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Managerial incentives and the decision to hire managers in markets with public and private firms
European Journal of Political Economy Vol. 17 Ž2001. 877–896 www.elsevier.comrlocatereconbase
Managerial incentives and the decision to hire managers in markets with public and private firms Mark D. White ) Department of Political Science, Economics, and Philosophy, College of Staten Islandr CUNY, 2800 Victory BouleÕard, Staten Island, NY 10314, USA Received 1 June 1999; received in revised form 1 May 2000; accepted 1 December 2000
Abstract This paper considers the managerial incentive contract when public and private firms compete in the same market. Social welfare is enhanced when all firms hire managers, but for different reasons than when all firms are privately owned. Incentives to hire managers differ in private and public firms; in equilibrium, only private firms hire managers. q 2001 Elsevier Science B.V. All rights reserved. JEL classification: L13; L32; D21 Keywords: Mixed oligopoly; Public enterprise; Managerial incentive contracts
This paper investigates managerial incentive contracts in an industry in which public firms with social welfare objectives compete with private firms that have profit objectives. 1 More precisely, I consider whether it is in all firms’ interests to hire managers, as is standard in the private sector, or whether incentives to hire managers are asymmetric because of the different objective functions.
)
Tel.: q1-718-982-3193; fax: q1-718-982-2888. E-mail address: [email protected] ŽM.D. White.. 1 Such industries are often called mixed oligopolies; prominent examples include the package and overnight mail delivery industries in the United States, in which the public United States Postal Service competes with private firms such as Federal Express and UPS, and the Indian airline industry in which state-owned Indian Airlines competes with several private airlines. 0176-2680r01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 7 6 - 2 6 8 0 Ž 0 1 . 0 0 0 6 0 - X
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The study of industries with private and public firms began with Merrill and Schneider Ž1966., and was further developed in the 1980s when game theory was applied by Cremer et al. Ž1989., De Fraja and Delbono Ž1989., and others.2 Strategic interaction between private and public firms is particularly relevant when governments privatize their state enterprises or open to competition markets that were previously monopolized by state enterprises Žsuch as telecommunications industries in European countries, Japan, Australia, New Zealand, Singapore, and elsewhere.. Little attention has been directed at investigating management of firms when private and public firms compete.3 The papers by Barros Ž1994, 1995. are notable exceptions, and I will discuss how these studies are related to the present paper. In the managerial incentive contract literature, which began in the mid-1980s, Fershtman and Judd Ž1987. and Sklivas Ž1987. demonstrated how firms can increase profits by precommiting to strategies that seem irrational in the short-term, but are beneficial in the long-term when the other firms’ actions are taken into account.4 Firm owners cannot themselves commit to pursuing non-profit-maximizing strategies, because owners of other firms will know that, when the firms actually make decisions, they will revert to profit-maximization, despite protests to the contrary.5 One way to credibly commit to a strategy other than profit-maximization is to hire a manager with complete discretion over the firm decisions, and assign him or her a contract that provides an incentive to pursue an alternative strategy. If a firm’s owners can convince their competitors that the manager is truly in charge and the owners no longer have control of the firm, a non-profitmaximizing strategy can be credible; therefore, this constitutes a method of strategic precommitment. Managerial incentive contracts can also help to solve delegation and principalragent problems in the event that a manager’s effort andror the output of the firm are not easily observable; in fact, it is this property that many feel justifies the managerial contract approach ŽBasu, 1993, Chapter 14.. The Fershtman–Judd–Sklivas ŽFJS. model has proven very popular in the industrial organizationrmanagerial economics literature, despite criticism Žagain, see Basu, 1993, Chapter 14.. Although the model has been extensively applied to competition among private firms, only Barros Ž1994, 1995. has applied the model to markets in which private and public firms compete.
2
See De Fraja and Delbono Ž1991. and Nett Ž1993. for reviews of the literature. For an overview of how scholars of management and operations research view the management of public enterprise, see Eliassen and Kooiman Ž1993.. 4 Vickers Ž1985. anticipated this development, but did not develop the managerial incentive contract model as thoroughly as did Fershtman and Judd, and Sklivas. 5 See Elster Ž1979. for further discussion of the difficulties involved in strategic precommitment. 3
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This paper departs from the studies by Barros by focusing on different issues. Barros emphasized the delegation aspects of managerial incentive contracts in the context of asymmetric information, which highlighted their usefulness in alleviating principleragent problems, whereas I choose to focus on the strategic benefits of such arrangements in situations of complete information. While Barros Ž1995. included both strategic effects and asymmetric information, I want to isolate the strategic benefits of managerial incentive contracts without the additional complexity introduced by modeling the information held by the parties. In the 1995 paper, Barros explained that, in an industry with one public and one private firm, allocative efficiency increases at the expense of productive efficiency when managers are hired by both firms, with a net positive effect on welfare, and that privatizing the public firm has a negative effect on welfare. We will see that these results can be proven Žsome with slight modifications. using my simplified approach, which allows the strategic interaction to be observed more easily. I also endogenize the decision whether or not to hire managers, as does Basu Ž1995. in the case of private firms. Barros Ž1995. showed that welfare is higher if both firms hire managers compared to when neither firm does, and I confirm this result with a general number of private firms in the industry. However, utilizing a simple game framework, I show that when a firm has the choice of whether or not to hire a manager, the sole subgame-perfect Nash equilibrium ŽSPNE. is that only private firms hire managers. In this equilibrium, only private firms produce output, while a public firm exists only to impose discipline on the private firms. This creates somewhat of a contestable market in the sense of Baumol et al. Ž1982.. I also show that this is the equilibrium of a larger game in which a public firm chooses whether to maximize social welfare, privatize and maximize profits, or shut down. The government will decide to allow the public firm to remain public and allow private firms to produce all output in a regime in which only they hire managers. Here, the very existence of a public firm enables welfare-increasing regulation of the industry, without requiring inefficient production by the public firm, which has higher marginal costs by assumption.6 Section 1 outlines and solves the basic model. Section 2 compares the results of the managerial model with those of the standard, nonmanagerial model, and in Section 3, I compare the results to an industry with private firms only to determine the effects of privatization on the managerial model. In Section 4, I endogenize the strategic decisions whether or not to hire managers. Section 5 analyzes the larger game, in which the public firm’s operation and shutdown decision is made before the managerial hiring decisions. I conclude in Section 6.
6
This naturally raises the issue of fixed cost; see Footnote 19 for a discussion of fixed cost and zero production by the public firm.
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1. Model and solution We assume that n G 1 private firms and one public firm compete in a Cournot game in a homogeneous-goods market with a linear Žinverse. demand curve p s a y Q, where p is the market price and Q is the total output of all n q 1 firms.7 The firms have asymmetric linear cost functions Ci Ž qi . s c i qi q Fi Ž i s 0,1,2, . . . ,n.; all firms’ fixed costs are zero.8 The owners of a private firm Žfirms i G 1. maximize profit: n
ž
/
p i s pqi y c i qi y Mi s a y Ý q j y c i qi y Mi , js0
Ž 1.
where qi is firm i’s output and Mi is its manager’s payoff Žif hired.. The public firm Žfirm 0. has an efficiency objective, defined as maximizing the unweighted sum of consumer surplus and the profits of the firms:9 n
W s CS q Ý p i s is0
1 2
n
ž / Ý qi
is0
2
n
qÝ is0
n
ž
/
a y Ý q j y c i qi y Mi . js0
Ž 2.
I assume c i s c1 for all i G 1 Ždue to symmetry among the private firms., and c 0 ) c1; if the public firm were as efficient as the private firms, it would be efficient for the public firm to produce the socially optimal output. This trivial solution is avoided by assuming that the public firm is relatively inefficient.10 The structure of the game is as follows: in stage one, each firm’s ownerradministrator assigns its manager a Fershtman–Judd–Sklivas ŽFJS. managerial contract, in which her payoff is based on a linear combination of her firm’s profits and revenues. In stage two, having accepted the contracts offered, each manager produces her payoff-maximizing output. Using the principle of backward induction, I first solve for the managers’ outputs as functions of their contract terms. Each firm’s manager chooses her firm’s output to maximize her compensation, given by the following managerial contract: Mi s a i bip i Ž qi . q Ž 1 y bi . R i Ž qi . q Ti ,
Ž 3.
in which p i is the profit, and R i is the revenue, earned by firm i when qi is produced. bi is the crucial contract term, while a i and Ti are adjustment terms; 7
The results of this model are not specific to this particular demand function, which is standard in the literature, and used for computational simplicity. 8 Again, see Footnote 19 for an exception to this. 9 We do not count the managers’ income in our welfare expression; we assume that the potential managers would earn their reservation utilities elsewhere, so the hiring decisions of the firms in this industry do not impact the managers’ well-being. 10 This assumption is not uncontroversial; see Bos ¨ Ž1991., Section 3.2, and Nett Ž1993., Section 2.3, for summaries of the empirical literature on the relative efficiency of private and public firms.
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the latter two terms are used to set the manager’s subgame-perfect Nash equilibrium ŽSPNE. compensation equal to her reservation utility. I assume that the payoffs to the managers Žtheir reservation utilities. are negligible compared to profits, such that the managers’ payoffs do not significantly affect either the hiring or shutdown decision. I make this assumption because my emphasis is on the strategic effect of hiring managers, not the impact of the managers’ payoffs on profits. For this reason, I will henceforth omit the managers’ payoffs from profit Žand welfare. expressions. Since bi , a i and Ti are given to the manager of firm i, each manager’s maximization problem is equivalent to: max bip i Ž qi . q Ž 1 y bi . R i Ž qi . qi
n
smax R i Ž qi . y bi Ci Ž qi . smax qi
qi
ž
/
a y Ý q j y bi c i qi . js0
Ž 4.
The contract term, bi , can thus be considered to be a discount factor on costs; the lower the assigned bi , the more the manager is instructed to discount costs. If a manager’s contract term is less than one Žperhaps even negative., her reaction function shifts outwards from its profit-maximizing position, a change which is representative of more aggressive competition on the part of the manager and the firm.11 If the contract term is equal to one, the manager simply maximizes profits, and if the contract term is greater than one, the manager is actually restrained, or less aggressive than when maximizing profits; we will see this possibility later in the public manager’s contract term. Fershtman and Judd Ž1987. and Sklivas Ž1987. find that, in a private duopoly with identical firms, it is a dominant strategy for each firm to instruct its manager to discount costs Žeach manager’s contract term is less than one.. The outcome of this game is a Prisoner’s Dilemma for the firms’ owners; each firm makes lower profits than if neither hired a manager, but social welfare is higher, due to increased output. In my model, since the managers are motivated only by their payoffs, and not whether the firms for whom they work are private or public, stage two of the game is identical to that of Fershtman and Judd and Sklivas. Solving the maximization problem of the manager of firm i, I derive her Cournot reaction function as a function of the assigned contract term, bi , and the other firms’ output Ždenoted by q j,y i .: n
ay qi Ž q j,y i , bi . s
11
q j y bi c i
Ý js0, j/i
2
.
