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JOURNAL OF COMPARATIVE ECONOMICS l&226-240 ( 1992) Competition Policy vs Horizontal Merger with Public, Entrepreneurial, and Labor-Managed Firms’ FLAVIO DELBONO AND GIANPAOLO ROSSINI Istituto di Scienze Economiche, Universitd di Verona, Via Dell’Artigliere, 19, 37129 Verona, Italy Received January 10, 199 1; revised January 16, 1992 Delbono, Flavio, and Rossini, Gianpaolo-Competition Policy vs Horizontal Merger with Public, Entrepreneurial, and Labor-Managed Firms The reorganization of existing state monopolies is a major issue of Eastern re- formers. Given a market monopolized by a labor-managed (LM) firm we try to compare a mixed duopoly with the case in which the original maximand of the LM monopoly is modified to take into account either entrepreneurial profits or social welfare. Welfare comparisons of the various market arrangements are then presented in order to provide some tentative policy conclusions. J. Comp. Econom., June 1992, 16( 2), pp. 226-240. Universita di Verona, 37129 Verona, Italy. o 1992 Academic Press, Inc. Journal of Economic Literature Classification Numbers: L12, L13, L32, PI 3. 1. INTRODUCTION Industrial policy measures in the future agenda of several Eastern Europe governments include both the splitting and the restructuring of property of most state-owned and collective firms.* Indeed, in some Eastern Europe economies an industry is sometimes monopolized either by a labor-managed (LM) firm or by a state-owned firm (S). The former is a company that maximizes revenue minus fixed costs per worker, while the latter is one that should maximize the sum of profits and consumers’ surplus. The latter termi- ’ Paper presented at the annual meeting of the ACES, Washington D.C., December 28-30, 1990. Egon Neuberger discussed this paper at the meeting, bringing up useful insights and helpful comments. We also thank Silvana Malle, Carlo Scarpa, Luca Fiorentini, and especially the editor and two anonymous referees for their invaluable remarks on earlier versions. Compu- tational help from Michele Burattoni is also acknowledged. The usual disclaimer applies. *See Lipton and Sachs (1990), Brus (l972), Roman (1985), Nuti (1988), and Grosfeld (1990). 0147-5967192 $5.00 Copyright 0 I992 by Academic Press. Inc. All rights of reproduction in any form reserved. 226

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JOURNAL OF COMPARATIVE ECONOMICS l&226-240 ( 1992)

Competition Policy vs Horizontal Merger with Public, Entrepreneurial, and Labor-Managed Firms’

FLAVIO DELBONO AND GIANPAOLO ROSSINI

Istituto di Scienze Economiche, Universitd di Verona, Via Dell’Artigliere, 19, 37129 Verona, Italy

Received January 10, 199 1; revised January 16, 1992

Delbono, Flavio, and Rossini, Gianpaolo-Competition Policy vs Horizontal Merger with Public, Entrepreneurial, and Labor-Managed Firms

The reorganization of existing state monopolies is a major issue of Eastern re- formers. Given a market monopolized by a labor-managed (LM) firm we try to compare a mixed duopoly with the case in which the original maximand of the LM monopoly is modified to take into account either entrepreneurial profits or social welfare. Welfare comparisons of the various market arrangements are then presented in order to provide some tentative policy conclusions. J. Comp. Econom., June 1992, 16( 2), pp. 226-240. Universita di Verona, 37129 Verona, Italy. o 1992 Academic

Press, Inc.

Journal of Economic Literature Classification Numbers: L12, L13, L32, PI 3.

1. INTRODUCTION

Industrial policy measures in the future agenda of several Eastern Europe governments include both the splitting and the restructuring of property of most state-owned and collective firms.* Indeed, in some Eastern Europe economies an industry is sometimes monopolized either by a labor-managed (LM) firm or by a state-owned firm (S). The former is a company that maximizes revenue minus fixed costs per worker, while the latter is one that should maximize the sum of profits and consumers’ surplus. The latter termi-

’ Paper presented at the annual meeting of the ACES, Washington D.C., December 28-30, 1990. Egon Neuberger discussed this paper at the meeting, bringing up useful insights and helpful comments. We also thank Silvana Malle, Carlo Scarpa, Luca Fiorentini, and especially the editor and two anonymous referees for their invaluable remarks on earlier versions. Compu- tational help from Michele Burattoni is also acknowledged. The usual disclaimer applies.

