Policy objectives and performance in a mixed market with bargaining

International Journal of Industrial Organization 17 (1999) 137–145

Policy objectives and performance in a mixed market with bargaining Johan Willner* ˚ ¨ Department of Economics, Abo Akademi University, Fanriksgatan 3 b, FIN-20500 Turku, Finland Accepted 4 July 1997

Abstract We analyse a mixed duopoly in which wages and salaries are determined by Nash bargaining and where the public firm’s unit costs depend on its objectives. Because of constant returns to scale, welfare maximisation without restriction would eliminate or significantly weaken the private firm. Therefore, we focus on constrained welfare maximisation, in which case unit costs are normally higher in the public firm. On the other hand, the private firm may even earn more than in a monopoly if the public firm maximises profits or if the constraint offers too much protection.  1999 Elsevier Science B.V. All rights reserved. Keywords: Public ownership; Mixed oligopoly; Bargaining JEL classification: L32; L 44

1. Introduction Many public firms around the world are being privatised; cost efficiency is often invoked as a main reason for this. However, there is a wide variety in terms of both objectives and constraints of public sector firms, and the empirical findings

* Corresponding author. Tel.: 1358 2 2654159; fax: 1358 2 2654677; e-mail: [email protected] 0167-7187 / 99 / $ – see front matter  1999 Elsevier Science B.V. All rights reserved. PII: S0167-7187( 97 )00036-2

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do not give unanimous support to the basic assumption of their cost inefficiency (see, for example, Millward, 1982, Boyd, 1986, and Willner, 1996). Firms in public ownership are often assumed to maximise welfare in a market where private and social costs and benefits differ. Recently, economists have focused on welfare maximisation as a strategy to enforce discipline among profit maximising firms ´ et al., 1989 or the survey by De Fraja and Delbono, (see, for example, Cremer 1990). Such a mixed oligopoly would, with some exceptions, provide higher welfare. We focus on one common explanation for cost differences in a mixed duopoly, namely the notion that public ownership leads to higher wages. This is often interpreted as inferior performance, but high wages and salaries are part of total surplus like profits if they are caused by rent capture: public ownership can therefore be considered beneficial even if wages are ‘excessive’ (De Fraja, 1993a). However, an analysis of welfare maximising equilibria can explain only partially the conflicting empirical findings. Therefore, we extend the analysis to other objectives than welfare maximisation, such as promoting the public or the private firm’s profits, and to bargaining as well. We fill a gap also by an explicit assumption that the public firm is not allowed to force its competitor out of business, as would be the case if output reaches its theoretically optimal level. Various refinements of the basic model have earlier been made to avoid such an outcome.1 However, this is of more than technical importance, because private firms often fear ‘unfair’ competition from firms in public ownership. We ignore incentives as a source of cost differences, inspired by a number of ´ recent theoretical contributions such as Pint (1991), Estrin and Perotin (1991) and De Fraja (1993b). For example, De Fraja shows that a public firm can be even more efficient, provided that welfare affects management compensation.2 We show in this paper that welfare maximisation (on the product market) is usually beneficial despite making the public firm appear less cost efficient than its private competitor. It also follows that it is not always better for a private firm to become a monopolist via privatisation and merger. It may be better to face competition, even from a firm in public ownership.

1

´ et al. (1989) assume an exogenous wage premium and require the public firm For example, Cremer to break even. De Fraja and Delbono (1989) assume increasing marginal costs, De Fraja (1993a) focuses on a weighted sum of profits and welfare while Willner (1994) models a capacity choice which implies endogenous differences in unit costs. 2 It has also been shown that X-inefficiency in a slack-ridden economy may be reduced if profit and welfare maximising firms interact, partly because the private firm is forced to become more efficient (De Fraja, 1991).

