Open Journal of Political Science
2013. Vol.3, No.4, 131-133
Published Online October 2013 in SciRes (http://www.scirp.org/journal/ojps) http://dx.doi.org/10.4236/ojps.2013.34018
Copyright © 2013 SciRe s . 131
Strategic Reason for Employing Workers with Public Service
Motivation
Wakana Hatada , Tomomichi Mizuno
Faculty of Economics, University of Nagasaki, Sasebo City, Nagasaki, Japan
Received June 20th, 2013 ; revised July 23rd, 2013; accepted August 7th, 2013
Copyright © 2013 Wakana Hatada, Tomomichi Mizuno. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any
medium, provided the original work is properly cited.
We construct a simple game-theoretic model in which one private firm and one public (or state-owned)
firm compete in quantity of goods produced or service provided. The private and public firms each decide
how many workers with public service motivation they will employ as part of an incentive scheme. We
assume that both firms produce homogeneous goods with a quadratic cost function but that the private
firm is more efficient than the public firm. Both firms are faced with linear inverse demand. We show that
whether public firms employ more workers with public service motivation than private firms depends on
the efficiency gap between the public and private sectors. This result explains why some literature in pub-
lic administration reports a significant difference in public service motivation between employees in the
private and public sectors and the other literature does not.
Keywords: Public Service Motivation; Oligopoly; Strategic Hiring Policy; Efficiency Gap
Introduction
One of the important issues in the literature of public admi-
nistration is whether employees of public (or state-owned)
firms and those of private firms are different in terms of
work-related values, reward preferences, needs, and personality
types (Wittmer, 1991). Following a prominent study of public
service motivation (Perry & Porter, 1982; Perry, 1996, 1997),
many papers study this issue1. However, overall, empirical
studies on this issue do not have consistent results. That is,
some studies show that employees of public and private firms
are different, but other studies do not show this. For example,
while Rainey (1982) reports a difference in preferences regard-
ing the value put on helping others, Gabris and Simo (1995)
show that there is no difference between workers in the public
and private sectors.
In order to explain why we cannot obtain robust evidence
about the difference in public service motivation between
workers in the public and private sectors, we provide a game-
theoretic model. Analyzing this model, we show that the strate-
gic incentive to employ workers with public service motivation
and the disparity in efficiency between the public and private
sectors accounts for the difference. That is, whether public
firms employ more workers with public service motivation than
private firms do depends on the efficiency gap between public
and private firms.
Our approach is relevant to the issue of delegation in micro-
economic theory and game theory (Vickers, 1985; Fershtman &
Judd, 1987). In the delegation model, the objective of the prin-
cipal is not the same as that of his agent. Thus, the principal
creates an incentive scheme for the agent. In our model, the
owners and governors of the firms in the public and private
sectors decide how many workers with public service motiva-
tion to employ. This decision works as a commitment of the
incentive scheme. This point is in contrast to previous studies.
This paper is organized as follows. In the next section, we
present the model. The third section calculates the equilibrium.
The final section offers a conclusion.
The Model
We provide a simple game-theoretic model. We assume a
public service market (e.g., the education industry or security
industry) where one private firm (firm P) and one state-owned
firm (firm S) compete in quantity of goods produced or service
provided2. In each firm, there is an owner (or governor) as prin-
cipal and a manager (or public servant) as agent. For the private
firm, the owner wants to maximize its profit; for the state-
owned firm, the governor wants to maximize social welfare3. In
order to maximize the owner’s objective, the owner (or gover-
nor) designs the objective function of the manager (or servant)
as the incentive scheme. For simplicity, following Vickers
(1985), we assume that the manager’s and servant’s objective
function (uP and uS) designed by owner and governor are:

1,
PPP PP
ux

 


1,
SSS SS
ux

 
2The assumption that there is only one private firm in the market is not
essential for our results. We can extend the model to an oligopoly market
with many firms.
3The oligopoly model with profit-maximizing private firms and welfare-
maximizing public firms is called a mixed oligopoly model. For surveys on
the mixed oligopoly model, see De Fraja and Delbono (1989) and Vickers
and Yarrow (1988).
1For the survey on publi c service motivation, see Perry (2 000).

W. HATADA, T. MIZUNO
where i
x
is the output of firm i, i

is the profit of firm i,
and i

is the incentive scheme chosen by the owner (or gov-
ernor) of firm i ()4. ,PS
We can interpret i

as the degree to which a private or
state-owned firm employs workers with public service motiva-
tion. The reason is explained as follows. If the firm employs
many workers with public service motivation, the firm will tend
to provide more public service. In other words, more workers
with public service motivation means a larger value of


,
iiPS
 . Since the owner or governor can decide whom to
hire, they indirectly choose the level of i

through their hiring
policy.
Given the incentive scheme, the manager chooses the output.
We consider the quadratic cost of firms: 2
P
x

for a private
firm and 2
S
x
for a state-owned firm, where

denotes the
difference in efficiency. Since in many industries, private firms
are more efficient than state-owned firm, we assume 01


.
We assume that the firms produce homogeneous goods and that
they face linear inverse demand: , where z is
price. 1zxP
S x
Under these setting, the profits of firms are:


