Voluntary export restraints and strategic technology transfers

Joumd of INTERMTIONAL ECONOMICS Journal of International Economics 40 (1996) 165-186

ElsGIER

Voluntary export restraints and strategic technology transfers E. Young Song Department

of Economics,

Vanderbilt

University,

Nashville,

TN 37235, USA

Received November 1993, revised version received March 1995

Abstract This paper investigates the effects of voluntary export restraints (VERs) in the presence of potential entrants and technology transfers. It builds a model of a licensing game in a Cournot oligopoly market, and examines conditions under which VERs induce restrained foreign firms to transfer technologies to potential suppliers. I show that a VER can decrease the profit and output of the domestic incumbent by perturbing the no-licensing equilibrium reached under free trade and inducing the market to move to a licensing equilibrium. Key words: Voluntary export restraints; Licensing; Cournot; Entry; Technology JEL classification:

F12; F13

1. Introduction Quantitative

import

restrictions

have been increasingly

used to protect

troubled industries. According to Bergsten (1975), legislated quotas were the dominant instrument of commercial policy from the 1930s until the 196Os,but from the early 196Os,voluntary export restraints (VERs) replaced the role of quotas (for economic and political reasons for the increasing use of VERs, see Destler, 1986). Faced with import restrictions, foreign firms responded by looking for loopholes in the system of protection. Instead of accepting export restraints passively, they upgraded the products to elicit more profits from restrained sales, switched to industries that were closely OO22-1996/96/$15.00@ 1996 Elsevier Science B.V. All rights reserved SSDI 0022-1996(95)01387-3

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related in production technology but not protected, and built ‘transplants’ to bypass trade restrictions. Many joint ventures, mergers and acquisitions were also motivated by current and expected trade restrictions. It has been noted by many trade experts that VERs have more loopholes than legislated quotas that cover all foreign suppliers. In contrast to quotas, VERs are selective. They are usually sought for the chief producers of ‘market disruptions’. The sales of small suppliers and potential entrants remain unrestrained. Consequently, even though VERs succeed in freezing sales of major foreign competitors, they are likely to boost the sales of unrestrained countries both because of the limits on supply from restrained countries and because they will want to establish the highest possible sales in anticipation of future VERs. (See the case studies of U.S. protection by Hufbauer et al. (1986) for the characteristics and the effects of VERs. To capture the boosting effect of VERs on imports from third-country suppliers, Dinopoulos and Kreinin (1989) construct a general equilibrium three-country model. Anderson (1992) presents a model that shows the stimulating effect of anticipated VERs on the current sales of foreign incumbents.) Furthermore, as Bergsten (1975) points out, “companies in restraining countries may foster such developments by investing in new production facilities in non-restraining countries.” There is widespread belief among experts that the Multi-Fiber Arrangement (MFA) made a major contribution in spreading the textile industry to developing countries. Keesing and Wolf (1980) note that “leading quota-restricted suppliers (Japan at one time and now South Korea and Taiwan), in a conscious attempt to escape quota limitations, set up clothing production for export in other low-wage countries. In the past this ‘quota jumping’ has played a major role in spreading the industry to Singapore, Macao, Thailand and Malaysia.” In other industries, we too can find cases in which the U.S. trade restrictions stimulated international technology transfers by restrained countries. The Japanese electronic companies tried to bypass quota limitations set up by the orderly Market Arrangement by investing in Taiwan and Korea. When the Japanese government negotiated a voluntary restraint agreement on its auto exports with the U.S., a Japanese company that was seriously constrained by the agreement made a joint-venture and licensing contract with a Korean automobile company whose entry into the U.S. and Canada markets was remarkable successful (see Handley (1988) and Armstrong and Treece (1989) for the Mitsubishi Motor Corporation’s efforts to get around the VER). This paper is a theoretical examination of this kind of reaction by restrained foreign companies. The paper presents a Cournot model of international duopoly, with the variation that, prior to production decisions, the duopoly has the option of licensing its technologies to potential entrants

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that are not subject to trade restrictions. Using a model of a licensing game, this paper shows that if the costs of technology transfer are not too high, a VER will induce restrained firms to transfer their technologies, though they have no incentives to do so under free trade. AVER makes licensing more attractive to the restrained firms for two reasons. First, licensing a superior technology to a potential entrant and retrieving its profit by license fees allow the restrained firm to bypass the restraint. Secondly, the decrease in the profit caused by a new entry becomes smaller since its output now bound by the VER does not decrease with a new entry. The protective effects of VERs are much reduced if technology transfers occur. Furthermore, the resultant increase in the total output can depress the protected incumbents’ profit and output below the levels under free trade. Protective measures can make the market move from a no-licensing equilibrium to a licensing equilibrium, and the results can be drastically different from what is expected by policymakers. This paper does not claim that trade restrictions play the most important role in international technology transfers. The purpose of this paper is to show that selective trade restrictions can induce international technology transfers even when other incentives for technology transfers are absent. What the paper attempts to do is a controlled experiment. Assumptions adopted in this paper should be interpreted as controls that eliminate other incentives for technology transfers. Additionally, our licensing game should be interpreted broadly. Selling strategically important inputs or foreign direct investments can be examined in the same framework without changing the basic results, if we interpret licensing fees appropriately. Section 2 sets up a model of a licensing game in a Cournot oligopoly. Section 3 investigates incumbents’ incentives for licensing potential entrants under free trade. We identify a commitment value of licensing in a Cournot oligopoly: an incumbent can effectively make a credible commitment to a larger level of output and force its rival’s output down its reaction function by licensing. Then, we specify conditions under which no-licensing is an equilibrium. Section 4 derives conditions under which the no-licensing equilibrium under free trade becomes impossible under a VER. Additionally, we examine the possibility that the profit and output of the domestic firm fall after imposition of a VER. Section 5 examines the linear demand case and calculates equilibria explicitly. Section 6 briefly comments on the model. Section 7 concludes this paper. 2. The model

