Supplier preferences and dumping: an analysis of Japanese corporate groups.

Kreinin, Mordechai E.

I. Introduction

While the nature and intensity of issues confronting the international economy change over time, the trade and investment tensions between the U.S. and Japan have continued unabated for many years. In part they find their origin in Japan's overall and bilateral trade surpluses, although these are generally recognized as macroeconomic phenomena. Apart from the trade imbalances, bilateral disputes arise also from the perceived inability of American exporters and investors to penetrate the Japanese market. There is empirical evidence indicating that the Japanese firms have a distinct preference to buy their needed machinery and other inputs from other Japanese firms [5; 6; 7]. It is the closed nature of Japan's market that triggered the bilateral negotiations known as Structural Impediments Initiative.

One reason for the difficulty faced by outsiders trying to sell in Japan is the way in which Japanese companies are organized. Keiretsu is a form of interlocking relationships among Japanese firms and industry groups [2] that allegedly enjoys advantages such as risk-sharing and stable inter-firm relations (which encourage efficient investment in relation-specific assets) and oligopolistic market power.(1) It has been suggested as a possible reason for low sales by non-Japanese firms to Japanese firms operating inside and outside of Japan. There is certainly a strong tendency for member companies of a Keiretsu to source from within their own corporate group.

This paper explores an economic rationale for this behavior by examining the implications of cross ownership and implicit contracts (long-term reciprocity), and shows that supplier preferences unambiguously increase the incidence of dumping. In this fashion the paper provides a link between two sets of stylized facts: supplier preferences by Japanese firms, and the numerous dumping complaints brought in the US. against large Japanese companies. Supplier preferences also increase the profits of firms which are directly involved in the arrangement, albeit at the expense of outside firms, and lead to lower prices for consumers.

In the next section we examine three models of supplier preferences that are based on cross ownership and implicit contracts. Alternative explanations of supplier preferences are provided in section III, while the effect of supplier preferences on dumping is analyzed in section IV and their implication for profits and consumer welfare are explored in section V. The final section summarizes our conclusions.

II. Models of Supplier Preferences

Consider three firms, A, B, and D, where A and B are Japanese firms which have cross ownership or an understanding of mutual reciprocity, while firm D is a non-Japanese firm not involved in any arrangement with A or B. From an analytical point of view, the national identity of these firms is not important. What is important is that A and B belong to some "alliance" either through cross ownership or the establishment of a long-term reciprocal relationship, but D is not part of that alliance.

In the following subsections we examine three models which generate rational supplier preferences.(2) The first model of unilateral cross ownership, which features a vertical production relationship between A and B, is a building block of the second model of bilateral cross ownership, which features a "symbiotic" or two-way production relationship between the firms. In contrast with some recent work which underscores the incentive of an integrated firm to set a high price for the export of an intermediate input to its foreign downstream competitor [10; 11; 12], our models attempt to explain why a downstream Japanese firm chooses to buy an intermediate input from an upstream Japanese firm when the former has the option of buying the same input from a non-Japanese firm at a lower price. The third model shows that A and B may give each other's products preferential treatment even without cross ownership. This result is consistent with the finding that cross ownership is only one of the factors which bind firms in a Keiretsu together [3].

This paper does not seek to explain the existence of Japanese corporate groups, but instead examines their implications for supplier preferences and dumping.

Supplier Preference under Unilateral Cross Ownership(3)

Let y be the quantity of A's sales, taken to be a function of its price p. To produce y, A requires a homogeneous input which is produced by both B and D. Let q be the price charged by B and [q.sup.*] be the price charged by D for this input and let the quantities of purchases from them be denoted by x and z, respectively. Throughout the rest of this paper, an asterisk signifies prices charged by the "outside" firm D. While it would be interesting to model explicitly the strategic interaction between B and D, for our purposes we simply assume that q and [q.sup.*] are oligopolistic prices which exceed the firms' respective marginal costs.

The cost of producing y besides this particular input is denoted by c(y; x + z). Suppose [Alpha](0 [less than] [Alpha]1) of B's shares are owned by A, then A's own profit plus its share of the part of B's profit which depends on A's input purchase decision are given by

[[Pi].sup.A] [equivalent to] py(p) - qx - [q.sup.*]z - c(y; x + z) + [Alpha][qx - g(x)], (1)

where g(x) is the additional costs to B of producing x, and [qx - g(x)] is the additional profits that B will make if A buys x of the input from B. The part of B's profit which is unrelated to A's purchase decision is left out as it will not affect the analysis.

