Chaebol and Catastrophe
Chaebol and Catastrophe: A New View of the Korean Business Groups and Their Role in the Financial Crisis*
Robert C. Feenstra Abstract Department of Economics We present a model of industrial organization that has multiple One Shields Avenue University of California stable equilibria and argue that the high-concentration equilibrium Davis, CA 95616 describes Korea’s economy and the low-concentration equilib- [email protected] rium describes Taiwan’s economy. Past industrial policy of the Gary G. Hamilton state may have put Korea’s economy in the high-concentration Department of Sociology equilibrium, but discontinuation of the policy did not cause the in- Box 353340 University of Washington dustrial organization to change because this is an economically vi- Seattle, WA 98195 able equilibrium. [email protected]
Eun Mie Lim The high-concentration equilibrium produces a narrower range of Department of Sociology final goods than the low-concentration equilibrium, which explains Box 353340 University of Washington why the 1996 collapse in semiconductor prices caused the less di- Seattle, WA 98195 versified Korean economy to contract more than the more diver- [email protected] sified Taiwanese economy. More importantly, this collapse in de- mand caused Korea’s economy to move to a new equilibrium that has a smaller number of business groups, as evidenced by the col- lapse of the second-tier chaebol and their absorption into the first-tier chaebol. This wave of bankruptcies, combined with the fi- nancially precarious state of the merchant banks, created an inves- tor panic that precipitated the crisis, which began with the 17 No- vember 1997 devaluation of the won. This is why economic fundamentals could explain the chaebol bankruptcies before that date and not those after that date. The logic of our model sug- gests that public policy should focus on reducing the vertical link- ages within business groups and not on reducing their horizontal linkages as the current “Big Deal” program of the government is doing.
* This paper was prepared for the Asian Economic Panel confer- ence, Seoul, Korea, 25–26 October 2001. It draws upon the forth- coming book Emergent Economics, Divergent Paths: Business Groups and Economic Organization in South Korea and Taiwan, by Robert Feenstra and Gary Hamilton, Cambridge University Press, as well as the dissertation research of Eun Mie Lim.
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1. Introduction
In the aftermath of the Asian ªnancial crisis, many economists in the United States have criticized the actions taken by the IMF, and in particular, its insistence that countries in crisis undertake contractionary monetary and ªscal policies as a condi- tion for receiving loans. Scholars such as Jeffrey Sachs (1998), Martin Feldstein (1998), and Joseph Stiglitz (2000) argue that imposition of this condition turned an initial liquidity crisis into a full-blown banking and ªnancial crisis.
We have no disagreement with these criticisms of the IMF and with a re-thinking of its appropriate role; focusing on the IMF, however, distracts attention from the ques- tion of what happened in South Korea and other countries of Asia, and why. The IMF did not enter Korea until December 1997, and by that time the ªnancial crisis was fully under way. To understand the origins of the crisis we need to go at least some months earlier, before the exchange rate devaluation of 17 November 1997, and even before the exchange rate crises elsewhere in Asia. Let us start at least at the beginning of 1997. On 23 January 1997, the Hanbo Steel group in Korea declared bankruptcy. It was unprecedented that any chaebol in Korea would be permitted to go bankrupt, and this was followed in the subsequent months by the bankruptcies of well-known groups such as Sammi, Jinro, Hanshin, and then Kia in July, which was the eighth largest chaebol. Two years later, Daewoo became the ªrst instance of a top ªve chaebol that was permitted to go bankrupt.
Including Daewoo, some 25 chaebol went bankrupt during 1997 and 1998, and fully 40 percent, or 10 out of 25, went bankrupt before the exchange rate crisis of 17 No- vember. Why did so many chaebol go bankrupt even before the exchange rate crisis, and what role did this play in the ªnancial crisis? It seems to us that these are the central questions that should be addressed and that need to be answered before Ko- rea pursues any reforms. It is impossible to answer these questions, however, with- out ªrst having a conceptual framework for thinking about the chaebol and their place in the economy.
