Equilibrium Costs of Efficient Internal Capital Markets*

Heitor AlmeidaNew York Universityhalmeida@stern.nyu.edu

Daniel WolfenzonNew York Universitydwolfenz@stern.nyu.edu

(This Draft: October 2, 2003 )

Abstract

We analyze how the efficiency of capital allocation depends on the prevalence of conglomeratesin an economy characterized by imperfect investor protection. We show that conglomerates thatallocate capital according to a �winner-picking� rule (Stein, 1997) may have negative effects on theequilibrium allocation of capital, once we consider the relationship between conglomeration and theability of other Þrms in the economy to raise capital. In particular, an increase in conglomerationmay exacerbate capital allocation distortions even when conglomerates� internal capital markets areefficient. This prediction is consistent with anecdotal evidence that the presence of business groupsinhibits the growth of new independent Þrms due to lack of Þnance. Our model also generatesadditional testable hypotheses.

Key words: capital allocation, conglomerates, investor protection, internal capital markets.JEL classiÞcation: G15, G31, D92.

*We wish to thank Yakov Amihud, Murillo Campello, Douglas Diamond, Arvind Krishnamurthy, HolgerMueller, Walter Novaes, Raghuram Rajan, Andrei Shleifer, Jeff Wurgler, Bernie Yeung, and conference par-ticipants at Berkeley University Haas School of Business, Stanford Graduate School of Business, Universityof Maryland, University of North Carolina at Chapel Hill, the Texas Finance Festival 2003, and the Þnanceworkshop at New York University for their comments and suggestions.

1 Introduction

During the 1990s business groups in developing countries, and specially in East Asia, have been

under pressure to restructure. Although widely regarded as the engine of economic growth in ear-

lier decades, business groups are now blamed by politicians and commentators for the economic

problems (slow growth, Þnancial crises, etc.) affecting some regions of the world. Those against

the busting up of business groups contend that these organizations substitute for missing markets

(Khanna and Palepu, 1997). For example, the presence of business groups may improve economic

efficiency because their internal capital markets allocate capital among member Þrms more effi-

ciently than the underdeveloped external capital market does (Stein, 1997). In contrast, those in

favor of dismantling business groups argue, among other things, that business groups inhibit the

growth of small independent Þrms by depriving these Þrms of Þnance.1

Existing models of internal capital markets consider conglomerates in isolation, abstracting from

the effects that conglomeration might have on other Þrms in the economy (see Stein, 2001, for a

survey of the literature on internal capital markets).2 However, the argument that conglomeration

makes it harder for small independent Þrms to raise Þnancing is directly suggestive of such exter-

nalities. Is it reasonable to expect that high conglomeration per se will have negative effects on

a country�s external capital market? If this conjecture is really true, it gives rise to an important

welfare and policy implication. Even if conglomerates� internal capital markets are efficient (in the

sense that conglomerates allocate capital to divisions with the highest growth opportunities), one

cannot infer that the presence of conglomerates should be encouraged, as Khanna and Palepu (1997)

suggest. In order to be able to address these questions we need an equilibrium model that considers

both internal and external capital markets, and the interactions between them. We present such a

framework in this paper.

In our model, capital allocation is constrained by the extent of legal protection of outside

investors against expropriation by the manager or �insiders�(La Porta et al. 1997, 1998). When

investor protection is low, there is a limit to the fraction of cash ßows that entrepreneurs can1See, for example, �Small business living with the crumbs,� The Financial Times, April 23, 1998.2We use the term conglomerate and business group interchangeably. Although these organizations are different in

many respects (for instance a business group is formed by legally independent Þrms while a conglomerate is typicallya single Þrm with multiple divisions) they both have internal markets that allocate capital among the member Þrmsin the case of business groups (Samphantharak, 2003) and among divisions in the case of conglomerates (Lamont,1997).

1

credibly commit to outside investors (limited pledgeability of cash ßows). Because of this friction,

the economy has a limited ability to direct capital to its best users: high productivity projects

cannot pledge a sufficiently high return to attract capital from low productivity projects.

In our framework it is possible that conglomerates hurt the equilibrium allocation of capital

even when they allocate capital internally to their best units. A stand-alone Þrm with a worthless

project has no better option than to supply the project�s capital to the external market. This

capital can then Þnd its way to a high productivity project. In contrast, a conglomerate allocates

the capital of a worthless project to its best unit, even if this unit is of mediocre productivity. A

conglomerate prefers this internal reallocation even when there are higher productivity projects

in the economy in need of capital, because, due to limited pledgeability, the high productivity

projects cannot properly compensate the conglomerate for its capital. In this case, the presence of

conglomerates further distorts the equilibrium capital allocation by reducing the supply of capital

to the external market.

An alternative explanation of this result is as follows. Conditional on liquidating a project, a

stand-alone Þrm deciding where to allocate the proceeds of the liquidation faces the same pledge-

ability problem for all Þrms in the economy. As a result, the stand alone Þrm ranks all projects in

the socially optimal way. However, conditional on liquidating one of its projects, the conglomerate

faces pledgeability problems only for Þrms outside the conglomerate. Thus, a conglomerate has a

bias towards internal reallocation. Increasing the degree of conglomeration can then further distort

capital allocation because the conglomerate may allocate capital to mediocre projects.

Our theory predicts that an exogenous decrease in conglomeration can improve the efficiency

of capital allocation. Clearly, the degree of conglomeration is not exogenous as individual Þrms

have the choice whether to conglomerate. However, there are also exogenous sources of variation

in the degree of conglomeration. For example, Khanna and Yafeh (2001, p.9) cite evidence that

current corporate grouping affiliation in Japan, South Korea and Eastern Europe is determined to a

large extent by history. Hoshi and Kashyap (2001) explain how the pre-war Zaibatsu (family-based

business groups) were dissolved by the U.S. occupation forces. Moreover, the recent reform of the

chaebol in South Korea shows that political pressure is a force that can shape business groups.

Even though we believe that it is meaningful to model exogenous variations in conglomeration,

we extend the model to allow Þrms to choose whether to form conglomerates or not. We show that

2

similar results hold when we the degree of conglomeration is endogenous. The model has multiple

equilibria with high and low levels of conglomeration and, under certain conditions, the equilibrium

with high level of conglomeration has worse capital allocation because of the negative externality

that conglomeration imposes on other Þrms in the economy.

This prediction is consistent with the anecdotal evidence mentioned above that the presence

of business groups in developing economies inhibits the growth of new independent Þrms due

to lack of Þnance. For example, it appears to be the case that one of the consequences of the

reform of the chaebols in South Korea is that more funds have become available to independent

Þrms.3 Our results also have implications for the recent debate on whether business groups in

developing countries should be dismantled. It has been documented that one of the roles of business

groups in developing countries is the allocation of capital among member Þrms (Hoshi, Kashyap,and

Scharfstein, 1991; Khanna and Palepu, 1997; Perotti and Gelfer, 2001). Khanna and Palepu (1999)

argue that because business groups provide an important substitute for the lack of active external

capital markets in developing countries, calls for their dismantlement should be ignored. The result

in this model suggests that business groups can simultaneously be detrimental to capital allocation

due to their negative effect on external markets, and be efficient at allocating capital internally.

The dismantling of efficient conglomerates may improve overall capital allocation by increasing

liquidation and fostering capital reallocation.