Since B and D produce a homogeneous input, the choice between them depends only on the relative magnitude of [q.sup.*] and [q.sub.e] [equivalent to] [q - [Alpha](q - g[prime](x))], where [q.sub.e] is the "effective" price of the input supplied by B. More specifically, A buys only from B if the effective price of x, [q.sub.e], is lower than that of z, [q.sup.*]. In other words, if the excess price charged by B is smaller than the extra profit per unit of B's output that A gets back from B through cross ownership, i.e.,

q - [q.sup.*] [less than] [Alpha](q - g[prime] (x)), (2)

where g[prime](x) is the derivative of g evaluated at the optimal x.

Thus, if q [greater than] [q.sup.*] and condition (2) holds, then A prefers to buy from B despite the fact that B charges a higher price for the same input than D.

Supplier Preference under Bilateral Cross Ownership(4)

Next, consider a situation in which A's output y is used by B as an input and B's output x is used by A as an input, a condition that can arise if both x and y are intermediate goods. Even if y is a final good such as electric fans and furniture, B may need it in its company as part of its production facilities. Such inter-firm demand could be common if A and B are diversified, multi-product firms. In what follows, it is assumed that A and B have bilateral cross ownership. Specifically, [Alpha] of B is owned by A and [Gamma] of A is owned by B, where both [Alpha] and [Gamma] are positive but smaller than unity. Firm D is a supplier of both x and y, but has no cross ownership with either A or B.

To address this slightly more complicated situation, additional notation is needed. As in the above section, let p be the price of A's output. In addition, let [p.sup.*] be the price of the same good charged by D. The price variables q and [q.sup.*] are as defined before. Let y be A's sales to B, [y.sub.0] be its sales to "final" customers, x be B's sales to A, and [x.sub.0] be B's sales to "final" customers. The total costs incurred by A less the cost of x and z are denoted by c([y.sub.0] + y; x + z) and those incurred by B less the costs of y and w are denoted by g([x.sub.0] + x, y + w), where w is the quantity of the good (same as that produced by A) that B buys from D at [p.sup.*].

As above, A's profit plus its share of B's profit is given by

[[Pi].sup.A] = P[y(p) + [y.sub.0](p)] - c([y.sub.0] + y; x + z) - qx - [q.sup.*]z

+ [Alpha][q(x + [x.sub.0]) - g(x + [x.sub.0]; y + w) - py - [p.sup.*]w]. (3)

Similarly, B's profit plus its share of A's profit is given by

[[Pi].sup.B] = q[x(q) + [x.sub.0](q)] - g(x + [x.sub.0]; y + w) - py - [p.sup.*]w

+ [Gamma][p(y + [y.sub.0]) - c(y + [y.sub.0]; x + z) - qx - [q.sup.*]z]. (4)

If the transactions between A and B are governed by an understanding of mutual reciprocity, then x and y are inter-dependent in that A's purchase of x from B is contingent upon B's purchase of y from A and vice versa. In the next subsection we shall show that this kind of implicit contract can lead to bilateral supplier preferences without any bilateral cross ownership. In this subsection, however, to focus on bilateral cross ownership as a cause of bilateral supplier preferences, we assume away any implicit contract between A and B. Under this circumstance, A regards its sales to B (namely, y) as independent of its choice between x and z and B regards its sales to A (namely, x) as independent of its choice between w and y. Consequently, the argument used earlier in this section indicates that A will buy its input only from B if the excess price charged by B is smaller than the extra profit per unit of B's output that A gets back from B through cross ownership, i.e.,

q - [q.sup.*] [less than] [Alpha](q - g[prime](x + [x.sub.0])), (5)

where g[prime] is evaluated at the optimal level of x and [x.sub.0].

Similarly, B will buy its input only from A if the excess price charged by A is smaller than the extra profit per unit of A's output that B gets back from A through cross ownership, i.e.,

p - [p.sup.*] [less than] [Gamma](p - c[prime](y + [y.sub.0])). (6)

If there is no cross ownership between A and B, then the right-hand side of both (5) and (6) is equal to zero, indicating that A will not buy from B if q [greater than] [q.sup.*] and B will not buy from A if p [greater than] [p.sup.*]. To see the following result, it is helpful to assume that both g[prime] and c[prime] are constant. However, it is not a necessary assumption at all.

