — a)cfn + a qdTherefore, m(E) > 0 for all E. Q.E.D.If qd >^, obviously the assumption in Lemma 7 holds since 71 77/ > 7rd . Even ifqd < qm, the assumption is not stringent. Let us rewrite the assumption as71- m^7rd>q171^qd1^C(qm)^C(qd) —p ( _ q in) ^ > p (qd )Or2^qin qd •By noting 2qd > qm , we can see that this assumption holds if the average cost doesnot increase in output very rapidly. We only preclude the rare case that a monopolist75produces a lot more than a duopolist but the monopolist's profit is only slightly higherthan the duopolist's.By definition, the expected returns to the bank from lending to firms y and xare derived by taking expectation of the same return function p(R, r) over differentdistributions Fy (R) and Fx (R) (see (70)) or equivalently, they can be calculated bytaking expectation of different return functions over the same distribution Fx (R). Forpurpose of comparison, we adopt the latter approach. Let R 0 and R 1 denote firm y'sminimum and maximum market returns and define e0 as a critical point such thatfirm y is at even, i.e., R(c0 ) = (1 + r)B — K. Then, R(€0 ) + m(€0 ) = (1 + r)B — Kand by (71) and Lemma 7, we obtainpy (r) = (1 — a)K + a I p(R, )dFy (R)fil-r)B-K-m(q)= (1 — a)K + a^[R + m(e) + K — (1 + r) jBc1Fx (R) + a(1 r)B0f0(1+0B-R> (1 — a)K + a^[R + K — (1 + r)B]c1F,(R) + a(1 + r)B(1+0.9-K> (1—a)K+a 10^[R + K — (1 + r)B]dFx (R) + all + r)B= px(r^ (72)Thus, inequality (72) indicates the benefit to the bank from loan redistribution,switching the loan from firm x to firm y.We now consider the general case of (i), i.e., when there are more than one indus-tries receiving loans in both countries. Following the same arguments above, we knowthat the home bank will be better off by cancelling a loan previously designated to a76firm whose foreign counterpart also receives a loan and offering the loan to anotherapplicant whose foreign counterpart does not receive a loan. The bank will stop do-ing so when all loans, which are previously designated to those firms whose foreigncounterparts also receive loans, have been cancelled or all applicants, whose foreigncounterparts do not receive loans, have received loans. This is because no further loanrelocation will be able to create a new potential monopolist by sacrificing a potentialduopolist and no gain will accrue to the bank. In case (ii), since all loan receiversare already potential monopolists in their respective product markets, clearly thereexists no benefit from any loan redistribution.The above discussion indicates that if the foreign bank does not change its timeof loan offer, the home bank would delay its loan offer. By so doing, the home bankcould avoid loan overlapping like case (i), which would often occur if it has madeits decision before it knows the foreign bank's offer, and therefore achieve a betteroutcome. Moreover, the above discussion also implies that the foreign bank equallybenefits from the home bank's delay of offer. To see why, recall from the special caseof (i) that the home bank gains from replacing a potential duopolist x with a potentialmonopolist y. Consequently, the foreign potential duopolist x becomes a potentialmonopolist, which gives the foreign bank a higher expected return. Therefore, boththe home bank and the foreign bank are (equally) better off if they announce their loanoffer sequentially instead of simultaneously.If the restriction that banks make their loan offer simultaneously is dropped off,banks might move sequentially and so the chance to see two-way trade will be greatly77reduced. In this case, production specialization occurs not because of any comparativeadvantage but because banks dislike competition.3.5 Concluding Remarks and Future ResearchSince developing new products is risky (it involves R&D uncertainty and demanduncertainty), credit is rationed in the presence of asymmetric information