Our conglomerate results contribute to the recent literature on whether internal capital markets

are efficient (Gertner, Scharfstein and Stein, 1994; Stein, 1997) or not (Shin and Stulz, 1998;

Rajan, Servaes and Zingales, 2000; Scharfstein and Stein 2000).4 The literature has focused on

conglomerates in isolation and thus has not generated equilibrium implications.5 We add to this

debate by suggesting that even when conglomerates improve the internal allocation of capital, they

can decrease the efficiency of the economy-wide allocation because of their negative impact on the

external market.

A more general formulation of our result is that local increases in pledgeability are not nec-3See The Financial Times, April 23, 1998, �Small business living with the crumbs� for an account of the difficulties

in obtaining Þnance that independent Þrms faced before the reform. See The Economist, April 17, 2003, �UnÞnishedbusiness� for an account of how the situation improved after some chaebols started to reform.

4See Stein (2001) for a survey. Other related theoretical papers (some of which we discuss below) are Fluck andLynch (1999), Inderst and Muller (2003), Matsusaka and Nanda (2002), and Heider (xxx).

5Maksimovic and Phillips (2001, 2002) are an exception: they analyze allocation decisions by conglomerates in anequilibrium context, but with no role for Þnancial imperfections.

3

-

Conglomeratesare formed

6

Productivity realized

Externalreallocationmarket

Internalreallocation inconglomerates

Cash ßowsrealized andpayments

t0 t1 t2

Figure 1: Timing of events

essarily socially beneÞcial. In our model, the conglomerate mitigates the limited pledgeability

problem for Þrms under the headquarter�s control. Similarly, one can think of a bank as mitigating

agency and information problems, but only for a subset of Þrms with direct relationships with the

bank. Our framework would then suggest that it is possible that banks have similar effects to

conglomerates: they might at the same time facilitate reallocation of capital across Þrms in their

local relationships, and decrease the efficiency of overall reallocation because they compromise re-

allocation of capital across Þrms with different banking relationships. Consistent with this idea,

the empirical literature generally Þnds that whether a Þnancial system is bank- or market-based

has an ambiguous effect on the efficiency of capital allocation (e.g., Beck and Levine, 2002, and

Demirguc-Kunt and Maksimovic, 2002).

In the next section we describe the model. In section 3 we brießy describe the intuition of the

main effect of the model. In section 4 we analyze the relation between the level of conglomeration

and the efficiency of capital allocation. In section 5 we solve for the equilibrium level of conglom-

eration. We summarize the empirical implications of our model in section 6, and present our Þnal

remarks in section 7. All proofs are relegated to the Appendix.

2 The model

In this section we develop our theoretical framework to analyze the effect of conglomeration in

the equilibrium allocation of capital. Parts of the model are similar to the model in Almeida and

Wolfenzon (2003).

The timing of events in the model is shown in Figure 1. There are three dates. At date t0,there is

a measure 1 of entrepreneurs each with one project (projects are described below). The investment

4

required at this point is one unit of capital. We assume that entrepreneurs have enough wealth to

Þnance their projects at date t0. At this date, entrepreneurs decide whether to form a conglomerate

or not. The productivity of the projects is not known at date t0 when conglomerates are formed,

however, it becomes public knowledge before date t1. In light of the new information, capital can be

reallocated among projects before cash ßows are realized at date t2. Reallocation can occur in the

external capital market or, when projects are in a conglomerate, reallocation can occur internally.

We assume that at date t1, in addition to the stand-alone Þrms and conglomerates, there is a group

of investors with an aggregate amount of capital equal to K.

2.1 Technologies

There are two types of technologies that pay off in period t2. We refer to the Þrst type of technologies

as projects. Each project is of inÞnitesimal size and has one unit of capital. At date t1, a project

can be liquidated, in which case the entire unit of capital is recovered. If a project is not liquidated,

it can receive additional capital or can simply be continued with no change until date t2. At date

t2, projects generate cash ßows.

Projects have different productivities. Each project�s type, s, can take three values: H (high

productivity projects), M (medium productivity projects), and L (low productivity projects) with

probabilities pH , pM , and pL (with pH + pM + pL = 1), respectively. The probability distribution

is independent across projects so that, at date t1, exactly a fraction pH , pM and pL of the projects

are of type H, M and L, respectively. For simplicity, we assume drastic decreasing returns to scale.

Depending on its type, each project generates YH , YM or YL (with YH > YM > YL ≡ 0) per unitinvested, but only for the Þrst two units (i.e., the initial unit with which the project is started at t0

and the unit that is potentially invested at t1). Additional units invested generate no cash ßows.

The second technology (�general technology�) is available to all agents in the economy at date

t1. We deÞne x(ω) as the per-unit pay off of the general technology with ω being the aggregate

amount of capital invested in it.

Assumption 1 The general technology satisÞes:a. ∂[ωx(ω)]

∂ω ≥ 0 c. x(1 +K) > 1b. x0(ω) ≤ 0

We assume that total output is increasing in the amount invested in the general technology

5

(assumption 1(a)) but that the per-unit payoff is decreasing (assumption 1(b)). Assumption 1(c)

guarantees that no capital is invested in storage at date t1.

To rank the productivity of the projects and the general technology, we assume that:

Assumption 2 YM > x(0)

The most productive technologies are good projects, followed by medium projects. By assump-

tion 2, medium projects are more productive than the general technology regardless of the amount

invested in the latter (since x(0) > x(ω) by assumption 1(b)). Finally, the bad projects are the

least productive.

2.2 Limited pledgeability of cash ßows

We consider an imperfection at the Þrm level: Þrms and conglomerates cannot pledge to outside

investors the entire cash ßow generated by projects. In particular, for date t2 cash ßows, we assume

that only a fraction λ of the returns of the second unit invested is pledgeable.6. We also assume

that the liquidation proceeds are fully pledgeable (we justify this assumption below).

The limited pledgeability assumption can be justiÞed as being a consequence of poor investor

protection, as shown in Shleifer and Wolfenzon (2002). In their model, insiders can expropri-

ate outside investors, but expropriation has costs that limit the optimal amount of expropriation

that the insider undertakes. Higher levels of protection of outside investors (i.e., higher costs of

expropriation) lead to lower expropriation and consequently higher pledgeability. To justify the

full pledgeability of cash ßows in the case of liquidation, we make the natural assumption that

liquidation proceeds are easier to verify than project returns.

Limited pledgeability also arises in other contracting frameworks. For example, limited pledge-

ability is a consequence of the inalienability of human capital (Hart and Moore 1994). Entrepreneurs

cannot contractually commit never to leave the Þrm. This leaves open the possibility that an en-

trepreneur could use the threat of withdrawing his human capital to renegotiate the agreed upon

payments. If the entrepreneur�s human capital is essential to the project, he will get a fraction of

the date t2 cash ßows. A natural assumption is that the entrepreneur�s human capital is not needed

to liquidate the Þrm. This justiÞes the fact that the entire liquidation proceeds are pledgeable, but6The assumption that the cash ßows from the Þrst unit are not pledgeable is made only for simplicity. It will

become clear our main results do not hinge on this assumption (see footnote ??)