PROPOSITION 1. Suppose g[prime] [less than] [q.sup.*] and c[prime] [less than] [p.sup.*]. Then A and B prefer to buy from one another even if p [greater than] [p.sup.*] and q [greater than] [q.sup.*] as long as

[Alpha] [greater than] (q - [q.sup.*])/(q - g[prime]) and [Gamma] [greater than] (p - [p.sup.*])/(p - c[prime]).

Implicit Contract or Reciprocity

Firms A and B may buy from each other rather than from D even in the absence of cross ownership if they mutually agree on an implicit contract arrangement of long-term reciprocity. More specifically, they would purchase from each other if A's (B's) loss due to its buying x from B (y from A) rather than from D is more than offset by the extra profit it would make from its sale of y to B (x to A) under an implicit contract arrangement.

As a bench mark, suppose that A and B are totally independent of one another. Then they would purchase inputs from D if D's prices are more attractive. Formally, the situation is described by the following two equations.

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

where "argmax" stands for "the argument which maximizes," C stands for A's total cost function, G stands for B's total cost function, and the prices of factors other than those under consideration are suppressed. Clearly, the same good can be sold at different prices only under imperfect competition and market segmentation.

Assuming that both [y.sub.0](P) and [x.sub.0](q) are downward sloping, we obtain [Mathematical Expression Omitted] and [Mathematical Expression Omitted], where the marginal costs C[prime] and G[prime] are for simplicity assumed to be constant. If A and B can simultaneously shift their purchases away from D and to one another while paying the same prices [q.sup.*] and [p.sup.*], respectively, then their profits are unambiguously higher because their outlays on inputs remain unchanged but now they both make additional profits from sales of outputs to each other.

That is to say, both A and B can increase their profits if they give one another lower prices than they charge other customers, i.e., [Mathematical Expression Omitted] and [Mathematical Expression Omitted]. A question rentals whether a mutually beneficial agreement of reciprocal purchases can be made without price discrimination between the firms (A and B) and their other customers. In the remainder of this section, we give an example in which A and B benefit from an implicit agreement of mutual purchases in the absence of price discrimination.

Let A's production function be given by y = A[x.sup.[Lambda]][l.sup.(1-[Lambda])], and B's production function be given by x = A[y.sup.[Lambda]][l.sup.(1-[Lambda])]. The common factor l is combined with x to produce y, and combined with y to produce x. To simplify the expressions, let us assume that the price of l is equal to unity and that A[[Lambda].sup.[Lambda]][(1 - [Lambda]).sup.(1-[Lambda])] = 1. Then C(y;q) = [q.sup.[Lambda]] [multiplied by] y, C(y;[q.sup.*]) = [q.sup.*[Lambda]] [multiplied by] y, G(x;p) = [p.sup.[Lambda]] [multiplied by] x, and G(x;[p.sup.*]) = [p.sup.*[Lambda]] [multiplied by] x. As a result, both the average cost and marginal cost of x are equal to [p.sup.[Lambda]], those of z are equal to [p.sup.*[Lambda]], those of y are equal to [q.sup.[Lambda]]; and those of w are equal to [p.sup.*[Lambda]]. If x and y are supplied competitively, then p = [p.sup.*] = 1 and q = [q.sup.*] = 1. Imperfect competition implies that q, [q.sup.*], p, and [p.sup.*] all exceed unity.

Suppose the "final" demand for x and y, faced by B and A, respectively, are linear and symmetric.

q = [Beta] - [Delta][x.sub.0], (9a)

and

p = [Beta] - [Delta][y.sub.0], (9b)

where [Beta] and [Delta] are positive constants. The profit-maximizing prices are

[Mathematical Expression Omitted]

and

[Mathematical Expression Omitted]

The firms' maximum profits are [[Pi].sup.A] = [([Beta] - C[prime]).sup.2]/4[Delta] and [[Pi].sup.B] = [([Beta] - G[prime]).sup.2]/4[Delta]. Since G[prime] = [p.sup.[Lambda]] or [p.sup.*[Lambda]], depending on the choice of supplier, and C[prime] = [q.sup.[Lambda]] or [q.sup.*[Lambda]], also depending on the choice of supplier, A and B's profits are clearly decreasing functions of the prices they pay for their respective intermediate inputs. Suppose [q.sup.*] = [p.sup.*] = r, then we have

[Mathematical Expression Omitted]

If [Beta] is sufficiently large that [Mathematical Expression Omitted], then without any agreement of reciprocity A and B will not buy from each other.