A more elaborate interpretation of a negative contract term is provided after Proposition 1.
Ž 5.
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We see that this is identical to the standard Cournot reaction function under linear demand and costs, except for the discounted marginal cost in the numerator. Solving all managers’ reaction functions simultaneously allows the stage-two equilibrium outputs to be derived as functions of the n q 1 contract terms: n
a y Ž n q 1 . bi c i q
Ý
bj c j
js0, j/i
qi Ž b 0 , . . . , bn . s
. Ž 6. nq2 Again, this is the standard result except for the firms’ discounted costs. In stage 1 of the game, the ownersradministrators take their managers’ output functions into account, and then simultaneously choose their contract terms to maximize their respective objective functions. Substituting Eq. Ž6. into Eqs. Ž1. and Ž2. and simultaneously solving the resulting first order conditions, we determine the optimal contract terms:
b0 s 1 y b1 s 1 y
a q n Ž n 2 q 2 n q 3 . c1 y Ž n3 q 2 n 2 q 3n q 1 . c 0 c0 n Ž n q 1 . Ž c 0 y c1 . c1
.
,
Ž 7.
Here, b 1 represents the private managers’ common contract term Židentical due to symmetry among the private firms.. The properties of the SPNE contract terms are summarized in Proposition 1. Proposition 1. In a linear-cost Cournot mixed oligopoly in which each firm assigns its manager a FJS contract, the SPNE contract terms haÕe the following properties. (a) Each priÕate manager’s contract term is less than one, and may be negatiÕe if the public firm’s marginal cost is large compared to that of the priÕate firms; (b) the public manager’s contract term is greater than (less than) one if the public firm’s marginal cost is large (small) enough relatiÕe to the priÕate firms’ marginal cost and the demand parameter (a), and may be negatiÕe; (c) the public manager’s contract term is lower (higher) than that of the priÕate managers if the public firm’s marginal cost is relatiÕely low (high); and (d) as the number of priÕate firms increases, the public manager’s contract term rises and the priÕate managers’ contract term falls.
All parts of Proposition 1 can be verified by observation and simple calculation; note that the asymmetry of the public and private firms’ objective functions is
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clearly reflected in their contract terms, b 0 and b 1. It is surprising that the public manager’s contract term can be larger than that of the private managers; we would expect to see the public manager instructed to be more aggressive Žlower b 0 . in order to boost total output and increase consumer surplus. This is true if the public firm’s marginal cost is relatively low, but if it is too high, the public firm would rather have the private firms produce more output in the interest of lowering total costs, and thus, the public manager will be commanded to Aback downB, possibly even to the point of overemphasizing costs Ž b 0 ) 1.. On the other hand, if either manager’s contract term is negative, then that manager’s firm wants her to expand output so much that it actually instructs the manager to give positive weight to costs; in this case, since marginal cost encourages production, it is diminishing marginal revenue Žin the negative range. alone that restrains the manager from producing past the owner’s wishes. Also, as the number of private firms increases, the public firm does not need to produce as much output, so its manager’s contract term rises, and the private contract term falls in response Žfor a fixed value of c 0 ..12 Substituting the SPNE contract terms ŽEq. Ž7.. into the managers’ output functions ŽEq. Ž6.., we can determine the SPNE individual and total outputs, consumer surplus, profits, and welfare: q 0 s a q n Ž n 2 q 2 n q 2 . c1 y Ž n q 1 . Ž n 2 q n q 1 . c 0 , 2
q1 s Ž n q 1 . Ž c 0 y c1 . , Q s q0 q nq1 s a q nc1 y Ž n q 1 . c 0 , CS s
a q nc1 y Ž n q 1 . c 0 2
2
,
p 0 s n Ž c 0 y c1 . a q n Ž n 2 q 2 n q 2 . c1 y Ž n q 1 . Ž n 2 q n q 1 . c 0 , 3
2
p 1 s Ž n q 1 . Ž c 0 y c1 . , Ws
2 2 Ž a y c0 . q n Ž 2 n2 q 3n q 2 . Ž c0 y c1 .
Ž 8. 2 If c 0 s c1 , we see that standard results obtain; the public firm produces the socially optimal level of output and the private firms produce nothing. It is for this reason that, if costs are linear, the public firm has to be less efficient to generate nontrivial results, in managerial as well as nonmanagerial settings. As the relative 12
The effect of n alone on the private managers’ contract term is ambiguous, depending critically on n itself, as well as the public manager’s contract term and marginal cost, as can be seen by differentiating the reaction function of b 1 in terms of b 0 with respect to n: Eb 1 Ž b 0 . En
s
Ž n2 y2. Ž aq b 0 c0 y2 c1 . 2
Ž n2 q nq2. c1
.
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884
inefficiency of the public firm increases, q1 rises and q0 falls, because the public firm AallowsB the more efficient private firms to produce more output. However, total output falls, because the private firms react conservatively to the drop in public output. Note that the expression for public output is strictly positive only if: c0 -
a q Ž n 3 q 2 n 2 q 2 n . c1 n3 q 2 n2 q 2 n q 1
s c0 ,
Ž 9.
where the polynomials have been expanded to make clear that the upper limit, c 0 , is a weighted average of the demand parameter a and the private firms’ marginal cost c1. As n grows, the weight on c1 increases as well; the public firm has to be relatively more efficient to stay in production. I will assume c 0 - c 0 for the rest of this paper; this guarantees positive public output in all the other models I shall consider Žthe model in which all firms hire managers is the most restrictive on the public firm, due to the increased output from the private firms.. This explains the seemingly odd result, observable from Eq. Ž8., that each private firm’s output increases and total output falls as the number of private firms increases: Eq1 En
EQ s 2 Ž n q 1 . Ž c 0 y c1 . ) 0,
En
s y Ž c 0 y c1 . - 0.
Ž 10 .
Note that these changes are functions of the cost difference between the public and private firms. As n increases, the public firm instructs its manager to produce less, allowing more output from the private firms Žas their managers’ contract terms are raised., but resulting in less total output. This is true for a fixed c 0 , but c 0 is more tightly constrained Ž c 0 decreases. as n increases. The maximum cost difference between the two types of firms must fall, partially offsetting the direct effect of n on these outcomes; if c 0 falls as n increases Žpossibly due to administrative or political pressure to cut costs in the face of growing private competition., public output could increase, each private firm’s output could fall, and total output could increase. Indeed, as n approaches infinity, this cost difference approaches zero, implying that price nears c 0 Žwhich itself approaches c1 . and the public firm produces nearly all output.
2. Comparing entrepreneurial and managerial oligopolies We can compare the results in Eq. Ž8. to those of the nonmanagerial, or entrepreneurial case,13 in which each owner or administrator simply maximizes 13
The use of the term AentrepreneurialB may seem inappropriate when one of the firms is owned and operated by the government; we use it merely for reasons of consistency with the literature.
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her objective function, whether it be profit or welfare. The following are the standard Cournot results when a public firm and private firms compete: q0 s a q nc1 y Ž n q 1 . c 0 , CS s Ws
Ž a y c0 . 2
q1 s c 0 y c1 ,
Q s a y c0 ,
2
,
2
p 0 s 0, p 1 s Ž c 0 y c1 . ,
2 2 Ž a y c 0 . q 2 n Ž c 0 y c1 .
. Ž 11 . 2 ŽThe assumption that c 0 - c 0 guarantees positive public output.. The differences between the managerial and entrepreneurial models are summarized in Proposition 2. Proposition 2. In a market with linear costs and Cournot competition between a public firm and priÕate firms, the following changes occur when the firms all hire managers and assign them FJS managerial contracts: (a) PriÕate output increases but public output drops, the net result being lower total output (higher price, lower consumer surplus); (b) priÕate profit rises, and public profit rises to become strictly positiÕe; and (c) welfare is higher. After managers are hired, he private firms produce more output and the public firm produces less Žin fact, the entrepreneurial public firm produces the same output as all the managerial firms together.. Total output is less in the managerial case, and the private firms make more profit because of an increase in output and price, while the public firm makes strictly positive profits.14 Finally, social welfare is higher with managerial firms; the additional profits in the managerial case overwhelm the loss in consumer surplus. This result about social welfare confirms Barros’ conclusion ŽBarros, 1995, p. 382, Proposition 3., who also finds that social welfare is higher in a mixed duopoly when both firms have managers, as opposed to the strictly nonmanagerial regime; qualitatively, the explicit inclusion of asymmetric information does not affect this result. In both my model and Barros’, social welfare increases when managers are hired in a mixed oligopoly because the drop in average and total costs due to the shifting of production from the public firm to the private firms more than compensates for the lower output; the increase in productive efficiency is greater than the fall in allocative efficiency. These results are in stark contrast to those of Fershtman and Judd and Sklivas, who considered only private firms. In each case, welfare rises, but the way in 14
Again, this assumes that the managers’ payoffs are negligible compared to profits.
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which this increase eventuates is quite different. With only private firms, social welfare increases when managers are hired, because each firm produces more output than they would without managers Žthe Prisoner’s Dilemma., but the resulting rise in consumer surplus dominates the fall in profits. When a public firm is present to compete with private firms, profits rise when managers are hired because they were abnormally low before managers due to high output Žand low price.. Consumer surplus falls, but not by much, because output is still relatively high in the managerial mixed oligopoly. The rise in profits dominates the fall in consumer surplus, again increasing social welfare, but by diametrically opposite means compared to the case of a market in which there are only private firms.15
3. Privatization I turn now to privatization; that is, the public firm administrators are instructed to maximize profit rather than social welfare. I assume Žfor this section. that all firms hire managers before privatization, and we will see that all firms will hire managers after privatization as well. Therefore, this section can be interpreted as comparing managerial mixed public and private, and only private, oligopoly. When there are only private firms,
b0 s 1 y n b1 s 1 y n q0 s q1 s Qs
a q n Ž n q 1 . c1 y Ž n 2 q n q 1 . c 0
Ž n2 q 2 n q 2. c0 a q Ž n q 1 . c 0 y Ž n q 2 . c1
Ž n 2 q 2 n q 2 . c1
,
,
Ž n q 1 . a q n Ž n q 1 . c1 y Ž n 2 q n q 1 . c 0 n2 q 2 n q 2 Ž n q 1 . a q Ž n q 1 . c 0 y Ž n q 2 . c1 n2 q 2 n q 2 Ž n q 1 . Ž n q 1 . a y nc1 y c0 n2 q 2 n q 2
,
,
,
15 Another phenomenon contributes to the odd results of this section: the form of the FJS managerial contract is not well-suited to a public firm. A public firm intends to maximizes social welfare, but when it assigns a FJS contract, it instructs its manager to maximize a linear combination of profits and revenues, a qualitatively different incentive scheme. The public firm administrators optimally structure the FJS contract to maximize welfare, but the manager can only see profits and revenues, not the larger picture, including consumer surplus and private profit. The public firm administrators would have more precise control over the manager if the scope of the contract were expanded to include these other welfare-related measures; for instance, they could affect the slope of the manager’s reaction function, impossible with an FJS contract. See White Ž1999. for an analysis of such an incentive scheme.