There are two incumbents competing in a single market, one domestic and the other foreign. The foreign incumbent will be referred to as firm F

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and the domestic incumbent will be referred to as firm D. They produce a homogeneous good, using technologies with constant unit costs.’ I assume that the two firms are equally efficient, and denote the common unit cost by c.” The market is also surrounded by a large number of potential entrants that can produce the same good. Initially, the potential entrants have the constant unit cost of c + k”, where k” is the initial cost disadvantage of potential entrants. All firms in the market are Cournot-Nash players. Each firm in the market chooses the output level to maximize the profit, regarding outputs of the other firms as given. The set of strategies for all players is the output interval [0, m) under free trade. When a VER is in effect, the set of strategies for the foreign incumbent is constrained to [0, q], where q is the level of the VER. The inverse demand function of the market will be denoted by p(Z), where 2 is the industry output. I assume that p(Z) is continuously differentiable, and satisfies the following conditions. Assumption Assumption

1. p’(Z) < 0 and p”(Z) s 0 , 2. 2( p”(Z))’ ap’(Z)p”‘(Z) .3

I will assume that k” is sufficiently large that potential entrants cannot enter the market without a technology transfer, both before and after imposition of a VER (I ignore the entry-promoting effects of protection by making this assumption; see Venables (1985) and Horstmann and Markusen (1986) for the entry-promoting effects of protection). Thus, without technology transfers, we will have the standard Cournot duopoly. The twist to this model is that the duopoly has the option of licensing its technologies to potential entrants. The incumbents have an innovation that can reduce k” to k. This cost-reducing innovation cannot be imitated. Technology transfers are made through the following two-part tariff licensing contract. The licensee pays a fixed fee of R for the accessto the technology and a royalty rate r per unit of output. I will use the auction mechanism analyzed by Katz and Shapiro (1986) to determine lixed license fees. The incumbent i (i = D or F) runs an Ivl unit, sealed bid auction with a royalty rate ri. In other words, the seller makes available a total of Ni licenses subject to buyers ‘The constant unit cost assumption also serves to eliminate the obvious incentive for licensing when marginal costs are increasing ‘The results of this paper do not depend on this symmetry assumption. I will focus my analysis on an incumbent’s incentive for licensing a potential entrant, not its incentive for licensing another incumbent. A licensing game among incumbents is examined by Katz and Shapiro (1985). 3This assumption is stronger than necessary. All we need is that the best response functions in the Cournot duopoly are not too concave.

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paying the royalty rate ri without setting a fixed fee. Potential entrants submit bids of R,P I will consider the following three-stage game. Stage 1: Incumbents simultaneously call (NF, rf) and (ND, rD). Stage 2: Potential entrants simultaneously submit bids of Ri to incumbents. Incumbents transfer technology to winning bidders. Stage 3: Firms, possibly with new entrants, play a Cournot game. We will solve for the subgame perfect Nash equilibrium of this game. In other words, we will solve the game by backward induction. Given the number of licensees, royalty rates, and fixed fees determined at stages 1 and 2, the stage 3 game is the standard Cournot oligopoly game. Games at stages 1 and 2 can be simplified by noting the following. A potential entrant at stage 2 will try to buy a license whenever it foresees that its profit net of license fees at stage 3 is non-negative. From the assumption that the number of potential entrants is large, we can show that competition among potential entrants drives up Ri sufficiently that the licensers extract the entire profits earned by licensees at stage 3. In addition, we can show that at stage 1, each incumbent wants to license to no more than one firm. The licenser can do as well by selling one license and charging a lower ri as by selling two or more licenses. Let us look at the stage 3 Cournot game. Suppose ND = NF = 1. Note that fixed licensing fees determined at stage 2 are already sunk for new entrants at stage 3. In addition, each incumbent regards the output of its licensee and thus license revenue as fixed when it chooses the level of output. Thus, players choose the output levels to maximize the following operating profits, regarding outputs of the other firms as given. xF E [0, 00)under free trade , X, E [0,

q]

(1)

under a VER ,

x, E [OY00)>

(2)

YF E VA9 7

(3)

‘The differences between their auction and ours are that sellers are allowed to charge a royalty rate, and two auctions are held simultaneously. This auction mechanism is adopted here mainly for analytical convenience. It serves to eliminate R, from the licenser’s strategy variables and allows our analysis to focus on the licenser’s choice of r,. As will become clear later, any mechanism that allows licensers to retrieve the profits of licensees in a lump-sum manner, such as repatriating the profit of a subsidiary created by direct investment, can replace the auction mechanism without changing the results.