6

only a fraction of the date t2 cash ßows are. Limited pledgeability is also an implication of the

Holmstrom and Tirole (1997) model of moral hazard in project choice. In that model project choice

cannot be speciÞed contractually. As a result, investors must leave a high enough fraction of the

payoff to entrepreneurs to induce them to choose the project with low private beneÞts but high

potential proÞtability. Since liquidation in our framework can be speciÞed contractually, there is

no need to leave anything to the entrepreneur when liquidation occurs. Again, this justiÞes the full

pledgeability of liquidation proceeds.

2.3 Conglomerate formation

At date t0 entrepreneurs can form conglomerates. We restrict attention to two-project conglomer-

ates. The intuition holds for conglomerates of any size, except in the extreme case in which all the

economy is in a single conglomerate. We assume that the entrepreneurs that form a conglomerate

share the payoffs at date 2.

We let c be the fraction of the projects that end up in conglomerates. Thus, there are c/2

conglomerates and 1−c projects in stand alone Þrms. We refer to c as the degree of conglomerationin the economy.

2.4 External capital markets

Before the external capital market operates, the type of the projects is realized. Six different types

of conglomerates emerge as a result. We denote each type by (s, t) where s, t = H,M,L refers to

the productivity of the projects in the conglomerate.

At date t1, some conglomerates opt out of the external capital market. That is, they decide

neither to supply nor to demand capital from the external capital market. In addition, some stand

alone projects and some conglomerates decide to liquidate their projects and supply the released

capital to the market. We let LQ be the set of projects that are liquidated and T be the amount

released from liquidation, T =Rj∈LQ dj. The total amount of capital to be allocated is K+T, where

K is the additional capital in the hands of investors. The remaining set of projects, C, demand

capital from the external market.

We model the external capital market as follows. Each continuing stand alone Þrm j, announces

P j , the amount it pays at date t2 for the Þrst unit of capital. Stand alone Þrms have no use for

7

additional units of capital and thus offer to pay zero for those units. Similarly a conglomerate with

a project j announces P j ,the amount is pays for the Þrst and second unit of capital it receives.

Next, date t1 investors (investors, stand-alone Þrms and conglomerates with capital to allocate in

the external market) allocate their capital to either the projects or to the general technology. An

allocation in the capital market can be described by rj , the probability that project j ∈ C gets

capital and ω, the amount allocated to the general technology. An equilibrium allocation must be

consistent with date t1 investor maximization and satisfy the market clearing condition

ω∗ +Zj∈C

rjdj = K + T. (1)

2.5 Internal capital markets

We assume that there are no agency problems inside the conglomerate. Once the external capital

markets closes, the conglomerate allocates the internal capital to the best possible use.

3 The main mechanism

In this section we explain the main mechanism driving the results. The next two sections formalize

this intuition. The most important result is that an increase in conglomeration may decrease the

efficiency of the economy-wide capital allocation even when conglomerates allocate capital to their

best projects.

We show that some conglomerates use only internal markets and do not participate in the

external capital market. Thus, an increase in the degree of conglomeration introduces a trade-off.

It reduces the number of transactions that take place in the external capital market, and increases

the number that take place in the various internal capital markets. Whether increasing the degree

of conglomeration is socially beneÞcial depends on which of these two markets (external or internal)

does a better job at allocating capital.

It would seem that, since conglomerates allocate capital to their best units whereas external

capital markets are plagued by pledgeability issues, it is always optimal to increase the degree of

conglomeration. However, this is not always the case. Conglomeration might hurt the efficiency

of capital allocation because the best project available to a conglomerate might not be the best

project available to the economy as a whole. In this case, increasing the number of conglomerates

8

exacerbates the initial capital allocation distortion. Conglomerate (M,L) always opts out of the

market and transfers capital from its project L to its project M . This conglomerate prefers this

internal allocation over supplying its funds to the market regardless of whether there are projects

of type H in the market that do not receive capital. This is because, due to limited pledgeability,

a project of type H cannot offer a sufficiently large fraction of the returns to make it worthwhile

for the conglomerate to supply its capital (we will show that this is the case since R∗ < YM ). If

instead these two projects were stand-alone projects, the Þrm with a project of type L would have

no better alternative than to supply its capital to the market. If the degree of pledgeability is not

too low, this unit of capital will Þnd its way to a project of type H. Therefore, as we show more

precisely in the next two sections, it is possible that an increase in conglomeration will decrease

the efficiency of economy-wide capital allocation.

4 Conglomerates and equilibrium capital allocation

We start by assuming that the degree of conglomeration in the economy, c, is exogenously given.

Clearly, the degree of conglomeration is not exogenous as individual Þrms have the choice whether

to conglomerate. Still, there are lessons to be learned to the extent that there is some exogenous

variation in conglomeration across countries. For example, Khanna and Yafeh (2001, p.9) cite

evidence that current corporate grouping affiliation in Japan, South Korea and Eastern Europe

is determined to a large extent by history. Hoshi and Kashyap (2001) explain how the pre-war

Zaibatsu (family-based business groups) were dissolved by the occupation forces. Moreover, the

recent reform of the chaebol in South Korea shows that political pressure is a force that can shape

business groups. In any case, we study the implications of endogenizing conglomeration in section

5.

We solve the model backwards. Since at date t2 no decisions are taken, we start by characterizing

the internal allocation of funds in a conglomerate.

4.1 Internal allocation of capital

After the external capital market has cleared, conglomerates allocate the capital they have to their

projects. Since there are no agency conßicts inside the conglomerate, headquarters allocate capital

to maximize the conglomerate�s payoff. The allocation rule inside the conglomerate is as follows. A

9

conglomerate that enters this stage with two additional units of capital (i.e., two units in addition

to the two units the projects started off with) allocates one to each project. A conglomerate

that enters with only one additional unit allocates it to its higher productivity project. Finally, a

conglomerate that enters with no additional capital transfers one unit of capital from its existing

lower productivity project to its higher productivity project.

For future reference, we deÞne, Pjas the maximum project j can credibly pledge to outsiders

in the date t1 reallocation market. If project j is in a stand-alone Þrm, Pj= λYs where s is

the productivity of the project. If project j is in a conglomerate, it is the conglomerate and not

the individual project that promises cash ßows to investors. Conglomerates can, for example, use

the pledgeability of one project to raise funds for the other project. However, with a suitable

deÞnition of Pjthat incorporates the information that project j is in a conglomerate, we are able

to solve the equilibrium as if all projects were stand-alone. This simpliÞes the analysis of the date

t1 reallocation market. A conglomerate allocates the Þrst unit of additional capital to its higher

productivity project. Thus, for project j of type s that is in a conglomerate (s, t) with Ys > Yt,

we deÞne Pj= λYs. The same conglomerate (s, t) can offer a maximum of λ(Ys + Yt)/2 per unit

when it raises two units of capital. Therefore for project j of type s in a conglomerate (s, t) with

Ys ≤ Yt, we deÞne P j = λ(Ys + Yt)/2.

4.2 Equilibrium of the external reallocation market

We can now treat each project as a stand alone project since the information that the project

is in a conglomerate is already incorporated in the deÞnition of P. We solve for the equilibrium

allocation for every possible subgame. A subgame is deÞned by a set of conglomerates that opt out

of the market, a set of projects (either stand-alone or divisions of a conglomerate), LQ, that are

liquidated and a set of projects C that continues and seeks additional Þnancing. Once we know

the equilibrium return and allocation rule for given values of LQ and C, we analyze the Þrm and

conglomerate�s decision to opt out of the market, liquidate, or continue and seek additional Þnance.