betweenlenders and borrowers. When credit rationing occurs, a country may not produce someproducts which it has the ability to produce and has no comparative disadvantage inproducing. A new product will be produced at home only if the innovating firm canborrow from a bank and also succeed in R&D. This may give partial explanation forthe indeterminacy of the pattern of international trade between two similar countries.For future research, this model can be used to examine trade policy implications inthe presence of credit rationing. In this regard, we now outline two possible directionsand discuss some potential difficult issues that certainly deserve special attention.Let us first consider the case in which the home government imposes a tariffon a particular product. The following discussion is based on our original modelin which the home and foreign banks make decisions simultaneously. Suppose thehome government announces a tariff rate on a product before banks set their interestrates. To derive a policy implication, we should pay special attention to the banks'determination on the interest rate of the loan intended to the protected firm andthe consequent market equilibrium of the corresponding product. However, sincebanks make their decisions on the interest rate for the protected firm basing on their78expectation about the return from such a lending, we shall first analyze the tariff'simpacts on the protected firm's profitability at a given interest rate and then returnto discuss the possible influences on the banks' decisions.As it is well known in the strategic trade literature, in a competition between ahome firm and a foreign firm, tariffs imposed by the home government will shift somemarket shares from the foreign firm to the home firm. Note also from the analysis inSection 3.2 that a firm's output decision is independent of the interest rate at whichit borrows. These together will imply that at any given interest rate the tariff willincrease the protected firm's expected profit.One should realize that a higher expected profit to a firm might not necessarilyimply a higher expected return to the bank from a loan to this firm or at least thisrelationship is not obvious since the bank's return is affected by not only the firm'sexpected market return but also the riskiness of the loan and a tariff may change theloan's riskiness through its impact on the firm's output decision. However, it may bepossible to show that under some not unrealistic assumptions the expected return tothe bank from the loan intended to the protected firm will also be increased at anygiven interest rate.It is then expected that all banks in the home country will compete among them-selves (by using interest rates) for the loan to the protected firm since it is moreprofitable than the loan to an average firm at the same interest rate. Presumably,elaboration on the model is needed for the existence of an equilibrium interest rate.Only after determining the equilibrium interest rate can we start discussing the tariff79implication. One of the most interesting questions is whether a tariff may help thetargeted industry get out of the credit rationing situation.Policy analysis can also be carried out for R&D subsidization. Presumably thesame qualitative results shall also be obtained as those from the case of tariffs. Awelfare comparison, however, might invite some difficulties.Another possibility for future work (not just for policy analysis) is to concentrateon R&D uncertainty in our original model by assuming no demand uncertainty. Thiswill be more interesting and will substantially simplify our analysis. However, wemust carefully model the R&D uncertainty in order to give rise to credit rationing.80References[1] Aryan, L. 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(1992), "Strategic Commercial Policy Revisited: A Supply-FunctionEquilibrium Model", American Economic Review 82(1), 84-99.