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@D=(p(z)-c-k-r,)Y,,

Y, E [OT4 f

(4)

xi is incumbent i’s output, and l?i is its operating profit. yi denotes the output of the entrant that has bought a license from incumbent i, and @j denotes its profit, net of the per-unit licensing fee but gross of the fixed fee. In Eqs. (3) and (4), we can see that an 2 is equal to x,+x, +y,+y,. incumbent can control the marginal cost of its licensee by controlling the royalty rate. Szidarovszky and Yakowitz (1982) show that under Assumption 1, the unique Cournot equilibrium of this game exits. Thus, we have a unique Cournot equilibrium corresponding to each pair of (rF, rD), and we can express the output levels of all players as functions of (rF, rD). (For notational simplicity, I will not use separate notations to denote these functions: outputs and profits below should be read as functions of (rF, rD).) Additionally, from Szidarovszky and Yakowitz (1982), we can show the following properties. Suppose y, > 0. If rF decreases, Pl. 2 strictly increases. P2. yF increases, and x,, xD, and yD decrease. This change is strict for a firm whose output level is inside the strategy interval. P3. QF increases, and Z&, II, and GD decrease. This change is strict for a firm whose output level is strictly positive. The symmetric result holds for rD. We can show that Pi through P3 hold if a decrease in rF changes y, from zero to a positive value. All these properties hold regardless of the existence of a VER. The four-firm Cournot game described above covers all possible outcomes of our licensing game. To see this, let us denote by 2’ the industry output in the Cournot duopoly where only two incumbents are in the market. Let r” =p(Z”) - c - k. Note that r” is equal to the per-unit profit rate a licensee can earn at the industry output level of 2’ before paying license fees. Suppose NF = 1 and rF 2 r”. By Pl, Z > Z” with a new entry. @$= (p(Z) c - k - r,)y, cannot be positive, regardless of firm D’s licensing strategy. Therefore, yF = 0. Then, R, is equal to zero (or equivalently, no firm buys a license from firm F) at the stage 2 game. Note that the outcome is identical to the one we will obtain when NF = 0. The strategy of calling the royalty rate of r” or a higher value with NF = 1 is equivalent to the no-licensing strategy of setting NF = 0. If (rF, rD) > (r’, r’), no licensee will be operating in the market and we will have the Cournot duopoly as the outcome. Therefore, without loss of generality, we can restrict ND and NF to one and allow incumbents to charge any royalty rate. Now look at the stage 2 game. Competition among bidders drives up Ri

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sufficiently that the net profits of licensees at stage 3 are zero. Thus, Ri = Qi for both licensers. At stage 1, each incumbent knows that given its rival’s choice of the royalty rate, it can determine the Cournot equilibrium at stage 3 by controlling its own royalty rate. It also knows that at stage 2, competition among potential entrants drives up the fixed fee sufficiently that it can extract the entire profit earned by its licensees at stage 3. The total profit of incumbent i = Lr, + (Ri + riyi) = (p(Z) - c)xi + (p(Z) - c - k)y, = (p(Z) c - k)(x, + yi) + kx,. Thus, incumbents at stage 1 maximize the following pay-off functions: L, = (p(zF + zD) - c - k)z, + kx, , L, = (p(zF + zD) - c - k)z, + kx, . Li is the pay-off to incumbent i. zF = xF + yF and zg = xg + yo. We can call zF the output of the foreign group composed of the domestic incumbent and its licensee. Similarly, we can call zg the output of the domestic group. Note that the pay-offs L, and L, are functions of (rF, rD). At stage 1, each incumbent will choose the royalty rate that maximizes its pay-off function, given its expectation of the other incumbent’s royalty rate. An equilibrium of our three-stage game is a Nash equilibrium pair (rg, r-z) for which LFG 6) 2 L,(r,, rz) for all rF, and L,(r;, ri) 2 LD(r:, rD) for all rD.

3. Strategic technology transfers In this section, we will examine equilibria of the licensing game under free trade. As we saw in the last section, if both incumbents choose the no-licensing strategy, we have the Cournot duopoly as the outcome. Denoting the Cournot duopoly by zero, each incumbent produces x0 and obtains the profit of no = (~(2”) - c)x’, where Z” =x0 +x0. I will call this duopoly equilibrium the no-licensing equilibrium. We first examine what conditions are necessary to sustain this no-licensing equilibrium. To examine the incumbents’ incentives for licensing, it will be convenient to reformulate the game in terms of group outputs. Suppose the domestic incumbent takes the no-licensing strategy and rD 2 r”. Fig. 1 shows the responses of zF, x, and xF as rF changes. If rF > r”, we have the no-licensing equilibrium and zF = xF = xg =x0. As rF decreases from r”, YF=ZF-XF becomes positive. By Pl and P2, zF strictly increases, while xg and xF decrease. As explained below, xF and x, are always identical because of the symmetry assumption. The foreign incumbent can obtain any zF 3 x0 by lowering rF sufficiently. Note that a unique value of rF corresponds to any ZF 2=x0; if zF =x0, we assign any rF 3 r”. Thus, unique values of xg and xF

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ZF, XD, XF t

r”

rF

Fig. 1. Response of outputs to the royalty rate.

correspond to each value of zF 3 x0. Given the royalty rate charged by the domestic incumbent, choosing rF is equivalent to choosing zF, and xD and xF can be expressed as functions of zF. When the domestic incumbent is not selling a license, these functions are the best response functions or the reaction functions in a Cournot duopoly. To see this, note that regardless of the value of rF, xD, xF, and zF must satisfy the following first order conditions for maximizing Eqs. (1) and (2), when xD and xF are positive: p’(x~+z,)x,+p(x,+zF)-c=o, P’(XD + ZF)XD+ P(XD + ZF) - c = 0 . From the second equation, we can express xD as a function of .zF, which is nothing but the best response function in a Cournot duopoly. This function will be denoted by p(z,). From the definition of x0, p(x”) =x0. By comparing the two equations, we can see that xF must always be equal to xD. Thus, xF = /3(zF). Therefore, when the domestic incumbent is taking the no-licensing strategy, the objective function of the foreign incumbent can be written as =::I% LF(ZF) = Mm,)

+4

-c - k)ZF + WZF).