The next Lemma characterizes the announcements, {P j}j∈C , and the resulting capital allocationas a function of the pledgeability parameter {P j}j∈C and the total amount of liquidation T. Thislemma is proved in Almeida and Wolfenzon (2003).

10

Lemma 1 There is a level R∗ such that date t1 investors allocate an amount ω∗ = x−1(R∗) to the

general technology and allocate capital to projects according to the following rule:

rj =

0 if P j < R∗

1 if P j > R∗ or, if P j = R∗ and P j > R∗

r if P j = Pj= R∗

(2)

with r ∈ [0, 1] chosen to satisfy the market clearing condition in equation (??). 7 Projects with

Pj ≥ R∗ offer to pay R∗, and projects with P j < R∗ are indifferent among all feasible offers.

The equilibrium strategy of date t1 investors (investors and stand-alone Þrms and conglomerates

that have decided to supply its capital to the external market) is to allocate their capital Þrst to

the projects offering the highest return and then to technologies in decreasing order of the offered

return. This implies that there is a cutoff value R∗ such that technologies offering strictly more

than R∗ get capital for sure and those offering strictly less than R∗ do not get capital. Technologies

offering exactly R∗ may or may not get capital. Also, investors are indifferent among all technologies

offering the same return. In particular, they are indifferent among all technologies offering exactly

R∗. If, for example, there are more projects offering R∗ than capital available, any allocation rule

to these projects is consistent with date t1 investors maximization behavior. However, in this case,

the only rule for which an equilibrium exists is one where all the projects that could have offered

more (projects with Pj> R∗) receive capital with probability 1.8

Given this allocation rule, it is optimal for all projects with Pj ≥ R∗ to offer exactly P j = R∗.

These projects beneÞt by raising capital at this price because they generate Ys out of this unit of

capital but pay only R∗ ≤ P j < Ys. They have no incentive to decrease the offer, because offersof less than R∗ receive no capital. Projects with P j > R∗ receive capital for sure so they have

no reason to increase their offer. Projects with Pj= R∗ do not necessarily receive capital with

probability 1 but, due to limited pledgeability, they cannot increase their offer. Finally, the storage

technology receives capital up to the point where its return is R∗.

Since, in equilibrium, all date t1 investors receive a return ofR∗, we refer to R∗ as the equilibrium

return of the reallocation market. It will be useful in what follows to derive a condition on the

7The level of R∗ can be found by solving: x−1(R∗) +

Z{j∈C|P j>R∗}

dj ≤ K + T ≤ x−1(R∗) +

Z{j∈C|P j≥R∗}

dj.

8 If a project with Pj> R∗ receives capital with probability less than 1 when it offers P j = R∗, then it will be

optimal for this project to offer R∗+ ² and receive capital for sure. Clearly, in this case an equilibrium does not existsince ² can always be made smaller.

11

equilibrium return R∗. By market clearing, ω∗ must satisfy 0 < ω∗ ≤ 1 + K. It follows that

x(1 +K) ≤ R∗ < x(0) and, by assumptions 1 and 2:

YL ≡ 0 < R∗ < YM < YH . (3)

We can use this inequality to analyze Þrm and conglomerate�s decision to opt out of the market,

liquidate, or continue and seek additional Þnance. For stand alone projects the decision is straight-

forward. Low productivity projects liquidate since they get R∗ in the market when they liquidate

but get zero if the continue. Similarly, conglomerate (L,L) liquidates and supplies it capital to the

market.

Stand alone projects of productivity M and H and conglomerates of type (H,H), (M,M) and

(H,M) do not liquidate since the capital they posses generates more cash ßow for them (either

YM or YH) if they continue than if the liquidate (R∗). These projects also beneÞt from raising

additional capital since they only pay R∗ but generate either YM or YH .

Finally conglomerates (H,L) and (M,L) do not participate in the external capital market.

They are (weakly) better off allocating capital internally than using the external capital market.

This is because the best they can do in the market is to supply the unit of capital in their low

productivity project and raise one unit for their higher productivity one. But they do not need

the market to accomplish this transaction. Furthermore, if the probability of raising capital in the

external market is less than one, they strictly prefer internal reallocation.

The equilibrium allocation can now be computed for any degree of conglomeration c. Stand-

alone projects L and projects of conglomerate (L,L) are liquidates. This deÞnes the set LQ. Since

there are a number (1−c)pL of stand-alone projects L and a number c2(pL)2 of conglomerates, eachwith two units of capital. The additional supply to the external capital market is

T = (1− c)pL + cp2L. (4)

A key feature of the model is that the higher the degree of conglomeration, the lower is the

amount of capital supplied to the external capital markets. The reason is that a stand-alone project

of productivity L always supplies its capital to the market since it has no other use for it. However,

conglomerates (M,L) and (H,L) opt out of the market because they prefer internal reallocation.

As the degree of conglomeration increases, the number of stand alone projects of productivity L

decreases and the number of conglomerates that opt out of the market increases.

12

The set of projects that continue, C, is formed by all stand-alone projects of productivity

M and H and all projects in conglomerates (H,H), (M,M) and (H,M). These are the projects

that demand capital. The Pj�s of these projects can be found by using the deÞnitions of section

4.1. A project j of productivity s in a conglomerate (s, s) has Pj= λYs and project j of type

H in a conglomerate (H,M) has Pj= λYH . That is, these projects can offer the same return

as a stand-alone project of the same productivity, and thus, in equilibrium, receive capital with

the same probability. However, project j of productivity M in a conglomerate (H,M) has Pj=

λ(YH +YM )/2 > λYM . This project can offer more than a stand-alone project of type M since the

conglomerate can use some of the cash ßows from the type H project to raise capital for the type

M project.9 As a result, project M in a conglomerate (H,M) receives capital before any other

project of type M .

Based on the discussion above, Pjtakes only three values: λYH , λ(YH + YM )/2, and λYM .

Projects with the same Pjoffer the same price in the reallocation market and hence receive capital

with the same probability. We deÞne rH , rHM , and rM as the probabilities that projects with Pj

of λYH , λ(YH + YM )/2, and λYM receive capital, respectively. Applying Lemma 1, with C being

the set of projects that continue and participate in the market and T given by equation 4, the

equilibrium rH , rHM , and rM can be obtained (these expressions are derived in the appendix).

4.3 Comparative statics on conglomeration

In the last section we described the equilibrium of the date t1 reallocation market when conglom-

erates are present. Taking the allocation rule derived, it is straight-forward to write the aggregate

payoff of the economy (see Appendix). The following proposition takes the degree of conglomeration

as exogenous and calculates its effect on the aggregate payoff of the economy.

Proposition 1 There are functions bλ1(c) < bλ2(c) such that:10a. For λ < bλ1(c), the aggregate payoff is increasing in the degree of conglomeration,b. For bλ1(c) < λ < bλ2(c), the aggregate payoff is decreasing in the degree of conglomeration, and9The conglomerate is thus relaxing the project M�s external Þnancing constraint. This effect is what Stein (2001)

calls the �more money� effect of conglomeration. The models in Fluck and Lynch (1999) and Inderst and Mueller(2003) feature a similar effect.10This derivative does not exist at λ = bλ1 and λ = bλ2.