Perhaps the most common framework for thinking about business groups, or the in- tegration of ªrms more generally, is the transactions cost approach. Initiated by Ron- ald Coase and greatly extended by Oliver Williamson (1975, 1985), transactions cost research was designed to explain why some industries are vertically integrated and others are not. The transactions cost approach typically relies on different industry characteristics (such as asset speciªcity of investments) to explain the extent of verti- cal integration across industries. When these ideas are applied to the business groups in Asia, as some authors have done (e.g., Chang and Choi 1988; Levy 1991),
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problems in the approach become apparent. In the ªrst place, the same industry is often organized quite differently across different countries (such as Korea and Tai- wan), so transactions costs are clearly not speciªc to industries. Furthermore, some of the other factors that might inºuence the level of transactions costs, such as the reliance or nonreliance on formal contracts, are actually quite similar across Korea and Taiwan. So we are hard-pressed to identify the contribution of transactions costs to the differing structure of business groups across these countries.
Government policies are another explanation for business groups, and the growth of the chaebol in South Korea is often attributed to the cheap credit that they received during the 1960s and 1970s. One drawback to this explanation, however, is that even when such policies are removed, the structure of business groups can remain intact for a considerable time, as happened in Korea. This is consistent with a policy-based explanation only if there is path dependence at work, that is, if past policies con- tinue to affect current structure. Path dependence, in turn, suggests the possibility of multiple equilibria in the structure of business groups, and this will be our focus in this paper.
We shall rely on an alternative reason for the formation of groups, suggested by Ghemawat and Khanna (1998) and Khanna (2001), and that is the market power ex- planation: by horizontally integrating, groups achieve the beneªts of setting prices across multiple markets (Bernheim and Whinston 1990), and by vertically integrat- ing, upstream producers can offer preferential prices to those downstream, thereby increasing their joint proªts [as originally noted by Spengler (1950)]. We shall exam- ine the incentives for integration in a monopolistic competition model with multiple upstream and downstream producers. A business group is deªned as a set of produ- cers that jointly maximize proªts.
Allowing for free entry of business groups and unafªliated ªrms, we demonstrate the presence of multiple equilibria in the economy that have varying degrees of verti- cal and horizontal integration. Thus, at given parameter values, we often ªnd a sta- ble high-concentration equilibrium, with a small number of strongly integrated busi- ness groups, and also a stable low-concentration equilibrium, with a larger number of less-integrated groups. The difference between these is that a small number of strongly integrated groups charge higher prices for external sales of the intermediate inputs, thereby inhibiting the entry of other business groups.
The ªnding of multiple equilibria offers a new perspective on the business groups in Korea. The chaebol should not be viewed as responses to transactions costs, nor as simply the result of industrial policies in Korea. Instead, they should be thought of
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as one of a small number of organizational forms consistent with proªt maximiza- tion and free entry. That other countries have different group structures reºects the prevailing historical conditions that have shaped the direction of each economy. The policy choices in Korea can be thought of as establishing initial conditions of the economy, but the fact that the chaebol have grown as large as they have reºects the fact that these groups are a stable form of economic organization. Even signiªcant policy changes, such as the end of industrial policies favoring the chaebol, should not be expected to break up this type of organization.
What about the effects of large shocks to the Korean economy, such as the Asian ªnancial crisis? As discussed in section 5, Korea experienced an abrupt fall in the growth and price of exports at the end of 1996. We view this as the proximate cause of the string of bankruptcies in 1997. In mathematical language, this is an example of a “catastrophe,” whereby a continuous change in some underlying variable (ex- ports) leads to a discontinuous change in a resulting variable (Woodcock and Davis 1978). Our hypothesis in this paper is that this notion of catastrophe may explain the string of bankruptcies in Korea during 1997, even before the exchange rate devalua- tion and ªnancial crisis.
We make the case for our hypothesis in three steps. First, we argue that the bank- ruptcies before 17 November are predicted well by the excessively high debt/equity ratios of the groups. In contrast, the bankruptcies after 17 November can be ex- plained not by the overall debt/equity ratios of these groups, but rather, by their ex- cessively high levels of short-term debt. In other words, the bankruptcies before 17 November show every indication that the capital market was working as it should have been, whereas the bankruptcies after 17 November show the character- istics of a ªnancial panic, in which banks are not willing to roll over short-term loans regardless of the performance of their debtors. Second, we demonstrate that a continuous change in some underlying variable, such as export sales, can lead to a discontinuous change in the number of groups. This is an example of a mathemati- cal catastrophe, which we believe provides an apt description for the unprecedented string of bankruptcies among the chaebol during the ªrst part of 1997. Third, we ex- plain how the interaction between the bankruptcies of chaebol and the precarious structure of the ªnancial system created the ªnancial crisis during the last quarter of 1997. This explanation relies on the details of ªnancial sector reform in Korea, which expanded the role of the merchant banks in ªnancing the chaebol. This ªnancing took the form of purchasing and distributing commercial paper for the chaebol and also borrowing abroad and re-lending to the chaebol. Both these activities exposed the merchant banks to considerable risk because of a mismatch between short-term and foreign-currency liabilities (borrowings) and long-term domestic currency as-
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sets (loans to the chaebol). This risk exposure, combined with the bankruptcies of the chaebol, proved to be more than the ªnancial system could withstand and led to a banking panic that precipitated the exchange rate crisis.
