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Incentive schemes as strategic variables: An application to a mixed duopoly
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InternatioJournal nal of International Journal of Industrial Organization 13 (1995) 373-386
ELSEVIER
Industrial Organization
Incentive schemes as strategic variables: An application to a mixed duopoly F~itima Barros Department of Economics, Universidade Cat61ica Portuguesa, Palma de Cima, 1600 Lisboa, Portugal
Accepted 21 September 1994
Abstract
In the context of asymmetry of information between firms' owners and their managers, we investigate the use of incentive contracts as strategic variables in a duopoly with a public and a private firm. By giving the public manager an incentive scheme based on a linear combination of profit and sales revenue, we show that welfare can be improved. Furthermore, we show that the government should not privatize the public company. Key words: Mixed oligopoly; Strategic contracts; Asymmetric information J E L classification: D82; L13; L32
I. I n t r o d u c t i o n
T h e strategic implications of incentive contracts have b e e n investigated in the c o n t e x t o f an oligopolistic industry. Vickers (1985), F e r s h t m a n and J u d d (1987), Sklivas (1987) and Katz (1991) have p o i n t e d out that the o w n e r of a firm m a y w a n t his m a n a g e r to pursue an objective different f r o m that of profit m a x i m i z a t i o n w h e n there is an i n t e r d e p e n d e n c e b e t w e e n firms. In particular, they have shown that a m a n a g e r ' s decisions based partly on non-profit considerations like sales can be m o r e profitable for o w n e r s than decisions driven solely by profit. T h e design of the incentive contract for the m a n a g e r then has the character o f a strategic variable (see also G a l - O r , 1993, and Sen, 1993). 0167-7187/95/$09.50 (~ 1995 Elsevier Science B.V. All rights reserved S S D I 0167-7187(94)00461-7
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In this p a p e r we analyze the design of incentive contracts when one of the firms m a y not be interested in maximizing profit. Some authors have shown that a public firm can be used as a possible alternative to m a r k e t regulation) If the public firm is instructed to maximize social welfare, then the public firm moves the m a r k e t outcome towards the social o p t i m u m and the g o v e r n m e n t can avoid direct regulation of the sector (with all the inherent informational problems). Alternatively, the government can use the public firm as a vehicle for gathering information from market activity since an insider firm has much m o r e information about the sector than a regulatory agency (see Garvie and Ware, 1991). Industries characterized by imperfect competition a m o n g private and public firms are called m i x e d oligopolies. T h e objective of the present p a p e r is to understand how results in mixed duopoly are affected by the explicit recognition that firms are run by m a n a g e r s , and owners can use incentive contracts in a strategic way. M o r e precisely, we consider that owners might base the m a n a g e r ' s compensation function upon a linear combination of profit and sales revenue as in F e r s h t m a n and Judd (1987) and we analyze the impact of introducing these contracts on the equilibrium of a mixed duopoly. This analysis is quite relevant because in the existing literature on mixed oligopoly the assumption generally used is that the public manager is instructed to maximize welfare while ignoring informational problems. Thus, the g o v e r n m e n t is presumed to have complete control of the m a n a g e r ' s actions. A question that can be raised is related to the usual assumption that the contract of the public manager is contingent upon realized social welfare. Since social welfare is a very complex concept, which depends also upon rivals' actions, it seems unreasonable to suppose that the public agent is offered such a contract. In particular some variables might not be observable to the government. Therefore, it is pertinent to consider a different class of contracts for the public manager. In our p a p e r we consider a homogeneous-goods duopolistic industry. The g o v e r n m e n t must decide whether to privatize a public firm or to retain control of the firm. The decision is made on the basis of the m a r k e t structure that leads to higher social welfare. Since both firms hire agents to play the game on the owners' behalf and there is full c o m m i t m e n t to the observable contracts, we face a situation where contracts have strategic value. As stated above, we assume that both owners (the private owner and the g o v e r n m e n t ) might base the m a n a g e r ' s compensation upon a linear combination of profit and sales revenue and we call such a contract a strategic
See Beato and Mas-Colell (1984), Cremer et al. (1989), Fershtman (1990) and De Fraja and Delbono (1989, 1990).
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Furthermore, it is assumed that the manager's effort is necessary for production and it is not observable by the owner. It is shown that at the equilibrium (hereafter called the Incentive Contract Equilibrium and denoted by ICE) both owners choose to base incentive schemes only partly on profits. But the private principal ties his manager's incentive more closely to profit than does the government. As a consequence the government makes its manager more aggressive than the private manager so the public firm produces a larger market share and makes higher profit than the private firm. The outcome in the ICE is similar to the classic Mixed Duopoly Equilibrium (MDE), where it is assumed that it is possible to induce a manager to act so as to maximize social welfare. However, the social welfare level at the ICE is higher than at the MDE. The explanation for this result is the following: since marginal cost is increasing, a larger asymmetry between the two firms' output increases industry average cost. At the M D E this asymmetry of production is larger than at the ICE, which means lower productive efficiency. Indeed, when both principals design strategic contracts, public production is lower than in the M D E , which means that the government induces the manager to be less aggressive than a welfaremaximizing manager. This is so because the private manager is also given the incentive to behave aggressively. On the contrary, the private firm produces larger output in the ICE than in the MDE. However, total production is lower in the ICE than in the M D E and this implies a reduction in consumer surplus. Nevertheless there is a more efficient distribution of industry supply in the ICE which leads to higher producer surplus. The net impact of introducing strategic contracts in the mixed duopoly is clear: total surplus is higher in the ICE than in the M D E because the reduction in consumer surplus is more than offset by the increase in producer surplus. We also show that the mixed duopoly yields higher social welfare than the private duopoly when principals implement strategic contracts for managers. T h e r e f o r e , the government should not privatize the public firm. The remainder of the paper is organized as follows. In Section 2 we present the model. In Section 3 we characterize the ICE in the mixed duopoly and we compare and discuss the results with those arising from the M D E . In Section 4 we compare the ICE in the mixed and private equilibrium. Our conclusions are found in Section 5. contract.