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2. Commercial objectives: a basic model of profit maximisation and bargaining In practice, public firms are often more or less commercial. A conventional oligopoly with a profit maximising commercial public firm is more than just the benchmark case for checking whether welfare maximisation works. The presence of such a firm matters through its impact on the market structure, and may occasionally even increase the private firm’s profits. There are two firms in the model; Firm 1 is in public ownership and Firm 2 is private. Marginal costs equal the wage rates w 1 and w 2 , because other variable costs are ignored and each unit of output requires one unit of labour. Demand is p 5 a 2 x, where p stands for price, x for quantity and a for a positive parameter; there is a discussion of robustness in Section 4. Wage negotiations take place locally before quantities are chosen. The bargaining strengths of workers and firms are a and 1 2 a under both types of ownership. As usual, the workers’ pay-off (rent) is the difference between the actual wage rate and a given competitive standard w 0 ; all other fall-back levels are zero. We use the superscript C for a Cournot duopoly. Calculating x C1 (w 1 , w 2 ), x 2C (w 1 , w 2 ), p C (w 1 , w 2 ), and is a standard procedure. It follows that 2 2 gross profits are (a 1 w 2 2 2w 1 ) / 9 and (a 1 w 1 2 2w 2 ) / 9. The Nash bargaining solution for Firm 1 is then obtained by maximising the following function; the expression for Firm 2 is similar:

F

a 1 w 2 2 2w 1 C B 1 5 (w 1 2 w 0 )a ]]]] 3

G

2( 12 a )

.

(1)

Inserting the solution w C (see Table 1) yields prices, quantities and gross profits as functions of a. Net profits are denoted by p.

Table 1 Cournot oligopoly and monopoly C

CC

M

w

a (a 2 w 0 ) w 0 1 ]]] 4 2 3a

a (a 2 w 0 ) w 0 1 ]]] 22a

a (a 2 w 0 ) w 0 1 ]]] 22a

xi

4(a 2 w 0 )(1 2 a ) ]]]] 3(4 2 3a )

2(1 2 a )(a 2 w 0 ) ]]]] 3(2 2 a )

(1 2 a )(a 2 w 0 ) ]]]] 22a

pi

F

4(a 2 w 0 )(1 2 a ) ]]]] 3(4 2 3a )

G

2

F

2(1 2 a )(a 2 w 0 ) ]]]] 3(2 2 a )

G

2

F

(1 2 a )(a 2 w 0 ) ]]]] (2 2 a )

G

2

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Welfare is approximated by the total surplus (see Section 3 below), which includes all rents earned by capitalists, managers and workers. However, welfare in the model is higher if and only if output is larger, because x will never exceed its first-best value. The outcome is summarised in Table 1 below, which includes the monopoly case (M) which would be the result of privatisation and take-over. As Table 1 shows, wages are higher for all values of a under monopoly. This depends on rent capture, as also suggested by empirical studies such as Katz and Summers (1989); MacPherson (1990); Stewart (1990); Cable and Machin (1991) and Machin (1991). Monopoly may benefit employees because it means central bargaining, while a duopoly enables firms to divide and rule. This is illustrated by the fact that central bargaining (CC) would lead to the monopoly wage in a duopoly as well.3 The wage rate is higher because we then maximise (w 2 w 0 )a p 12 a subject to a relationship between p1 1 p2 and w. The objective function a is formally equivalent under local bargaining ((w 1 2 w 0 )a p 12 ), but the constraint 1 is then less generous and relates w 1 to p1 . Welfare is always lower in a monopoly, but not necessarily because of higher profits. Normally, the higher price more than compensates for the fact that a larger part of the rents are captured by the workers as bargaining becomes centralised because of monopolisation. However, if workers are extremely strong, the net effect on profits is negative. As follows from Table 1, it is better to have a competitor, and thus to divide the workers, if a .0.80.