Now consider a mutual agreement between A and B to buy all their intermediate inputs from each other. The effective prices of x and y, respectively, under the agreement are given by

[Mathematical Expression Omitted]

and

[Mathematical Expression Omitted]

where x([q.sub.e]) and y([p.sub.e]) signify the dependence of input demand on the effective prices. Equation (12a) ((12b), respectively) indicates that the effective price of x to A (y to B) when it buys the input from B (A) under a reciprocity agreement is equal to the posted price it actually pays to B (A) less the profit it makes from the sale of y (x) to B (A) divided by the volume of x (y). Given the symmetric structure of the problem, it is not difficult to check that x = y, and [q.sub.e] = [p.sub.e] = 1 [less than] r.(5) Replacing r in (11) by [q.sub.e] = [p.sub.e], we obtain the firms' optimal prices, [Mathematical Expression Omitted]. A comparison of prices yields the following proposition.

PROPOSITION 2. If the final de demand for A and B's outputs is sufficiently large in that ([Beta] + 1)/2 [greater than] r, then the firms buy their intermediate inputs from one another at prices above those offered by D.

The assumption of complete symmetry used to derive Proposition 2 is admittedly restrictive. However, the purpose of the above example is to illustrate the possibility that there are conditions under which A and B buy their intermediate inputs from one another at prices above those offered by D.

It is well known that if A and B are two divisions of an integrated firm, then the optimal price of x charged to Division A is x's marginal cost and that of y charged to Division B is y's marginal cost. In essence, when A and B are independent firms, the implicit contract allows them to move closer to the more efficient outcome of an integrated firm without blatant price discrimination against other users of their outputs or without incurring the managerial costs associated with an integrated firm. In the presence of cross ownership or an implicit agreement of reciprocity, the effective price of x to A, [q.sub.e], is below [q.sup.*] despite the fact that q [greater than] [q.sup.*], and the effective price of y to B, [p.sub.e], is below [p.sup.*] despite the fact that p [greater than] [p.sup.*]. An implicit agreement of mutual purchases can also contribute to lower effective costs through stable demand and production, a linkage which is not captured in the above analysis.(6)

III. Alternative Explanations of Supplier Preferences

While this paper provides a possible rational explanation of Keiretsu behavior and supplier preferences, there are other explanations that may be unique to Japan. In the survey of Australian subsidiaries reported by Kreinin [5], respondents suggested such reasons as "we are certain of the high quality of Japanese machines, so why re-invent the wheel and conduct a global search?" and "we are bound by custom to source from our traditional suppliers in Japan." In other words, Japanese customs and tradition dictate buying from suppliers with whom the firm has a long standing relationship, even if the good can be obtained elsewhere on better terms. And competitive bids require much work and deviation from this tradition. One Australian respondent even suggested that the "Japanese take a nationalist view of buying," and hence prefer to source in Japan. Such motives are usually absent in Western firms, even where inter-locking directorships exist.

IV. Supplier Preference and Dumping

We next examine the effect of supplier preference on the incidence of "dumping". Applying Shephard's lemma, one can show that a decrease in the price of an input decreases marginal cost if the input is normal.(7) Under the assumption that input x is normal, the inequality [q.sub.e] [less than] [q.sup.*] implies that

C[prime](y;[q.sub.e]) [less than] C[prime](y;[q.sup.*]). (13)

Using (13), Figure 1 demonstrates that supplier preferences increase the incidence of dumping. It is seen that A would sell only in its domestic market if it buys its input from D since C[prime](y;[q.sup.*]) is too high to export profitably. But it would "dump" - in the sense of charging a price [p.sup.f] in the export market below that charged in the domestic market - if it can buy its input from B at a lower effective price due to cross ownership or implicit contracts.(8) Given C[prime](y;[q.sub.e]), A's total output is [Mathematical Expression Omitted], [Mathematical Expression Omitted] is supplied to the domestic market at [Mathematical Expression Omitted], and [Mathematical Expression Omitted] is supplied to the foreign market at an exogenously given price [p.sub.f]. As in other cases of price discrimination, the total output and its division between the two markets are optimal. At Z and V

[Mathematical Expression Omitted]

When measured in terms of the nominal costs of inputs, A's total costs are higher under q than under [q.sup.*]. To the extent that [Mathematical Expression Omitted], we also have dumping in the sense that marginal costs as measured by nominal costs on the books exceed the price charged in the export market.

V. Supplier Preferences, Profits, and Welfare

In all three models of supplier preferences analyzed in section II, A and B's total profits (i.e., own profit plus share of the other firm's profit) are higher with supplier preferences than without.