2. The model
We consider a market where two firms produce a homogeneous good. One firm is private while the other is public. Private ownership means that
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the owner's goal is profit maximization; public ownership implies an objective of social welfare maximization, i.e. the sum of consumer and producer surpluses and managers' utilities. For simplicity demand is assumed to be linear and is given by P = a - Q,
(1)
where P denotes the market price, Q = ql + q2 and qi is firm i's output. 2.1. The firms
Each owner hires an agent and gives him the authority to make all production decisions. We then have a four-player game: for each of the two firms we have an owner (principal) and a manager (agent). On grounds of tractability, we restrict consideration to risk neutrality for all players. Each agent chooses an unobservable action e i E [0, ~[ called effort. A manager's effort is one of the inputs necessary for production. Moreover, managers are assumed to be identical and their utility function is described by e2 i
U~(Y/,e,)= Y ~ - b - ~ - ,
b~>0,
(2)
where Y~ denotes manager i's compensation function and be~/2 is the disutility from effort. The manager's reservation utility is normalized to zero. Managers' willingness to exert effort depends solely on the incentive scheme stipulated by the contract. Ownership type determines a principal's objective and consequently the contract form. Therefore, the manager's action is conditioned via the contract and the fact that a firm is private or public is not, per se, a determinant of the manager's efficiency: under the same contract a public manager is as efficient as a private one. Principal i's strategy is his manager's compensation function Y,; manager i's strategy is the choice of his effort level, e i. Both firms have the same technology given by the production function qi = Oi + ei,
Vi,
(3)
where 0~ is a random productivity parameter with mean 0 and variance o-z and is independently distributed across firms. A low 0i might represent a disruption in the production process perhaps due to a high percentage of malfunctioning machines or a high amount of labor turnover. To achieve a particular rate of production when 0~ is lower, the manager must spend more effort with the production process; for example, organizing the repair or replacement of the machines and training and monitoring new workers.
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Furthermore, both firms face a linear production cost equal to C(qi) = cqi, where a > c > 0.
2.2. Information structure A t date 1 the government must decide whether the public firm is privatized or remains under public control. Once firms' property rights are clearly defined, the owner of each firm offers an employment contract to his manager, which the manager can either accept or reject. At that time, neither party knows the realization of 0 but its distribution is c o m m o n knowledge. At date 2 nature draws the value of 0. At date 3, managers observe the realization of their 0 and decide on the level of effort. A f t e r the contracting stage, contracts are publicly announced and principals are fully committed to this contract (no renegotiation is allowed). In the second stage, when production decisions are taken, agent i knows the rival agent's contract but cannot observe the realization of the rival's productivity parameter, 0r. Principals are constrained by their information set: they are fully informed about agents' utility functions but cannot observe the effort exerted by their managers. In consequence, they cannot contract upon the effort value. F u r t h e r m o r e , each owner does not observe the realization of 0 ex post so he cannot determine whether a low output was due to a low productivity state or to managerial slack. We consider here that the owner only observes the value of sales and profits of his firm. Therefore contracts can be conditional only on these variables that are ex post observable to principals. 2
2.3. Strategic incentive contracts We analyze the equilibrium in a framework where both principals offer contracts that are linear in the firm's gross profit and sales revenue. Such a strategic contract is defined by the following compensation function:
Yi(q,, q~) = ,~iYri(qi, q~) +
(1 -
A,)Ri(q,, qj) + T~,
i ~j,
(4)
where 7ri and R i stand for firm i's sales revenue and gross profit, respectively, and T i denotes a fixed transfer (it can be either positive or negative). M a n a g e r i's compensation function is then defined by the pair (Ai, 7",). For values of A ~ < I ( A ~ > I ) manager i receives an incentive to be more 2Like Fershtman and Judd (1987) and Sklivas (1987) we exclude output from the contract because the owner may not be able to observe it directly. It seems more reasonable to assume that the owner designs his manager's contract contingent upon sales and profit because these variables are made available for accounting purposes.
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aggressive (less aggressive) than a profit-maximizer in the product market which is reflected by producing a larger output. We do not impose any range on values for A, as long as each firm has positive output. The solution concept is a subgame perfect Nash equilibrium.
3. Mixed duopoly In this section we focus on the situation where the government maintains control of the public firm. In Section 4 we consider the privatization decision. Public ownership means that the firm might pursue goals other than profit maximization. Under the assumptions of the model, ownership alteration does not imply any change in either the firm's cost function or the principal's information structure. Moreover, we do not consider any specific regulatory rule: our objective is to look at the public firm in the market only as a regulation mechanism. We start by looking for the equilibrium in the second stage. Let a subscript s denote the public firm and a subscript p the private one. Each manager chooses the level of output (and consequently the effort level) that maximizes his expected utility given the pairs (h,, Ti) and (hi, Tj). Since the effort choice determines the level of output, for a given realization of O, we can write a manager's maximization program as a function of the output level. Both problems are equivalent and it is easier for our analysis to set it up in terms of output rather than effort: maXqiE° [Ui] = (a - qi
--
Eo [qj(Oj)])qi
-
Aicq,
d- r i -
b
(qi - Oi) 2
2
'
(5)
for i = s , p , j = s , p a n d i ¢ j . The first-order conditions of (5) yield the following best reply function for manager i: a + bOi - cA, - E o [qj(Oj)] q * ( E o [ q j ( O j ) ] ; Ai) -
2+ b
(6)
fori=s,p andiCj. Thus, quantity levels, at the second-stage equilibrium, are a function of the contracts designed in the previous stage: q~(A i, Aj) =
(1 + b ) ( a + bO,) - (2 + b)cA, + cAj (3 + b)(1 + b)
b E - 0,)
(3 + b)(1 + b)
(7)
for i = s , p , j = s , p a n d i ¢ j . Firm i's output (consequently, manager i's effort) is decreasing with Ai and increasing with Aj for i ¢ j . When As = Ap = 1, we obtain the regular Cournot equilibrium (RCE) with two profit-maximizing firms.