In summary, our application of the concept of a mathematical catastrophe offers a new and intriguing explanation for the events in Korea during early 1997. But argu- ing that the chaebol can experience discontinuous changes in organization, or a ca- tastrophe, is not the same as saying they can or should be eliminated. The Korean government is now attempting to dismantle the chaebol in what is known as the Big Deal. We will argue that the policies being undertaken as part of the Big Deal are ill conceived and need to be rethought to avoid harming the economy.
2. A model of business groups
Figure 1 shows an economy divided into two sectors: an upstream sector producing intermediate inputs from labor, and a downstream sector using these intermediate inputs to produce a ªnal good that is sold to consumers. The intermediate inputs are not traded internationally, but the ªnal good is. Suppose that both the sectors are characterized by product differentiation, so that each ªrm charges a price that is above its marginal cost of production. We allow free entry of ªrms in both the up- stream and downstream sectors to drive proªts to zero. We also allow the free entry of business groups.
In contrast to conventional treatments of monopolistic competition, we will also al- low groups to produce multiple varieties of inputs and outputs.1 In particular, there will be an incentive to produce both upstream and downstream products to take ad- vantage of the efªciencies from marginal cost pricing of the intermediate inputs. When the groups sell inputs internally at marginal cost, however, the selling ªrms will not be covering their ªxed costs of research and development. Therefore, it will be necessary for other ªrms in the group to make a ªnancial transfer to cover these losses. Naturally, this sets up a principal-agent problem, whereby the transfers made to a subsidiary ªrm are not necessarily efªcient, because of incomplete information. We will model this as a ªxed cost for each business group, which we will call “gover- nance costs.” Modeling these costs in any detail is well beyond the scope of our model. So we will simply assume that they take the form of a ªxed cost associated with the running of a business group, as well as additional costs associated with each intermediate and ªnal product produced by the group (over and above the
1 The equilibrium concept we use is most similar to the “vertical equilibrium” investigated by Perry (1989, 229–35).
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Figure 1. Model of business groups
research and development costs that an unafªliated ªrm would incur for such products).
We will consider only symmetric equilibria, in which each business group produces
the same number Mb of intermediate inputs and Nb of ªnal goods. The proªts of each business group are denoted by b, and the total number of groups is G. In addition, we will allow for unafªliated (or competitive) upstream ªrms, producing Mc inputs and earning proªts xc, together with a number of unafªliated down- stream ªrms, producing Nc ªnal goods and earning proªts yc. In the free-entry equilibrium, all these proªts must be nonpositive. We assume that there is a single factor of production called labor and choose the wage rate as the numeraire.
We assume that each business group is able to choose the number and price of in- puts and outputs, taking as given the simultaneous decisions of other groups and unafªliated ªrms. Even though decisions are made simultaneously, business groups will recognize that if they sell intermediate inputs to other groups, thereby lowering those groups’ costs, this will be reºected in the prices charged by those groups for their ªnal goods. In other words, each group takes the markups of other groups rather than the prices of the ªnal goods as given in the Nash equilibrium. So the strategies chosen by each business consist of the markup of the ªnal-goods price µ over marginal cost (denoted by b), the price of intermediates, and the number of in- puts and output varieties produced. These variables are chosen to maximize the joint proªts of a group:
max µ Π=µφ − − + ~ −− −α {,pMbbbb , , N } bNy b[( b b1 ) b kM yb ] b[xb()],pkbxb1 (1)
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where Nb is the number and yb is the output of each ªnal good, produced with mar- µ ginal cost b and ªxed costs kyb and sold at price qb b b;Mb is the number of inter- ~ mediate inputs, produced with marginal cost of unity and ªxed cost of kxb;xb is the 2 quantity sold of each intermediate input outside the group, at price pb; and is the level of ªxed governance costs associated with the running of a business group.