(5)

Similarly, when the foreign incumbent is taking the no-licensing strategy, the objective function of the domestic incumbent is given by max L,(b) ZD3X0

= (PW,)

+ zD) -c - W,

+ Mz,)

.

(6)

Thus, to sustain the duopoly as an equilibrium in our licensing game, each incumbent should not want to increase its group output above x0, given that the other firm calls the royalty rate of r” or a higher value.

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To single out the strategic benefit of technology transfer in our licensing game, let us consider the case k = 0. We obtain the following proposition. Proposition 1. Suppose the cost disadvantage of the licensee is zero (i.e. k = 0). Zf the rival does not sell a license, an incumbent can attain the Stackeiberg leader profit by selling a license to a potential entrant. Thus, no-licensing cannot be an equilibrium. Proof. If k = 0 and the rival does not sell a license, the objective of the foreign incumbent, for example, becomes max WF) ZF”XO

= (PWF)

+ ZF) - C)ZF.

The solution of the problem is the output level of the Stackelberg leader. Since it is greater than x0, an incumbent always sells a license to a potential entrant if its rival does not. The no-licensing equilibrium is impossible. 0 This result is not surprising if we understand that licensing a potential entrant can be regarded as breaking a firm into two independent firms when k = 0. Szidarovszky and Yakowitz (1982) and Salant et al. (1983) show that if we split a firm into two independent firms in a Cournot oligopoly, the joint profit of the two firms can be higher than the profit of the single firm. By splitting a firm, one can credibly make a commitment to a larger amount of output, decreasing the output of the other incumbent down its best response function. We will call a technology transfer motivated by this incentive a strategic technology transfer. To avoid the ‘excessive’ incentive for licensing, Katz and Shapiro (1985, 1986) restricted licensing contracts to a fixed fee type.5 Instead, I will restrict my attention to the case where k is strictly positive, allowing a licenser to collect license fees through a two-part tariff contract (see Section 6 for a comment on the role of the two-part tariff licensing). From now on, I will adopt the following assumption. Assumption

-P ‘(x0) 3. k a& = 1 _ p,(xo) (PV”)

- 4 > 0.

5 Katz and Shapiro (1985) show that licensing always occurs for non-drastic innovations if an inovator can sell a superior technology to another incumbent through a two-part tariff licensing contract. Licensing increases the industry profit by reducing the unit cost of the licensee, and two-part tariff licensing allows the splitting of the increased industry profit such that both the licenser and the licensee enjoy higher profits. Proposition 1 holds in our model for a different reason. In contrast to selling a license to an incumbent, allowing a currently inactive firm to enter the market by licensing decreases the industry profit. In our model, licensing occurs because of its commitment value.

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Assumption 3 requires that k is greater than a fraction of the profit margin of the incumbents in the duopoly, the fraction determined by the slope of the best response function. The following proposition immediately follows. Proposition free trade.

2. Under Assumption

3, no-licensing

is an equilibrium

under

+p(Z”) - c) +p’(Z”)xo@‘(xo) At zi =x0, dL,ldz, = (p’(Z”)x” k(1 - p’(x’)) = -(p(Z”) - c)p’(x”) - k(1 -p’(x”)) ~0 since p’(Z”)xo + p(Z”) - c = 0. We can show that Assumption 2 implies that L,(z,) is concave in zi for zi ax0 if k sp(Z”) - c. Thus, Li(zi) < Li(xo) = 17’ for all zi 3~‘. If k >p(Z”) - c, L,(z,) 6 Li(xo) always. Each incumbent has no incentive to sell a license if its rival is not selling one. 0 Proof.

From the proof, we can see that Assumption 3 is also necessary to sustain the no-licensing equilibrium. What Proposition 2 shows is that to prevent licensing, k should be large enough to offset the strategic benefit of the commitment to a larger level of output. k does not have to be the difference between the licenser’s operating marginal cost and that of the licensee. A technology transfer entails significant costs arising from the need for information exchange and learning. One can interpret k as reflecting the costs of technology transfer that increase proportionally with the licensee’s scale of entryP Of course, a licensee can have a higher marginal cost than its licenser. k will be positive if the technology transferred affects only a part of the production process or if the licensee has a disadvantage in factor costs or transportation costs. It can also reflect product differentiation in favor of the existing firms, if we redefine the units of outputs appropriately. The purpose of this paper is to show that a VER can reduce the profit of the domestic incumbent by inducing the restrained foreign firm to set up an additional production facility in a new location, which was unprofitable before the restriction. This result does not depend on Assumption 3. If k is less than k, licensing occurs under free trade. Section 6 shows that in this case also, a restriction can lower the profit of the domestic incumbent by increasing the output level of the foreign group. I adopt Assumption 3 here to prevent licensing before a trade restriction, which greatly simplifies the following analysis. Proposition 2 also shows that only one incumbent selling a license cannot be an equilibrium. One additional kind of equilibrium that is possible is 6 In our model, it does not matter whether the licenser or the licensee bears these costs directly. In either case, the licenser maximizes the same joint profit in (5) or (6). Section 6 discusses the case where these costs are fixed.

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17.5

licensing by both firms. An incumbent may want to sell a license once the rival sells one, even if it does not sell as long as the rival does not. We can have multiple equilibria. The following proposition shows that if both licensing and no-licensing are possible in equilibrium, the no-licensing equilibrium Pareto-dominates a licensing equilibrium for incumbents. Proposition incumbent’s

3. If both incumbents are licensing in an equilibrium, each profit is strictly lower than that in the no-licensing equilibrium.