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In the principal subgame, owner i, i = s, p, chooses the optimal contract (A/, Ti) by maximizing his payoff taking into account the anticipated equilibrium outcome of the managers' subgame and agent i's individual participation constraint. Recall that the government's goal is social welfare (W) maximization. We define social welfare as the total surplus which is equivalent to the sum of the consumer surplus and the firms' profits net of the agents' effort disutility (agents' compensations are just transfers between firms and their agents so they cancel out). The public principal solves the following program:
Fqs+qp
m~x~ ~ ~ E0~ %I~/~s, ~., ~ 0s, 0pl] = E0~0p k fo ,a -~, ~ -Clqs + qp~ b (qs - 0s) 2 2
b.(qp - Op);]
2
'
(8)
s.t. ~>0,
,
(9)
where qs = qs(As, Zp, 0s) and qp = qp(As,/~p, 0p). Since the private principal maximizes his net profit, he solves the following program: max Eos.op[Pp(.)] = E0s %[Trp(A,, Ap, 0s, 0p) - Yp(As, Ap, Tp, 0p, 0s)] ,
Ap,Tp
(lo) s.t. ~>0,
(ll)
where Pp stands for the private principal's payoff (the firm's profit net of the manager's compensation). The best reply functions are
As*(Ap) = 1 -
(t~ - CAp)(b + 1) 2 - 2c(1 - Ap) c(1 + 7b + 5b 2 + b 3) ' (h - c ) ( b +
Av ( A s ) = l
1)
-
c(1
c(2+b)(Z+4b+b
-
As) 2) '
(12) (13)
where h -= a + bO. Note that the best reply functions in the principal subgame might have different signs to their slopes: the slope is negative for the private firm but it
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is positive for the public firm when b > X / 2 - 1. This fact allows us to conclude that the private firm wants its manager to be less aggressive in the product market (higher value of Ap) when the rival firm gives an incentive to its manager to be more aggressive (lower value of Ap) in order to avoid a significant decrease in price level. However, the behavior of the public firm depends on the marginal cost function. If marginal cost increases sharply (b > ~ - 1 ) , then the public firm will want its manager to be less aggressive (higher value of As) when the private firm gives less incentive to its manager to be aggressive (higher value of Ap). This results from the fact that the private firm's profit and consumer surplus also enter the objective function of the public firm. Thus, the positive slope of its best reply function is due to the public firm being interested in decreasing the gap between public and private production (and consequently in decreasing the average cost of the industry supply), when the value of b is significantly high. Since the individual rationality constraint holds as an equality, then T~ = E0[Y~(. ) - b(q, - 0,)2/2]. The following proposition sums up the equilibrium contracts.
Proposition 1. A t the ICE, 1 > Ap > & and E0[qJ > E0[qp ]. Proof. By solving the above programs we have: (1 + 5b + 4b 2 + b3)(gt - c) A* = 1 - c(1 + 12b + 16b 2 + 7b 3 + b 4) < 1,
(14)
b(b + 2)(h - c) Ap = l - c ( l + 1 2 b + 1 6 b 2 + 7 b 3 + b 4) < 1 '
(15)
and clearly Ap > AS since ~/> c and b/> 0 by assumption. Also, from (7) and using (14) and (15): (1 + 6b + 5b 2 + b3)(d - c) E°[q*] - 1 + 1 ~ + i-~-2 + T-~3 + ~ '
(16)
b(2 + b)2(a - c) E ° [ q ; ] = 1 + 12b + 16b 2 + 7b 3 + b 4"
(17)
It can then be checked that Eo[q*~]>Eo[qp ] for b ~ 0 .
[]
Proposition 1 shows that it is not in the interest of the owners to base their incentive schemes on profits alone. Since &, Ap < 1, both principals give their managers an incentive to be more aggressive than in the regular Cournot equilibrium. The equilibrium contracts are, however, very different. Since A~< Ap, the private principal ties his manager's incentive more
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closely to case that penalized rewarded
381
profit than does the public principal. In fact, it may well be the As < 0 and Ap > 0 , which implies that the public manager is for profits and overcompensated for sales, while his rival is by profits. This case arises when the parameters satisfy O
1 + 5b + 4b 2 + b 3
<
a--c
c
<
o
b(b + 2)'
where v - 1 + 12b + 16b z + 7b 3 + b 4. This result clearly shows the government's concern for consumers. Note that the private firm is out of the market when the effort cost is zero (b = 0). This means that when the marginal production cost is constant and identical for both firms, the welfare-maximizing firm supplies the entire market .3 Proposition 2. The public firm makes strictly higher expected profits than the private firm. Proof. Straightforward computations yield (1 + b)3(3 + b) - Zo[
which is positive.
p] =
- c) 2
202
,
[]
Clearly, the different nature of the firms' property rights yields a strategic advantage to the public firm. The fact that the public owner aims to maximize social welfare is a credible commitment to induce the public manager to behave more aggressively than the private manager and to produce beyond the profit-maximizing level. What happens when we compare the incentive contract equilibrium with the outcome of a mixed duopoly in the traditional literature? 4 In these models strategic delegation is not considered so that the public manager maximizes social welfare and the private firm maximizes profit. We denote the associated equilibrium as the mixed duopoly equilibrium (MDE). In the M D E the welfare-maximizing manager produces more aggressively than the private manager. As in the ICE there is a large difference between public and private production. The impact of introducing incentive contracts in the mixed duopoly is stated by the following proposition: 3This result is well known in mixed oligopoly theory (see De Fraja and Delbono, 1989, 1990). 4This corresponds to the case where there is no agency problem and the public manager maximizes welfare.
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Proposition 3. In the M D E the difference between the levels of production of the public and private firm is larger than in the ICE. However E o[Q MDE]> E0 [Q ~CE], which implies that the total expected output is more competitive in the M D E than in the ICE and there is a loss in terms of allocative efficiency in the ICE when compared with the MDE. Proof. The expected outputs at the M D E are Eo[qs]--
(1 + b)(a - c) l+3b+b 2 '
(18)
b(a - c)
(19)
E o [ O ~ ] - 1 + 3b + b 2'
Simple computations show that Eo[Os]>Eo[q*] and Eo[ ~ l < E o [ q p ]. Clearly, from (16), (17) and (18), (19),
Eo[QMDEI>Eo[Q'CE] t. ~
It is easy to see that the introduction of incentive contracts leads to a more efficent allocation of production between both firms: the public firm no longer needs to produce such a large quantity as in the M D E because the private firm also gives incentive to its manager to produce beyond the profit-maximization level. Hence, there is a transfer of production from the public firm to the private firm. Since the marginal cost associated with the effort is increasing with the production level, this transfer corresponds to a gain in terms of productive efficiency. However, the reduction in public production more than offsets the increase in private production leading to a loss in terms of allocative efficiency. The impact of introducing incentive contracts results in the public firm making its manager less aggressive than in the M D E . On the contrary, the private firm makes its manager more aggressive and increases its profit. The net effect on social welfare then depends upon the trade-off between the gain in productive efficiency in the ICE and the gain in allocative efficiency in the MDE. Proposition 4. In the mixed duopoly, social welfare at the ICE is higher than at the MDE. Proof. The difference between the expected social surplus in the ICE regime and the M D E regime equals: a(t~ - c) 2 - bfltr 2, where /3 --- (4 + 6b + b2)/ (2(1 + b)(2 + b) 2) and a =- b2(1 + b)[(1 + b)(2 + b)(2 + 16b + l l b 2 + 2b 3) + v]/[2(1 + 3 b + b2)2v2]. [] From Proposition 4 we conclude that the reduction in consumer surplus is more than offset by the increase in producer surplus. With this class of linear contracts we achieve an equilibrium that is more efficient (in terms of total
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surplus) than the regular Cournot equilibrium of a mixed duopoly. This is due to the strategic interaction between firms and the commitment value of managerial contracts.