13

c. For λ > bλ2(c), the aggregate payoff is non-decreasing in the degree of conglomeration.For low levels of pledgeability, the external market does a poor job of allocating capital. Since

conglomerates allocate capital to their best units irrespective of the level of pledgeability, a higher

degree of conglomeration increases the number of efficient capital transfers that take place in the

economy, thereby increasing the aggregate payoff. This explains part (a).

In region (b) the market does a better job of allocating capital than in region (a). In particular,

the functions bλ1 and bλ2 are chosen such that, in this region, rH is large but less than 1. Increasingthe number of conglomerates exacerbates the existing distortion in capital allocation in this range.

Notice that conglomerates of type (M,L) always opt out of the market and allocate capital from

their type L project to their type M project. However, if instead these projects were stand-alone

projects, the capital in the type L project would be supplied to the market. Since in this range

of pledgeability the external capital market works relatively well, these units of capital would Þnd

their way to type H projects.

The bias towards internal investment is due to limited pledgeability. A conglomerate of type

(M,L) does not supply capital to the market but rather allocates it internally (even when there is

unsatisÞed demand from projects of type H), since projects of type H cannot offer a sufficiently

high return. In this range, the maximum return a type H project can offer is lower than the

cash ßows a project of type M generates (i.e., λYH < YM ) and thus it is privately optimal for

the conglomerate to allocate internally whereas it is socially optimal to supply its capital to the

market.

Finally, for higher levels of pledgeability, increasing conglomeration is never detrimental to

the aggregate payoff because all projects of type H receive capital in the external capital market

(rH = 1). As a result, transfers that take place inside the (M,L) conglomerates are no longer

suboptimal since the best project in need of capital for the economy as a whole is now project M .

5 The equilibrium level of conglomeration

In the previous section we analyzed the effect of conglomeration on the efficiency of capital alloca-

tion. The main result is that, even when conglomerates are efficient at allocating capital internally,

they might reduce the efficiency of economy-wide capital allocation. In this section we analyze

14

the equilibrium level of conglomeration. Proofs of the results discussed in this section are in the

Appendix.

As we described above, at date t0, entrepreneurs with projects can decide to form a two-project

conglomerate or remain a stand-alone Þrm. We assume that there is a cost d of conglomeration.

This can be thought of as the organizational costs incurred by the conglomerate due to its higher

complexity. In addition, d can capture other beneÞts and costs of conglomeration. For example,

Claessens et al. (2002) conclude from various case studies of business groups in East Asia that

their �dominance lies in the privileges they solicit from the government.� Countries where these

privileges are high have a smaller d.

At date t0, the equilibrium level of conglomeration must satisfy:

UC − 2USA = d, (5)

where UC is the expected payoff of a two-project conglomerate and USA is the expected payoff of

a stand-alone project.

Figure 2, panel B shows UC−2USA as a function of c (the degree of conglomeration). Recall thatlow levels of conglomeration are associated with a large supply of capital to the market. In Þgure

2, panel B, when conglomeration is low the supply of capital is sufficiently large so that all good

projects receive capital. Notice this corresponds to the case where supply is at c =c in the panel

A of Figure 2. An increase in conglomeration reduces the supply of funds and consequently raises

the interest rate. Since a stand-alone Þrm supplies its capital to the external market more often, it

beneÞts from this increase more than a conglomerate does (i.e., UC − 2USA falls). For moderatelevels of conglomeration, further increases in the degree of conglomeration reduce supply so much

that some good projects are unable to raise capital. Since stand-alone projects rely completely

on the external market to raise capital whereas conglomerates rely only to some extent (they can

use their internal capital markets) the payoff of a stand-alone Þrm falls relative to the payoff of a

conglomerate (i.e., UC − 2USA increases). Finally, for very high levels of conglomeration, no goodproject raises capital and any increase in conglomeration (contraction in supply) translates to an

increase in the interest rate. Again this beneÞts stand-alone projects and UC − 2USA falls again.As can be seen in the panel B of Figure 2 there are two equilibrium levels of conglomeration c

15

and c with c< c.11 Figure 2, panel A, shows the date t1 reallocation market at these two levels of

conglomeration. When c is low, the supply of capital to the external market is large (because there

are few conglomerates) and so all good projects in the economy (regardless of whether they are

part of conglomerates) receive capital. In turn, because the market works well, it is beneÞcial for

entrepreneurs to keep their projects as stand-alone Þrms rather than to conglomerate. Thus there

is an equilibrium with low c. Alternatively, when c is high, the supply of capital to the market

is small (because there are so many conglomerates) and so no good project raises capital in the

external capital market. In turn, because the external market works poorly, entrepreneurs choose

to conglomerate. Thus, there is an equilibrium with high c.

As we show in the Appendix, under certain conditions the low conglomeration equilibrium will

be better from a social point of view. This result holds even when we do not count the cost of

conglomeration d in the aggregate payoff. Including this cost will only make this result stronger

as the number of conglomerates and hence the total cost of conglomeration is lower in the low

conglomeration equilibrium. The results in this section show that the main insight of the previous

section remains when we endogenize the degree of conglomeration in the economy. In the �bad�

equilibrium, there is too much conglomeration from a social point of view because even when capital

is allocated efficiently inside the conglomerate the reallocation of capital across conglomerates is

reduced. The economy would beneÞt from a decrease in the number of conglomerates, but individual

Þrms will not choose to perform this change on their own.

6 Empirical Implications

Our theory suggests that a decrease in the degree of conglomeration in economies with imperfect

investor protection can improve the efficiency of capital allocation. Conglomeration imposes a

negative externality to other Þrms because internal reallocation dries up the external market and

makes it more difficult for good projects to raise funds. This is true even when we allow the degree

of conglomeration in the economy to be endogenous.

We are unable to provide systematic evidence for this implication because we lack data to

build an �aggregate conglomeration� index for a large enough sample of countries. In principle,

this measure could be constructed. For example, for East Asia, Claessens, Fan and Lang (2002)11The third equilibrium (the middle one) is unstable and hence we do not discuss it further.

16

measure the fraction of Þrms that are affiliated with business groups. However, we do not have

enough observations to perform a statistical analysis. With a large enough sample of countries,

future research could examine the empirical relationship between conglomeration and measures of

the efficiency of capital allocation, such as Wurgler�s (2000).12 Our prediction is that conglomeration

may have a negative effect on the equilibrium efficiency of investment, even after controlling for

other determinants of investment efficiency such as investor protection and economic development.

Of course, one should worry about whether the reduction in external market activity that the

presence of the conglomerates entails is a Þrst order effect. Although there is no systematic study

on this issue, the sheer size of business groups as a fraction of the economy in some countries

suggests that this can be the case. Claessens, Djankov, Fan, and Lang (2000) Þnd that in 8 out

of the 9 Asian countries they study, the top 15 family groups control more that 20% of the listed

corporate assets. In a sample of 13 Western European countries, Faccio and Lang (2002) Þnd that

in 9 countries the top 15 family groups control more than 20% of the listed corporate assets. Given

that business groups consist of such a large fraction of the capital market in some countries, it is

highly plausible that their actions could have Þrst-order effects on the behavior of the market as a

whole.

Our results have implications for a recent debate about whether business groups should be

dismantled in developing countries (Khanna and Palepu 1999). An argument against dismantling

business groups is that their internal capital markets provide a substitute for the lack of external

capital markets. Our results suggest that even when business groups allocate capital to their best

units, their presence can hurt economy wide capital allocation by reducing external market activity.