*See Lipton and Sachs (1990), Brus (l972), Roman (1985), Nuti (1988), and Grosfeld (1990).

0147-5967192 $5.00 Copyright 0 I992 by Academic Press. Inc. All rights of reproduction in any form reserved.

226

MARKETS WITH HETEROGENEOUS FIRMS 227

nology does not fully convey the scope and constraints of industrial organiza- tions operating in those countries, where the actual firms may not be accu- rately represented by the current labels of public and labor-managed firms. Our investigation seeks to shed light on policy measures that are under scru- tiny in such countries, absent central planning.

We investigate the social welfare consequences of two types of change in the ownership and market organization in reforming economies: the cre- ation of both a mixed duopoly and a horizontal merger between an LM firm and a profit-seeking enterprise (P) . The cases in which an S firm coexists and competes with P firms and in which an S and a P firm merge have been analyzed recently.3 Other contributions to the field concern international mixed duopolies, made up of P and LM firm~.~

Starting from a situation where an LM firm with two plants monopolizes an entire industry we envisage two scenarios: (i) a duopoly in which one plant, formerly managed by the LM monopoly, is now controlled either by a P or by an S company; and (ii) a company whose objective function com- bines that of the original LM firm and the goal of either a P or an S firrn5 The latter scenario may be thought of as the outcome of a horizontal merger between two companies identical in all respects but their objective functions. We shall assess the consequences of both a change in the goal pursued in the industry and liberalization, in that such an arrangement breaks up existing monopolies. In other words, we explore what happens if either competition or merger with a P firm, on the one hand, or an S firm, on the other hand, takes place.

The coexistence of a P or S and an LM decision maker entails the interven- tion of a social framer, but the effect on social welfare depends on the agents’ behavior, which is cooperative in the case of a merger and noncooperative under duopoly. Considering a merger between the P and LM firms, more weight to profit seeking is given with respect to the initial situation, but there is no competition since the monopolistic structure remains. The creation of a mixed duopoly, however, can be thought of as an instance of competition policy. Our research might thus be seen as a preliminary attempt to combine theoretical ingredients from comparative economics, industrial economics, and public economics to the objective of tackling a relevant policy issue.

3 See Delbono and Scarpa ( 1990). 4 See Horowitz (1991), Okuguchi (1991), and Mai and Hwang (1989). 5 One can think of geographically local industries such as transport or other services. To

consider an initial monopoly with two plants may seem a rather restrictive assumption. Below we consider as status quo an n-plant LM industry. Despite the prevalence of state-owned enter- prises in Eastern countries, their actual rules of behavior hardly fit the standard theoretical setting according to which public firms are modeled in modem economics. As is well docu- mented (Lee and Nellis, 1990), such firms seem to be somehow closer to LM companies than to social welfare maximizers. Hence, our status quo appears sufficiently descriptive of a good chunk of industries in Eastern countries.

228 DELBONO AND ROSSINI

We develop a simple partial equilibrium model allowing us to explore the conditions under which a horizontal merger between an LM and a P firm is socially superior to the status quo and to a mixed duopoly with the same firms. We repeat the exercise when the partner or rival of the LM firm behaves like an S enterprise. We show that giving some weight to entrepre- neurial profits in the industry is always beneficial with respect to the status quo. This is true for either type of industrial partner, P or S, and for either type of market solution, horizontal merger or noncooperative duopoly.

Our perspective is that of an external regulator, who can be thought of as a social framer, aiming at maximizing social welfare by modifying the objec- tive functions to be maximized by an industry’s decision makers.6 More precisely, we have to choose between two policy instruments: creating a horizontal merger or a mixed duopoly.

The paper is organized as follows. Section 2 presents the model and charac- terizes the status quo. Section 3 explores the creation of(i) a duopoly formed by an LM and a P firm in a Cournot-Nash setting, and (ii) a horizontal merger between the same agents. In Section 4 the same analysis is carried out for the case in which the P firm is replaced by an S firm. This generates another case of mixed duopoly and another case of horizontal merger. In Section 5 the model presented in Section 2 is extended to consider the case of more than two plants, under both duopoly and oligopoly settings. The wel- fare consequences of the various arrangements are compared in Section 6, and Section 7 contains some concluding remarks.

