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Archives of Business Research – Vol. 13, No. 1
Publication Date: January 25, 2025
DOI:10.14738/abr.131.18144.
Fujita, Y., & Kaji, C. (2025). Does Higher Wages Prevent Workers from Transferring to Other Organizations? Archives of Business
Research, 13(1). 01-06.
Services for Science and Education – United Kingdom
Does Higher Wages Prevent Workers from Transferring to Other
Organizations?
Yasunori Fujita
Keio University, Japan
Chihiro Kaji
General Incorporated Association, Chisho-kai
ABSTRACT
The idea that raising wages does not always lead to higher labor productivity has
been explored in various works, with pioneering work being Solow (1957), which
highlights the importance of technological progress. This was followed by Shapiro
and Stiglitz (1984), which demonstrate that excessively high wages can make
workers complacent or less motivated, and Blanchard and Summers (1986), which
reveal that even with higher wages, productivity does not improve, among others.
This paper takes a different approach by developing a theoretical model to explore
the possibility of headhunting. Specifically, the model we propose involves external
organizations that attempt to recruit workers from the organization in question.
We examine scenarios in which wage increases prompt employees to leave for
other organizations.
Keywords: wage increases, productivity, headhunting, theoretical model, optimal wage.
INTRODUCTION
The idea that raising wages does not always result in higher labor productivity has been
examined, with Solow (1957) being the pioneering work that emphasizes the importance of
technological progress, showing that wage increases may not lead to productivity gains unless
there are technological improvements. Shapiro and Stiglitz (1984) demonstrate that
excessively high wages can make workers complacent or less motivated, to cause inefficiencies
like overconfidence and reduced effort, which ultimately diminish productivity. Blanchard and
Summers (1986) highlight wage rigidity and reveal that even with higher wages, productivity
does not improve, particularly if firms do not adapt to technological advances or other
productivity-boosting measures.
Card and Krueger (1994), focusing on the complexity of the relationship between wage
increases and productivity, make it clear that factors such as market conditions, technological
advancements and so on influence whether higher wages bring about greater output. Frey and
Osterloh (2002) examine if high wages reduce intrinsic motivation and reduce overall
productivity.
This paper takes a different approach by developing a theoretical model, as in Fujita (2022),
and exploring the possibility of headhunting. Specifically, the model we propose involves
external organizations that attempt to recruit workers from the organization in question. We
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Archives of Business Research (ABR) Vol. 13, Issue 1, January-2025
Services for Science and Education – United Kingdom
will examine scenarios in which wage increases prompt employees to leave for other
organizations.
Structure of the present paper is as follows: Section 2 presents the basic model, and Section 3
explores situations where wage increases lead workers to switch to other companies. In Section
4, we determine the optimal wage for the organization in question. Concluding remarks are
provided in Section 5.
BASIC MODEL
Let us consider an organization A that consists of a manager and workers. For simplicity of
analysis, we assume that the workers are identical and each worker provides one unit of
service, with quality increasing as the worker's effort level rises, which in turn leads to a higher
income. We also assume that each worker experiences more disutility if she/he exerts more
effort and that the disutility increases at an increasing rate. In the following, letting x denote the
effort level of each worker and letting d be a positive constant, we specify the disutility function
D(x) as dx2.
If we let w denote the wage level of w for each worker, benefit of each worker B is expressed as
B=wx-dx2. (1)
Assuming that each worker determines the effort level x so as to maximize B given the wage
level w the manager offers, the maximization condition for each worker is
dB
dx
=w-2dx=0, (2)
which determines the optimal effort level x* for each worker to be
x
∗ =
w
2d
. (3)
By inserting (3) into (1), we have the maximum benefit of each worker B* as
B*=
w2
4d
. (4)
Now, let us assume that there are other organizations which are eager to hire the workers in
the organization A. Let us also assume that workers who exert more effort in the organization
A are more likely to be hired in other organizations, while the probability of being hired
becomes less when the workers in the organization A claim higher income from other
organizations.
In the following, by letting P denote the probability of workers being hired by organizations
other than the organization A and letting z denote the wages the workers want from other
organizations we express this situation as a function P=P(x*,z), where ∂P
∂x
∗ > 0 and ∂P
∂z <
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Fujita, Y., & Kaji, C. (2025). Does Higher Wages Prevent Workers from Transferring to Other Organizations? Archives of Business Research, 13(1). 01-
06.
URL: http://doi.org/10.14738/abr.131.18144
0,which leads to the condition the workers in the organization A do not transfer to other
organizations as follows.
P(x*,z)z<w. (5)
3. Situations where increasing wages leads workers to switch to other companies
If we specify the probability function P(x*, z) as
P(x
∗
, z) = 1 −
1
x
∗ +
1
z
, if x*<z, (6)
P(x
∗
, z) = 1 if x*≥ z,
for the simplicity of the analysis, then we obtain
z <
w−1
1−
2d
w
, if z >
w
2d
, (7)
z < w, if z≤
w
2d
,
by making use of (3) and (6).
Thus, we can plot the region that satisfies the condition (7) in w-z space in two cases: as shown
in Figure 1 for 0 ≤ z ≤
1
2
and as shown in Figure 2 for z ≥
1
2
, with the minimal point located at
point M ( 2d + √4d
2 − d ,
(4d+2√4d2−d−1)(2d+√4d2−d)
√4d2−d)
). The dotted regions in both figures
represent the areas where workers in the organization A transfer to other organizations.
Figure 1: Areas where workers transfer to other organizations for 0 ≤ d ≤
1
2