4. Mixed vs. private duopoly
The next question that we address is the following: Is the mixed duopoly socially preferable to a private duopoly when principals can give strategic contracts to their agents? In the mixed duopoly total industry supply is expected to be higher than in the private duopoly. However, we have already seen that a large asymmetry of firms' production levels leads to higher average cost of industry supply (and thus to a loss in productive efficiency) than when production is equally distributed among firms--which is the case of the private duopoly, when firms are both profit maximizers. In what follows we investigate whether the government should privatize the public firm. Fershtman and Judd (1987) have shown that a contract with Ai = 1 is a dominated strategy for a firm in a private duopoly. The main result is that the production of each firm increases but at the equilibrium each firm gets lower profits than in the regular Cournot case. In order to answer the aforementioned question we must compare the outcome of the ICE in the mixed and private duopolies. Proposition 5. A t the I C E o f a mixed duopoly, expected consumer surplus is higher and expected producer surplus is lower than at the I C E o f a private duopoly. Proof. Computing the ICE of the private duopoly yields a contract parameter of
fi-c )~,=l-c(5+5b+b2)
'
Vi,
(20)
(2 + b)(a - c) 5+5b+b 2 '
Vi.
(21)
and a production level of E°[4]-
Obviously A* <'~i E o [ ~ i l > E o [ q p ] and it is straightforward to show that E 0[QICE] > E0 [2~i]. Hence, expected consumer surplus is higher in the mixed duopoly than in the private duopoly. Computing the difference between firms' expected profits in both regimes yields:
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384
+ b)2bY2)2v2(dt _ c) 2 • 0, Eo[Trs q- "/rp- 2~/] = - 2(5 +(15b + where y - 8 + 121b + 450b 2 + 668b 3 + 494b 4 + 192b s + 38b 6 + 3b 7.
[]
This result is very intuitive: due to the presence of the welfare-maximizing firm, the private firm ties its manager incentive more closely to profit than in the case when the rival firm is a private firm. Consequently, it produces less than in the private duopoly. We now have to check whether the net effect of a mixed duopoly on welfare is positive. This leads to:
Proposition 6. The ICE of a mixed duopoly can be sustained as a subgame perfect equilibrium of the extended game where the government decides about the firm's ownership. Proof. Straightforward computations yield the following result for the difference between expected social welfare of the mixed and the private duopoly: E0[AW ] = Z ( t / - c) 2, where Z ~ (1 + b)3(1 + 10b + 48b 2 + 66b 3 + 38b 4 + 10b 5 + b6)/((2(5 + 5b + b2)Zv2)). Clearly, this difference is positive and is decreasing with b. [] Proposition 6 states that the government should not privatize the public firm. The I C E in the mixed duopoly leads to an i m p r o v e m e n t in terms of social welfare although the private firm gets lower profits than in the setting where it competes against another private firm.
5. Conclusion We have presented an alternative formulation for a mixed duopoly. Unlike previous work which presumes that a public manager can be induced to maximize social welfare, we assume here that a government is constrained to writing contracts that m a k e a m a n a g e r ' s compensation depend on only observable variables, specifically profit and revenue. This allow us to p e r f o r m for a mixed duopoly the same exercise as Fershtman and Judd (1987) have done for a private duopoly, considering that incentive contracts can be used as strategic variables. We show that it is in the interest of both principals to design a contract that induces their managers to deviate from profit maximization. Moreover, the private principal ties his m a n a g e r ' s incentive m o r e closely to profit than does the public principal. As a consequence the public firm produces a larger m a r k e t share and makes higher profits than the private firm. We
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conclude that strategic contracts are welfare-improving relative to the situation where the government could write a contract contingent upon social welfare, and strategic contracts would not be considered. This effect of considering strategic contracts is explained by a more efficient allocation of production between both firms. We also show that the mixed duopoly with strategic contracts is welfare-improving so the government should not change the ownership structure of the public firm. These findings apply to the duopoly case and we can expect that similar results could be verified in markets where the number of competing firms is small. However, if the market is sufficiently competitive (a large number of firms) and marginal cost increases sharply, then we might expect that the g o v e r n m e n t should privatize the public firm (see De Fraja and Delbono, 1989, and Barros, 1994). When the market is more competitive, it is more likely that the gain in terms of allocative efficiency does not offset the loss in terms of the productive inefficiency associated with the large asymmetry between public and private production (and the consequent high average cost of the industry supply).
Acknowledgements I wish to thank Jacques Cr6mer, Massimo Motta, Jacques Thisse, Joseph E. Harrington as editor and two referees for their helpful suggestions on an earlier version of this paper. The usual caveat applies. Financial support from the E E C Commission (S.P.E.S.) is gratefully acknowledged,
References Barros, F., 1994, Delegation and efficiency in a mixed oligopoly, Annales d'Economie et de Statistique 33, 51-72. Beato, P. and A. Mas-Colell, 1984, The marginal cost pricing as a regulation mechanism in mixed markets, in: M. Marchand, P. Pestieau and H. Tulkens, eds., The performance of public enterprises (North-Holland, Amsterdam). Cremer, H., M. Marchand and J.F. Thisse, 1989, The public firm as an instrument for regulating an oligopolistic market, Oxford Economic Papers 41,283-301. De Fraja, G. and F. Delbono, 1989, Alternative strategies for a public enterprise in oligopoly, Oxford Economic Papers 41, 303-311. De Fraja, G. and F. Deibono, 1990, Game theoretic models of mixed oligopoly, Journal of Economic Survey 4, 1-16. Fershtman, C., 1990, Market structure: The case of privatization, Economica 57, 319-328. Fershtman, C. and K. Judd, 1987, Equilibrium incentives in oligopoly, American Economic Review 77, 927-940. Gal-Or, E., 1993, Internal organization and managerial compensation in oligopoly, International Journal of Industrial Organization 11, 157-183.