2. THE MODEL Consider an LM firm producing a homogeneous good whose market de-

mand function is

p=a-Q, (1) where p is price, Q is total output, and a is a positive parameter. Production takes place in two identical plants, each of which operates according to the production function ’

9, = vi., i= 1,2, (2) where li and qi denote, respectively, the quantity of labor employed and the output of the ith plant. The corresponding short-run cost function is*

c(a) = F + q:, (3)

6 In this sense our approach is close in spirit to the one presented in Shapiro and Willig (1990).

’ For simplicity we focus, on the case oftwo plants; in Section 5 we provide an extension to the caseofn> 2.

‘All workers are assumed identical in terms of membership share and number of hours provided to the firm.

MARKETS WITH HETEROGENEOUS FIRMS 229

where F is a positive fixed cost and the level of money wage has been normal- ized to 1.

The LM enterprise maximizes

v = PQ-2F c L

(where L = I, + 1,)) which can be written as

(a-Q>Q-2F 4: + 4: ’

(4)

(5)

where Q = q1 + q2. The first-order condition is also sufficient to calculate the optimal level of

total output 9

a*=: ifa 3 12F

= 0 otherwise, (6)

where a2 2 12 F emerges from the condition that price be greater than or equal to the average cost. In equilibrium each plant produces E//2, because with the convex cost function as described by (3) it would be inefficient to have identical plants producing different levels of output.

In the same industry a P monopolist with two plants would produce Qz= a / 3 if a 2 2 12 F, and zero otherwise. The inequality a2 > 12 F guarantees LM members a remuneration at least as great as the market wage.

Social welfare ( W) will be measured, as usual in partial equilibrium analy- sis, by the area between the demand curve and the cost curve. This is the well-known sum of consumers’ and producers’ surplu~.‘~ Hence, IV, gross of fixed costs, is given by

w=aQ-$-$‘q?. (7) i=l

The equilibrium level of W under monopoly of the LM firm is given by ”

w:=4Fp -4-3

’ The average total cost curve is decreasing at g Indeed, in each plant, the U-shaped average total cost is minimized when qi = p. The LM monopolist produces qz= 2 F/a in each plant. The condition a2 > 12 F implies that \rF < 2 F/a. This is crucial for the equilibrium to be sensible as shown by Cremer and Cremer ( 1990).

” The exact distribution of net surplus, defined as income minus fixed costs minus variable costs evaluated at the market wage, is discussed below.

” When both plants produce the same level of output, Eq. (7) reduces to W = aQ - Q*.

230 DELBONO AND ROSSINI

while the equilibrium level of W under P monopoly is

IV,*= gZ2. (9)

A straightforward comparison between ( 8 ) and ( 9 ) shows that when a 2 / F > 12, then IV,? > IV,*. In the following sections, I%‘,* will represent the basis of comparison for the design of industrial policies that we are going to in- vestigate.

When both plants produce the same level of output, the condition of sustainability can be written as

a-Q> fQ2+2F , Q ’

which yields

3Q2-2aQ+4F<O,

and imposes the restriction on Q and on the parameters,

a- A v- a+@ 3

<Q<------ 3 ’

where A = a2 - 12F.

(10)

3. AN LM FIRM AND A P FIRM 3.1. Mixed Duopoly

Now suppose that all workers of the LM monopoly, regardless of the plant in which they work, give up half of their membership rights. Assume that the total capital of the original LM monopolist is represented by the value of the two plants, and that one plant is taken over by a P company.