Our results might also help explain why governments need to take an active role in dismantling

conglomerates. Individual conglomerates have no incentives to dismantle since they would not be

properly compensated by the capital they provide to the external market.

One example is the case of South Korea. Up until the 90�s, the Korean conglomerates, or

chaebols, were credited with being one of the most important factors in Korea�s rapid growth.

However, in the 90�s, the chaebols were seen as an obstacle to growth. One of the reasons for

this perception is that the chaebols inhibited the growth of small and medium sized Þrms, among12Almeida and Wolfenzon (2003) use a similar procedure to examine the relationship between an index of aggregate

external Þnance dependence and the efficiency of capital allocation.

17

other things, because most of the Þnance available was channelled to the chaebols (see The Financial

Times, April 23, 1998, �Small business living with the crumbs�).13 From the late 1990s, the Korean

government has been exerting pressure on the chaebols to slim their empires. As a consequence,

�with the chaebol no longer dominating access to South Korea�s huge pool of savings, credit began

to ßow to small- and medium-sized Þrms� (The Economist, April 17, 2003, �UnÞnished business�).

This example is consistent with our model. First, when conglomeration was high, independent Þrms

could not get capital. Second, despite this fact, the conglomerates did not voluntarily dismantle

and thus government action was required. Finally, after the conglomerates had started reforming,

more Þnancing was made available to independent Þrms.

We are not the Þrst to point out that conglomerates may have a negative effect on the alloca-

tion of capital. Other models also have the implication that, as the Þnancing-related beneÞts of

conglomeration decrease, costs of conglomeration such as less effective monitoring (Stein, 1997), co-

ordination costs (Fluck and Lynch, 1999), free cash-ßow (Matsusaka and Nanda, 2002 and Inderst

and Mueller, 2003) and incentive problems (Gautier and Heider, 2003) make conglomerates less

desirable. However, most of the literature focuses on conglomerates in isolation and thus has no

implications for the efficiency of economy-wide capital allocation. More importantly, an implication

of our main result is that it is not possible to extrapolate results about the efficiency of capital

allocation from models of conglomerates in isolation. In our set up conglomerates are assumed to

allocate capital efficiently. Yet, under certain conditions, increases in conglomeration actually hurt

economy-wide capital allocation.

7 Conclusion

We develop an equilibrium model to understand how the efficiency of capital allocation depends on

the degree of conglomeration. We show that an increase in conglomeration can be detrimental to

capital allocation even when conglomerates have efficient internal capital markets.

Our model is consistent with anecdotal evidence on the role of business groups in developing

countries. The model gives a rationale for why the presence of business groups may inhibit the

growth of new independent Þrms due to lack of Þnance. Our results also suggest that efficient13Too much political power (as evidenced by a number of corruption scandals), almost total control of product

markets and excessive debt levels are other reasons why the chaebols were believed to be hampering growth.

18

internal capital markets is not a sufficient condition to advocate the presence of conglomerates in

developing economies. Conglomeration may impose a negative externality to other Þrms by making

it more difficult for good projects outside the conglomerate to raise funds. While the economy as

a whole might beneÞt from having fewer conglomerates, individual Þrms cannot be expected to

bust up these conglomerates on their own. Our model thus suggests that there might be a role for

policies that directly discourage the presence of conglomerates in developing economies.

One way to reinterpret our conglomerate result is that, in an equilibrium framework, mitigating

an agency cost for only a few Þrms is not necessarily socially beneÞcial. This insight could poten-

tially be extended to the literature on Þnancial intermediaries (e.g. Bencivenga and Smith, 1991;

Boyd and Smith, 1992; King and Levine, 1993; Galetovic, 1996). This literature has argued that

Þnancial intermediaries perform several roles that aid the allocation of capital, such as discovering

information about productivity, pooling funds and diversifying risks. In the context of our model,

this reasoning suggests that Þnancial intermediaries could increase pledgeability of cash ßows in

the economy. However, our results on conglomeration suggest that it is important that banks in-

crease the aggregate pledgeability level in the economy (our parameter λ), as opposed to increasing

pledgeability locally for a group of Þrms with more direct relationships with banks. If the latter

occurs, banks might have similar effects to conglomerates: they might at the same time facilitate

reallocation of capital across Þrms in their local relationships, and decrease the efficiency of overall

reallocation because they compromise reallocation of capital across Þrms with different banking

relationships.

19

References

Almeida, H. and D. Wolfenzon, 2003, The effect of external Þnance on the equilibrium allocationof capital, forthcoming, Journal of Financial Economics.

Beck, T. and R. Levine, 2002, Industry-growth and capital allocation: does having a market- orbank-based system matter?, Journal of Financial Economics 64, 147-180.

Bencivenga, V. and B. Smith, 1991, Financial intermediation and endogenous growth, Review ofEconomic Studies 58, 195-209.

Boyd, J. and B. Smith, 1992, Intermediation and the equilibrium allocation of investment capital:implications for economic development, Journal of Monetary Economics 30, 409-432.

Claessens, S., S. Djankov, J. Fan, and L. Lang, 2002, The cost of group affiliation: evidence fromeast Asia, manuscript, World Bank.

Claessens, S., S. Djankov, and L. Lang, 2000, The separation of ownership and control in EastAsian corporations, Journal of Financial Economics 58, 81�112.

Demirguc-Kunt, A., and V. Maksimovic, 2002, Funding growth in bank-based and market-basedÞnancial systems: evidence from Þrm-level data, Journal of Financial Economics 65, 337-363.

Faccio, M. and L. Lang, 2002, The ultimate ownership of Western European corporations, Journalof Financial Economics 65, 365-395.

Fluck, Z., and A. Lynch, 1999, Why do Þrms merge and then divest? A theory of Þnancial synergy,Journal of Business 72, 319-46.

Galetovic, A., 1996, Specialization, intermediation, and growth, Journal of Monetary Economics38, 549-559.

Gertner, R., D. Scharfstein, and J. Stein, 1994, Internal versus external capital markets, QuarterlyJournal of Economics 109, 1211-30.

Hart, O., and J. Moore, 1994, A theory of debt based on the inalienability of human capital,Quarterly Journal of Economics 109, 841-79

Gautier, A. and F. Heider, 2003, The beneÞts and costs of winner-picking: Redistribution versusincentives, working paper, New York University.

Holmstrom, B., and J. Tirole, 1997, Financial intermediation, loanable funds and the real sector,Quarterly Journal of Economics 112, 663-691.

Hoshi, T., and A. Kashyap, 2001, Corporate Financing and Governance in Japan, MIT Press,Cambridge, MA.

Hoshi, T., A. Kashyap, and D. Scharfstein, 1991, Corporate structure, liquidity and investment:Evidence from Japanese industrial groups, Quarterly Journal of Economics February, 33-60.

Inderst, R., and H. Mueller, 2003, Internal vs. external Þnancing: An optimal contracting ap-proach, Journal of Finance, forthcoming.

Khanna, T., and K. Palepu, 1997, Why focused strategies may be wrong for emerging countries,Harvard Business Review 75, 41-51.

20

Khanna, T., and K. Palepu, 1999, The right way to restructure conglomerates in emerging markets,Harvard Business Review 77, 125-134.

Khanna, T., and Y. Yafeh, 2001, Business groups and risk sharing around the world, HarvardBusiness School Working Paper.