3. Constrained welfare maximisation Suppose that Firm 1 maximises welfare and Firm 2 profits. If Firm 1 simply maximises total surplus, Firm 2 would not operate or would be marginalised, producing the amount w 1 2w 2 only. Some economists therefore focus on a weighted sum of profits and welfare. However, a public firm might in practice get less precise instructions, such as serving society as well as possible, while making some profits and not becoming too dominant. We interpret this as welfare maximisation with the restriction that the price should not be allowed fall below a floor m.4 For Firm 2, low values of m mean competition and high values protection. Thus, the public firm maximises total surplus, which is ax 2 ]21 x 2 2 w 1 x 1 2 w 2 x 2 ,

3

As in the Nordic cases, there may be central bargaining even in mixed markets. Alternatively, we might require that the private firm’s output should exceed some minimum value, in which case the results are similar. 4

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subject to the constraint a 2 x > m, while the private firm maximises p Ni 5 (a 2 x 2 w 2 )x 2 . It obvious that the constraint is binding, because otherwise we would get p5w 1 , in which case x 2 would be only max[0, w 1 2 w 2 ]. Thus, x 1 adapts so as to keep the price at m. The public firm’s pay-off in the bargaining situation is not welfare but profits, unlike in the earlier literature. Otherwise, higher wages and salaries in the public firm would be a trivial outcome. Combining the reaction functions and inserting solutions yield prices, quantities and gross profits as functions of the wage rates. Using the superscript W, Nash bargaining means maximising: a 12 a BW , 1 5 (w 1 2 w 0 ) [m(a 2 2m 1 w 2 )(m 2 w 1 )

(2)

B 2 5 (w 2 2 w 0 )a (m 2 w 2 )2(12 a ) ,

(3)

W

Straightforward calculations now yield the results summarised in Table 2. Firm 2 would not produce at all if m , w 0 , and there is an upper boundary above which Firm 1 would not produce: m 2 w0 22a 0 , ]] , L1 5 ]] . a 2 w0 4 2 3a

(4)

The upper boundary of the feasible region is monotone and increasing from 0.5 to 1.0 in the relevant interval. It is obvious that unit costs (wages) are always higher in the public firm, despite

Table 2 The mixed duopoly wW 1

a m 1 (1 2 a )w 0

wW 2

2(1 2 a ) a ]] m 1 ]] w 0 22a 22a

xW 1

(4 2 3a )m 2 2(1 2 a )w 0 a 2 ]]]]]] 22a

xW 2

2(1 2 a )(m 2 w 0 ) ]]]] 22a

pW 1

(2 2 a )(a 2 w 0 ) 2 (4 2 3a )(m 2 w 0 ) (1 2 a )(m 2 w 0 ) ]]]]]]]] 22a

pW 2

F

2(1 2 a )(m 2 w 0 ) ]]]] 22a

G

2

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the focus on profits in the bargaining situation.5 However, welfare is higher than in W C C C the Cournot case (x W 1 1 x 2 . x 1 1 x 2 ), provided that m , p . Using Table 1 and Table 2 shows that this means m2w 42a ]]0 , L2 5 ]]] . a 2 w0 3(4 2 3a )

(5)

This boundary is monotonically increasing from 0.33 to 1.0 in the relevant interval. Firm 1 can also be captured to serve other purposes by authorities which set m too high. State monopoly capitalism can be interpreted as a symbiotic relationship where public intervention is used to promote private profits. Thus, private sector profits are higher than in the conventional duopoly under the following condition: m2w 2(2 2 a ) ]]0 . L3 5 ]]] . a 2 w0 3(4 2 3a )

(6)

This boundary is monotone and increasing from 0.33 for a 5 0 to 0.67 for a 51.0. The intuition for why private sector profits can be higher than in a conventional duopoly is is the fact that the public firm then produces less than its profit maximising output, thus causing a similar outcome as when sticking to a collusive solution while the other firm is non-cooperative. Private profits may even be higher than in a monopoly if (m 2 w 0 ) /(a 2 w 0 ) . 0.5, because a high value of m increases the profit margin. Note however that both welfare and private sector profits are higher than in a conventional duopoly in the region between L2 and L3 ; this is possible because the latter is not Pareto optimal. It is now fashionable to emphasise profitability, but this should not be an end in itself for a public firm. However, Firm 1 may become more profitable than Firm 2 as a by-product of improving welfare. Its output is higher, but its profit margin is lower because of the wage disadvantage. The wage disadvantage is higher for high W values of m and intermediate values of a. More precisely, p W 1 . p 2 under the following condition: m2w (2 2 a )2 ]]0 , L4 5 ]]]]]2 . a 2 w0 12 2 14a 1 3a

(7)

This boundary lies below L2 but connects the same end-points. By combining L1 –L4 we get regions representing different combinations of bargaining power and protection for Firm 2. The properties of each major area is displayed in Fig. 1; it is straightforward characterise the two smaller regions.