M.D. White r European Journal of Political Economy 17 (2001) 877–896 2
CS s
p0s
p1s Ws
Ž n q 1 . Ž n q 1 . a y nc1 y c0 2 Ž n2 q 2 n q 2.
2
2
,
Ž n q 1 . a q n Ž n q 1 . c1 y Ž n 2 q n q 1 . c 0 Ž n2 q 2 n q 2.
2
,
2
Ž n q 1 . a q Ž n q 1 . c 0 y Ž n q 2 . c1 Ž n2 q 2 n q 2.
887
2
,
2
nq1 2
2 Ž n q 2 n q 2.
2
= Ž n 2 q 2 n q 3 . Ž a y c1 . Ž n q 1 . a y Ž n y 1 . c1 y 2 c 0 2
q Ž 2 n 4 q 6 n 3 q 10 n 2 q 7n q 3 . Ž c 0 y c1 . .
Ž 12 .
The results of now privatizing the public firm are summarized in the following proposition. Proposition 3. When all firms hire managers to whom they assign FJS contracts both before and after priÕatization, the consequences of priÕatizing the public firm are: (a) If c 0 is relatiÕely low, the priÕate managers’ contract term falls, while that of the public manager rises, public and total output fall, and priÕate output and profit rise; if c 0 is relatiÕely high, these effects are reÕersed, (b) public profit rises and social welfare falls, unless c 0 lies in an intermediate range between its highest and lowest possible Õalues. The first part of Proposition 3 describes the following changes Žthe superscripts m and p represent the cases of mixed public and private firms, and private firms only.:
b 0p y b 0m s
n2 q n q 2 2
Ž n q 2 n q 2. c0
q0p y q0m s y
n2 q n q 1
b 1p y b 1m s y
q1p y q1m s
n 2
Ž n q 2 n q 2 . c1
u,
nq1
u, n q2nq2 n qnq2 1 Qp y Qm s y 2 u, n q2nq2 nq1 p 1p y p 1m s a q Ž n3 q 3n 2 q 5n q 3 . c 0 2 2 n q 2 n q 2 Ž . 2
u,
u,
y Ž n q 1 . Ž n 2 q 2 n q 3 . c1 u ,
2
Ž 13 .
M.D. White r European Journal of Political Economy 17 (2001) 877–896
888
where
u s a q n Ž n2 q 3n q 3 . c1 y Ž n3 q 3n 2 q 3n q 1 . c 0 ,
Ž 14 .
which can be either positive or negative while c 0 - c 0 . If u ) 0, these changes are the AstandardB privatization results, while if u - 0, all of the standard results are reversed; privatization can actually raise output from the public firm, as well as total output and consumer surplus.16 In explaining these results, we must keep in mind that the owners Žor administrators. of the firms control only the contract terms, not output directly. If c 0 is low enough, then the public firm’s b 0 will be low initially and rise after privatization; when public, it can instruct its manager to be more aggressive to boost allocative efficiency because its costs are not high enough to significantly reduce productive efficiency. That in turn prompts the private firms to raise b 1 , and the outputs follow Žpublic output is higher and private output is lower.. After privatization, the public firm no longer has an incentive to have such an aggressive manager, so its contract term, b 0 , rises and its output falls; the private contract term and output move in opposite directions, and private profit increases due to higher output and price. These results are all reversed if c 0 is high enough, which is surprising, because it implies that the public firm’s output actually increases after privatization. If c 0 is high enough to render u - 0, then the public firm sets a higher contract term, b 0 , than after privatization; its lack of direct control over production requires it to limit the AaggressivenessB of the manager, thus reducing its output relative to its privatized output. Before privatization, the public firm would rather lower its own output so the more efficient private firms will increase their output, sacrificing some consumer surplus in the interest of lowering average industry costs. After privatization, the public firm is concerned only with its own profit, and thus lowers its manager’s contract term, which increases its output. As before, the private variables move in lockstep, private output and profit falling and the private managers’ contract term rising. As indicated in the second part of Proposition 3, the changes in public profit and welfare are more complicated: p 0p yp 0m s
Ž nq1. aq Ž n5 q3n4 q6 n3 q6 n2 q3n . c1 y Ž n5 q3n4 q6n3 q6n2 q4 nq1. c 0 Ž n2 q2 nq2.
2
u,
Ž 15 . 16 See Pal and White Ž1998. for another circumstance under which this result obtains, stemming from the use of production subsidies as a strategic trade policy instrument in an international mixed oligopoly.
M.D. White r European Journal of Political Economy 17 (2001) 877–896
889
W pyW m a q Ž 2 n4 q 5n 3 q 7n 2 q 3n . c1 y Ž 2 n 4 q 5n 3 q 7n 2 q 3n q 1 . c 0 sy u. 2 2 Ž n2 q 2 n q 2. Ž 16 . For each expression above, the polynomial in the numerator can be either positive or negative. For low values of c0 , both u and these polynomials will be positive, so public profit rises and welfare falls with privatization, the usual result. But c 0 can be high enough to reverse these signs even while u ) 0, so public profit falls and social welfare increases Žnote that the critical value of c 0 is slightly different for the two changes above.. Public profit will fall because at high values of c 0 , price is not increasing enough to recover the loss of revenue from reduced output. At lower values of c 0 , price would increase enough to cover the lost sales, and public profit would increase. Similarly, welfare rises when c 0 is high, because the fall in consumer surplus is smaller Žpublic output falls less., and the increase in private profit is able to overwhelm it, even including the possible decline in public profit. At lower values of c 0 , the fall in consumer surplus dominates the welfare change, and welfare falls. If c 0 is high enough to imply u - 0, the usual effects on public profit and welfare are restored, just as the effects on the other outcomes are reversed. When c 0 is sufficiently high, the increase in public output compensates for the lower price, so public profit rises, and consumer surplus and public profit rise enough to overwhelm the fall in the one private firm’s profit, so welfare increases. In Barros Ž1995., due to the quadratic cost function used therein, welfare is always higher before privatization due to higher consumer surplus dominating lower profits, which occurs in my model only in the case described here, when the public firm’s constant marginal cost is relatively large.
4. Endogenization of managerial hiring decisions In the previous three sections, I implicitly assumed that when both a public firm and private firm are present, the decision to hire managers is exogenous for all firms. In this section, I endogenize this decision, which effectively adds a preliminary stage to the game, in which each firm chooses whether or not to hire a manager, and then the appropriate one- or two-stage game is played to determine SPNE outputs. We have the results for the all-managerial case Žfrom Section 2. and the all-entrepreneurial case Žfrom Section 3., but we still need to solve the models in which managers are hired by only the public firm or the private firms. We do this briefly in Section 4.1, and then proceed with solving the managerial game in Section 4.2.
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4.1. Mixed oligopolies with asymmetric managerial hiring The properties of the two versions of the model in which only one type of firm hires a manager are summarized in Proposition 4. Proposition 4. When only one type of firm hires a manager, the results of the two models are: (a) When only the public firm hires a manager, compared to when all firms haÕe managers, the public manager’s contract term is smaller, public output is higher, priÕate output is halÕed, and total output remains the same, implying lower priÕate profit and higher public profit, resulting in lower social welfare; (b) when only the priÕate firms hire managers, together they produce all of the total output, and the public firm produces nothing; compared to when all firms haÕe managers, total output and priÕate profit are higher, public profit is zero (and therefore lower), and social welfare is higher. In the first part of Proposition 4, only the public firm hires a manager. In this case, the stage 2 outputs of the manager and the private firm owners are identical to Eq. Ž6., with only the public firm’s costs discounted Žor, equivalently, setting b 1 s 1.. The public firm administrator then chooses the public firm manager’s contract term to maximize social welfare:
b0 s 1 y
a q n Ž n q 3 . c1 y Ž n 2 q 3n q 1 . c0 c0
.
Ž 17 .
This contract term results in the following outputs, profits and social welfare: q 0 s a q n Ž n q 2 . c1 y Ž n 2 q 2 n q 1 . c 0 ,
q1 s Ž n q 1 . Ž c 0 y c1 . ,
Q s a q nc1 y Ž n q 1 . c 0 ,
p0s
Ž n q 1 . a q n Ž n q 2 . c1 y Ž n 2 q 2 n q 1 . c 0 Ž n2 q 2 n q 2. 2
2
p 1 s Ž n q 1 . Ž c 0 y c1 . , CS s Ws
2
,
a q nc1 y Ž n q 1 . c 0
2 2 Ž a y c 0 . q n Ž n q 1 . Ž c 0 y c1 .
2
2
2 .
2
,
Ž 18 .
Total output is the same as when all firms have managers; the production is merely distributed less efficiently Žpositive public output is guaranteed by c 0 - c 0 .. The changes in profits follow from the changes in outputs since price is the same, and the increase in total costs lowers welfare Žsince consumer surplus and total revenue are unchanged..
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In the second part of Proposition 4, only private firms hire managers; in this case, we have a significantly different model. In the previous model, the private firms did not hire managers, which was equivalent to assuming that they did hire them and assigned a common contract term of b 1 s 1. However, we cannot perform this operation in the case where only the private firms hire managers, because the public firm’s objective, maximization of social welfare, does not correspond to assigning its manager a contract term b 0 s 1. The public firm’s objective function and contract structure are qualitatively different, whereas in the case of the private firm, they are related. In this model, the individual and total outputs as functions of the private managers’ contract terms are: n
q i s c 0 y b i c1 Ž i s 1 . . . n . ,
q 0 s a q Ý b i c1 y Ž n q 1 . c 0 , is1
Q s a y c0 ,
Ž 19 .
which are familiar as the standard Cournot–Nash mixed oligopoly results ŽEq. Ž11.. with discounted private marginal cost. Obviously, each private firm’s output falls and public output rises when bi rises. Total output, and therefore, price and consumer surplus, remain constant; the private contract terms only affect the distribution of production. Since price is constant and greater than the private firms’ marginal cost, each private firm’s marginal profit on every unit produced is positive. Therefore, the private firm owners will set their managers’ contract terms to such a level that they will produce all of the total output.This is verified by examining a private firm’s profit as a function of its contract term:
p i Ž b i . s Ž c 0 y c1 . Ž c 0 y b i c1 . ,
Ž 20 .
which is clearly maximized by lowering bi as far as possible Žnote that the other private firms’ contract terms do not appear in this expression, having been canceled out by public output in computing the market price.. If we assume that all private firms’ contract terms are equal, the lowest feasible value of bi is the value at which the private firms split total output equally:
bi s 1 y
a q nc1 y Ž n q 1 . c 0 nc1
.
