By considering a mixed oligopoly and considering that public firms are less efficient than private firms, White (2001) shows that if private firms hire managers then the public firm does not do so. We show in this paper that if we consider that a private firm competes with a firm that is owned jointly by both the private and public sectors (a semipublic firm) and that all the firms are equally efficient, then in equilibrium both firms hire managers.Mixed duopoly, Semipublic Firms, Managerial incentive contracts, Cournot competition

Juan Carlos Barcena-Ruiz

English

Research Papers in Economics

     
 
 
  
  
Volume 30, Issue 1 
  
Strategic Delegation and Semipublic Firms 
  
 
 
Juan Carlos Barcena-Ruiz  
Universidad del Pais Vasco 
Abstract 
By considering a mixed oligopoly and considering that public firms are less efficient than private firms, White (2001) 
shows that if private firms hire managers then the public firm does not do so. We show in this paper that if we 
consider that a private firm competes with a firm that is owned jointly by both the private and public sectors (a 
semipublic firm) and that all the firms are equally efficient, then in equilibrium both firms hire managers.
Financial support from Departamento de Educación, Universidades e Investigación del Gobierno Vasco (IT-223-07) and Ministerio de 
Ciencia y Tecnología and FEDER (ECO2009-07939) is gratefully acknowledged. 
Citation: Juan Carlos Barcena-Ruiz, (2010) ''Strategic Delegation and Semipublic Firms'', Economics Bulletin, Vol. 30 no.1 pp. 744-750. 
Submitted: Feb 09 2010.   Published: March 17, 2010. 
 
        
1 
 
1. Introduction 
 
The literature on strategic delegation, which started with Vickers (1985), Fershtman and Judd 
(1987), and Sklivas (1987), analyzes the strategic value for shareholders of publicly observed 
irreversible  incentive  contracts  based  on sales and profits (not only profits). Basu (1995) 
shows that if all private firms are identical and all managers have the same reservation utility 
level all private firms hire managers.  
  Barros  (1995)  and  White  (2001)  extend  the  above  analysis,  assuming  Cournot 
competition,  to  markets  in  which  private  and  public  firms  compete.  Barros  (1995) 
investigates the use of incentive contracts as strategic variables in a mixed duopoly. White 
(2001) extends the analysis of Barros (1995) considering a mixed oligopoly. He shows that 
when firms have the choice of whether or not to hire managers, in equilibrium only private 
firms do so. In this equilibrium, only private firms produce output, while a public firm exists 
only to impose discipline on private firms.
1  
  We extend the model of White (2001) by considering a semipublic firm rather than a 
public firm. We consider an oligopoly containing one semipublic firm and one private firm 
that produce a homogeneous good. The semipublic firm maximizes the weighted average of 
the payoff of the government and its own profit. The private firm maximizes profits. These 
firms have identical constant marginal costs of production. The owners of the firms chose 
whether to delegate production decisions to managers or not. We obtain that in equilibrium it 
is  a  dominant  strategy  for  the  owners  of  both  firms  to  hire  managers.  Therefore,  in 
equilibrium they both do so. Thus we obtain a different result from White (2001), who finds 
that only the private firm hires a manager. 
Our  result  differs  from  that  of  White  (2001)  due  to  two  factors:  first,  we  consider  a 
semipublic firm (whose objective function is the weighted average of social welfare and its own 
profit) while White (2001) considers a public firm (that maximizes social welfare). Second, we 
assume that the constant marginal production costs of all firms are identical whereas White 
assumes  that  the  public  firm  has  a  higher  constant  marginal  cost  than  private  firms.  Both 
differences are necessary to obtain the contrasting result. If we consider that the semipublic 
firm has a greater marginal cost than the private firm then the semipublic firm does not hire a 
manager when the government owns a great enough percentage of the shares in this firm. In 
this case, the semipublic firm behaves in a similar way to a public firm and, thus, the same 
result is obtained as in White (2001). On the other hand, if we assume that all firms have the 
same marginal cost of production and that the private firm competes in the product market 
with a public firm instead of a semipublic firm we obtain that the private firm does not 
produce. Therefore, to obtain that it is a dominant strategy for the semipublic firm to hire a 
manager, it is necessary to assume that both firms are equally efficient. 
  The rest of the paper is organized as follows. Section 2 presents the model. Section 3 
analyzes whether or not firms hire managers. Conclusions are drawn in section 4. 
 