5 The result that average costs are higher in the public firm can be extended. As shown in a preliminary version, it also holds true if there are managerial salaries as well if the total revenues net of wages are divided between owners and managers through Nash bargaining.

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Fig. 1. Comparison of profits and wages in the mixed oligopoly.

Region III conforms to prejudice in the sense that profits are lower and costs higher in Firm 1 than in Firm 2. Note that a low value of (m2w 0 ) /(a2w 0 ) implies low salaries in both firms, but they will be higher in Firm 1 in region IV, because of higher total rents.

4. Some comments on robustness and extensions As some results might be sensitive to changes in the assumptions, a short discussion on alternative specifications is needed. For example, suppose that inverse demand is of the form p 5 A /x 1 / e , where A is a shift parameter and e the (absolute value) of the demand elasticity. Setting e51 yields the same wage rates as in Section 3; unit costs are therefore always higher in the public firm. It turns

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out that a cannot be larger than 0.5, but all values of m.w 0 are now feasible, because the demand function has no intercepts. With these exceptions, the regions that we get are ordered in a similar way. On the other hand, comparing a conventional duopoly with monopoly requires e.1; the permissible range of a is then increasing in e. It turns out that the threshold value of a that causes a duopolist to earn more than a monopolist may be much lower than in the linear case. For example, elasticities of 1.2, 2.0 and 4.0, which require a to be lower than 0.167, 0.500 and 0.750, are associated with the thresholds 0.166, 0.412 and 0.518. We have assumed equal bargaining strengths. However, suppose that a1 5 a2 5 a0 in a conventional duopoly and that a1 ± a2 under welfare maximisation. We then get w 1 5 a1 m 1 (1 2 a1 )w 0 and w 2 5 [a2 m 1 2(1 2 a2 )w 0 ] /(2 2 a2 ). If, for example, a2 5 0.5, unit costs are higher in Firm 1 unless a1 , 0.33. Note also that the condition for welfare to increase depends on a0 only, because x w 5a2m. Reaction functions can be asymmetric for other reasons than welfare maximisation. If the public firm is a Stackelberg leader, its wages would be higher than in Firm 2 because of higher total rents. If it is a follower, it would appear as more efficient even when causing the private leader to earn higher profits than in a monopoly. Wages in Firm 1 and Firm 2 are always equal if there is central bargaining, but conclusions would otherwise be similar. However, the condition for welfare to be improved is stronger in the sense that it cannot be satisfied if a .0.67. If negotiations cannot be decentralised, the authorities have to choose between adopting commercial objetives and removing the constraint, in which case the industry would become nationalised. In other versions of the model we can get a W small region where c W 1 , c 2 , but these solutions are inferior from a welfare standpoint. More details on some of the alternative versions are available on request.

5. Concluding remarks This theoretical exercise suggests that welfare maximisation is normally beneficial and associated with higher unit costs for the public firm. However, many firms in public ownership are commercial. Unit costs are then equal in the Cournot case, but otherwise they may differ according to the slopes of the reaction functions. These predictions might explain why the empirical findings do not suggest any simple relationship between ownership and costs. Privatisation is often associated with commercial objectives which may not even be desirable, but the analysis suggests that they can be achieved without a change of ownership. However, a future government might change priorities; this is less likely if firms first have to be re-nationalised. The analysis also suggests that privatisation is likely to be preceded by an anti-union policy if workers are strong.

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Acknowledgements Constructive comments by colleagues at University of Warwick, University of ˚ Birmingham, Abo Akademi University, the 1995 EARIE-conference and by the editor and referees are gratefully acknowledged.

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