Ž 21 .
Substituting this value into Eq. Ž19. gives us the following outputs, profits and social welfare: q1 s
a y c0 n
,
q0 s 0,
p 0 s 0, CS s
Ž a y c0 . 2
Q s nq1 s a y c 0 , 2
,
Ws
p1s
Ž a y c 0 . Ž c 0 y c1 .
Ž a y c 0 . Ž a q c 0 y 2 c1 . 2
n .
,
Ž 22 .
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Even if n is small Žpossibly one., the private firms cannot achieve the normally low Cournot total output due to the threat of public production. In this way, the public firm creates a contestable market, wherein the private firms’ ability to abuse market power is curtailed by potential competition Žsimilar to Baumol’s contestable markets theory; see Baumol et al., 1982.. Social welfare is higher than when all firms have managers Žgiven the relevant assumption of c 0 - c 0 ., since total output is higher and produced solely by the more efficient firms. 4.2. Managerial game solution Now we have all of the results required for the managerial game; the solution is given in Proposition 5. Proposition 5. The subgame-perfect Nash equilibrium with a public firm and priÕate firms in which each firm chooses whether or not to hire a manager is: the priÕate firms hire managers and the public firm does not. We will prove this proposition using a payoff matrix, which is shown in Table 1 below. We will try to find a Žsubgame-perfect. Nash equilibrium solution to this game. First, we analyze a representative private firm owner’s decision, and find that the private firms will always hire managers. If the public firm hires a manager, then each private firm’s profit is higher if it hires a manager Žassuming a negligible payoff to its manager.. If the public firm does not hire a manager, again private profit is increased by hiring a manager Žgiven our assumption that c 0 - c 0 .. Hiring a manager is therefore a strictly dominant strategy for the private firm, as it is in the original FJS analysis; in both models, the optimal contract term for a private firm is different than one, which implies that pure profit-maximization is a strictly dominated strategy. From Table 1, we can see that the public firm will always do the opposite of what the private firms do; if the private firms hire managers, the public firm will not hire one, and vice versa. When private firms hire managers, welfare is higher
Table 1
Private managers
Public manager
No public manager
p 1 s Ž nq1. 3 Ž c0 y c1 . 2 ,
p 1s
Ws No private managers
Ž ay c0 . 2q n Ž 2 n2 q3nq2.Ž c0 y c1 . 2 2 .2 Ž
p 1 s Ž nq1 Ws
.2
c 0 y c1 ,
Ž ay c0 . 2q n Ž nq1.Ž c0 y c1 . 2 2
Ws
Ž ay c0 .Ž c0 y c1 . n
,
Ž ay c0 . Ž aq c0 y2 c1 . 2
p 1 s Ž c 0 y c1 . 2 , Ws
Ž ay c0 . 2q2 n Ž c0 y c1 . 2 2
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if the public firm does not hire one Žguaranteed by c 0 - c 0 ., and when the private firms do not hire managers, welfare is always increased by hiring a public manager. Since the optimal strategy for the public firm is to do the opposite of what the private firms do, the SPNE solution to this game is: the private firms hire managers and the public firm does not. Under our cost assumptions, private firms will always hire managers, and the public firm maximizes social welfare by doing the opposite, not hiring a manager. Here, the precommitment ability possible under a managerial regime does not seem to enable the public firm to increase social welfare when the private firms hire managers. When the public firm does not hire a manager, compared to when it does, total output is higher, public profit is zero Žlower., and the change in private profit is ambiguous; however, the net result is unambiguously higher welfare. This seems odd, because we solved for an optimal contract term for the public manager; why, then, does not hiring a manager provide higher social welfare than hiring one with the AoptimalB contract? Recall that for the public firm, assigning an FJS contract is qualitatively different from maximizing its true objective function, welfare. While the contract term derived for the public manager maximizes social welfare assuming a manager is hired, it does not necessarily maximize social welfare when the option of not hiring a manager is included as well. No FJS contract achieves a level of social welfare as high as simple welfare-maximization; the form of the FJS contract is not sufficiently well-suited to social welfare maximization to provide any net strategic advantage.17
5. Privatizationr r managerial game A final question we may ask is: given the solution of the game in which all firms have the option of hiring a manager, what are the effects of privatization? In other words, with the solution of the above game, will privatization raise or lower social welfare? The answer to this question is given in Proposition 6. Proposition 6. In a multistage game in which the public firm decides whether to operate as a public firm, shut down, or priÕatize, and then the firms decide whether or not to hire managers, the subgame-perfect Nash equilibrium solution is as in Proposition 5: the public firm operates as a public firm (but does not produce), and only the priÕate firms hire managers (and produce all output). If we assume that the privatized industry will take the standard FJS managerial form, we can simply compare welfare in the private managerial industry from Eq. 17
See Footnote 15.
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Ž12., to that of the mixed publicrprivate industry in which only the private firms hire managers as given in Eq. Ž22.: Wp y Wm s y
a q Ž 2 n3 q 7n 2 q 11n q 7 . c 0 y Ž 2 n 3 q 7n 2 q 11n q 8 . c1 2 Ž n2 q 2 n q 2.
2
= a q n Ž n q 1 . c1 y Ž n 2 q n q 1 . c 0 .
Ž 23 .
Expression Ž23. is strictly negative if the final bracketed term is positive, which is guaranteed by the necessary condition for production by the privatized public firm. So the private managerial form, when feasible, is always welfare-inferior to the mixed case in which a public firm is present to constrain the behavior of private firms.18 In conclusion, in a larger game in which the government first chooses whether or not to privatize the public firm, and if not, then chooses whether or not to hire a manager, the SPNE solution is for the public firm to remain government-operated and to do so without a manager, resulting in the private firms’ assuming all production under threat of public firm participation. Price is maintained at c 0 , while all production is undertaken by the more efficient firms.19
6. Conclusions and extensions In this paper, I have investigated managerial incentives in a market where a public firm competes with private firms, focusing on endogenizing the managerial hiring decision. Previously, the literature considered only cases in which either all firms hired managers or all did not, and the result was that the managerial case provided both higher social welfare and higher private profits; these results are confirmed with my model. When, however, the managerial hiring decision is endogenous, the only subgame-perfect Nash equilibrium is that only private firms hire managers and undertake all production, and are constrained by the public 18
Even if the public firm’s costs fall after privatization, privatization still lowers welfare if the public firm’s original c 0 - w aqŽ n2 q2 nq2 )c1 xrŽ n2 q2 nq3.. 19 The issue of fixed costs becomes particularly relevant at this point. While the public firm produces no output in the SPNE, it must not shut down completely; it must stand ready to produce in order to retain its disciplinary powers and ensure that the private firms produce the ArightB output. In other words, the public firm will still incur any fixed costs it may have, although it produces nothing. Though we assume no fixed costs, a certain level of fixed costs for the public firm can be tolerated without altering the results of the model. This fixed cost must be balanced against the cost of allowing the private firms an unrestrained oligopoly. The larger the SPNE output, the higher the losses from private oligopoly, and the higher the fixed costs that can be incurred by the public firm while producing no output. Only if the SPNE output is relatively small and the fixed costs are high will the results of the model be altered.
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firm, which forces the private firms to produce above their normal oligopoly output, as in a contestable market. The public firm is a means, therefore, of regulating the industry, without requiring any production that be would be inefficient, compared to private production Žthough some fixed costs would be incurred.. This contrasts with results that require the public firm to produce positive output in order to be a means of regulation.20 I also analyzed a larger game, in which the public firm first decides whether to remain public, privatize, or shut down, and then all firms decide whether or not to hire managers. The solution to the managerial game holds as a SPNE in this larger game; the public firm will remain public, not hire a manager, and AallowB the private firms to produce all output. Privatization never raises social welfare, unlike in the case in which all firms have managers, in which case, privatization may raise social welfare under certain cost conditions. Extensions to this paper would generalize the assumptions of the model, regarding cost and demand functions, the form of the managerial contracts, and the nature of competition,21 as well as reintroducing asymmetric information.
Acknowledgements I thank Debashis Pal, Wolfgang Mayer, H.W. Whitmore, Frans van Winden, Arye L. Hillman, and two anonymous referees for helpful comments, and the Taft Fellowship at the University of Cincinnati for financial assistance. All remaining errors are of course my own.
References ´ Barros, F., 1994. Delegation and efficiency in a mixed oligopoly. Annales d’Economie et de Statistique 33, 51–72. Barros, F., 1995. Incentive schemes as strategic variables: an application to a mixed duopoly. International Journal of Industrial Organization 13, 373–386. Basu, K., 1993. Lectures in Industrial Organization Theory. Blackwell, Oxford. Basu, K., 1995. Stackelberg equilibrium in oligopoly: an explanation based on managerial incentives. Economics Letters 49, 459–464. Baumol, W.J. et al., 1982. Contestable Markets and the Theory of Industry Structure. Harcourt, Brace, Jovanovich, New York. 20 See De Fraja and Delbono Ž1987. for an example of this sort of result within price competition Žsee also De Fraja and Delbono, 1991, pp. 11–12.. 21 For instance, under Bertrand competition when a public firm and private firms produce differentiated products, private output falls when managers are hired, while public output rises, which is the opposite of the effects in the paper under Cournot competition. Also, the changes in private profit and welfare depend critically on the strength of the cross-price effects between the two markets. These results encourage further study of this model; I thank an anonymous referee for the suggestion.