2. The model 
 
We consider an economy made up of two firms that produce a homogeneous good. One firm 
is jointly owned by the public sector and private domestic shareholders (semipublic) and the 
other firm is privately owned. They are denoted by 0 and 1, respectively. The inverse demand 
                                                 
1  Bárcena-Ruiz  (2009)  extends  this  analysis  assuming  a  mixed  duopoly  and  Bertrand  competition  with 
heterogeneous goods. He shows that both the public and private firms hire managers. This is in contrast with the 
result obtained under Cournot competition, where only the private firm hires a manager.    
2 
 
function is given by: p = a – q0 – q1, where p is the price of the good and qi is the amount of 
the good produced by firm i. All firms have constant identical marginal costs of production of 
c, which means that they are equally efficient. Thus, the profit of firm i is given by: 
pi = (p – c) qi, i = 0, 1.                    (1) 
As usual, social welfare comprises the consumer surplus, CS, and the producer surplus, 
PS. Thus, the social welfare function can be expressed as: W=CS+PS, where CS=(q0+q1)2/2 
and PS=p0+p1.  
  The government owns a percent of the shares in the semipublic firm, where aÎ(0, 1). 
Following Matsumura (1998) and Bárcena-Ruiz and Garzón (2010), we consider that this 
firm chooses the output level, q0, that maximizes the weighted average of the payoff of the 
government and its own profit (denoted as weighted welfare): 
V = a W + (1 – a) p0,                      (2) 
where  p0  is  given  by  (1),  for  i=0.  The  private  firm  chooses  the  output  level,  q1,  that 
maximizes its profit given by (1), for i=1.  
  The owners of the firms may delegate price decisions to their managers. If they do this 
they  offer  linear  incentive  schemes  to  their  managers.  The  incentive  schemes  are  of  the 
following type: the managers, who are risk neutral, are paid on the margin according to a 
linear combination of profits and sales revenue. Formally, the manager of firm i (manager i) 
has the following objective function: 
Oi = bi pi + (1 – bi) Si, i = 0, 1,                 (3) 
where pi and Si are profits and sales revenue, respectively, and bi is the incentive parameter 
chosen by the owner of firm i (owner i).
2 It has to be noted that the semipublic firm’s manager is 
given the same type of contract as the private manager, one based on profit and sales revenue. 
  We propose a three stage game with the following timing. In the first stage, the owners 
of the firms decide whether or not to hire a manager. In the second stage, if they have hired a 
manager the owners of the firms choose the incentive parameters of their managers. Finally, 
in the third stage, the owners or the managers of the firms decide on production. To obtain a 
subgame perfect equilibrium, the game is solved backwards. 
 
3. Results 
 
Given that the owners of the firms may hire a manager or not, there are four possible cases: 
both firms hire managers, neither firm hires a manager, only the semipublic firm hires a 
manager and only the private firm hires a manager. 
 
3.1 Both firms hire managers 
 
 In  this  case,  in  the  third  stage,  manager  i  chooses  the  value  of  qi,  that  maximizes  his 
objective function, given by (3). Solving these problems we obtain:  
) 2 (
3
1
0 1 1 b b c c a q + - = ,  ) 2 (
3
1
1 0 0 b b c c a q + - = .              (4) 
                                                 
2 As in Fershtman and Judd (1987), we assume that each owner offers its managers “take it or leave it” incentive 
schemes. Manager i receives a payoff Ai+giOi, where Ai and gi are constant, gi>0. Manager i is risk neutral and 
maximizes Oi; owner i chooses Ai and gi so that the manager gets only his opportunity cost, which is normalized 
to zero. We assume that owners can commit themselves to incentive schemes.    
3 
 