2
1,
P
PSP P
x
xxx   


2
1.
SPSSS
x
xx x   
Social welfare is PS SW CS

 

, where the consumer
surplus is 22
PS
CSx x . Then, the maximization prob-
lems of owner, governor, manager, and servant are max
P
P


,
, max
S
SW



max 1
P
P
PP
xxP

  , and


max 1
S
SS
xxS S

  ,
respectively. The timing of the game is as follows. In the first
stage, the owner (or governor) of firm


,iPS chooses the
incentive scheme i

. After the manager (or servant) of firm i
observes the incentive scheme, they choose the output i
x
in
the second stage. We solve the model using backward induc-
tion.
Calculating Equilibrium
In the second stage, the maximization problems of manager
and servant are:




2
max1 1,
P
PPPPS PP
x
x
xxx x  

 
 
 
2
max1 1.
S
SSSPS SS
x
x
xxxx 
 
 

The first-order conditions lead to the outcome in the second
stage:

34 ,
1178
SP
P
SP
x




 


 
1221
.
1178
SP
S
SP
x

 


 
 
In the first stage, the maximization problems of owner and
governor are:


2
max 1,
P
P
SP P
x
xx x

 



2
2
2
max 1
2
1.
S
PS
PSP P
PSSS
xx
x
xx x
xxxx




  



 

Note that the governor maximizes social welfare SW. Putting
the outcome in the second stage into these maximization prob-
lems and using the first-order condition, we obtain the outcome
in the first stage:


2
41 1
if ,
35 86488
3otherwise.
27 32
P




 






2
2
322 161
if ,
28 104648
0ot
S
 

 




herwise.
This result is illustrated in Figure 1. In this figure, the pri-
vate firm employs more workers with public service motivation
if

is small, and fewer workers with public service motiva-
tion if

is large. When the private firm is more efficient,

is closer to zero. Hence, the equilibrium structure of employ-
ment depends on the difference in the firms’ efficiency. Solving
PS

  for

, we have the following proposition.
Proposition: PS

  if and only if


1939 160.3058  .
The intuition behind this proposition is explained as follows.
In our model, large


,
iiPS
  works as a commitment de-
vice for large output. When the private firm is quite efficient
(

is small), the private firm obtains high gain from this
commitment because of large margin (price minus marginal
cost). Hence, the private firm with small

tends to set a large
value for P

. This means that the private firm employs many
workers with public service motivation. On the other hand,
since the state-owned firm maximizes social welfare, it is con-
cerned about efficient production. That is, if the private firm is
quite efficient, the state-owned firm wants to move production
from the state-owned firm to the private firm. For this to hap-
pen, the state-owned firm must commit to a small output. In
other words, the state-owned firm chooses small S

. Hence, in
this case, the state-owned firm employs fewer workers with
public service motivation. The converse of above argument is
4One might think that the incentive scheme of the state-owned firm should
b
e a convex combination of the output and social welfare. In this case, the
governor of a state-owned firm chooses the incentive scheme that causes the
servant to maximize social welfare. That is, the objective functions of the
governor and servant are the same in equilibrium. Even so, the owner of the
private firm chooses a positive θP. Hence, our main result is robust to this
modification.
Figure 1.
Equilibrium choice of θi.
Copyright © 2013 SciRe s . 132

W. HATADA, T. MIZUNO
Copyright © 2013 SciRe s . 133
also true: the private firm chooses small P

and the state-
owned firm chooses large S

, when the private firm is ineffi-
cient (

is large). Therefore, in the converse case, the state-
owned firm employs more workers with public service motiva-
tion than does the private firm.
Our result can provide an explanation for why some litera-
ture reports significant difference in public service motivation
between employees in the private and state-owned sectors and
other literature does not. Since each study uses data from a
different industry, the efficiency gap between private and
state-owned firms is different in each study. With regard to our
results, in order to obtain robust evidence about the relationship
between the type of firm (private versus state-owned) and the
level of public service motivation in workers, we need to con-
trol for the strategic effect of hiring policy. If we used data on
the efficiency gap between private and state-owned firms and
estimated the relationship between the type of firm and the
level of public service motivation of workers, we could remove
this strategic effect of hiring policy from the estimated results.
Conclusion
We consider a simple model and show that the equilibrium
tendency of employing workers with public service motivation
depends on the difference between public and private firms’
efficiency levels. Hence, we provide the answer for why previ-
ous literature on public service motivation cannot obtain robust
evidence on the difference between workers in the public and
private sectors. Since we focus on the strategic reason for em-
ploying workers with public service motivation, we use a game-
theoretic model. However, every industry is not oligopolistic.
Therefore, in order to answer our question in competitive in-
dustries, we should create a model without strategic interaction.
Although this issue is important, it is a consideration for future
research.
Acknowledgements
We thank financial support from University of Nagasaki. The
second author gratefully acknowledges financial support from
the Ministry of Education, Science, Sports and Culture in the
form of a Grant-in-Aid for Young Scientists (B). Needless to
say, all remaining errors are ours.
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