Proof. Suppose, for example, rD is raised to r” in an equilibrium where y, >O and y, >O. As y, drops to zero, Z decreases, while zF and xF increase by Pl and P2. Thus, L, becomes strictly higher when the domestic incumbent does not sell a license. By Proposition 2, this L, is, in turn, less than the duopoly profit 17’. Similarly, L, is less than L!‘. 0

Even when both types of equilibrium are possible, the no-licensing equilibrium seems more likely since it Pareto-dominates a licensing equilibrium. It is likely to be the focal point of the game, and it is also renegotiation proof.

4. VERs and strategic technology transfers In this section, we examine how VERs affect our licensing game. The effect of a VER comes simply as a shrinkage of the foreign incumbent’s strategy interval to [0, q], where q is strictly less than x0. By the discriminatory nature of the restriction, strategy intervals of potentials entrants remain unchanged. As a reference point, we first examine the effects of a VER in a conventional Cournot duopoly market. As the VER is imposed, the foreign incumbent’s best response function p(x,) becomes kinked at xF = q. xF decreases to q, and xD increases to p(q). The profit of the domestic firm increases since it becomes higher at every value of xD when the rival’s output is lower. The opposite holds for the foreign firm’s profit. It is also easy to show that the industry output 2 declines and the price rises. This result conforms to conventional wisdom. A limit on foreign sales succeeds in increasing the domestic firm’s market share and profit. However, effects can be different if technology transfers can be used to circumvent restrictions. An important observation from the last section is that the duopoly equilibrium under free trade is a subtle situation where potential entrants surrounding the market are deterred from entry by large cost disadvantages, and each incumbent has no incentive for a technology transfer when its rival

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does not. A VER can perturb the no-licensing equilibrium reached under free trade and induce the market to move to a licensing equilibrium. I will denote the value of variable x corresponding to the VER level of q by x(q). Again, denoting the no-licensing equilibrium by superscript 0, xo,(q)=q x0 in the no-licensing equilibrium. II;(q) < 17’ and 17:(q) > no. Recall that Pl through P3 hold also under a VER. The argument in Section 3 can be used again to show that choosing the royalty rate is equivalent to choosing the group output level, given the rival’s licensing strategy. Let us start with the domestic incumbent’s incentive to sell a license. Proposition 4. Under a VER, the domestic incumbent has no incentive to sell a license if the foreign incumbent does not sell one. Proof. Note that 17;(q) is the profit of a monopolist facing the demand curve p(xo + q). There is no way of increasing the profit over the monopolist profit as long as xF = q. The domestic incumbent can choose a high value of zD such that xF = p(z,)
The situation is different for the foreign incumbent. Suppose the domestic incumbent does not sell a license. The best response function of the domestic incumbent does not change with a VER since it is not constrained. From the first order conditions for Eqs. (1) through (4), we can easily show that if q G p(z,), the VER is binding and xF = q, and if q > /?(z,), the VER is unbinding and xF = /?(z,). Let p-’ be the inverse function of @.Since p is a decreasing function, q < x0 < p( q)-l. Thus, when the domestic incumbent does not sell a license, the foreign incumbent faces the following objective function: max 2F-l UZF)

= (PWF)

+ ZF) - c - k)z, + &I 3

where q Sz,S/3(q)-’ = (PWZF)

+ ZF) - c - kk,

where zF > p( q)-l .’

+ WZF)

7 (7)

’ For a strictly positive k, it is never optimal for the foreign incumbent to shut down its own plant in the face of a VER. If it does, its pay-off function becomes LF(zp) = (p(p(zF) + zF) c - k)z, for all q and it is always below the one in (7), for which the foreign incumbent should operate both plants.

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Let us define the following functions, which will be used to prove the next two propositions: S(z) = (p@(z) + z) - c)z, H(z) = S(z) - kz. S is the profit function of a Stackelberg leader with the unit cost of c. H is the profit function of a Stackelberg leader with the unit cost of c + k. Assumption 2 guarantees strict concavity of S and H. Note the following. S’(q) =P’(P(q) + q)@‘(q) + l)q +P(P(q) + 4)) -c > S’(x”) ==p’(z”)(p’(xO) + 1)x0 +p(z”) - c = -p’(x”)(p(z”) 4 < 9(x”)

< S’(q) .

- c) ,

(8) (9) (10)

The first inequality in (10) holds because l/( 1 - p’(x”)) < 1. The second inequality comes from the fact that S” < 0 and q
Proposition k 2 S’(q).

= WzF) + kq 9

where q c zF s /3( q)-l

= H(z,)

where zF > p( q)-l .

+ kj3(zF) ,

5. No-licensing

LT an equilibrium

(11)

under a VER if and only if

If k 2 S’(q), H’(zF) = S’(z,) - k s 0 at zF = q. In Eq. (ll), L,(z,) is decreasing for all z F 5 q since H(z,) is concave and p(zF) is decreasing. The foreign incumbent does not want to sell a license if the domestic incumbent does not sell one. Combined with Proposition 4, no-licensing is an equilibrium. Suppose k < S’(q). Then, H’(zF) = S’(z,) - k > 0 at zF = q. Thus, L,(z,) = H(zF) + kq is strictly increasing at zF = q. The foreign incumbent will sell a license and the no-licensing cannot be an equilibrium. Cl Proof.