  In the second stage, the owner of the semipublic firm chooses the incentive parameter b0 
that maximizes weighted welfare. Simultaneously, the owner of the private firm chooses the 
incentive parameter b1 that maximizes its profit. The superscript YY denotes that both firms 
hire managers. Solving these problems, we obtain:  
c
c a YY
) 4 5 (
1 0 a
b
-
-
- = , 
c
c a YY
) 4 5 (
) )( 1 (
1 1 a
a
b
-
- -
- = ,  1 1 0 < <
YY YY b b , 
a
a
4 5
) )( 2 (
0 -
- -
=
c a
q
YY ,  
a
a
4 5
) )( 1 ( 2
1 -
- -
=
c a
q
YY ,  2
2
0 ) 4 5 (
) )( 2 )( 1 (
a
a a
p
-
- - -
=
c a YY ,  2
2 2
1 ) 4 5 (
) ( ) 1 ( 2
a
a
p
-
- -
=
c a YY ,  
2
2 2
) 4 5 ( 2
) ( ) 3 4 (
a
a
-
- -
=
c a
CS
YY ,  2
2 3 2
) 4 5 ( 2
) )( 13 30 14 4 (
a
a a a
-
- + - +
=
c a
V
YY . 
  As is well known(see Fershtman and Judd, 1987), the private firm chooses an incentive 
parameter lower than one to provide incentives to its manager to be aggressive in the product 
market (i.e. to produce more) in order to gain market share at the expense of the other firm. 
The owner of the semipublic firm provides incentives to its manager to be aggressive in the 
product  market  for  two  reasons.  First,  the  owner  of  the  semipublic  firm  takes  consumer 
surplus into account and thus wants to produce more than a private firm. Second, quantities 
are  strategic  substitutes  and  thus  the  semipublic  firm  wants  to  gain  market  share  at  the 
expense  of  its  rival.  Therefore,  the  owner  of  the  semipublic  firm  chooses  an  incentive 
parameter lower than that of the private firm (
YY YY
1 0 b b < ).  
 
3.2 Neither firm hires a manager 
 
In the third stage, the private firm chooses the value of q1 that maximizes its profit given by 
(1), for i=1. Simultaneously, the semipublic firm chooses the value of q0 that maximizes its 
objective  function,  given  by  (2).  The  superscript  NN  denotes  that  neither  firm  hires  a 
manager. Solving these problems, we obtain:  
a 2 3
0 -
-
=
c a
q
NN , 
a
a
2 3
) )( 1 (
1 -
- -
=
c a
q
NN ,  2
2
0 ) 2 3 (
) )( 1 (
a
a
p
-
- -
=
c a NN ,  2
2 2
1 ) 2 3 (
) ( ) 1 (
a
a
p
-
- -
=
c a NN ,  
2
2 2
) 2 3 ( 2
) ( ) 2 (
a
a
-
- -
=
c a
CS
NN ,  2
2 3 2
) 2 3 ( 2
) )( 3 8 4 2 (
a
a a a
-
- + - +
=
c a
V
NN . 
 
3.3 Only the semipublic firm hires a manager 
 
In the third stage, the manager of the semipublic firm and the owner of the private firm 
choose their firms’ outputs to maximize their respective objective functions. Solving these 
problems we obtain expression (4) for b1=1. In the second stage, the owner of the public firm 
chooses the incentive parameter b0 that maximizes weighted welfare. The superscript YN 
denotes that the semipublic firm hires a manager when the other firm does not do so. Solving 
this problem, we obtain:  
1
) 3 4 (
) (
1 0 <
-
-
- =
c
c a YN
a
b , 
a
a
3 4
) )( 2 (
0 -
- -
=
c a
q
YN , 
a
a
3 4
) )( 1 (
1 -
- -
=
c a
q
YN ,  2
2 2
1 ) 3 4 (
) ( ) 1 (
a
a
p
-
- -
=
c a YN ,  
2
2
0 ) 3 4 (
) )( 2 )( 1 (
a
a a
p
-
- - -
=
c a YN ,  2
2 2
) 3 4 ( 2
) ( ) 2 3 (
a
a
-
- -
=
c a
CS
YN , 
) 3 4 ( 2
) )( 2 2 1 (
2 2
a
a a
-
- - +
=
c a
V
YN .    
4 
 