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Bos, ¨ D., 1991. Privatization: A Theoretical Treatment. Clarendon Press, Oxford. Cremer, H. et al., 1989. The public firm as an instrument for regulating an oligopolistic market. Oxford Economic Papers 41, 283–301. De Fraja, G., Delbono, F., 1987. Oligopoly, public firm, and welfare maximization: a game-theoretic analysis. Giornale degli Economisti e Annali di Economia 46, 417–435. De Fraja, G., Delbono, F., 1989. Alternative strategies of a public enterprise in oligopoly. Oxford Economic Papers 41, 302–311. De Fraja, G., Delbono, F., 1991. Game theoretic models of mixed oligopoly. Journal of Economic Surveys 4, 1–17. Eliassen, K.A., Kooiman, J. ŽEds.., Managing Public Organizations: Lessons from Contemporary European Experience. SAGE Publications, London. Elster, J., 1979. Ulysses and the Sirens: Studies in Rationality and Irrationality. Cambridge Univ. Press, Paris. Fershtman, C., Judd, K.L., 1987. Equilibrium incentives in oligopoly. American Economic Review 77, 927–940. Merrill, W.C., Schneider, N., 1966. Government firms in oligopoly industries: a short-run analysis. Quarterly Journal of Economics 80, 400–412. Nett, L., 1993. Mixed oligopoly with homogeneous goods. Annals of Public and Cooperative Economics 64, 367–393. Pal, D., White, M.D., 1998. Mixed oligopoly, privatization and strategic trade policy. Southern Economic Journal 65, 264–281. Sklivas, S.D., 1987. The strategic choice of managerial incentives. Rand Journal of Economics 18, 452–458. Vickers, J., 1985. Delegation and the theory of the firm. Economic Journal ŽSupplement. 95, 138–147. White, M.D., 1999. Welfare-based incentives for public firm in mixed oligopoly. Working paper.
Managerial incentives and the decision to hire managers in markets with public and private firms Mark D. White ) Department of Political Science, Economics, and Philosophy, College of Staten Islandr CUNY, 2800 Victory BouleÕard, Staten Island, NY 10314, USA Received 1 June 1999; received in revised form 1 May 2000; accepted 1 December 2000
Abstract This paper considers the managerial incentive contract when public and private firms compete in the same market. Social welfare is enhanced when all firms hire managers, but for different reasons than when all firms are privately owned. Incentives to hire managers differ in private and public firms; in equilibrium, only private firms hire managers. q 2001 Elsevier Science B.V. All rights reserved. JEL classification: L13; L32; D21 Keywords: Mixed oligopoly; Public enterprise; Managerial incentive contracts
This paper investigates managerial incentive contracts in an industry in which public firms with social welfare objectives compete with private firms that have profit objectives. 1 More precisely, I consider whether it is in all firms’ interests to hire managers, as is standard in the private sector, or whether incentives to hire managers are asymmetric because of the different objective functions.
)
Tel.: q1-718-982-3193; fax: q1-718-982-2888. E-mail address: [email protected] ŽM.D. White.. 1 Such industries are often called mixed oligopolies; prominent examples include the package and overnight mail delivery industries in the United States, in which the public United States Postal Service competes with private firms such as Federal Express and UPS, and the Indian airline industry in which state-owned Indian Airlines competes with several private airlines. 0176-2680r01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 7 6 - 2 6 8 0 Ž 0 1 . 0 0 0 6 0 - X
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The study of industries with private and public firms began with Merrill and Schneider Ž1966., and was further developed in the 1980s when game theory was applied by Cremer et al. Ž1989., De Fraja and Delbono Ž1989., and others.2 Strategic interaction between private and public firms is particularly relevant when governments privatize their state enterprises or open to competition markets that were previously monopolized by state enterprises Žsuch as telecommunications industries in European countries, Japan, Australia, New Zealand, Singapore, and elsewhere.. Little attention has been directed at investigating management of firms when private and public firms compete.3 The papers by Barros Ž1994, 1995. are notable exceptions, and I will discuss how these studies are related to the present paper. In the managerial incentive contract literature, which began in the mid-1980s, Fershtman and Judd Ž1987. and Sklivas Ž1987. demonstrated how firms can increase profits by precommiting to strategies that seem irrational in the short-term, but are beneficial in the long-term when the other firms’ actions are taken into account.4 Firm owners cannot themselves commit to pursuing non-profit-maximizing strategies, because owners of other firms will know that, when the firms actually make decisions, they will revert to profit-maximization, despite protests to the contrary.5 One way to credibly commit to a strategy other than profit-maximization is to hire a manager with complete discretion over the firm decisions, and assign him or her a contract that provides an incentive to pursue an alternative strategy. If a firm’s owners can convince their competitors that the manager is truly in charge and the owners no longer have control of the firm, a non-profitmaximizing strategy can be credible; therefore, this constitutes a method of strategic precommitment. Managerial incentive contracts can also help to solve delegation and principalragent problems in the event that a manager’s effort andror the output of the firm are not easily observable; in fact, it is this property that many feel justifies the managerial contract approach ŽBasu, 1993, Chapter 14.. The Fershtman–Judd–Sklivas ŽFJS. model has proven very popular in the industrial organizationrmanagerial economics literature, despite criticism Žagain, see Basu, 1993, Chapter 14.. Although the model has been extensively applied to competition among private firms, only Barros Ž1994, 1995. has applied the model to markets in which private and public firms compete.
2
See De Fraja and Delbono Ž1991. and Nett Ž1993. for reviews of the literature. For an overview of how scholars of management and operations research view the management of public enterprise, see Eliassen and Kooiman Ž1993.. 4 Vickers Ž1985. anticipated this development, but did not develop the managerial incentive contract model as thoroughly as did Fershtman and Judd, and Sklivas. 5 See Elster Ž1979. for further discussion of the difficulties involved in strategic precommitment. 3
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This paper departs from the studies by Barros by focusing on different issues. Barros emphasized the delegation aspects of managerial incentive contracts in the context of asymmetric information, which highlighted their usefulness in alleviating principleragent problems, whereas I choose to focus on the strategic benefits of such arrangements in situations of complete information. While Barros Ž1995. included both strategic effects and asymmetric information, I want to isolate the strategic benefits of managerial incentive contracts without the additional complexity introduced by modeling the information held by the parties. In the 1995 paper, Barros explained that, in an industry with one public and one private firm, allocative efficiency increases at the expense of productive efficiency when managers are hired by both firms, with a net positive effect on welfare, and that privatizing the public firm has a negative effect on welfare. We will see that these results can be proven Žsome with slight modifications. using my simplified approach, which allows the strategic interaction to be observed more easily. I also endogenize the decision whether or not to hire managers, as does Basu Ž1995. in the case of private firms. Barros Ž1995. showed that welfare is higher if both firms hire managers compared to when neither firm does, and I confirm this result with a general number of private firms in the industry. However, utilizing a simple game framework, I show that when a firm has the choice of whether or not to hire a manager, the sole subgame-perfect Nash equilibrium ŽSPNE. is that only private firms hire managers. In this equilibrium, only private firms produce output, while a public firm exists only to impose discipline on the private firms. This creates somewhat of a contestable market in the sense of Baumol et al. Ž1982.. I also show that this is the equilibrium of a larger game in which a public firm chooses whether to maximize social welfare, privatize and maximize profits, or shut down. The government will decide to allow the public firm to remain public and allow private firms to produce all output in a regime in which only they hire managers. Here, the very existence of a public firm enables welfare-increasing regulation of the industry, without requiring inefficient production by the public firm, which has higher marginal costs by assumption.6 Section 1 outlines and solves the basic model. Section 2 compares the results of the managerial model with those of the standard, nonmanagerial model, and in Section 3, I compare the results to an industry with private firms only to determine the effects of privatization on the managerial model. In Section 4, I endogenize the strategic decisions whether or not to hire managers. Section 5 analyzes the larger game, in which the public firm’s operation and shutdown decision is made before the managerial hiring decisions. I conclude in Section 6.
6
This naturally raises the issue of fixed cost; see Footnote 19 for a discussion of fixed cost and zero production by the public firm.
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1. Model and solution We assume that n G 1 private firms and one public firm compete in a Cournot game in a homogeneous-goods market with a linear Žinverse. demand curve p s a y Q, where p is the market price and Q is the total output of all n q 1 firms.7 The firms have asymmetric linear cost functions Ci Ž qi . s c i qi q Fi Ž i s 0,1,2, . . . ,n.; all firms’ fixed costs are zero.8 The owners of a private firm Žfirms i G 1. maximize profit: n
ž
/
p i s pqi y c i qi y Mi s a y Ý q j y c i qi y Mi , js0
Ž 1.
where qi is firm i’s output and Mi is its manager’s payoff Žif hired.. The public firm Žfirm 0. has an efficiency objective, defined as maximizing the unweighted sum of consumer surplus and the profits of the firms:9 n
W s CS q Ý p i s is0
1 2
n
ž / Ý qi
is0
2
n
qÝ is0
n
ž
/
a y Ý q j y c i qi y Mi . js0
Ž 2.
I assume c i s c1 for all i G 1 Ždue to symmetry among the private firms., and c 0 ) c1; if the public firm were as efficient as the private firms, it would be efficient for the public firm to produce the socially optimal output. This trivial solution is avoided by assuming that the public firm is relatively inefficient.10 The structure of the game is as follows: in stage one, each firm’s ownerradministrator assigns its manager a Fershtman–Judd–Sklivas ŽFJS. managerial contract, in which her payoff is based on a linear combination of her firm’s profits and revenues. In stage two, having accepted the contracts offered, each manager produces her payoff-maximizing output. Using the principle of backward induction, I first solve for the managers’ outputs as functions of their contract terms. Each firm’s manager chooses her firm’s output to maximize her compensation, given by the following managerial contract: Mi s a i bip i Ž qi . q Ž 1 y bi . R i Ž qi . q Ti ,
Ž 3.
in which p i is the profit, and R i is the revenue, earned by firm i when qi is produced. bi is the crucial contract term, while a i and Ti are adjustment terms; 7
The results of this model are not specific to this particular demand function, which is standard in the literature, and used for computational simplicity. 8 Again, see Footnote 19 for an exception to this. 9 We do not count the managers’ income in our welfare expression; we assume that the potential managers would earn their reservation utilities elsewhere, so the hiring decisions of the firms in this industry do not impact the managers’ well-being. 10 This assumption is not uncontroversial; see Bos ¨ Ž1991., Section 3.2, and Nett Ž1993., Section 2.3, for summaries of the empirical literature on the relative efficiency of private and public firms.
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the latter two terms are used to set the manager’s subgame-perfect Nash equilibrium ŽSPNE. compensation equal to her reservation utility. I assume that the payoffs to the managers Žtheir reservation utilities. are negligible compared to profits, such that the managers’ payoffs do not significantly affect either the hiring or shutdown decision. I make this assumption because my emphasis is on the strategic effect of hiring managers, not the impact of the managers’ payoffs on profits. For this reason, I will henceforth omit the managers’ payoffs from profit Žand welfare. expressions. Since bi , a i and Ti are given to the manager of firm i, each manager’s maximization problem is equivalent to: max bip i Ž qi . q Ž 1 y bi . R i Ž qi . qi
n
smax R i Ž qi . y bi Ci Ž qi . smax qi
qi
ž
/
a y Ý q j y bi c i qi . js0
Ž 4.