King , R., and R. Levine, 1993, Finance, entrepreneurship and growth, Journal of MonetaryEconomics 32, 513-542.

La Porta, R., F. Lopez-De-Silanes, and A. Shleifer, and R. Vishny, 1997, Legal determinants ofexternal Þnance, Journal of Finance 52, 1131-1150.

La Porta, R., F. Lopez-De-Silanes, and A. Shleifer, and R. Vishny, 1998, Law and Þnance, Journalof Political Economy 106, 1113-1155.

Maksimovic, V., and G. Phillips, 2001, The market for corporate assets: Who engages in mergersand asset sales and are there efficiency gains?, Journal of Finance 56, 2019-2065.

Maksimovic, V., and G. Phillips, 2002, Do conglomerate Þrms allocate resources inefficiently acrossindustries?, Journal of Finance 57, 721-769.

Matsusaka, J., and V. Nanda, 2002, Internal capital markets and corporate refocusing, Journal ofFinancial Intermediation 11, 176-211.

Perotti, E. and S. Gelfer, 2001, Red barons or robber barons? Governance and investment inRussian Þnancial-industrial groups, European Economic Review 45, 1601-1617.

Rajan, R., H. Servaes, and L. Zingales, 2000, The cost of diversity: The diversiÞcation discountand inefficient investment, Journal of Finance 55, 35-80.

Samphantharak, K., 2003, Internal capital markets in business groups, Working paper Universityof Chicago.

Scharfstein, D., and J. Stein, 2000, The dark side of internal capital markets: Divisional rent-seeking and inefficient investment, Journal of Finance 55, 2537-64.

Shin, H., and R. Stulz, 1998, Are Internal Capital Markets Efficient?, Quarterly Journal of Eco-nomics 113, 531-52.

Shleifer, A., and D. Wolfenzon, 2002, Investor protection and equity markets, Journal of FinancialEconomics 66, 3-27.

Stein, J., 1997, Internal capital markets and the competition for corporate resources, Journal ofFinance 52, 111-133.

Stein, J., 2001, Agency, information and corporate investment, forthcoming in the Handbook ofEconomics and Finance, edited by G. Constantinides, M. Harris and R. Stulz.

Wurgler, J., 2000, Financial markets and the allocation of capital, Journal of Financial Economics58, 187-214.

21

Figure 3

6

-

R

Capital

Panel A

λYH

R

R

ω̄ K + T3 K + T2 K + T1

Supply at c = c̄

Supply at c = c

6

-

UC − 2USA

Conglomeration

Panel B

d

c1 c2 c3 c̄c

AppendixProof of Lemma 1

See Almeida and Wolfenzon (2003). ¥

Proof of Proposition 1Direct application of Lemma ??, with C being the set of projects that are not liquidated and that belong to

conglomerates that do not opt out of the external capital market, leads to:

rH =

0 if λYH < x(K + T )

K+T−x−1(λYH )pH−cpLpH if x(K + T ) ≤ λYH < x(K + T − pH + cpLpH)

1 if λYH ≥ x(K + T − pH + cpLpH)

rHM =

0 if λYHM < x(K + T − pH + cpLpH)

K+T−pH+cpLpH−x−1(λYHM )cpHpM

if x(K + T − pH + cpLpH) ≤ λYHM << x(K + T − pH + cpLpH − cpMpH)

1 if λYHM ≥ x(K + T − pH + cpLpH − cpMpH)

rM =

0 if λYM < x(K + T − pH + cpLpH − cpMpH)

K+T−−pH+cpLpH−cpHpM−x−1(λYM )

(1−c)pM+cp2M

if x(K + T − pH + cpLpH − cpMpH) ≤ λYM << x(K + T − pH + cpLpH − cpMpH − (1− c)pM − cp2M )

1 if λYM ≥ x(K + T − pH + cpLpH − cpMpH − (1− c)pM − cp2M )where YHM ≡ (YH +YM )/2. The deÞnition of rH , rHM and rM motivate the deÞnition of the following functions

of λ : eλ1 = x(K + T )/YH , eλ2 = x(K + T − pH + cpLpH)/YH , eλ3 = x(K + T − pH + cpLpH)/YHM , eλ4 = x(K +

T − pH + cpLpH − cpMpH)/YHM , eλ5 = x(K + T − pH + cpLpH − cpMpH)/YM and eλ6 = x(K + T − pH + cpLpH −cpMpH − (1− c)pM − cp2M )/YM . For any c, the value of these functions satisfy eλ1 < eλ2 < · · · < eλ6.

To lighten notation we let r0t ≡ ∂rt∂c

for t = H, HM, and M and f(ω) = ωx(ω). The aggregate payoff function isgiven by:

Π = f(ω) + (1− c) [pH(YH + rHYH) + pM (YM + rMYM )]+

c

2

·p2H(2)(YH + rHYH) + p

2M (2)(YM + rMYM ) + 2pHpM (2YH + rHYM + rHMYM )+2pHpL(2YH) + 2pMpL(2YM )

¸where ω = K + (1 − c)pL + cp2L − rH(pH − cpLpH) − rHM (cpHpM ) − rM ((1 − c)pM + cp2M ). We analyze

dΠdcin all

the regions deÞned by eλk k = 1, 2 . . . 6. We denote by ∂Π∂cthe derivative of Π wrt c assuming rH , rHM and rM are

constants:

∂Π

∂c= pLpH(1− rH)(YH − f 0(ω)) + pHpM (1− rH)(YH − YM )+ (6)

+ pM (1− pM )(1− rM )(YM − f 0(ω)) + pHpM (rHM − 1)(YM − f 0(ω))

For λ < eλ1, rH = rHM = rM = 0 and since r0H = r0HM = r0M = 0 we can use equation 6 to obtain dΠdc= ∂Π

∂c=

pLpH(YH − f 0(ω)) + pHpM (YH − YM ) + pMpL(YM − f 0(ω)) > 0 since f 0(ω) = x(ω) + ωx0(ω) ≤ x(ω) < YM < YH .

For eλ1 < λ < eλ2, rH ∈ (0, 1), rHM = 0 and rM = 0 also r0H 6= 0 and r0HM = r0M = 0. Also in this region, simplealgebra leads to ∂ω

∂c= 0. Thus, dΠ

dc= pLpH(1−rH)YH+pHpM (1−rH)(YH−YM )+pMpLYM+r0H [(1−c)pHYH+cp2HYH+

cpHpMYM ] and r0H =−pL+p2L+rHpHpL

pH−cpLpH . In the limit as λ→ eλ2, rH → 1 and dΠdc= pMpLYM−pMpL[γYH+(1−γ)YM ] <

0 where γ = (1−c+cpH)/(1−cpL). Also ∂∂λ

¡dΠdc

¢= ∂

∂rH

¡dΠdc

¢∂rH∂λ. Since x() is a decreasing function ∂rH

∂λis increasing.

And since ∂∂rH

¡dΠdc

¢= −pHpLYH − pHpM (YH − YM ) + pHpL[γYH + (1− γ)YM ] < 0 then ∂

∂λ

¡dΠdc

¢< 0.