The two firms, P and LM, play a one-shot noncooperative game in output levels. The P firm chooses qP so as to maximize

VP = (a - Qh, - si - F, (11)

whereas the LM firm chooses its output q, to maximize

v = (a - Qk - F c 4: . (12)

The two first-order conditions, which are also sufficient for a maximum, yield the reaction functions

i&J = -!?L- ifq, <a- a - qp

2m

= 0 otherwise (13)

MARKETS WITH HETEROGENEOUS FIRMS 231

a-2 2F r

a a

* %

FIGURE 1

for the LM firm, and

i&(4,)= (n4qc) ifq,<a--2m

= 0 otherwise (14) for the P firm (see Fig. 1 where c is the label for an LM plant and p is for a P plant) b

Confining our attention to interior solutions, in which both firrns produce output, requires a2 > yF.12

PROPOSITION 1. There exists a unique, locally stable, Cournot-Nash equi- librium for the mixed duopoly, made up by an LM and a P firm (dcp), denoted (4,“: q,*); moreover, q,* > q,* > 0.

I* The output of the LM firm remains in the region of decreasing average total cost.

232 DELBONO AND ROSSINI

Proof: It suffices to show that if a2 > YF the intersection between the two 13) and ( 14) is unique and is such that q,* < a - 2w

As

where A = 9a2 + 32F, both q: and q,*are strictly positive if a2 > ?I;. Uniqueness follows from the fact that gC( qp) is continuous and monotonic- ally increasing for qp E [ 0, a - 2p?l and &,( qJ is continuous and monoton- ically decreasing for qc E [0, a - 21J2F]. Finally, straightforward algebra shows that the equilibrium is locally stable and that a2 > YF implies @ ’ cc. Q.E.D.

The expressions of q,*and q& through (7)) will allow us to calculate the equilibrium level of social welfare in dep.

3.2. Horizontal Merger

Suppose now that a fraction of the total members shares of the LM monop- oly, representing the assets of the company, is turned into shares and sold to an outsider P firm. We require that members of the original LM monopoly dismiss a corresponding fraction of their own membership. In other words, the industry is still monopolized, as in the status quo, but the entry of P executives alters the objective function of the monopolist. The resulting setting might be thought of as the outcome of a horizontal merger between two firms identical in all respects but their respective goals. Then the new firm chooses qmcp to maximize

V mcp = avp + (1 - a)V,, (15) where (Y E 10, 1 [ is an indicator of the weight of profits, i.e., a weight indicator of the profit seeking shareholders in the corporate board, in the payoff of the new firm.”

I3 We need not specify any rule governing the distribution of net surplus of the new firm, because we are interested only in the total level of social welfare and not in the composition of net producers’ surplus accruing to each partner. As a referee pointed out, one may wonder about how workers are paid. One can think of each worker splitting his total labor time between the two firms according to the relative output of each firm. As a result, each worker works in the same proportions as any other in both firms. If this arrangement is not feasible, it is possible to design other compensation schemes giving rise to the same result, that is, equal revenue across workers, labelled j. Such a scheme should require that

R, = wl; + SC/y

under the constraint that rtM = lLM and 17 = I’ V j, so that R, = R V j, where SC is net surplus per unit of time worked in the LM firm.

MARKETS WITH HETEROGENEOUS FIRMS 233

Maximizing ( 15 ) with respect to qmcP yields the following first order condi- tion, which is sufficient for a maximum:

G&,Ja - Qncp) + 2( 1 - a)(4F - fan,,) = 0. (16)

Again, both plants produce the same level of output in equilibrium. Let q* be the solution(s) of ( 16)) so that

&* dh(q)lda -=- dor Wq)l&

=s dh(q)/dol > 0,

where = ’ reads “has the same sign of “; h(q) is the left-hand side of ( 16 ) and we are taking advantage of the second-order condition for a maximum. Moreover,

&* - =’ dh(q)/dF > 0 dF

and

&* 2 - =‘dh(q)/du < or > 0 as (Y < or > - da q2+2’

From the above comparative statics we can conclude that (i) increasing the weight of P boosts output, and (ii) there is a threshold value for (Y beyond which the perverse behavior of the LM firm vanishes in the merger solution.

Unfortunately, ( 16 ) cannot be handled analytically; therefore, we resort to a numerical treatment. We shall calculate q&, for different values of the parameters CX, a, F, and then we shall calculate the resulting level of social welfare, as given by the expression in footnote 10.