When k < S’(q), H’(zF) is positive at zF = q. The profit of the foreign incumbent, which behaves like a Stackelberg leader with the unit cost of c + k as long as the VER is binding, is increasing at the VER level of output. If no-licensing were the equilibrium under free trade, a VER must move the market to a licensing equilibrium. Note also that since S is concave, S’(q) increases as q falls. The interval of k in which no-licensing is impossible enlarges as the VER becomes more severe. In the case k < S’(q), only two kinds of equilibrium are possible by Propositions 4 and 5: only licensing by the foreign incumbent or by both incumbents. In either case, compared to the duopoly under the VER, the output and profit of the domestic incumbent are lower. The protective effects of the VER will be weakened. However, the domestic incumbent may have to face a worse outcome if k is close to &. The next proposition shows the interesting possibility that the profit and output of the domestic incumbent actually fall after a VER.

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Proposition 6. Suppose k G k < S’(x’). In any possible equilibrium under a VER, the domestic incumbent’s profit and output are lower than those in the free trade duopoly. Proof. We first examine an equilibrium in which only the foreign incumbent sells a license. By the hypothesis, H’(q) and H/(x’) are strictly positive. Since x0 < p-l(q), we can see from (11) that LF(zF) is strictly increasing for zF E [q, x0]. Thus, denoting the equilibrium values by asterisks, zz>x” and xi = p(z~) (~(2; +x2) - c)x; = L;. N ow examine the case where both incumbents sell licenses in equilibrium. We have two possibilities. If the entry of two additional firms increases the industry output sufficiently, q will be unbinding in equilibrium. In this case, the equilibrium is identical to the free trade licensing equilibrium. By Proposition 3, Li < 17’. By P2, X: < x0. The proof for the other case, where q remains binding in equilibrium, is in the appendix. 0

Therefore, if & G k < S’(x’), and no-licensing was the equilibrium under free trade, a VER must move the market to a licensing equilibrium where the profit and the output of the domestic incumbent are lower than the free trade levels. Note in this case, H(zF) = S(z,) - kz, is increasing at zF =x0. Recall that L&z,) = H(z,) + kx, when the domestic incumbent is not selling a license. The foreign incumbent did not want to sell a license under free trade because the fall in xF after licensing is large enough to offset the increase in H. With a VER, this effect vanishes since xF is fixed to q. The foreign incumbent wants to increase zF above x0 since H(z,) is increasing at zF = x0. The VER makes licensing more attractive to the restrained firm for two reasons. First, an entry of a licensee allows the firm to bypass the restraint. Secondly, the cost of a new entry decreases since its output now bound by the VER does not decrease with a new entry. One may conjecture that it may be possible that the foreign incumbent’s profit increases despite the restraint. Finally, we show that this is impossible. Proposition 7. In an equilibrium under a VER, the foreign incumbent’s profit is always lower than the free trade duopoly profit.

The proof is omitted, Proposition 7 simply follows from the fact that the pay-off function of the foreign incumbent shifts down with the imposition of a VER, and with an entry of the domestic incumbent’s licensee. Thus, if & 6 k < S’(x”), the profits of both incumbents fall after a restraint if the no-licensing were the equilibrium under free trade. New entries caused by the restrained firm’s licensing increase the industry output, decreasing the

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price. In this case, a VER makes consumers better off but it causes the market to move to an equilibrium that is worse for both incumbents.

5. Linear example In this section, I will examine the linear demand case and calculate equilibria explicitly. Even in the linear demand case, the calculation involved is quite complicated. Rather than going into details of derivation, I will briefly sketch the results. Consider the linear demand function p(Z) = a - bZ. In the free trade duopoly, each incumbent produces x0 = (a - c)/3b and enjoys the profit margin p(Z”) -c = (a - c)/3. In the following, I will normalize every output variable by dividing it by the duopoly output level (a - c) /3b, and every price or cost variable by dividing it by the duopoly profit margin (a - c)/3. Thus, in the following, xi, yi, and zi should be interpreted as xjIxo, yiIxo, and zilxo, respectively, and ri should be interpreted as r,l(p(Z’) - c). Similarly, q means the VER level as a ratio to x0, and k denotes the cost disadvantage of a licensee as a ratio to p(Z”) - c. To prevent any entry without technology transfer, it is sufficient to assume that k”, as a ratio to p(Z”) - c, is greater than 3/2. First, we examine equilibria under free trade. The normalized best response function is given by p(x,) = 312 - l&5+. Thus, & = -p’(x”)l(l /3‘(x0)) = l/3 and Assumption 3 becomes k 2 l/3. By Proposition 2, nolicensing is an equilibrium for this range of k. Let us check whether licensing by both incumbents can also be an equilibrium. In this equilibrium, y, > 0 and yD > 0. In addition, L, should be maximized, given the rival’s royalty rate. These conditions imply that rD = rF = (13k - 3)/7, x,=x,=(Sk+3)/7,

(12) yD=y,=6(1-2k)/7,

z,=z,=(9-4k)/7.