The contract term, bi , can thus be considered to be a discount factor on costs; the lower the assigned bi , the more the manager is instructed to discount costs. If a manager’s contract term is less than one Žperhaps even negative., her reaction function shifts outwards from its profit-maximizing position, a change which is representative of more aggressive competition on the part of the manager and the firm.11 If the contract term is equal to one, the manager simply maximizes profits, and if the contract term is greater than one, the manager is actually restrained, or less aggressive than when maximizing profits; we will see this possibility later in the public manager’s contract term. Fershtman and Judd Ž1987. and Sklivas Ž1987. find that, in a private duopoly with identical firms, it is a dominant strategy for each firm to instruct its manager to discount costs Žeach manager’s contract term is less than one.. The outcome of this game is a Prisoner’s Dilemma for the firms’ owners; each firm makes lower profits than if neither hired a manager, but social welfare is higher, due to increased output. In my model, since the managers are motivated only by their payoffs, and not whether the firms for whom they work are private or public, stage two of the game is identical to that of Fershtman and Judd and Sklivas. Solving the maximization problem of the manager of firm i, I derive her Cournot reaction function as a function of the assigned contract term, bi , and the other firms’ output Ždenoted by q j,y i .: n
ay qi Ž q j,y i , bi . s
11
q j y bi c i
Ý js0, j/i
2
.
A more elaborate interpretation of a negative contract term is provided after Proposition 1.
Ž 5.
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We see that this is identical to the standard Cournot reaction function under linear demand and costs, except for the discounted marginal cost in the numerator. Solving all managers’ reaction functions simultaneously allows the stage-two equilibrium outputs to be derived as functions of the n q 1 contract terms: n
a y Ž n q 1 . bi c i q
Ý
bj c j
js0, j/i
qi Ž b 0 , . . . , bn . s
. Ž 6. nq2 Again, this is the standard result except for the firms’ discounted costs. In stage 1 of the game, the ownersradministrators take their managers’ output functions into account, and then simultaneously choose their contract terms to maximize their respective objective functions. Substituting Eq. Ž6. into Eqs. Ž1. and Ž2. and simultaneously solving the resulting first order conditions, we determine the optimal contract terms:
b0 s 1 y b1 s 1 y
a q n Ž n 2 q 2 n q 3 . c1 y Ž n3 q 2 n 2 q 3n q 1 . c 0 c0 n Ž n q 1 . Ž c 0 y c1 . c1
.
,
Ž 7.
Here, b 1 represents the private managers’ common contract term Židentical due to symmetry among the private firms.. The properties of the SPNE contract terms are summarized in Proposition 1. Proposition 1. In a linear-cost Cournot mixed oligopoly in which each firm assigns its manager a FJS contract, the SPNE contract terms haÕe the following properties. (a) Each priÕate manager’s contract term is less than one, and may be negatiÕe if the public firm’s marginal cost is large compared to that of the priÕate firms; (b) the public manager’s contract term is greater than (less than) one if the public firm’s marginal cost is large (small) enough relatiÕe to the priÕate firms’ marginal cost and the demand parameter (a), and may be negatiÕe; (c) the public manager’s contract term is lower (higher) than that of the priÕate managers if the public firm’s marginal cost is relatiÕely low (high); and (d) as the number of priÕate firms increases, the public manager’s contract term rises and the priÕate managers’ contract term falls.
All parts of Proposition 1 can be verified by observation and simple calculation; note that the asymmetry of the public and private firms’ objective functions is
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clearly reflected in their contract terms, b 0 and b 1. It is surprising that the public manager’s contract term can be larger than that of the private managers; we would expect to see the public manager instructed to be more aggressive Žlower b 0 . in order to boost total output and increase consumer surplus. This is true if the public firm’s marginal cost is relatively low, but if it is too high, the public firm would rather have the private firms produce more output in the interest of lowering total costs, and thus, the public manager will be commanded to Aback downB, possibly even to the point of overemphasizing costs Ž b 0 ) 1.. On the other hand, if either manager’s contract term is negative, then that manager’s firm wants her to expand output so much that it actually instructs the manager to give positive weight to costs; in this case, since marginal cost encourages production, it is diminishing marginal revenue Žin the negative range. alone that restrains the manager from producing past the owner’s wishes. Also, as the number of private firms increases, the public firm does not need to produce as much output, so its manager’s contract term rises, and the private contract term falls in response Žfor a fixed value of c 0 ..12 Substituting the SPNE contract terms ŽEq. Ž7.. into the managers’ output functions ŽEq. Ž6.., we can determine the SPNE individual and total outputs, consumer surplus, profits, and welfare: q 0 s a q n Ž n 2 q 2 n q 2 . c1 y Ž n q 1 . Ž n 2 q n q 1 . c 0 , 2
q1 s Ž n q 1 . Ž c 0 y c1 . , Q s q0 q nq1 s a q nc1 y Ž n q 1 . c 0 , CS s
a q nc1 y Ž n q 1 . c 0 2
2
,
p 0 s n Ž c 0 y c1 . a q n Ž n 2 q 2 n q 2 . c1 y Ž n q 1 . Ž n 2 q n q 1 . c 0 , 3
2
p 1 s Ž n q 1 . Ž c 0 y c1 . , Ws
2 2 Ž a y c0 . q n Ž 2 n2 q 3n q 2 . Ž c0 y c1 .
Ž 8. 2 If c 0 s c1 , we see that standard results obtain; the public firm produces the socially optimal level of output and the private firms produce nothing. It is for this reason that, if costs are linear, the public firm has to be less efficient to generate nontrivial results, in managerial as well as nonmanagerial settings. As the relative 12
The effect of n alone on the private managers’ contract term is ambiguous, depending critically on n itself, as well as the public manager’s contract term and marginal cost, as can be seen by differentiating the reaction function of b 1 in terms of b 0 with respect to n: Eb 1 Ž b 0 . En
s
Ž n2 y2. Ž aq b 0 c0 y2 c1 . 2
Ž n2 q nq2. c1
.
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inefficiency of the public firm increases, q1 rises and q0 falls, because the public firm AallowsB the more efficient private firms to produce more output. However, total output falls, because the private firms react conservatively to the drop in public output. Note that the expression for public output is strictly positive only if: c0 -
a q Ž n 3 q 2 n 2 q 2 n . c1 n3 q 2 n2 q 2 n q 1
s c0 ,
Ž 9.
where the polynomials have been expanded to make clear that the upper limit, c 0 , is a weighted average of the demand parameter a and the private firms’ marginal cost c1. As n grows, the weight on c1 increases as well; the public firm has to be relatively more efficient to stay in production. I will assume c 0 - c 0 for the rest of this paper; this guarantees positive public output in all the other models I shall consider Žthe model in which all firms hire managers is the most restrictive on the public firm, due to the increased output from the private firms.. This explains the seemingly odd result, observable from Eq. Ž8., that each private firm’s output increases and total output falls as the number of private firms increases: Eq1 En
EQ s 2 Ž n q 1 . Ž c 0 y c1 . ) 0,
En
s y Ž c 0 y c1 . - 0.
Ž 10 .
Note that these changes are functions of the cost difference between the public and private firms. As n increases, the public firm instructs its manager to produce less, allowing more output from the private firms Žas their managers’ contract terms are raised., but resulting in less total output. This is true for a fixed c 0 , but c 0 is more tightly constrained Ž c 0 decreases. as n increases. The maximum cost difference between the two types of firms must fall, partially offsetting the direct effect of n on these outcomes; if c 0 falls as n increases Žpossibly due to administrative or political pressure to cut costs in the face of growing private competition., public output could increase, each private firm’s output could fall, and total output could increase. Indeed, as n approaches infinity, this cost difference approaches zero, implying that price nears c 0 Žwhich itself approaches c1 . and the public firm produces nearly all output.
2. Comparing entrepreneurial and managerial oligopolies We can compare the results in Eq. Ž8. to those of the nonmanagerial, or entrepreneurial case,13 in which each owner or administrator simply maximizes 13
The use of the term AentrepreneurialB may seem inappropriate when one of the firms is owned and operated by the government; we use it merely for reasons of consistency with the literature.
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her objective function, whether it be profit or welfare. The following are the standard Cournot results when a public firm and private firms compete: q0 s a q nc1 y Ž n q 1 . c 0 , CS s Ws
Ž a y c0 . 2
q1 s c 0 y c1 ,
Q s a y c0 ,
2
,
2
p 0 s 0, p 1 s Ž c 0 y c1 . ,
2 2 Ž a y c 0 . q 2 n Ž c 0 y c1 .
. Ž 11 . 2 ŽThe assumption that c 0 - c 0 guarantees positive public output.. The differences between the managerial and entrepreneurial models are summarized in Proposition 2. Proposition 2. In a market with linear costs and Cournot competition between a public firm and priÕate firms, the following changes occur when the firms all hire managers and assign them FJS managerial contracts: (a) PriÕate output increases but public output drops, the net result being lower total output (higher price, lower consumer surplus); (b) priÕate profit rises, and public profit rises to become strictly positiÕe; and (c) welfare is higher. After managers are hired, he private firms produce more output and the public firm produces less Žin fact, the entrepreneurial public firm produces the same output as all the managerial firms together.. Total output is less in the managerial case, and the private firms make more profit because of an increase in output and price, while the public firm makes strictly positive profits.14 Finally, social welfare is higher with managerial firms; the additional profits in the managerial case overwhelm the loss in consumer surplus. This result about social welfare confirms Barros’ conclusion ŽBarros, 1995, p. 382, Proposition 3., who also finds that social welfare is higher in a mixed duopoly when both firms have managers, as opposed to the strictly nonmanagerial regime; qualitatively, the explicit inclusion of asymmetric information does not affect this result. In both my model and Barros’, social welfare increases when managers are hired in a mixed oligopoly because the drop in average and total costs due to the shifting of production from the public firm to the private firms more than compensates for the lower output; the increase in productive efficiency is greater than the fall in allocative efficiency. These results are in stark contrast to those of Fershtman and Judd and Sklivas, who considered only private firms. In each case, welfare rises, but the way in 14
Again, this assumes that the managers’ payoffs are negligible compared to profits.