Again, it is worth specifying how workers could be paid in this regime. First of all, it is immaterial to distinguish between the two plants as they produce the same output level. Then, each worker is paid the hourly money wage plus a dividend that is the ratio between the fraction of total surplus accruing to workers and the total number of workers. Such a fraction will be the result of a sharing rule, related to (Y, that dictates how net surplus is split between the two shareholders.

4. AN LM FIRM AND AN S FIRM 4.1. Mixed Duopoly

Along the same line as in Section 3 we assume that one plant is managed by a firm behaving like a social welfare maximizer. The new firm, called an S firm, will run one of the two plants formerly belonging to the LM enterprise in the status quo. We next analyze the Coumot-Nash equilibrium arising in such mixed duopoly and postpone the analysis of a horizontal merger to the next subsection.

234 DELBONO AND ROSSINI

The LM firm still chooses q, in order to maximize ( 12)) whereas the S firm chooses q, to maximize social welfare, i.e., the sum of producers and con- sumers surpluses:

s

Q v,= w= (a - z)dz - qf - q: - 2F

0

=aQ-$-q;-q;-2F.

The two first-order conditions, which are also sufficient, yield

2F 4,(4s) = - if q, <a-

a - 4, 2@

= 0 otherwise

for the LM firm, and

(17)

(18)

= 0 otherwise (19)

for the S firm (see Fig. 2). These expressions, through ( 7 ), will allow us to calculate the equilibrium

level of social welfare. We still confine our attention to interior solutions. This requires a2 > 18F.

PROPOSITION 2. There exists a unique, locally stable, Cournot-Nash equi- librium for the dcs, denoted (qz q,*); moreover q,* > q$

ProoJ Follows the same procedure as the proof of Proposition 1, once it is noted that in this case q,* = fi-aandq,*=(2a-fi)/3,whereA=a2+ 6F. Q.E.D.

4.2. Horizontal Merger

Suppose now that the framer wants to assess the impact of a merger be- tween the LM firm and the S firm. Everything replicates Section 3.2 but for the objective of the non-LM firm.

The new firm will choose qmcS to maximize

V mcs = PK + ( 1 - B)V,, (20)

where B E IO, 1 [ is a weight indicator of social welfare in the payoff of the new firm. Maximizing V,, with respect to qmcS yields the following first- order condition, which is still sufficient for a maximum:

Pqida - 2q,,,) + 2( 1 - P)(4F - aqmcs) = 0. (21)

MARKETS WITH HETEROGENEOUS FIRMS 235

qs

a-25

i

* qs

FIGURES

The same qualitative properties of ( 16) still apply to (2 1) . As for ( 16)) (2 1) is not amenable to analytical treatment and, therefore, we are com- pelled to resort to numerical resolution within the viable region of the param- eters ( a2 > 18 F) . Once we have calculated q,&, we can proceed, using the expression in footnote 10, to obtain the associated level of social welfare.

5. EXTENSIONS 5.1. Two Firms, n Plants

Consider an LM monopoly with IZ > 2 plants. Proceeding as in Section 2, the equilibrium output level, when positive, is

(22)

236 DELBONO AND ROSSINI

In the same industry, a P monopolist would produce

Qp*= an 2(n+ 1)’ (23)

Suppose now that k plants are managed by the LM company while m plants are controlled by a P firm, with m + k = n. In the interior Nash equilibrium of this mixed duopoly output levels in the two firms are

SC?= f a*(m + 2)2 + 16F(km2 + km) - a(m + 2)

2m (24)

9: = 3am + 2a - f( 3am + 2a)* - 8m(m + l)(a* - 2kF)

4(m + 1) * (25)

If the original LM monopoly is turned into a mixed firm as in Section 3.2, the first-order condition dictates

f[ an - 2q,,,(n + l)] + ‘(l - cr$2nF- “) = 0. (26) mcp

In the next section we shall perform numerical analysis for the case n = 3 in order to compare social welfare in the various regimes.

5.2. A Mixed Oligopoly with n Firms For the sake of completeness we also provide a preliminary characteriza-

tion of a mixed oligopoly. We now consider the transformation of the origi- nal status quo, an n plants LM monopoly, into a mixed oligopoly in which m P companies compete with k LM firms. The first-order conditions to be used for computing the Nash equilibrium of this oligopoly are

qf(k - 1) - qr(a - mqh) + 2F = 0 (27) for each of the k LM firms and

a-kg,-(3+m)q,=O (28) for each of the m P firms, where 1 = 1. . . k denotes LM firms and h = 1 . . . m denotes P firms.