Note that in addition to the external sale of inputs at price pb, the group will also sell its inputs internally at a marginal cost of unity, and we will denote the internal
quantity sold by xb. It is quite possible that the proªts earned by the upstream ªrms, which are represented by the second bracketed term on the right-hand side of (1), are negative, because these inputs are sold internally at marginal cost. Thus, we would expect some transfer from the downstream to the upstream ªrms to cover these losses. Our key simplifying assumption on the governance costs is that they don’t depend on the amount of the transfer, though they can depend on the numbers of upstream and downstream ªrms in a group. It is this simplifying assumption that allows us to ignore the transfer in the speciªcation of (1).
The marginal cost of producing each output variety is given by the CES function
− β 1 βσσ−− φ =+−+11 1− σ bbwM[() G1 Mp bbcc Mp ], (2)
where w is the wage rate, and labor is a proportion of marginal costs; Mb inputs
are purchased internally at the price of unity; by symmetry, Mb inputs are also pur- chased from each of (G 1) other business groups at the price of pb; and Mc inputs are purchased from unafªliated upstream ªrms at the price of pc. We will set w 1 by choice of numeraire and suppress it in all that follows. The elasticity of substitu- tion between inputs, denoted by σ, is assumed to exceed unity. With a large number of inputs, the elasticity of substitution σ also equals the price elasticity of demand for any input, so we shall use these terms interchangeably.
Turning to the unafªliated ªrms, the upstream ªrms maximize proªts:
max Π= −− pxcccc xp(),1 k xc (3)
where xc is the output of each intermediate input, sold at price pc and produced with
marginal cost of unityand ªxed costskxc. The elasticity of demand facing these ªrms
2 It makes no difference whether we specify (1) in terms of the optimal price of inputs or their optimal markup. This does matter for ªnal goods, however: because the strategies consist of markups for ªnal goods, business groups then realize that if they expand Mb or lower pb, thereby reducing b for other groups, this will be reºected in a lower ªnal-goods price qb b b from those other groups.
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is σ, so that with marginal costs of unity, the markup of the optimal price over mar - ginal costs equals
p σ c = . (4) 11 σ −
Of course, this gives a positive solution for the price if and only if σ 1, as we as- sume. The unafªliated downstream ªrms maximize proªts given by
max Π= −φ − qyccccycc yq(), k (5)
where yc is the output of each ªnal good, sold at price qc and produced with mar- φ ginal cost c and ªxed costs kyc . The marginal cost of producing each output variety is
− β 1 −−σσ φ =+11 1− σ cbbcc[],GM p M p (6)
where Mb inputs are purchased from G other business groups at the price of pb, and
Mc inputs are purchased from unafªliated upstream ªrms at the price of pc. Since w 1, it is apparent that the marginal costs for a business group in (2) are less than those for an unafªliated ªrm in (6), because the business groups are able to purchase their own inputs at the cost of unity.
On the demand side, we will assume a constant elasticity of substitution between output varieties, denoted by . Then for each unafªliated downstream ªrm, the markup of the optimal price over marginal costs equals
q η c = . (7) φ η − c 1
In general, the business groups will charge markups for inputs and outputs that are higher than those in (6) and (7). This occurs for two reasons: (1) each business group
sells a range of Mb inputs and Nb outputs (rather than just one variety of each), so there will be an incentive to charge higher prices because of multimarket sales; and
(2) the prices for inputs sold externally (pb) will be increased because this creates higher costs for rival business groups and therefore less downstream competition. The solution for the optimal markups for business groups is obtained by solving the control problem (1).3
Before ªnding this solution, however, it is useful to consider the possible conªg- urations of groups and unafªliated ªrms that can arise in a zero-proªt equilibrium.
3 The equilibria of the model are formally solved in Feenstra, Huang, and Hamilton (2002).
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Which conªgurations are possible will depend on the level of governance costs within the groups. If these costs are zero, then a group will be more efªcient than a like number of unafªliated upstream and downstream ªrms (because of its internal marginal cost pricing of inputs). Then in a zero-proªt equilibrium for groups, the proªts of unafªliated ªrms will be negative, and they will never enter. Conversely, if the governance costs are large, then both upstream and downstream unafªliated ªrms, together with groups, may very well occur in a zero-proªt equilibrium. This is probably realistic, but having all types of ªrms makes the computation of equilibria intractable. We will take a middle-of-the-road approach and assume that the gover- nance costs are large enough to allow the possibility that either upstream or down- stream unafªliated ªrms may enter but small enough to prevent entry of both types.