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Garvie, D. and R. Ware, 1991, Public firms as regulatory and auditing instruments, Discussion Paper no. 809, Queen's University. Katz, M., 1991, Game playing agents: Contracts as precommitments, RAND Journal of Economics 22, 307-327. Sen, A., 1993, Entry and managerial incentives, International Journal of Industrial Organization 11, 123-137. Sklivas, S.D., 1987, The strategic choice of management incentives, RAND Journal of Economics 18, 452-458. Vickers, J., 1985, Delegation and the theory of the firm, Economic Journal, Suppl. 95, 138-147.
InternatioJournal nal of International Journal of Industrial Organization 13 (1995) 373-386
ELSEVIER
Industrial Organization
Incentive schemes as strategic variables: An application to a mixed duopoly F~itima Barros Department of Economics, Universidade Cat61ica Portuguesa, Palma de Cima, 1600 Lisboa, Portugal
Accepted 21 September 1994
Abstract
In the context of asymmetry of information between firms' owners and their managers, we investigate the use of incentive contracts as strategic variables in a duopoly with a public and a private firm. By giving the public manager an incentive scheme based on a linear combination of profit and sales revenue, we show that welfare can be improved. Furthermore, we show that the government should not privatize the public company. Key words: Mixed oligopoly; Strategic contracts; Asymmetric information J E L classification: D82; L13; L32
I. I n t r o d u c t i o n
T h e strategic implications of incentive contracts have b e e n investigated in the c o n t e x t o f an oligopolistic industry. Vickers (1985), F e r s h t m a n and J u d d (1987), Sklivas (1987) and Katz (1991) have p o i n t e d out that the o w n e r of a firm m a y w a n t his m a n a g e r to pursue an objective different f r o m that of profit m a x i m i z a t i o n w h e n there is an i n t e r d e p e n d e n c e b e t w e e n firms. In particular, they have shown that a m a n a g e r ' s decisions based partly on non-profit considerations like sales can be m o r e profitable for o w n e r s than decisions driven solely by profit. T h e design of the incentive contract for the m a n a g e r then has the character o f a strategic variable (see also G a l - O r , 1993, and Sen, 1993). 0167-7187/95/$09.50 (~ 1995 Elsevier Science B.V. All rights reserved S S D I 0167-7187(94)00461-7
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In this p a p e r we analyze the design of incentive contracts when one of the firms m a y not be interested in maximizing profit. Some authors have shown that a public firm can be used as a possible alternative to m a r k e t regulation) If the public firm is instructed to maximize social welfare, then the public firm moves the m a r k e t outcome towards the social o p t i m u m and the g o v e r n m e n t can avoid direct regulation of the sector (with all the inherent informational problems). Alternatively, the government can use the public firm as a vehicle for gathering information from market activity since an insider firm has much m o r e information about the sector than a regulatory agency (see Garvie and Ware, 1991). Industries characterized by imperfect competition a m o n g private and public firms are called m i x e d oligopolies. T h e objective of the present p a p e r is to understand how results in mixed duopoly are affected by the explicit recognition that firms are run by m a n a g e r s , and owners can use incentive contracts in a strategic way. M o r e precisely, we consider that owners might base the m a n a g e r ' s compensation function upon a linear combination of profit and sales revenue as in F e r s h t m a n and Judd (1987) and we analyze the impact of introducing these contracts on the equilibrium of a mixed duopoly. This analysis is quite relevant because in the existing literature on mixed oligopoly the assumption generally used is that the public manager is instructed to maximize welfare while ignoring informational problems. Thus, the g o v e r n m e n t is presumed to have complete control of the m a n a g e r ' s actions. A question that can be raised is related to the usual assumption that the contract of the public manager is contingent upon realized social welfare. Since social welfare is a very complex concept, which depends also upon rivals' actions, it seems unreasonable to suppose that the public agent is offered such a contract. In particular some variables might not be observable to the government. Therefore, it is pertinent to consider a different class of contracts for the public manager. In our p a p e r we consider a homogeneous-goods duopolistic industry. The g o v e r n m e n t must decide whether to privatize a public firm or to retain control of the firm. The decision is made on the basis of the m a r k e t structure that leads to higher social welfare. Since both firms hire agents to play the game on the owners' behalf and there is full c o m m i t m e n t to the observable contracts, we face a situation where contracts have strategic value. As stated above, we assume that both owners (the private owner and the g o v e r n m e n t ) might base the m a n a g e r ' s compensation upon a linear combination of profit and sales revenue and we call such a contract a strategic
See Beato and Mas-Colell (1984), Cremer et al. (1989), Fershtman (1990) and De Fraja and Delbono (1989, 1990).
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Furthermore, it is assumed that the manager's effort is necessary for production and it is not observable by the owner. It is shown that at the equilibrium (hereafter called the Incentive Contract Equilibrium and denoted by ICE) both owners choose to base incentive schemes only partly on profits. But the private principal ties his manager's incentive more closely to profit than does the government. As a consequence the government makes its manager more aggressive than the private manager so the public firm produces a larger market share and makes higher profit than the private firm. The outcome in the ICE is similar to the classic Mixed Duopoly Equilibrium (MDE), where it is assumed that it is possible to induce a manager to act so as to maximize social welfare. However, the social welfare level at the ICE is higher than at the MDE. The explanation for this result is the following: since marginal cost is increasing, a larger asymmetry between the two firms' output increases industry average cost. At the M D E this asymmetry of production is larger than at the ICE, which means lower productive efficiency. Indeed, when both principals design strategic contracts, public production is lower than in the M D E , which means that the government induces the manager to be less aggressive than a welfaremaximizing manager. This is so because the private manager is also given the incentive to behave aggressively. On the contrary, the private firm produces larger output in the ICE than in the MDE. However, total production is lower in the ICE than in the M D E and this implies a reduction in consumer surplus. Nevertheless there is a more efficient distribution of industry supply in the ICE which leads to higher producer surplus. The net impact of introducing strategic contracts in the mixed duopoly is clear: total surplus is higher in the ICE than in the M D E because the reduction in consumer surplus is more than offset by the increase in producer surplus. We also show that the mixed duopoly yields higher social welfare than the private duopoly when principals implement strategic contracts for managers. T h e r e f o r e , the government should not privatize the public firm. The remainder of the paper is organized as follows. In Section 2 we present the model. In Section 3 we characterize the ICE in the mixed duopoly and we compare and discuss the results with those arising from the M D E . In Section 4 we compare the ICE in the mixed and private equilibrium. Our conclusions are found in Section 5. contract.