6. WELFARE COMPARISONS In this section we compare social welfare across the various market re-

gimes portrayed in previous sections. We employ numerical analysis since some of the relevant equations are not amenable to analytical treatment. To this end, we set one numerical level of market size and allow the fixed cost to vary within its feasible region, and (Y or ,f3 to vary between zero and one.14

I4 The sustainability condition (price not lower than average cost) requires F not to be too large with respect to market size.

MARKETS WITH HETEROGENEOUS FIRMS 231

We first consider the changes caused by the participation of P agents in a previously monopolised LM industry. Relying upon Sections 3 and 5, we compare the following regimes: status quo, P monopoly, mixed duopoly, and horizontal merger. This comparison will be performed when the in- dustry is endowed with two or three plants. We then undertake the same comparison when the market arrangement involves an S firm.

Finally we provide an overall assessment of all regimes. Our claims are based upon a fairly large set of numerical simulations; the ones reported here only aim at conveying some quantitative flavor of the welfare comparisons.

6.1. Overall Claims

Tables 1 and 2 summarize the outcomes of our numerical exercise. We have calculated the level of social welfare in the status quo, in the mixed, P and LM duopoly, S and LM duopoly, respectively labeled dcp and dcs, and in the merger, between the aforementioned firms, mcp and mcs. In the case of P + LM we provide data also for the case of three plants.

Claim 1. Both the dcp and the mcp yield a higher social welfare than the sq (status quo).

This is true regardless of the values of the four parameters, a, F, CY, n . Once profit seeking matters, irrespective of the degree of rivalry in the industry, we get a definite welfare improvement. In order to compare the social desirabil- ity of either arrangement with respect to the status quo, we have to consider fixed costs vis a vis market size.

Claim 2. dcp is superior to mcp when (Y is close to zero, provided F is not too large.

In the other cases mcp is socially superior. Hence, once F is kept fixed, there exists a critical value IX* such that, for (Y > (Y* mcp dominates dcp and vice versa. From the comparative statics of Section 3, the critical (Y* also depends on market size. Indeed, for a given F, (Y* decreases as market size increases.

When we have a three-plant duopoly it is socially more desirable to have two plants in the P firm and one in the LM rather than the opposite. As the number of plants attributed to the P firm grows, we move toward welfare levels closer to those reached by the merger when (Y > CY*. In other words, the solution of the mixed duopoly tends to the one of the merger, for (Y > (Y*, as the number of plants of the P firm increases while the LM keeps only one plant.

When we consider Table 2, mcs and dcs, we get a first result paralleling Claim 1:

238 DELBONO AND ROSIN1

TABLE 1

Two plants a = 100

alpha F w dcp .Ol 0.1 0.3 0.5 0.7 0.9

0.1 0.4 1562.6 0.4 1 4.0 1564.4 4.0 3 12.0 1568.0 12.0 6 23.9 1573.5 23.9 8 32.1 1577.1 31.9

50 196.0 1651.4 199.8 200 736.0 1886.0 1968.2

2203.1 2217.4 2220.1 2203.1 2217.4 2220.1 2203.1 2217.4 2220.1 2203.1 2217.4 2220.1 2203.5 2217.4 2220.1 2204.5 2217.8 2220.4 2207.9 2218.4 2220.8

Three plants a = 100

2221.4 2222.1 2221.4 2222.1 2221.4 2222.1 2221.4 2222.1 2221.4 2222.1 2221.4 2222.1 2221.4 2222.1

F sq .Ol 0.1 alpha

0.3 0.5 0.7 0.9

0.1 0.0 1 6.0 3 18.0 6 35.9 8 47.8

50 292.5 200 1080.0

F

0.0 0.2 0.2 0.4 0.5 3.1

30.1

36.8 2565.7 2575.1 2577.0 2577.7 2549.5 2571.0 2575.1 2577.0 2577.7 2549.5 2571.0 2575.1 2577.0 2577.7 2550.0 2571.0 2575.1 2577.0 2577.7 2550.0 2571.0 2575.1 2577.0 2577.7 2551.9 2571.7 2575.5 2577.0 2577.7 2559.2 2573.2 2576.2 2577.7 2577.7

dcp lc+2p” dcp 2c + Ip

0.1 2224.4 1047.8 1 2224.4 1577.5 3 2231.0 1577.5 6 2237.9 1589.9 8 2238.0 1589.9

50 2301.6 2055.9 200 2501.5 2180.3

a Here c is the label for an LM plant, p for a P plant.