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which this increase eventuates is quite different. With only private firms, social welfare increases when managers are hired, because each firm produces more output than they would without managers Žthe Prisoner’s Dilemma., but the resulting rise in consumer surplus dominates the fall in profits. When a public firm is present to compete with private firms, profits rise when managers are hired because they were abnormally low before managers due to high output Žand low price.. Consumer surplus falls, but not by much, because output is still relatively high in the managerial mixed oligopoly. The rise in profits dominates the fall in consumer surplus, again increasing social welfare, but by diametrically opposite means compared to the case of a market in which there are only private firms.15
3. Privatization I turn now to privatization; that is, the public firm administrators are instructed to maximize profit rather than social welfare. I assume Žfor this section. that all firms hire managers before privatization, and we will see that all firms will hire managers after privatization as well. Therefore, this section can be interpreted as comparing managerial mixed public and private, and only private, oligopoly. When there are only private firms,
b0 s 1 y n b1 s 1 y n q0 s q1 s Qs
a q n Ž n q 1 . c1 y Ž n 2 q n q 1 . c 0
Ž n2 q 2 n q 2. c0 a q Ž n q 1 . c 0 y Ž n q 2 . c1
Ž n 2 q 2 n q 2 . c1
,
,
Ž n q 1 . a q n Ž n q 1 . c1 y Ž n 2 q n q 1 . c 0 n2 q 2 n q 2 Ž n q 1 . a q Ž n q 1 . c 0 y Ž n q 2 . c1 n2 q 2 n q 2 Ž n q 1 . Ž n q 1 . a y nc1 y c0 n2 q 2 n q 2
,
,
,
15 Another phenomenon contributes to the odd results of this section: the form of the FJS managerial contract is not well-suited to a public firm. A public firm intends to maximizes social welfare, but when it assigns a FJS contract, it instructs its manager to maximize a linear combination of profits and revenues, a qualitatively different incentive scheme. The public firm administrators optimally structure the FJS contract to maximize welfare, but the manager can only see profits and revenues, not the larger picture, including consumer surplus and private profit. The public firm administrators would have more precise control over the manager if the scope of the contract were expanded to include these other welfare-related measures; for instance, they could affect the slope of the manager’s reaction function, impossible with an FJS contract. See White Ž1999. for an analysis of such an incentive scheme.
M.D. White r European Journal of Political Economy 17 (2001) 877–896 2
CS s
p0s
p1s Ws
Ž n q 1 . Ž n q 1 . a y nc1 y c0 2 Ž n2 q 2 n q 2.
2
2
,
Ž n q 1 . a q n Ž n q 1 . c1 y Ž n 2 q n q 1 . c 0 Ž n2 q 2 n q 2.
2
,
2
Ž n q 1 . a q Ž n q 1 . c 0 y Ž n q 2 . c1 Ž n2 q 2 n q 2.
887
2
,
2
nq1 2
2 Ž n q 2 n q 2.
2
= Ž n 2 q 2 n q 3 . Ž a y c1 . Ž n q 1 . a y Ž n y 1 . c1 y 2 c 0 2
q Ž 2 n 4 q 6 n 3 q 10 n 2 q 7n q 3 . Ž c 0 y c1 . .
Ž 12 .
The results of now privatizing the public firm are summarized in the following proposition. Proposition 3. When all firms hire managers to whom they assign FJS contracts both before and after priÕatization, the consequences of priÕatizing the public firm are: (a) If c 0 is relatiÕely low, the priÕate managers’ contract term falls, while that of the public manager rises, public and total output fall, and priÕate output and profit rise; if c 0 is relatiÕely high, these effects are reÕersed, (b) public profit rises and social welfare falls, unless c 0 lies in an intermediate range between its highest and lowest possible Õalues. The first part of Proposition 3 describes the following changes Žthe superscripts m and p represent the cases of mixed public and private firms, and private firms only.:
b 0p y b 0m s
n2 q n q 2 2
Ž n q 2 n q 2. c0
q0p y q0m s y
n2 q n q 1
b 1p y b 1m s y
q1p y q1m s
n 2
Ž n q 2 n q 2 . c1
u,
nq1
u, n q2nq2 n qnq2 1 Qp y Qm s y 2 u, n q2nq2 nq1 p 1p y p 1m s a q Ž n3 q 3n 2 q 5n q 3 . c 0 2 2 n q 2 n q 2 Ž . 2
u,
u,
y Ž n q 1 . Ž n 2 q 2 n q 3 . c1 u ,
2
Ž 13 .
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888
where
u s a q n Ž n2 q 3n q 3 . c1 y Ž n3 q 3n 2 q 3n q 1 . c 0 ,
Ž 14 .
which can be either positive or negative while c 0 - c 0 . If u ) 0, these changes are the AstandardB privatization results, while if u - 0, all of the standard results are reversed; privatization can actually raise output from the public firm, as well as total output and consumer surplus.16 In explaining these results, we must keep in mind that the owners Žor administrators. of the firms control only the contract terms, not output directly. If c 0 is low enough, then the public firm’s b 0 will be low initially and rise after privatization; when public, it can instruct its manager to be more aggressive to boost allocative efficiency because its costs are not high enough to significantly reduce productive efficiency. That in turn prompts the private firms to raise b 1 , and the outputs follow Žpublic output is higher and private output is lower.. After privatization, the public firm no longer has an incentive to have such an aggressive manager, so its contract term, b 0 , rises and its output falls; the private contract term and output move in opposite directions, and private profit increases due to higher output and price. These results are all reversed if c 0 is high enough, which is surprising, because it implies that the public firm’s output actually increases after privatization. If c 0 is high enough to render u - 0, then the public firm sets a higher contract term, b 0 , than after privatization; its lack of direct control over production requires it to limit the AaggressivenessB of the manager, thus reducing its output relative to its privatized output. Before privatization, the public firm would rather lower its own output so the more efficient private firms will increase their output, sacrificing some consumer surplus in the interest of lowering average industry costs. After privatization, the public firm is concerned only with its own profit, and thus lowers its manager’s contract term, which increases its output. As before, the private variables move in lockstep, private output and profit falling and the private managers’ contract term rising. As indicated in the second part of Proposition 3, the changes in public profit and welfare are more complicated: p 0p yp 0m s
Ž nq1. aq Ž n5 q3n4 q6 n3 q6 n2 q3n . c1 y Ž n5 q3n4 q6n3 q6n2 q4 nq1. c 0 Ž n2 q2 nq2.
2
u,
Ž 15 . 16 See Pal and White Ž1998. for another circumstance under which this result obtains, stemming from the use of production subsidies as a strategic trade policy instrument in an international mixed oligopoly.
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W pyW m a q Ž 2 n4 q 5n 3 q 7n 2 q 3n . c1 y Ž 2 n 4 q 5n 3 q 7n 2 q 3n q 1 . c 0 sy u. 2 2 Ž n2 q 2 n q 2. Ž 16 . For each expression above, the polynomial in the numerator can be either positive or negative. For low values of c0 , both u and these polynomials will be positive, so public profit rises and welfare falls with privatization, the usual result. But c 0 can be high enough to reverse these signs even while u ) 0, so public profit falls and social welfare increases Žnote that the critical value of c 0 is slightly different for the two changes above.. Public profit will fall because at high values of c 0 , price is not increasing enough to recover the loss of revenue from reduced output. At lower values of c 0 , price would increase enough to cover the lost sales, and public profit would increase. Similarly, welfare rises when c 0 is high, because the fall in consumer surplus is smaller Žpublic output falls less., and the increase in private profit is able to overwhelm it, even including the possible decline in public profit. At lower values of c 0 , the fall in consumer surplus dominates the welfare change, and welfare falls. If c 0 is high enough to imply u - 0, the usual effects on public profit and welfare are restored, just as the effects on the other outcomes are reversed. When c 0 is sufficiently high, the increase in public output compensates for the lower price, so public profit rises, and consumer surplus and public profit rise enough to overwhelm the fall in the one private firm’s profit, so welfare increases. In Barros Ž1995., due to the quadratic cost function used therein, welfare is always higher before privatization due to higher consumer surplus dominating lower profits, which occurs in my model only in the case described here, when the public firm’s constant marginal cost is relatively large.
4. Endogenization of managerial hiring decisions In the previous three sections, I implicitly assumed that when both a public firm and private firm are present, the decision to hire managers is exogenous for all firms. In this section, I endogenize this decision, which effectively adds a preliminary stage to the game, in which each firm chooses whether or not to hire a manager, and then the appropriate one- or two-stage game is played to determine SPNE outputs. We have the results for the all-managerial case Žfrom Section 2. and the all-entrepreneurial case Žfrom Section 3., but we still need to solve the models in which managers are hired by only the public firm or the private firms. We do this briefly in Section 4.1, and then proceed with solving the managerial game in Section 4.2.
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4.1. Mixed oligopolies with asymmetric managerial hiring The properties of the two versions of the model in which only one type of firm hires a manager are summarized in Proposition 4. Proposition 4. When only one type of firm hires a manager, the results of the two models are: (a) When only the public firm hires a manager, compared to when all firms haÕe managers, the public manager’s contract term is smaller, public output is higher, priÕate output is halÕed, and total output remains the same, implying lower priÕate profit and higher public profit, resulting in lower social welfare; (b) when only the priÕate firms hire managers, together they produce all of the total output, and the public firm produces nothing; compared to when all firms haÕe managers, total output and priÕate profit are higher, public profit is zero (and therefore lower), and social welfare is higher. In the first part of Proposition 4, only the public firm hires a manager. In this case, the stage 2 outputs of the manager and the private firm owners are identical to Eq. Ž6., with only the public firm’s costs discounted Žor, equivalently, setting b 1 s 1.. The public firm administrator then chooses the public firm manager’s contract term to maximize social welfare:
b0 s 1 y
a q n Ž n q 3 . c1 y Ž n 2 q 3n q 1 . c0 c0
.
Ž 17 .
This contract term results in the following outputs, profits and social welfare: q 0 s a q n Ž n q 2 . c1 y Ž n 2 q 2 n q 1 . c 0 ,
q1 s Ž n q 1 . Ž c 0 y c1 . ,
Q s a q nc1 y Ž n q 1 . c 0 ,
p0s
Ž n q 1 . a q n Ž n q 2 . c1 y Ž n 2 q 2 n q 1 . c 0 Ž n2 q 2 n q 2. 2
2
p 1 s Ž n q 1 . Ž c 0 y c1 . , CS s Ws
2
,
a q nc1 y Ž n q 1 . c 0
2 2 Ž a y c 0 . q n Ž n q 1 . Ž c 0 y c1 .
2
2
2 .
2
,
Ž 18 .
Total output is the same as when all firms have managers; the production is merely distributed less efficiently Žpositive public output is guaranteed by c 0 - c 0 .. The changes in profits follow from the changes in outputs since price is the same, and the increase in total costs lowers welfare Žsince consumer surplus and total revenue are unchanged..