2. The model
We consider a market where two firms produce a homogeneous good. One firm is private while the other is public. Private ownership means that
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the owner's goal is profit maximization; public ownership implies an objective of social welfare maximization, i.e. the sum of consumer and producer surpluses and managers' utilities. For simplicity demand is assumed to be linear and is given by P = a - Q,
(1)
where P denotes the market price, Q = ql + q2 and qi is firm i's output. 2.1. The firms
Each owner hires an agent and gives him the authority to make all production decisions. We then have a four-player game: for each of the two firms we have an owner (principal) and a manager (agent). On grounds of tractability, we restrict consideration to risk neutrality for all players. Each agent chooses an unobservable action e i E [0, ~[ called effort. A manager's effort is one of the inputs necessary for production. Moreover, managers are assumed to be identical and their utility function is described by e2 i
U~(Y/,e,)= Y ~ - b - ~ - ,
b~>0,
(2)
where Y~ denotes manager i's compensation function and be~/2 is the disutility from effort. The manager's reservation utility is normalized to zero. Managers' willingness to exert effort depends solely on the incentive scheme stipulated by the contract. Ownership type determines a principal's objective and consequently the contract form. Therefore, the manager's action is conditioned via the contract and the fact that a firm is private or public is not, per se, a determinant of the manager's efficiency: under the same contract a public manager is as efficient as a private one. Principal i's strategy is his manager's compensation function Y,; manager i's strategy is the choice of his effort level, e i. Both firms have the same technology given by the production function qi = Oi + ei,
Vi,
(3)
where 0~ is a random productivity parameter with mean 0 and variance o-z and is independently distributed across firms. A low 0i might represent a disruption in the production process perhaps due to a high percentage of malfunctioning machines or a high amount of labor turnover. To achieve a particular rate of production when 0~ is lower, the manager must spend more effort with the production process; for example, organizing the repair or replacement of the machines and training and monitoring new workers.
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Furthermore, both firms face a linear production cost equal to C(qi) = cqi, where a > c > 0.
2.2. Information structure A t date 1 the government must decide whether the public firm is privatized or remains under public control. Once firms' property rights are clearly defined, the owner of each firm offers an employment contract to his manager, which the manager can either accept or reject. At that time, neither party knows the realization of 0 but its distribution is c o m m o n knowledge. At date 2 nature draws the value of 0. At date 3, managers observe the realization of their 0 and decide on the level of effort. A f t e r the contracting stage, contracts are publicly announced and principals are fully committed to this contract (no renegotiation is allowed). In the second stage, when production decisions are taken, agent i knows the rival agent's contract but cannot observe the realization of the rival's productivity parameter, 0r. Principals are constrained by their information set: they are fully informed about agents' utility functions but cannot observe the effort exerted by their managers. In consequence, they cannot contract upon the effort value. F u r t h e r m o r e , each owner does not observe the realization of 0 ex post so he cannot determine whether a low output was due to a low productivity state or to managerial slack. We consider here that the owner only observes the value of sales and profits of his firm. Therefore contracts can be conditional only on these variables that are ex post observable to principals. 2
2.3. Strategic incentive contracts We analyze the equilibrium in a framework where both principals offer contracts that are linear in the firm's gross profit and sales revenue. Such a strategic contract is defined by the following compensation function:
Yi(q,, q~) = ,~iYri(qi, q~) +
(1 -
A,)Ri(q,, qj) + T~,
i ~j,
(4)
where 7ri and R i stand for firm i's sales revenue and gross profit, respectively, and T i denotes a fixed transfer (it can be either positive or negative). M a n a g e r i's compensation function is then defined by the pair (Ai, 7",). For values of A ~ < I ( A ~ > I ) manager i receives an incentive to be more 2Like Fershtman and Judd (1987) and Sklivas (1987) we exclude output from the contract because the owner may not be able to observe it directly. It seems more reasonable to assume that the owner designs his manager's contract contingent upon sales and profit because these variables are made available for accounting purposes.
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aggressive (less aggressive) than a profit-maximizer in the product market which is reflected by producing a larger output. We do not impose any range on values for A, as long as each firm has positive output. The solution concept is a subgame perfect Nash equilibrium.
3. Mixed duopoly In this section we focus on the situation where the government maintains control of the public firm. In Section 4 we consider the privatization decision. Public ownership means that the firm might pursue goals other than profit maximization. Under the assumptions of the model, ownership alteration does not imply any change in either the firm's cost function or the principal's information structure. Moreover, we do not consider any specific regulatory rule: our objective is to look at the public firm in the market only as a regulation mechanism. We start by looking for the equilibrium in the second stage. Let a subscript s denote the public firm and a subscript p the private one. Each manager chooses the level of output (and consequently the effort level) that maximizes his expected utility given the pairs (h,, Ti) and (hi, Tj). Since the effort choice determines the level of output, for a given realization of O, we can write a manager's maximization program as a function of the output level. Both problems are equivalent and it is easier for our analysis to set it up in terms of output rather than effort: maXqiE° [Ui] = (a - qi
--
Eo [qj(Oj)])qi
-
Aicq,
d- r i -
b
(qi - Oi) 2
2
'
(5)
for i = s , p , j = s , p a n d i ¢ j . The first-order conditions of (5) yield the following best reply function for manager i: a + bOi - cA, - E o [qj(Oj)] q * ( E o [ q j ( O j ) ] ; Ai) -
2+ b
(6)
fori=s,p andiCj. Thus, quantity levels, at the second-stage equilibrium, are a function of the contracts designed in the previous stage: q~(A i, Aj) =
(1 + b ) ( a + bO,) - (2 + b)cA, + cAj (3 + b)(1 + b)
b E - 0,)
(3 + b)(1 + b)
(7)
for i = s , p , j = s , p a n d i ¢ j . Firm i's output (consequently, manager i's effort) is decreasing with Ai and increasing with Aj for i ¢ j . When As = Ap = 1, we obtain the regular Cournot equilibrium (RCE) with two profit-maximizing firms.