[28] Maggi, G., (1992), "Strategic Trade Policy under Asymmetric Information",Stanford University, mimeo.[29] Pomfret, R. (1991), "International Trade Policy with Imperfect Competition",Johns Hopkins University, Mimeo.[30] Prusa, T.J. (1990), "An Incentive Compatible Approach to the Transfer PricingProblem", Journal of International Economics 28, 155-172.[31] Rothschild, M. and J.E. Stiglitz (1970), "Increasing Risk: I, A Definition",Journal of Economic Theory 2, 225-253.[32] Singh, N. and X. Vives (1984), "Price and Quantity Competition in a Differen-tiated Duopoly", Rand Journal of Economics 15(4), 546-554.[33] Stegeman, K. (1989), "Policy Rivalry among Industrial States: What Can WeLearn from Models of Strategic Trade Policy?" International Organization 43,73-100.[34] Stiglitz, J.E. and A. Weiss (1981), "Credit Rationing in Markets with ImperfectInformation", American Economic Review 71(3), 393-410.82[35] Vernon, R. (1966), "International Investment and International Trade in theProduct Cycle", Quarterly Journal of Economics 80, 190-207.[36] Wong, K. (1990), "Incentive Incompatible, Immiserizing Export Subsidies",University of Washington Discussion Paper No. 9020.83APPENDIX IA. Proof of Lemma 1:(i). Given any strategy of the foreign firm, the domestic firm faces the residualdemand (4).If the domestic firm maximizes its expected profit E7r 1 by choice of quantities,then the optimal quantity isql = 2B1 + c2 — 82and the maximum expected profit given s i and s 2 is(A1 ± Si — Ci) 2E 7r1q = 2(2B1 c2 — s2) •However, If the domestic firm chooses a price to maximize its expected profit, theoptimal price isP1 = (A1 — si C1)B1 (e2 S2)A1 2B1 + c2 — 82and the maximum expected profit given s 1 and 8 2 isE7r ip = E7ril0_2(c2 — s9)2.,8?^• (76)The first result of the lemma follows.). The proof for the foreign firm is similar. We have, if the foreign firm sets aquantity,A2 —Cl^(A2 — c 1 ) 2= ^ and E79, =^2B2 c2^2(2B2 + c2) •A1 + 81 — c1(73)(74)(75)84If the foreign firm sets a price, then(A2 + ci)B2 + C2A2 P2 =2B2 + C2and ET2p = ET2q^2B; •a 2 C9Therefore, the second result of the lemma follows.(iii). (5) is obtained by using (73) and (74) in the welfare function W if c2 > 82,but using (75) and (76) if c 2 < s 2 . Q.E.D.B. Proof of Lemma 2:First, we show N > -w6q when d i. < d < d2 , where d1 = \/bkc2 /(b + c2 ) andd2 = Vkc2 . Define a function g(y) ^(k-d-9)2 for y < d. Then by (18) and(k—y)[k(k—y)-2d2 ](20), WQ —^>^— c i ) 2 [g(0) — g(d7)]. But ag(y)10y = —2d(k — d — y)[(k —d)(k — y) — d2]I(k — y) 2 [k(k — y) — 2d2 } 2 < 0 since k — d — y > 2(b — d)-1- c2 > 0 and(k — d)(k — y) — d2 > (k — d) 2 — d2 > (b + e2) 2 — d2 > 0. Thus g(0) > g(d-y). So thedesired inequality holds within the given range.Second, we extend the result to the case d < d 1 without comparing them directly.Suppose that the domestic firm still sets a price when d < d 1 . Then the optimalexpected net-subsidy profit when the domestic firm sets a price iswpq = (a — c i ) 2 (k — d-y — d) 2^0-2 C22(k — d7)[k(k — d-y) — 2d2]^2b2^for d < d2which can be obtained by going through the two-stage game without having theconstraint s2 > c2 . From above, we can infer N > -lir for d < d2 . However, both1/1/Pq and Wm are derived by maximizing the same objective functions but the formerhas one more constraint s2 > C9. Thus W/cp' < 4VQq for d < d 1 since the maximized85profit with more constraints can not be greater than the one with fewer constraints.The result follows. Q.E.D.C. Proof of Lemma 3:First, we showwqp (a — c i ) 2 (k — d) 22k2 (h —24P)^wb^(CI^C1) 2 [h^2(N3 + C2) ,63-YPQ^2[h — 7 2 (3 + c2 )] 2 (h — 24)a2 ( — c2)213 2(77)(78)According to (5) in Lemma 1, in a (q,p) competition, the government's problem canbe written asmax[ — ci)2(2Bi + c2 — 282) ] s.t.