 
3.4 Only the private firm hires a manager 
 
In the third stage, the manager of the private firm and the owner of the semipublic firm 
choose  their  firms’  quantities  to  maximize  their  objective  functions.  The  superscript  NY 
denotes  that  the  semipublic  firm  does  not  hire  a  manager  when  the  other  firm  hires  a 
manager. Solving these problems we obtain: 
a
a b a
2 3
) 2 ( ) 1 ( 1
1 -
- - + -
=
c c a
q , 
a
b
2 3
2 1
0 -
+ -
=
c c a
q . 
  In the second stage, the owner of the private firm chooses the incentive parameter b1 that 
maximizes its profit. Solving this problem, we get:  
1
) 2 ( 2
) (
1 1 <
-
-
- =
c
c a NY
a
b , 
) 2 ( 2
0 a -
-
=
c a
q
NY , 
2
1
c a
q
NY -
= ,  2
2
0 ) 2 ( 4
) )( 1 (
a
a
p
-
- -
=
c a NY ,  
) 2 ( 4
) )( 1 (
2
1 a
a
p
-
- -
=
c a NY ,  2
2 2
) 2 ( 8
) ( ) 3 (
a
a
-
- -
=
c a
CS
NY , 
) 2 ( 8
) )( 3 6 1 (
2 2
a
a a
-
- - +
=
c a
V
NY . 
 
3.5 Owners’ decisions as to whether or not hire a manager 
 
It remains to solve the first stage of the game. In this stage, the owners of the firms decide 
whether or not to hire managers. From the results obtained in the four cases considered, the 
following is obtained.  
 
Proposition 1. It is a dominant strategy for the private firm to hire a manager. 
 
  It is easy to see that 
YN YY
1 1 p p >  and 
NN NY
1 1 p p > . Therefore, the owner of the private firm 
hires a manager independently of whether or not the semipublic firm does so.  
When the semipublic firm does not hire a manager, the profit obtained by the private firm 
is greater if it hires a manager than if it does not do so (
NN NY
1 1 p p > ). As reaction functions in 
quantities are downward sloping, if the semipublic firm does not hire a manager the private 
firm wants to hire a manager, thus becoming the leader in incentives; this permits the private 
firm to gain market share and profits at the expense of its rival.  
When the semipublic firm hires a manager, the profit obtained by the private firm is 
greater if it hires a manager than if it does not do so (
YN YY
1 1 p p > ), since in the latter case the 
private  firm  loses  market  share  at  the  expense  of  the  semipublic  firm.  As  quantities  are 
strategic substitutes, the leader firm in incentives is more aggressive in the product market 
than the follower firm; thus, the private firm wants to hire a manager to avoid becoming the 
follower in incentives. 
 
Proposition 2. It is a dominant strategy for the semipublic firm to hire a manager. 
 
  It is easy to see that 
NN YN V V >  and 
NY YY V V > , therefore the semipublic firm hires a 
manager independently of whether the private firm hires a manager or not.  
  When the private firm does not hire a manager, the best response of the semipublic firm is to 
hire  a  manger  (
NN YN V V > ).  To  explain  this  result  all  three  components  of  the  objective 
function of the semipublic firm have to be taken into account: the profit of the semipublic firm, 
the weighted profit of the private firm, and the weighted consumer surplus. Weighted welfare    
5 
 