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In the principal subgame, owner i, i = s, p, chooses the optimal contract (A/, Ti) by maximizing his payoff taking into account the anticipated equilibrium outcome of the managers' subgame and agent i's individual participation constraint. Recall that the government's goal is social welfare (W) maximization. We define social welfare as the total surplus which is equivalent to the sum of the consumer surplus and the firms' profits net of the agents' effort disutility (agents' compensations are just transfers between firms and their agents so they cancel out). The public principal solves the following program:
Fqs+qp
m~x~ ~ ~ E0~ %I~/~s, ~., ~ 0s, 0pl] = E0~0p k fo ,a -~, ~ -Clqs + qp~ b (qs - 0s) 2 2
b.(qp - Op);]
2
'
(8)
s.t. ~>0,
,
(9)
where qs = qs(As, Zp, 0s) and qp = qp(As,/~p, 0p). Since the private principal maximizes his net profit, he solves the following program: max Eos.op[Pp(.)] = E0s %[Trp(A,, Ap, 0s, 0p) - Yp(As, Ap, Tp, 0p, 0s)] ,
Ap,Tp
(lo) s.t. ~>0,
(ll)
where Pp stands for the private principal's payoff (the firm's profit net of the manager's compensation). The best reply functions are
As*(Ap) = 1 -
(t~ - CAp)(b + 1) 2 - 2c(1 - Ap) c(1 + 7b + 5b 2 + b 3) ' (h - c ) ( b +
Av ( A s ) = l
1)
-
c(1
c(2+b)(Z+4b+b
-
As) 2) '
(12) (13)
where h -= a + bO. Note that the best reply functions in the principal subgame might have different signs to their slopes: the slope is negative for the private firm but it
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is positive for the public firm when b > X / 2 - 1. This fact allows us to conclude that the private firm wants its manager to be less aggressive in the product market (higher value of Ap) when the rival firm gives an incentive to its manager to be more aggressive (lower value of Ap) in order to avoid a significant decrease in price level. However, the behavior of the public firm depends on the marginal cost function. If marginal cost increases sharply (b > ~ - 1 ) , then the public firm will want its manager to be less aggressive (higher value of As) when the private firm gives less incentive to its manager to be aggressive (higher value of Ap). This results from the fact that the private firm's profit and consumer surplus also enter the objective function of the public firm. Thus, the positive slope of its best reply function is due to the public firm being interested in decreasing the gap between public and private production (and consequently in decreasing the average cost of the industry supply), when the value of b is significantly high. Since the individual rationality constraint holds as an equality, then T~ = E0[Y~(. ) - b(q, - 0,)2/2]. The following proposition sums up the equilibrium contracts.
Proposition 1. A t the ICE, 1 > Ap > & and E0[qJ > E0[qp ]. Proof. By solving the above programs we have: (1 + 5b + 4b 2 + b3)(gt - c) A* = 1 - c(1 + 12b + 16b 2 + 7b 3 + b 4) < 1,
(14)
b(b + 2)(h - c) Ap = l - c ( l + 1 2 b + 1 6 b 2 + 7 b 3 + b 4) < 1 '
(15)
and clearly Ap > AS since ~/> c and b/> 0 by assumption. Also, from (7) and using (14) and (15): (1 + 6b + 5b 2 + b3)(d - c) E°[q*] - 1 + 1 ~ + i-~-2 + T-~3 + ~ '
(16)
b(2 + b)2(a - c) E ° [ q ; ] = 1 + 12b + 16b 2 + 7b 3 + b 4"
(17)
It can then be checked that Eo[q*~]>Eo[qp ] for b ~ 0 .
[]
Proposition 1 shows that it is not in the interest of the owners to base their incentive schemes on profits alone. Since &, Ap < 1, both principals give their managers an incentive to be more aggressive than in the regular Cournot equilibrium. The equilibrium contracts are, however, very different. Since A~< Ap, the private principal ties his manager's incentive more
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closely to case that penalized rewarded
381
profit than does the public principal. In fact, it may well be the As < 0 and Ap > 0 , which implies that the public manager is for profits and overcompensated for sales, while his rival is by profits. This case arises when the parameters satisfy O
1 + 5b + 4b 2 + b 3
<
a--c
c
<
o
b(b + 2)'
where v - 1 + 12b + 16b z + 7b 3 + b 4. This result clearly shows the government's concern for consumers. Note that the private firm is out of the market when the effort cost is zero (b = 0). This means that when the marginal production cost is constant and identical for both firms, the welfare-maximizing firm supplies the entire market .3 Proposition 2. The public firm makes strictly higher expected profits than the private firm. Proof. Straightforward computations yield (1 + b)3(3 + b) - Zo[
which is positive.
p] =
- c) 2
202
,
[]
Clearly, the different nature of the firms' property rights yields a strategic advantage to the public firm. The fact that the public owner aims to maximize social welfare is a credible commitment to induce the public manager to behave more aggressively than the private manager and to produce beyond the profit-maximizing level. What happens when we compare the incentive contract equilibrium with the outcome of a mixed duopoly in the traditional literature? 4 In these models strategic delegation is not considered so that the public manager maximizes social welfare and the private firm maximizes profit. We denote the associated equilibrium as the mixed duopoly equilibrium (MDE). In the M D E the welfare-maximizing manager produces more aggressively than the private manager. As in the ICE there is a large difference between public and private production. The impact of introducing incentive contracts in the mixed duopoly is stated by the following proposition: 3This result is well known in mixed oligopoly theory (see De Fraja and Delbono, 1989, 1990). 4This corresponds to the case where there is no agency problem and the public manager maximizes welfare.