But this is at the expense of profits earned by the outside firm, D. in the case where preferences are not based on cross-ownership, but on an implicit contract, each firm's own profit must be higher. In the case of unilateral cross ownership, however, A's profit from its own operation must be lower with supplier preferences for two reasons. First, A pays a higher price for x(q [greater than] [q.sup.*]). Second, it does not optimize with respect to q. Given that its output supply and input demand decisions are guided by [q.sub.e], which is smaller than q, it "over-supplies" and "fails" to minimize its nominal costs.

Supplier preferences not only increase the profits of firms which are directly involved in the transactions, but also benefit their final consumers in the form of lower prices. The situation is similar to vertical integration which, by eliminating successive monopoly or oligopoly, usually benefits final consumers as well as increases the upstream and downstream firms' total profits [4]. Indeed, Keiretsu is a loose form of integration, vertical or "symbiotic."

VI. Conclusions

This paper explores the causes and consequences of the preferences of Japanese companies to source from sister companies within the same industrial group. To some extent the analysis applies to certain conglomerate corporations where similar conditions obtain. We have examined models of cross ownership and implicit contract, providing an economic rationale for this behavior. In turn such preferences are shown to lead to a higher incidence of dumping. This happens because the preferences reduce the "true" or "effective" marginal cost of the output to a level where it pays to export part of the output at world market prices which are below the oligopoly prices charged in the home market. Without supplier preferences the marginal cost curve is so high that the entire output is sold at home. In this fashion the paper provides a link between two sets of stylized facts: supplier preferences within a Japanese Keiretsu, and the numerous dumping complaints brought in the U.S. against large Japanese companies.(9) Furthermore, supplier preferences increase the profits of the participating firms but lower the profits of outside firms as well as prices charged the consumers. In essence, supplier preferences are an arrangement which is a substitute for agglomeration and vertical integration.(10)

Although the result that supplier preferences lead to dumping is not necessarily caused by deliberate government policy, it does have the effect of increasing the global market share of Japanese firms and with it their share in global profits. To the extent that the industrial arrangements discussed here are encouraged by "administrative guidance," this can certainly be labelled "strategic trade policy." But even in the absence of governmental encouragement, Japan's trading partners need to consider whether the outcome described here should be countered by their own strategic trade policy.

1. See Gerlach [3] for a discussion of some of these advantages.

2. As described in Kreinin [5, 533-34], an advisor sent by the parent company of a Japanese foreign subsidiary would typically try to influence purchase decisions of the subsidiary. This sophisticated organizational structure suggests that the behavior of Japanese firms in pursuing supplier preferences are not irrational.

3. Fung [2] developed a somewhat different model to analyze the implications of cross ownership for international trade. In his model, there are two downstream firms, one Japanese and one American, which engage in Cournot competition in a final good market. A Japanese upstream firm is an exclusive supplier of an intermediate input to the Japanese downstream firm. In setting its price, the upstream firm takes into account the fact that a lower price of the intermediate input will increase the Japanese downstream firm's market shares and profits, and in turn its own profits through cross shareholding. In contrast, our focus is on the choice of input suppliers. Thus, in this section a Japanese downstream firm partially owns a Japanese upstream firm and takes into account the effect of its purchase decision on that particular upstream firm's profits. Nevertheless, both approaches reach the conclusion that cross ownership has the effect of increasing sales by Japanese firms.

4. For statistics of cross ownership, see Fung [2, Table 5.4].

5. The other solution [q.sub.e] = [p.sub.e] = 0 is ignored because it entails losses by both firms.

6. For a theoretical analysis of Keiretsu as means of risk-sharing, see Aoki [1]; for an empirical study of the effect of Keiretsu on stable profits, see Nakatani [9].

7. [Delta]C[prime]/[Delta]q = [Delta]([Delta]C/[Delta]y)/[Delta]q = [Delta]([Delta]C/[Delta]q)/[Delta]y = [Delta]x/[Delta]y, where the last equality follows from Shepard's lemma.

8. Suppose the export market is not characterized by perfect competition as assumed above, but instead is characterized by some form of oligopolistic (such as Bertrand or Cournot) competition. A reduction in A's effective marginal cost of production due to cross ownership or implicit contracts would similarly increase the chance that A sells to the export market.

9. Even if dumping cases were used by U.S. firms mainly to harass their Japanese competitors, it is likely that the target Japanese firms have lower costs and exert greater pressure on U.S. firms.

10. Our interpretation of supplier preference and corporate alliance is consistent with the view of some experts on corporate strategy [3; 8].

References

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