(13) Note that this licensing equilibrium is possible if and only if k < l/2 such that yD = y, > 0. Therefore, if l/3 G k < l/2, both the no-licensing and the above licensing equilibrium are equilibria under free trade. However, for incumbents, the no-licensing equilibrium Pareto-dominates the licensing equilibrium. If k 3 l/2, no-licensing is the unique equilibrium. Now examine how the equilibrium configuration changes under a VER. From Eqs. (8) and (9), S’(x”) = l/2 and S’(q) = 3/2- q. Therefore, if k < 312 -4, no-licensing cannot be an equilibrium by Proposition 5. By Proposition 6, if l/3
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selling a license, the VER must be binding. Additionally, we can show that an equilibrium where both firms are selling licenses and the VER is strictly binding is impossible. Therefore, we have only three possible equilibria: the no-licensing equilibrium where xF = q and xg = /3(q), or the licensing equilibrium where only the foreign incumbent is selling a license with the VER binding, or the free trade licensing equilibrium described in Eqs. (12) and (13). In the second equilibrium, Eq. (11) implies that z, must be maximizing H(zF). From this, we can show that the following must hold: rD is prohibitively high, rF = -314 + ll2k + q , xF=q,

xD =3/4+1/2k,

y,=3/2-k-q,

(14) y,=O.

(15)

To support this equilibrium, y, = 3/2 - k - q > 0. Additionally, the domestic incumbent must have no incentive for licensing if rF = -3/4 + 1/2k + q. Tedious calculations show that this is true if and only if q < l/8(-18 + 4k + 12-m). Therefore, if these two conditions hold, the outcome defined in Eqs. (14) and (15) is an equilibrium. Finally, going back to the free trade licensing equilibrium in Eqs. (12) and (13), we can show that this is an equilibrium under a VER if and only if q > (8k + 3)/7, such that the foreign incumbent can produce xF = (8k + 3)/7. Fig. 2 summarizes the discussion above. The curve dividing regions A and B is q = l/8 (- 18 + 4k + 12-m). In region E, no-licensing is the unique equilibrium. In regions C and D, the equilibrium where only the foreign incumbent is selling a license is the unique equilibrium. In region B, this equilibrium and where both incumbents are selling licenses are two equilibria. In region A, licensing by both incumbents is the unique equilibrium. 4 1

113

312

l/2

Fig. 2. The licensing region.

k

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Now we can examine the effects of VERs on the market outcome. In region E, no-licensing is the equilibrium both before and after a VER and the conventional analysis is valid. In region D, the market must move from the no-licensing equilibrium to the licensing equilibrium where only the foreign firm is selling a license. The profit of the domestic incumbent under the VER is still higher than the free trade level but the protective effects of the VER are weakened by a new entry. In regions A, B, and C, both no-licensing and licensing by both incumbents were possible under free trade. If the no-licensing equilibrium were the equilibrium under free trade, aVER must move the market to one of the two licensing equilibria, and the profit and output of the domestic incumbents decrease. An interesting property to note is that in the equilibrium where only the foreign firm is selling a license, a decrease in the VER level does not change the market outcome. As Eqs. (14) and (15) show, if the restriction becomes severe and 9 decreases, the foreign incumbent simply lowers the royalty rate to maintain the same group output level. Note also that in region A, a VER level that is slightly smaller than the free trade output level is sufficient to perturb the no-licensing equilibrium. 6. Some remarks In this section, I will briefly comment on a few issues related to the model. 6.1. Independence of the licensee

The result that the profit of the domestic incumbent can be lower under a VER hinges on the assumption that the licensee is a firm making independent decisions at the stage 3 Cournot game. If the licenser and the licensee are perceived as a single firm with multiple plants, the market becomes a Cournot duopoly. AVER always increases the domestic incumbent’s profit since the foreign incumbent must face a higher unit cost to bypass the restriction. This is also the case if the foreign incumbent chooses the royalty rate, not prior to the Cournot game, but simultaneously with production decisions, taking the rival’s output level as given. 6.2. The form of the licensing contract

Although the licenser and the licensee are firms making independent decisions at the stage 3 Coumot game, the ability to choose the royalty rate gives the licenser a perfect control over its licensee’s output. The two-part tariff licensing is optimal to the licenser, but one may question the empirical

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relevance of the perfect controllability assumption. Allowing only a fixed fee in licensing does not change the basic results of the paper. The licenser loses a continuous control over the group output level, but the option to sell a license still gives the licenser a discrete choice over the group output level. In this case also, we can identify a range of parameters in which a VER moves the market to a licensing equilibrium and reduces the profit of the domestic incumbent. 6.3. The size of k The possibility that the profit of the domestic incumbent falls after a VER does not depend on Assumption 3. Suppose 0 < k
= MP”(z,)

+ zF) - c - k)z, + W+)

-

PG is the best response of the domestic group, which can be derived from (A.3) and (A.4) in the appendix. The relationship between xF and zF, which is denoted by xF(zF) above, can be derived from the first order condition for the foreign incumbent at the stage 3 game. By P2, x is decreasing in zF. Since L,(z,) is maximized under free trade, (p(p E;
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to sell a license and choose the group output level of z*. Again, the profit of the domestic incumbent falls if this happens.8 So far we have assumed that the size of k is exogenously given to the licenser. What happens if the licenser has the ability to choose k by controlling the quality of the technology transferred? In our model, the licenser always chooses the technology with the lowest k when it sells a license. By reducing k and raising the royalty rate by the same amount, the licenser can achieve the same group output. This means that at every group level, the joint profit in (5) and (6) becomes higher with a lower kp Thus, when k is variable, k in the paper should be interpreted as the minimum value of k that can be achieved by the licenser. As explained above, the profit of the domestic incumbent can fall after a VER for a wide range of minimum values for k. 6.4. Price versus quantity competition