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Proposition 3. In the M D E the difference between the levels of production of the public and private firm is larger than in the ICE. However E o[Q MDE]> E0 [Q ~CE], which implies that the total expected output is more competitive in the M D E than in the ICE and there is a loss in terms of allocative efficiency in the ICE when compared with the MDE. Proof. The expected outputs at the M D E are Eo[qs]--
(1 + b)(a - c) l+3b+b 2 '
(18)
b(a - c)
(19)
E o [ O ~ ] - 1 + 3b + b 2'
Simple computations show that Eo[Os]>Eo[q*] and Eo[ ~ l < E o [ q p ]. Clearly, from (16), (17) and (18), (19),
Eo[QMDEI>Eo[Q'CE] t. ~
It is easy to see that the introduction of incentive contracts leads to a more efficent allocation of production between both firms: the public firm no longer needs to produce such a large quantity as in the M D E because the private firm also gives incentive to its manager to produce beyond the profit-maximization level. Hence, there is a transfer of production from the public firm to the private firm. Since the marginal cost associated with the effort is increasing with the production level, this transfer corresponds to a gain in terms of productive efficiency. However, the reduction in public production more than offsets the increase in private production leading to a loss in terms of allocative efficiency. The impact of introducing incentive contracts results in the public firm making its manager less aggressive than in the M D E . On the contrary, the private firm makes its manager more aggressive and increases its profit. The net effect on social welfare then depends upon the trade-off between the gain in productive efficiency in the ICE and the gain in allocative efficiency in the MDE. Proposition 4. In the mixed duopoly, social welfare at the ICE is higher than at the MDE. Proof. The difference between the expected social surplus in the ICE regime and the M D E regime equals: a(t~ - c) 2 - bfltr 2, where /3 --- (4 + 6b + b2)/ (2(1 + b)(2 + b) 2) and a =- b2(1 + b)[(1 + b)(2 + b)(2 + 16b + l l b 2 + 2b 3) + v]/[2(1 + 3 b + b2)2v2]. [] From Proposition 4 we conclude that the reduction in consumer surplus is more than offset by the increase in producer surplus. With this class of linear contracts we achieve an equilibrium that is more efficient (in terms of total
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surplus) than the regular Cournot equilibrium of a mixed duopoly. This is due to the strategic interaction between firms and the commitment value of managerial contracts.
4. Mixed vs. private duopoly
The next question that we address is the following: Is the mixed duopoly socially preferable to a private duopoly when principals can give strategic contracts to their agents? In the mixed duopoly total industry supply is expected to be higher than in the private duopoly. However, we have already seen that a large asymmetry of firms' production levels leads to higher average cost of industry supply (and thus to a loss in productive efficiency) than when production is equally distributed among firms--which is the case of the private duopoly, when firms are both profit maximizers. In what follows we investigate whether the government should privatize the public firm. Fershtman and Judd (1987) have shown that a contract with Ai = 1 is a dominated strategy for a firm in a private duopoly. The main result is that the production of each firm increases but at the equilibrium each firm gets lower profits than in the regular Cournot case. In order to answer the aforementioned question we must compare the outcome of the ICE in the mixed and private duopolies. Proposition 5. A t the I C E o f a mixed duopoly, expected consumer surplus is higher and expected producer surplus is lower than at the I C E o f a private duopoly. Proof. Computing the ICE of the private duopoly yields a contract parameter of
fi-c )~,=l-c(5+5b+b2)
'
Vi,
(20)
(2 + b)(a - c) 5+5b+b 2 '
Vi.
(21)
and a production level of E°[4]-
Obviously A* <'~i
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+ b)2bY2)2v2(dt _ c) 2 • 0, Eo[Trs q- "/rp- 2~/] = - 2(5 +(15b + where y - 8 + 121b + 450b 2 + 668b 3 + 494b 4 + 192b s + 38b 6 + 3b 7.
[]
This result is very intuitive: due to the presence of the welfare-maximizing firm, the private firm ties its manager incentive more closely to profit than in the case when the rival firm is a private firm. Consequently, it produces less than in the private duopoly. We now have to check whether the net effect of a mixed duopoly on welfare is positive. This leads to:
Proposition 6. The ICE of a mixed duopoly can be sustained as a subgame perfect equilibrium of the extended game where the government decides about the firm's ownership. Proof. Straightforward computations yield the following result for the difference between expected social welfare of the mixed and the private duopoly: E0[AW ] = Z ( t / - c) 2, where Z ~ (1 + b)3(1 + 10b + 48b 2 + 66b 3 + 38b 4 + 10b 5 + b6)/((2(5 + 5b + b2)Zv2)). Clearly, this difference is positive and is decreasing with b. [] Proposition 6 states that the government should not privatize the public firm. The I C E in the mixed duopoly leads to an i m p r o v e m e n t in terms of social welfare although the private firm gets lower profits than in the setting where it competes against another private firm.
5. Conclusion We have presented an alternative formulation for a mixed duopoly. Unlike previous work which presumes that a public manager can be induced to maximize social welfare, we assume here that a government is constrained to writing contracts that m a k e a m a n a g e r ' s compensation depend on only observable variables, specifically profit and revenue. This allow us to p e r f o r m for a mixed duopoly the same exercise as Fershtman and Judd (1987) have done for a private duopoly, considering that incentive contracts can be used as strategic variables. We show that it is in the interest of both principals to design a contract that induces their managers to deviate from profit maximization. Moreover, the private principal ties his m a n a g e r ' s incentive m o r e closely to profit than does the public principal. As a consequence the public firm produces a larger m a r k e t share and makes higher profits than the private firm. We
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conclude that strategic contracts are welfare-improving relative to the situation where the government could write a contract contingent upon social welfare, and strategic contracts would not be considered. This effect of considering strategic contracts is explained by a more efficient allocation of production between both firms. We also show that the mixed duopoly with strategic contracts is welfare-improving so the government should not change the ownership structure of the public firm. These findings apply to the duopoly case and we can expect that similar results could be verified in markets where the number of competing firms is small. However, if the market is sufficiently competitive (a large number of firms) and marginal cost increases sharply, then we might expect that the g o v e r n m e n t should privatize the public firm (see De Fraja and Delbono, 1989, and Barros, 1994). When the market is more competitive, it is more likely that the gain in terms of allocative efficiency does not offset the loss in terms of the productive inefficiency associated with the large asymmetry between public and private production (and the consequent high average cost of the industry supply).
Acknowledgements I wish to thank Jacques Cr6mer, Massimo Motta, Jacques Thisse, Joseph E. Harrington as editor and two referees for their helpful suggestions on an earlier version of this paper. The usual caveat applies. Financial support from the E E C Commission (S.P.E.S.) is gratefully acknowledged,
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