With these assumptions, the equilibria will be one of three possible conªgurations, shown in ªgure 2:
1. V-groups. The business groups prevent the entry of unafªliated producers in both the upstream and downstream sectors (Mc Nc 0) and are therefore strongly vertically integrated. 2. D-groups. Business groups are the only ªrms in the downstream sector (Nc 0) and are vertically integrated upstream and purchase inputs from some unafªliated upstream ªrms (Mc 0). 3. U-groups. Business groups are the only ªrms in the upstream sector (Mc 0) and are vertically integrated downstream but also compete with some unafªliated downstream ªrms (Nc 0).
Our terminology does not make any presumption about the horizontal integration of the various types of groups: this is something that we will have to determine in equilibrium. In fact, it will turn out that the largest V-groups are also spread hori- zontally over a wide range of products, much like the largest chaebol in Korea.
In order to observe a U-group or D-group equilibrium, we further need to rule out the possibility that all unafªliated ªrms would want to merge with a business group. We do this by supposing that unafªliated ªrms have lower ªxed costs associ- ated with product development, which are automatically increased if that ªrm is Ն part of a group: that is, we will assume that kyb kyc and kxb kxc, with these in- equalities holding as strict when needed to make mergers unproªtable. These extra ªxed costs should be interpreted as governance costs that are additional to the ªxed costs of . The precise speciªcation of ªxed costs to achieve this will depend on the equilibrium. This ad hoc assumption is a compromise between tractability (prevent- ing all ªrms from entering) and interest (having the possibility that some unafªliated ªrms will enter and not merge). This still leaves the possibility of merg-
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Figure 2. Types of business groups
ers across groups. To rule out this activity we appeal to some extra costs associated with governing a group of increasing size, which lie outside the notation of our model.
3. Computing equilibria of the model
3.1 When will groups sell inputs to each other? For convenience, we will focus initially on the V-groups. A key choice variable of the business groups is the price that groups charge for the intermediate inputs sold to other groups. This reºects the competition that groups perceive that they face with each other. If group A believes that selling an input to group B confers a substantial ad- vantage to that group, in the sense that group B can produce the downstream good at lower cost and therefore compete more aggressively downstream, then group A
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could decide not to sell this input even at a very high price. We are interested in knowing when this type of outcome will occur.
We ªrst review some well-known results. An unafªliated ªrm will ªnd it most proªtable to set the price for an input it is selling in inverse relation to its elasticity of demand: this is the familiar Lerner pricing rule in (4). In our model the elasticity of demand and elasticity of substitution for inputs are both measured by σ. When the elasticity approaches unity, then the ªrm does not lose any sales revenue at all from increasing its price, so it will set its price arbitrarily high. Since inªnite prices make no sense, this leads to the well-known result that the elasticity of demand for any ªrm with some ability to set its price (i.e., some market power) must be greater than unity.
How does this Lerner pricing rule change when a group is selling the intermediate input to another group? We expect that the competition in the downstream market will lead the group to set a price higher than would an unafªliated ªrm, because not only does the group want to maximize its proªts from selling the intermediate in- put, it also does not want to give a cost advantage to the purchasing group, since these groups compete in the downstream market. How intense is this competition? That clearly depends on how many groups are in the economy. We expect to ªnd that the smaller the number of business groups competing head to head down- stream, the higher the prices of the intermediate inputs.
We can now answer the question of when a group would want to sell to other groups at all. Such sales will not occur if the optimal price for the intermediate input is arbitrarily high, approaching inªnity. In conventional models, inªnite prices do not make any sense, but in our model these prices apply only to external sales, whereas the internal sales still occur at marginal cost. We ªnd that the groups do not sell to each other (i.e., the external prices are inªnite) whenever the elasticity of sub- stitution is less than or equal to G/(G 1), where G is the number of business groups (see ªgure 3).