This paper is intended for evaluating the long-run effects of VERs. Kreps and Scheinkman (1983) justify the Cournot model as a two-stage game in which firms compete in prices with capacity constraints in the short run, and engage in a capacity choice game in the long run. In view of this interpretation, the Cournot model seems more appropriate for the purpose of this paper. Decisions on technology transfer involve a horizon at least as long as that of investment decisions. However, results of game theoretic models often depend on the choice of strategy variable. The results of this paper depend on two properties of the Cournot model: a binding VER reduces the profit of the restricted firm, and a new entry decreasesthe profit of the domestic incumbent. Thus, it is important to check how these properties change when firms compete by price and sell differentiated products. Harris (1985) and Krishna (1989) study the Bertrand competition model and show that if the level of a VER is close enough to the free trade a T must be sunk for the incumbents. Otherwise, the foreign incumbent can shut down its own plant, making the additional fixed cost zero. k can be negative if a new plant has advantage in factor or transportation costs. In this case, we do not have to use the licensing game to show that the profit of the domestic incumbent can fall after a VER. If a VER is severe enough to cause the foreign firm to shift its production to the new plant, its marginal cost falls even though it has to pay an additional fixed cost. The profit of the domestic firm will fall even in the absence of the commitment value of licensing. Thus, the point of this paper lies in showing that the profit of the domestic firm can fall even when k is zero or positive. 9This is not true when the licenser cannot use the two-part tariff licensing. Even when k is low, the restricted firm may not want to sell a license since the licensee’s entry can increase the group output level too much, lowering the joint profit below the no-licensing level. This can be prevented by choosing a technology with a higher k. The variability of k gives the licenser a better control over the group output level and increases the possibility of licensing.

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level of output, the profit of the restrained firm increases rather than decreases. Thus, a minor restriction does not cause licensing in this model. However, a severe enough restriction starts to decrease the foreign firm’s profit, (VERs are usually imposed at levels close to the current sales of restrained firms; however, VERs can become severely binding as the market grows over time). We can show that there is a threshold level of a VER under which licensing always occurs. The possibility of licensing decreases the protective effects of aVER just as in the Cournot model, but only when the restriction is severe. Is it still possible that the profit of the domestic incumbent falls after a VER? Suppose the licensee has to enter the market with a product identical to its licenser’s at a unit cost equal to or higher than its licenser’s Note that the entry of another firm producing the rival product does not shift down the profit function of the domestic incumbent as long as the price of the rival product does not go down. We can show that faced with a VER, the foreign incumbent chooses a royalty rate such that the price of its product increases relative to the free trade level. The profit of the domestic incumbent cannot fall in this case. However, we can consider another case where a technology transfer gives the licensee the ability to manufacture a product that is differentiated from the existing products. Now, there is a profit-stealing effect of a new entry per se. Introducing a new variety into the market shifts down the profit functions of incumbents as in the monopolistic competition models. In this case, we can construct an example in which the profit of the domestic incumbent falls with a VER. 6.5. Location of new entrants The licensees in the model may be from the domestic country or they can be firms from third countries that are not subject to VERs. If the licensees are domestic firms, the total output of domestic firms will increase even when the domestic incumbent’s output falls. If they come from a third country, the total output of domestic firms will fall after a VER when k is relatively small. 7. Policy implications and conclusion In many markets, technological difference works as a main entry barrier and these markets are surrounded by numerous potential entrants eager to acquire necessary technologies. Firms’ decisions on technology transfer respond sensitively to policy environment. A policy that does not recognize the existence of potential entrants and technological barriers can result in a totally unexpected outcome. Using a Cournot oligopoly model, this paper has shown that the imposi-

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tion of selective quotas like VERs can actually decrease the domestic profit, output, and employment. The result of this paper can be used both as a case for free trade and as a case for grim protectionism. However, if the complete blockade of new entries is impracticable, quantitative trade restrictions targeted at major foreign producers should be used cautiously. Even when the market share of new entrants can be frozen by VERs, if this is done with significant lags, new restrictions will have little effect on the outcome, or may call for another round of restrictions caused by technology transfers from new incumbents to second-tier developing countries.

Acknowledgments

I am grateful to Kala Krishna and two anonymous referees for their helpful comments on earlier versions of this paper. All remaining errors are mine.

Appendix In an equilibrium where both firms binding, xD
are selling licenses and q is strictly

Proof. The following conditions should be met in equilibrium. P(ZF + ZD) - c + PYZF + ZD)4 ’ 0

64.1)

p(zF+zD)-c-k-rTF+p’(zF+zD)yF=O

(A.21

p(z,+z,)-c+p’(z,+z,)x,=O

(A.3)

~(2, + zD) - c - k - rD + p’(zF + zD)y, = 0

(A.4)

dL,ldz,

= p(z, + zD) - c - k + p’(z, + zD)zF( 1 + dz,/dz,)

=0 0-w

dL,ldz,

=p(zF + zD) -c - k +p’(z, +kdx,/dz,=O.

+

zD)zD(l + dz,/dz,) (A4

From Eqs. (A.3) and (A.4), we can derive dz,/dz,, which measures the slope of the domestic group’s best response function at a given rD. From Eqs. (A.l) and (A.2), we can derive dz,/dz,, which is the slope of the foreign group’s best response function at a given rF. Plugging these values into (A.5) and (A.6), and noting that dx,/dz, < 0, we can get the following inequality,

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ZD/(2 +p’lp’y,)

<2,/(3

+pf’/p’zo)

.

This implies that zD < zF. Suppose zF CX’. Then, zD x0, contradicting that zD x0 and xD C x0. Then, no = (p(x” + x0) - c)x” a (p(x” + z,) - c)z, > (P(ZF + ZD) - c)zD ’ (P(ZF + zD ) - c)zD -ky,=(p(z,+z,)-c-k)z,+kx,=L,. 0

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