If dΠdc

¯̄̄eλ1 ≤ 0 then we deÞne bλ1 = eλ1. If dΠdc ¯̄̄eλ1 > 0 then since ∂

∂λ

¡dΠdc

¢< 0 and dΠ

dc

¯̄̄eλ2 < 0, there is a λ∗ ∈ (eλ1, eλ2)

such that dΠdc|λ∗ = 0. In this case we deÞne bλ1 = λ∗. We also deÞne bλ2 = eλ2. So far we have shown that to the left

of bλ1, dΠdc is positive, and from bλ1 to bλ2, dΠdc is negative. Left to prove is that to the right of bλ2, dΠdc is non-negative.For eλ2 < λ < eλ3, rH = 1, rHM = rM = 0 and r0H = r0HM = r0M = 0. Using equation 6, dΠ

dc= ∂Π

∂c=

pMpL(YM − f 0(ω)) > 0.For eλ3 < λ < eλ4, rH = 1, rHM ∈ (0, 1), rM = 0 and r0HM 6= 0 and r0H = r0M = 0. Also in this region, simple algebra

leads to ∂ω∂c= 0. Thus, dΠ

dc= pMpLYM + pHpMrHMYM + cpHpMr

0HMYM and r0HM =

−pL+p2L−+pHpL+rHMpHpMcpHpM

.

Substituting the value of r0HM and simplifying leads to dΠdc= 0.

For eλ4 < λ < eλ5, rH = 1, rHM = 1, rM = 0 and r0H = r0HM = r0M = 0. Using equation 6, dΠdc

= ∂Π∂c

=pM (1− pM )(YM − f 0(ω)) > 0

1

For eλ5 < λ < eλ6, rH = 1, rHM = 1, rM ∈ (0, 1) and r0M 6= 0 and r0HM = r0M = 0. Also in this region, simplealgebra leads to ∂ω

∂c= 0. dΠ

dc= pMpLYM + pHpMYM − pMrMYM + p2MrMYM + r0M ((1 − c)pMYM + cp2MYM ) and

r0M =−pL+p2L+pLpH−pHpM−rM (−pM+p2M )

(1−c)pM+cp2M

. Substituting the value of r0M and simplifying leads to dΠdc= 0.

Finally, for λ > eλ6, rH = 1, rHM = 1, rM = 1 and r0H = r0HM = r0M = 0. Using equation 6, dΠdc= ∂Π

∂c= 0.

Thus, to the right of bλ2, dΠdc is non-negative.¥Proof of results of section 5We modify the model so that Þrms choose whether to conglomerate at date t0. If two Þrms choose to conglomerate

they pay a cost d. This cost can be thought of as organizational costs that the conglomerate incurs due to its highercomplexity.

Let USA be the expected payoff of a stand-alone project and UC be the expected payoff of a conglomerate(excluding the cost k). Then

USA = pH(YH + rH(YH −R)) + pM (YM + rM (YM −R)) + pLRUC = p2H(2YH + 2rH(YH −R)) + p2M (2YM + 2rM (YM −R)) + 2pHpM (2YH + rH(YM −R) + rHM (YM −R))

+ 2pHpL(2YH) + 2pMpL(2YM )

Characterizing the equilibrium level of conglomeration

To concentrate on the most interesting region of the parameter space, we assume that

Assumption 3

a. x(K + p2L) > λYH

b. x(K + pL − pH) < λYHM

Figure 2, panel A shows the reallocation market for different levels of conglomeration. In this Þgure K + T3 ≡x−1(λYH) and K + T2 ≡ x−1(λYH) + pH − cpLpH , and K + T3 ≡ x−1(λYHM ) + pH − cpLpH . Figure 2, panelB shows UC − 2USA as a function of c. In this Þgure, c1 =

K+pL−x−1(λYHM )−pHpL−p2L−pLpH

, c2 =K+pL−x−1(λYH)−pH

pL−p2L−pLpH, and

c3 =K+pL−x−1(λYH)

pL−p2L.(Assumption 3 (a) guarantees that c3 < 1 and assumption 3 (b) guarantees that c1 > 0). These

values are chosen so that when c ∈ (c1, c2] then the supply of capital K+T ∈ [K+T2,K+T1), when c ∈ (c2, c3] thenK + T ∈ [K + T3,K + T2), and when c ∈ (c3, 1] then K + T < K + T3. To compute UC − 2USA, we need the date t1equilibrium allocation ( rH , rHM , and rM ) and return R.We get these values from Þgure 2, panel A. For example, inthe region where K+T ∈ [K+T2,K +T1), rH = 1 and rHM = rM = 0 and R is calculated where demand intersectssupply. In the region where K + T ∈ [K + T3,K + T2), rH ∈ (0, 1], rHM = rM = 0 and R = λYH . Finally, in theregion where K+T > K+T3, rH = rHM = rM = 0 and R is again calculated where demand intersects supply. Nextwe take the date t1 equilibrium values and plug them in USA − 2UC .

In Þgure 2, panel B, the level of d satisÞes

d ∈ [max{2pHpL(YH − x(K + p2L)) + 2pMpL(YM − x(K + p2L)) + 2pHpM (YH − YM ), 2pMpL(YM − λYH)}, (7)

min{2pHpL(YH − λYH) + 2pMpL(YM − λYH) + 2pHpM (YH − YM ), 2pMpL(YM − λYHM )].In this case there are two equilibria, the high conglomeration equilibrium at c and the low conglomeration

equilibrium at c (the equilibrium level of c between other c and c is not stable so we do not consider it in thediscussion). As can be seen from Þgure 2, panel A, in the high conglomeration equilibrium, there is little supplyof funds to the market and as a result the reallocation market works poorly (no reallocation to good projects). Asa result it does not pay to be a stand alone. In the low conglomeration equilibrium, the supply of funds is largerand as a result the external market works better. Since good projects do get capital in equilibrium, it pays to be astand-alone project.¥

Welfare comparison between the two equilibria

For a sufficiently steep x(.) function, the equilibrium with low conglomeration is better from society�s point ofview. In this proof, we assume also that d satisÞes the condition in equation 7.

First we deÞne what we mean by a �steeper� x(.) function. We start with any x(.) function that leads to twoequilibrium levels of conglomeration c and c with respective date t1 equilibrium return R and R. We also deÞne ω as

2

the amount of capital going to the general technology in the high conglomeration equilibrium. We consider a familyof x(.) functions that pass through the high conglomeration equilibrium, that is all x(.)function in this family satisfyx(ω) = R. For each x(.) we deÞne ∆ω as x(ω +∆ω) =R. That is, ∆ω is the additional amount of capital that hasto be invested in the general technology to drive the return down from R to R. Intuitively, the smaller the ∆ω, the�steeper� the x(.) function.

We show that there is a leveld∆ω such that for all x(.) functions in the family deÞned above with ∆ω <d∆ω, thelow conglomeration equilibrium is the better one.

First, notice that for a given set of parameters {YH , YM , pH , pL.pM , d} the equilibrium returns R to R satisfy:

2pMpL(YM −R) = d2pHpLYH − 2pMpLYM −R(2pHpL + 2pMpL) + 2pHpM (YH − YM ) = d

These expressions are the expansion of USA − 2UC at the low and high conglomeration equilibria. From theexpressions, it is clear that the return in the date t1 reallocation market is not affected by the x(.) function . However,the level of c at the low conglomeration equilibrium will be not be the same as different amounts of capital need to bereleased to the external market to achieve a return of R. In other words, for the family of x(.) functions we consider,there are two equilibria: (c,R), and (c(∆ω),R).The only unknown is c(∆ω).

3