Our goal now is to “ªll in” the regions of ªgure 3 with equilibria from the theoreti- cal model. To do so, we pick a value for the elasticity of substitution for inputs, . In our model, we suppose that this same value applies to all possible inputs in the economy (another value of the elasticity applies to all ªnal goods).4 We then solve
4 Initially, we used an elasticity of substitution for ªnal goods equal to 5. Although we found both V-group and U-group equilibria at this value, it was difªcult to ªnd D-group equilibria in which the unafªliated downstream ªrms had no incentive to enter. To limit such an incen- tive, it was necessary to use lower values for the ªnal demand elasticity, especially when the
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Figure 3. Regions where groups do and do not sell inputs
for an equilibrium satisfying proªt maximization and free entry of all business groups (later we also add unafªliated ªrms) and full employment of resources in the economy. This allows us to determine the number of groups, G, in equilibrium. This exercise is then repeated for every other value of the elasticity: in each case, we ªnd the number of groups and the prices they would charge for inputs and ªnal goods.
3.2 Equilibria with vertically integrated groups For an economy with only V-groups, the results are summarized in ªgure 4. We see that for elasticities less than about 2.5, the equilibrium number of groups is small enough that the groups do not sell any intermediate inputs to each other. Now con- sider values of the elasticity exceeding 2.5. This moves us into the region above the line σ G/(G 1), so that groups begin selling inputs to each other. What, then, is the equilibrium number of groups in the economy? It would appear that this de- pends on the price charged for the intermediate inputs. If this price is high, it would prevent business groups (and unafªliated ªrms) from entering, whereas if this price is low, then more groups would want to enter. But we have already argued that the equilibrium price of the intermediate inputs depends on the number of business groups: when there are fewer groups, each has a larger share of the downstream market and would want to charge a higher price for the intermediate inputs used by their rivals. So now there is a circularity in the argument: the equilibrium number of groups will depend on the price of the intermediate inputs, but the price charged for these inputs will depend on the number of groups. This kind of circular reasoning is precisely what gives rise to multiple equilibria in any economic model, and our styl-
elasticity of substitution for inputs itself was low. Accordingly, all our equilibria are com- puted with an elasticity of substitution for ªnal goods equal to 5 for σ Ն 2.65 and equal to 1.9·σ for σ Յ 2.60.
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ized economy is no exception. We therefore expect to observe two types of equilib- ria: those with a small number of business groups and a high price for the interme- diate inputs, and those with a large number of groups and a lower price of the intermediate inputs.
This line of reasoning is conªrmed when we actually solve for the equilibria. For elasticities just slightly greater than 2.5, there is a still a unique number of groups G consistent with equilibrium. For elasticities between about 2.8 and 3.2, however, we ªnd that there are three equilibria, giving the S-shaped curve shown in ªgure 4. We have checked the stability of the V-group equilibria by slightly increasing the num- ber of groups beyond the equilibrium number and computing whether proªts of the groups rise or fall: if proªts fall, then the number of groups will return to its equilib- rium number, so the equilibrium is stable; but if the proªts rise, then even more groups would be induced to enter, and the equilibrium is unstable.
The stable V-group equilibria are illustrated with solid triangles in ªgure 4, and the unstable ones are represented by open triangles. To further explore how these multi- ple equilibria arise, in ªgure 5 we plot the optimal price for the intermediate input.5 For values of the elasticity less than 2.5, the business groups do not sell to each other; that is, the price of the inputs is inªnite. For slightly higher values of the elas- ticity, the price begins to fall, and when the elasticity reaches 2.8, multiple equilibria with high and low prices appear. The high-price equilibria support a small number of business groups, and the low-price equilibria support a larger number of groups, with an intermediate case in between. The intermediate case is unstable, whereas the high-price and low-price equilibria are stable.
3.3 Upstream and downstream business groups We now add the possibility of unafªliated ªrms locating in the upstream or down- stream markets. Because there is free entry of these ªrms, they will choose to enter whenever the proªts available cover the ªxed costs of entry. We allow entry into both the upstream and downstream markets, but we do not expect both to occur si- multaneously, because the business groups in the model are inherently more efª- cient than a similar-sized combination of upstream and downstream ªrms. So we adjust this governance cost in our model, so that upstream or downstream ªrms are proªtable in at least some equilibria in order to obtain a wide range of possible equi- librium conªgurations.
5 Note that the marginal cost of intermediate inputs, which equals the internal price within a group, has been set at unity in the model.
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Figure 4. Number of V-groups