Claim 3. Both the dcs and the mcs yield a higher social welfare than sq.

CZaim 4. mcs is always superior to dcs, except for low values of F vis Avis market size.

This is due to a rather unusual feature of the maximand of mcs: even for values of ,6 very close to zero, the equilibrium level of output approaches the equilibrium level of output when /3 is close to one. With a low F vis a vis market size, there is a L?* such that for p < /3* dcs is superior to mcs.

MARKETS WITH HETEROGENEOUS FIRMS 239

TABLE 2

SOCIAL WELFARE: STATUS Quo (sq), MIXED DUO~~LY (dcs), MERGER (mcs)

Two plants a = 100

beta F sq dcs .Ol 0.1 0.3 0.5 0.7 0.9

0.1 0.4 1666.9 2476.4 2500.0 2500.0 2500.0 2500.0 2500 1 4.0 1668.7. 2476.5 2500.0 2500.0 2500.0 3 12.0 1672.7 2416.6 2500.0 2500.0 6 23.9 1678.6 2476.7 2500.0 8 32.1 1682.6 2476.8 2500.0

50 196.0 1763.0 200 736.0 2010.0

7. CONCLUDING REMARKS

We have investigated the effects on social welfare of two types of industrial policies in an industry initially monopolized by an LM firm. We envisaged a social framer who intervenes in the industry, either implementing a mixed noncooperative duopoly or devising a horizontal agreement giving rise to a merger. Both industrial arrangements have been studied with two different partners: a profit-seeking (P) company and a welfare-maximizing (S) com- pany. The four regimes resulting from this framework have been compared to the status quo. It appears that competition policy aiming at the creation of a mixed duopoly leads to a definite welfare improvement with respect to the status quo.

The behavior of the firms after the reorganization depends on the weight given to each partner. There is a threshold value of this weight. Below it, the behavior of the merger replicates the well-known LM allocative inefficiency. Above it, we are left only with the allocative loss of a monopoly, which decreases if the partner of the LM firm is an S firm.

Although our conclusions have been obtained within a highly stylized model, we think they may enlighten various effects of different industrial policies. For instance, the fact that a merger solution is better than a duopo- listic one only beyond a critical level of the weight parameter (a) implies that competition policy is superior if P agents do not have at least some say in the merger. Below the critical level of the weight parameter (Y, the merger solu- tion is socially superior to noncooperative duopoly only at high levels of fixed costs vis a vis market size. When firms are small compared to the market, duopoly is better. The welfare improvement from changing regimes decreases as fixed costs increase. Indeed, in order to have a larger improve- ment with respect to the status quo it might be better to let private, and perhaps public, shareholders enter the company, with some weight, rather than splitting the initial monopoly and adopting a duopoly solution.

240 DELBONO AND ROSSINI

Some of the limitations of this model point to potential extensions. A first route could amount to making endogenous, via bargaining, the weight of different goals in the objective function of the enterprise resulting from the merger.15 Further we have focused on a closed economy. To investigate the effects of opening the economy to international trade seems a rather promis- ing avenue for future research.16

REFERENCES

Brus, Wlodzimietz, The Market in a Socialist Economy. London: Routledge and Kegan Paul, 1972.

Cremer, Helmuth, and Cremer, Jacques, “Employee Control and Oligopoly in a Free Market Economy.” Mimeo, Virginia Polytechnic Institute & State University, June 29, 1990.

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is For an attempt to pursue this route see Rossini and Scarpa ( 199 1) . I6 See Horowitz (1991), Mai and Hwang (1989), and Okuguchi (1991).