can  be  written  as  V= 0 p + 1 ap + CS a ;  therefore, 
NN YN V V >   if 
YN
0 p +
YN
1 ap +
YN CS a > 
NN
0 p +
NN
1 ap +
NN CS a .  Moreover,  it  can  be  shown  that 
NN YN NN YN q q q q 1 1 0 0 > > >   and 
> +
YN YN q q 1 0
NN NN q q 1 0 + . Therefore, the semipublic firm produces more than the private firm, 
and the highest output of the industry is obtained when the semipublic firm hires a manager. As 
a result: (i) 
YN
0 p >
NN
0 p  if and only if a<a= ) 17 7 (
8
1
- »0.3596, (ii) 
YN
1 ap <
NN
1 ap , and (iii) 
YN CS a >
NN CS a . Then, if a<a, (i) and (iii) dominate (ii), implying that 
NN YN V V > ; if a≥a, 
(iii) has a greater effect than (i) and (ii), which means that 
NN YN V V > .  
  When the private firm hires a manager, the best response of the semipublic firm is to hire 
a manger (
NY YY V V > ). Therefore: 
YY
0 p +
YY
1 ap +
YY CS a >
NY
0 p +
NY
1 ap + 
NY CS a . It is easy to 
see that in this case: (i) 
NY YY
0 0 p p > , (ii) 
NY YY
1 1 ap ap < , and (iii) 
NY YY CS CS a a >  if and only 
if a<1/2. Then, if a<1/2, (i) and (iii) dominate (ii); if a>1/2, (i) dominates (ii) and (iii). 
 
Proposition 3. In equilibrium, both the private firm and the semipublic firm hire managers. 
  
  We have seen in Propositions 1 and 2 that it is a dominant strategy for both firms to hire a 
manager. So in equilibrium both firms hire managers. Besides, it can be shown that 
YY NN
1 1 p p >  
if  and  only  if  a< 8 / 1 1-   and 
NN YY V V > .  Therefore,  if  parameter  a  is  low  enough 
(a< 8 / 1 1- ) there is a Prisoners’ Dilemma and both firms would prefer not to hire a manager. 
 
4. Conclusion 
 
The literature that analyzes mixed oligopolies has dedicated little attention to investigating 
whether  firms  want  to  hire  managers  or  not.  However,  this  question  has  received  great 
attention under private oligopolies. White (2001) extends this analysis considering a mixed 
oligopoly. He shows that when firms have the choice of whether or not to hire managers, in 
equilibrium  only  private  firms  do  so.  In  this  paper  we  consider  a  market  in  which  a 
semipublic firm and a private firm compete. These firms have identical constant marginal 
costs of production. The owners of the firms chose whether to delegate production decisions 
to managers or not. We obtain that in equilibrium both firms hire managers.  
 
References 
 
Bárcena-Ruiz, J.C. (2009) “The Decision to Hire Managers in Mixed Markets under Bertrand 
Competition” The Japanese Economic Review 60, 376-388. 
Bárcena-Ruiz, J.C. and M.B. Garzón (2010) “Endogenous Timing in a Mixed Oligopoly with 
Semipublic  Firms”  Portuguese  Economic  Journal,  forthcoming,  DOI  10.1007/s10258-
010-0054-8. 
Barros,  F. (1995) “Incentive Schemes as Strategic Variables: An Application to a Mixed 
Duopoly” International Journal of industrial Organization 13, 373-386. 
Basu, K. (1995) “Stackelberg Equilibrium in Oligopoly: an Explanation Based on Managerial 
Incentives” Economic Letters 49, 459-464.  
Fershtman,  C.  and  K.L.  Judd  (1987)  “Equilibrium  Incentives  in  Oligopoly”  American 
Economic Review 77, 927-940.    
6 
 
Matsumura, T. (1998) “Partial privatization in mixed duopoly” Journal of Public Economics 
70, 473-483. 
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”  The  Economic  Journal  95 
(supplement), 138-147. 
White, M.D. (2001) “Managerial Incentives and the Decision to Hire Managers in Markets 
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Strategic Delegation and Semipublic Firms

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