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In the second part of Proposition 4, only private firms hire managers; in this case, we have a significantly different model. In the previous model, the private firms did not hire managers, which was equivalent to assuming that they did hire them and assigned a common contract term of b 1 s 1. However, we cannot perform this operation in the case where only the private firms hire managers, because the public firm’s objective, maximization of social welfare, does not correspond to assigning its manager a contract term b 0 s 1. The public firm’s objective function and contract structure are qualitatively different, whereas in the case of the private firm, they are related. In this model, the individual and total outputs as functions of the private managers’ contract terms are: n
q i s c 0 y b i c1 Ž i s 1 . . . n . ,
q 0 s a q Ý b i c1 y Ž n q 1 . c 0 , is1
Q s a y c0 ,
Ž 19 .
which are familiar as the standard Cournot–Nash mixed oligopoly results ŽEq. Ž11.. with discounted private marginal cost. Obviously, each private firm’s output falls and public output rises when bi rises. Total output, and therefore, price and consumer surplus, remain constant; the private contract terms only affect the distribution of production. Since price is constant and greater than the private firms’ marginal cost, each private firm’s marginal profit on every unit produced is positive. Therefore, the private firm owners will set their managers’ contract terms to such a level that they will produce all of the total output.This is verified by examining a private firm’s profit as a function of its contract term:
p i Ž b i . s Ž c 0 y c1 . Ž c 0 y b i c1 . ,
Ž 20 .
which is clearly maximized by lowering bi as far as possible Žnote that the other private firms’ contract terms do not appear in this expression, having been canceled out by public output in computing the market price.. If we assume that all private firms’ contract terms are equal, the lowest feasible value of bi is the value at which the private firms split total output equally:
bi s 1 y
a q nc1 y Ž n q 1 . c 0 nc1
.
Ž 21 .
Substituting this value into Eq. Ž19. gives us the following outputs, profits and social welfare: q1 s
a y c0 n
,
q0 s 0,
p 0 s 0, CS s
Ž a y c0 . 2
Q s nq1 s a y c 0 , 2
,
Ws
p1s
Ž a y c 0 . Ž c 0 y c1 .
Ž a y c 0 . Ž a q c 0 y 2 c1 . 2
n .
,
Ž 22 .
892
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Even if n is small Žpossibly one., the private firms cannot achieve the normally low Cournot total output due to the threat of public production. In this way, the public firm creates a contestable market, wherein the private firms’ ability to abuse market power is curtailed by potential competition Žsimilar to Baumol’s contestable markets theory; see Baumol et al., 1982.. Social welfare is higher than when all firms have managers Žgiven the relevant assumption of c 0 - c 0 ., since total output is higher and produced solely by the more efficient firms. 4.2. Managerial game solution Now we have all of the results required for the managerial game; the solution is given in Proposition 5. Proposition 5. The subgame-perfect Nash equilibrium with a public firm and priÕate firms in which each firm chooses whether or not to hire a manager is: the priÕate firms hire managers and the public firm does not. We will prove this proposition using a payoff matrix, which is shown in Table 1 below. We will try to find a Žsubgame-perfect. Nash equilibrium solution to this game. First, we analyze a representative private firm owner’s decision, and find that the private firms will always hire managers. If the public firm hires a manager, then each private firm’s profit is higher if it hires a manager Žassuming a negligible payoff to its manager.. If the public firm does not hire a manager, again private profit is increased by hiring a manager Žgiven our assumption that c 0 - c 0 .. Hiring a manager is therefore a strictly dominant strategy for the private firm, as it is in the original FJS analysis; in both models, the optimal contract term for a private firm is different than one, which implies that pure profit-maximization is a strictly dominated strategy. From Table 1, we can see that the public firm will always do the opposite of what the private firms do; if the private firms hire managers, the public firm will not hire one, and vice versa. When private firms hire managers, welfare is higher
Table 1
Private managers
Public manager
No public manager
p 1 s Ž nq1. 3 Ž c0 y c1 . 2 ,
p 1s
Ws No private managers
Ž ay c0 . 2q n Ž 2 n2 q3nq2.Ž c0 y c1 . 2 2 .2 Ž
p 1 s Ž nq1 Ws
.2
c 0 y c1 ,
Ž ay c0 . 2q n Ž nq1.Ž c0 y c1 . 2 2
Ws
Ž ay c0 .Ž c0 y c1 . n
,
Ž ay c0 . Ž aq c0 y2 c1 . 2
p 1 s Ž c 0 y c1 . 2 , Ws
Ž ay c0 . 2q2 n Ž c0 y c1 . 2 2
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if the public firm does not hire one Žguaranteed by c 0 - c 0 ., and when the private firms do not hire managers, welfare is always increased by hiring a public manager. Since the optimal strategy for the public firm is to do the opposite of what the private firms do, the SPNE solution to this game is: the private firms hire managers and the public firm does not. Under our cost assumptions, private firms will always hire managers, and the public firm maximizes social welfare by doing the opposite, not hiring a manager. Here, the precommitment ability possible under a managerial regime does not seem to enable the public firm to increase social welfare when the private firms hire managers. When the public firm does not hire a manager, compared to when it does, total output is higher, public profit is zero Žlower., and the change in private profit is ambiguous; however, the net result is unambiguously higher welfare. This seems odd, because we solved for an optimal contract term for the public manager; why, then, does not hiring a manager provide higher social welfare than hiring one with the AoptimalB contract? Recall that for the public firm, assigning an FJS contract is qualitatively different from maximizing its true objective function, welfare. While the contract term derived for the public manager maximizes social welfare assuming a manager is hired, it does not necessarily maximize social welfare when the option of not hiring a manager is included as well. No FJS contract achieves a level of social welfare as high as simple welfare-maximization; the form of the FJS contract is not sufficiently well-suited to social welfare maximization to provide any net strategic advantage.17
5. Privatizationr r managerial game A final question we may ask is: given the solution of the game in which all firms have the option of hiring a manager, what are the effects of privatization? In other words, with the solution of the above game, will privatization raise or lower social welfare? The answer to this question is given in Proposition 6. Proposition 6. In a multistage game in which the public firm decides whether to operate as a public firm, shut down, or priÕatize, and then the firms decide whether or not to hire managers, the subgame-perfect Nash equilibrium solution is as in Proposition 5: the public firm operates as a public firm (but does not produce), and only the priÕate firms hire managers (and produce all output). If we assume that the privatized industry will take the standard FJS managerial form, we can simply compare welfare in the private managerial industry from Eq. 17
See Footnote 15.
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Ž12., to that of the mixed publicrprivate industry in which only the private firms hire managers as given in Eq. Ž22.: Wp y Wm s y
a q Ž 2 n3 q 7n 2 q 11n q 7 . c 0 y Ž 2 n 3 q 7n 2 q 11n q 8 . c1 2 Ž n2 q 2 n q 2.
2
= a q n Ž n q 1 . c1 y Ž n 2 q n q 1 . c 0 .
Ž 23 .
Expression Ž23. is strictly negative if the final bracketed term is positive, which is guaranteed by the necessary condition for production by the privatized public firm. So the private managerial form, when feasible, is always welfare-inferior to the mixed case in which a public firm is present to constrain the behavior of private firms.18 In conclusion, in a larger game in which the government first chooses whether or not to privatize the public firm, and if not, then chooses whether or not to hire a manager, the SPNE solution is for the public firm to remain government-operated and to do so without a manager, resulting in the private firms’ assuming all production under threat of public firm participation. Price is maintained at c 0 , while all production is undertaken by the more efficient firms.19
6. Conclusions and extensions In this paper, I have investigated managerial incentives in a market where a public firm competes with private firms, focusing on endogenizing the managerial hiring decision. Previously, the literature considered only cases in which either all firms hired managers or all did not, and the result was that the managerial case provided both higher social welfare and higher private profits; these results are confirmed with my model. When, however, the managerial hiring decision is endogenous, the only subgame-perfect Nash equilibrium is that only private firms hire managers and undertake all production, and are constrained by the public 18
Even if the public firm’s costs fall after privatization, privatization still lowers welfare if the public firm’s original c 0 - w aqŽ n2 q2 nq2 )c1 xrŽ n2 q2 nq3.. 19 The issue of fixed costs becomes particularly relevant at this point. While the public firm produces no output in the SPNE, it must not shut down completely; it must stand ready to produce in order to retain its disciplinary powers and ensure that the private firms produce the ArightB output. In other words, the public firm will still incur any fixed costs it may have, although it produces nothing. Though we assume no fixed costs, a certain level of fixed costs for the public firm can be tolerated without altering the results of the model. This fixed cost must be balanced against the cost of allowing the private firms an unrestrained oligopoly. The larger the SPNE output, the higher the losses from private oligopoly, and the higher the fixed costs that can be incurred by the public firm while producing no output. Only if the SPNE output is relatively small and the fixed costs are high will the results of the model be altered.
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firm, which forces the private firms to produce above their normal oligopoly output, as in a contestable market. The public firm is a means, therefore, of regulating the industry, without requiring any production that be would be inefficient, compared to private production Žthough some fixed costs would be incurred.. This contrasts with results that require the public firm to produce positive output in order to be a means of regulation.20 I also analyzed a larger game, in which the public firm first decides whether to remain public, privatize, or shut down, and then all firms decide whether or not to hire managers. The solution to the managerial game holds as a SPNE in this larger game; the public firm will remain public, not hire a manager, and AallowB the private firms to produce all output. Privatization never raises social welfare, unlike in the case in which all firms have managers, in which case, privatization may raise social welfare under certain cost conditions. Extensions to this paper would generalize the assumptions of the model, regarding cost and demand functions, the form of the managerial contracts, and the nature of competition,21 as well as reintroducing asymmetric information.
Acknowledgements I thank Debashis Pal, Wolfgang Mayer, H.W. Whitmore, Frans van Winden, Arye L. Hillman, and two anonymous referees for helpful comments, and the Taft Fellowship at the University of Cincinnati for financial assistance. All remaining errors are of course my own.
References ´ Barros, F., 1994. Delegation and efficiency in a mixed oligopoly. Annales d’Economie et de Statistique 33, 51–72. Barros, F., 1995. Incentive schemes as strategic variables: an application to a mixed duopoly. International Journal of Industrial Organization 13, 373–386. Basu, K., 1993. Lectures in Industrial Organization Theory. Blackwell, Oxford. Basu, K., 1995. Stackelberg equilibrium in oligopoly: an explanation based on managerial incentives. Economics Letters 49, 459–464. Baumol, W.J. et al., 1982. Contestable Markets and the Theory of Industry Structure. Harcourt, Brace, Jovanovich, New York. 20 See De Fraja and Delbono Ž1987. for an example of this sort of result within price competition Žsee also De Fraja and Delbono, 1991, pp. 11–12.. 21 For instance, under Bertrand competition when a public firm and private firms produce differentiated products, private output falls when managers are hired, while public output rises, which is the opposite of the effects in the paper under Cournot competition. Also, the changes in private profit and welfare depend critically on the strength of the cross-price effects between the two markets. These results encourage further study of this model; I thank an anonymous referee for the suggestion.
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