^= a + -y13;, 82 < C2.32^2(2B1 + c2 — s 2 ) 2Since d > —kbc2/(b c2 ), the optimal tax is an interior solution. Then from theF.O.C. we may obtain A l — ci = 2-y(h — s 2 )(h — 2s 2 )(V-). Thus,wqp^-y2 (h — 28 2 ) 3 ( ap' )2.282^382Differentiating (24) w.r.t. s 2 yields(79)014^d(b+ c2)(a — ci)(k —d) = (a — ci)(k — d) 7k(h —28. 2) 2as2 k2(h — 2s2 )2Substituting the above into (79) gives (77). We can also obtain (78) in the same way(but omit).Second, we show(a — c i ) 2 (k — d) 214/- 2P = ^2k(k 2 — 2d2 ) (80)86wa? =  (a — ci) 2 (k — d — d'y)2  + a2(—c2) 2(k — d7)[k(k — d7)-2d2 ]^2,32 • (81)Note that h = k — 2d-y. If we substitute this and (26) into (77), we have WaP =—ci ) 2 (k d) 2 /[k —2d7+2d7(b+c2)/k]. Note also that 2d7(b+c2) = 2dy(k—b)2kd-y — 2bdy = 2kd2 — 2d2 . Then (80) follows. To show (81), we haveh — 2 (3 + c2 ) = h — 7 2 (h — 3). (1 — 7 2 )(k — 2(17) + 32 2 = (1 — 72 )(k — d7)since /3 = (1 — 7 2 )b and 7 2b = d-y. Note that 3-y = b(1 — 72 )7 = (1 — 7 2)d, soh — 7 2 (3 + c2) — 132 = (1 — 72 )(k — d-y — d). Note also thath — 2s b2 = h+21372 (3 + c2)^h(1 — -Y 2 )(k — d-y) +2137 2 (,4 + C2) h — 7 2 (3 + c2) h — 72 (13 + c2)but the numerator = (1 — 7 2 )[h(k — d-y)+2b-y2 (h — 3)] = (1 — 2 2 )[(k —2d7)(k— d7) +2d-y(k — 2d7 — 3)] = (1 — 2 2 )[k(k — d-y) — 2d2] because d2 + = b and by = d. Afterusing all these results and substituting them into (78), (81) follows.The rest of the proof is the same as that of Lemma 2. Note that the condition thata2 (—c2 )/2/32 is small is necessary because it is a positive component in W. Q.E.D.D. Proof of Proposition 1:(27) is an immediate result of Lemma 2, Lemma 3. (15), and (26). (28) followsbecause of (14) and (80). Q.E.D.E. Proof of (29):First, h — 7 2 (h —^— 3y = h(1 — 2 2 ) — 37(1 —^= (1 — 7)[h + 7(h — ,3)].Substituting this into (12) yields87= s2^h2 — (h — ,3)72 c2b (a — )[h — -Y2 (h — ,3) — /3-y] (82)b /37 2 (a — c].)(h — 0)[h — 7 2 (h — 0) — 071 si =^[h — (h — I3 )7 2}[h2 (h — /3)72 c2]Second, from the F.O.C. of maximizing W /,' we obtain a + -y — cl =(7'2k), butfrom (10) apVas i = — 37(h — 13)/[h 2 — 72 (h — 13) 2 ]. Using these results, the maximumexpected welfare becomes1^(s b ) 2^2(T/T7 1,),^ ). + ^\ -- c 2)2h ' 72( psi^)2a 2/(32_  (a — ci) 2 [h — 72 (0 + c2) 07]2 2[h — 7 2 (13+ c2)][h2 — 72 (3 + c2)c2]0.2 _22 03 ^•(83)Finally, we show [h — 7 2 (13 + c2 )](h — 24) = h2 — (I3 + c2 )c2. Utilizing (23) wehave LHS = [h 7 2 ( 3 c2)][h h2/37 23+cc22j1 = h 2 — h7 2(,3 c2) 20720 + c2) =h2 — 72 (13 c2 )(h — 213) = RHS. Using this result and comparing (83) with (78), (29)immediately follows. Q.E.D.88(a — CL — CH) 2 7r (t*) = (a — — cH ) 2 *,TH (t ,;) Tr4b^L.4bAPPENDIX IIA. Proof of Lemma 4:By (35), 7F L (t H) 7 11 (tH) = 4(CH --cd(a—cL—cH-F2sH)19b. Since r L (tL )^7FL(tH)from the separation constraint, we obtain71.L(t.L) — ,TH( tH ) > _49b (CH — cL )(a — CL — CH + 28 H ).Similarly,7r-H (tH ) — 7F L (tL) > — —4 (c, — cL )(a — CL — CH + 2sL).9bCombining (84) and (85) yields9b(c, — cL )(a —^9b— cH + ^< —4(cH — cL )(a — cL — c, + 2sSo s L > s„. Using 711 (tH ) > T-H(t i,) once again, we have^(a — 2c, + 2s,) 2^(a — 2c, + 2sL)2TH > ^ 7-L9b 9bwhich confirms TH < TL . Q.E.D.B. Proof of Proposition 3:We shall show that t* induces separation. By using optimal subsidy levels (37)and the normalization 7," = 0, we obtain(84)(85)(a^2C L) 2(t *L ) = .L,4b^TL ,(7F H (rH) =_. a — 2c,) 2  4b89Therefore, 7L(t*) > 7L(t*H ) iffTL < -1[(a — 2cL ) 2 — (a — CL — ) 2] = — (c, — ) 2 + — (c, — CL)(a — — cll )4b^ 4b^2band 7H(t*H ) >^iff1 1^ 1--4T [(a — CL — CH) 2 - (a — 2cH) 2, = — CL)(a — CL — CH) — 4b (CH — CL ) 2 .Hence the separation constraints are satisfied iff1^1--4b(cH — CL)2 <2b(CH — cL)(a —^1— CH) < —( CH — CL) 2 .4bObviously, 7- '," defined as in (39) satisfies the above condition. Thus t* induces sepa-ration. Q.E.D.90P2 APSL = PPL P1 PSH = PPHRPL RSL^RI^RSHRpllR2P 2H -P2P2LFigure 291)6.- P1R 2q SH^CI PH^q1^qPL^qSLFigure 1q

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