Parents’ Decision-Making on the Consumption
of Private Tutoring of Private and Charter
School Going Children:
A Game Theoretic Approach
Dr. Sakib Mahmud
UW-Superior
Dr. Tanzeem Ali
Center for Astronomy and Physics Education
Research CAPER, USA
Private Tutoring
How it is defined?
“Private tutoring covers tutoring in academic subjects by
tutors for financial gains and in addition to the provision of
mainstream schooling” (Bray, 2003)
“Private tutoring (PT) or after school tutoring learning
experiences may serve as an unexplored Shadow education
system” (Bray, 1999)
“PT as shadow education is a metaphor to signify its
hidden nature and the way in which it mirrors the formal
system in scope, intensity and size.” (Marimuthuet al., 1991)
Private Tutoring or Shadow Education
Use of the “Shadow” Metaphor
The “shadow” metaphor fits in three ways:
1) PT exists because of a perceived or real deficiency
in mainstream education systems;
2) Shape and size of mainstream education systems
change so do the sizes, function and shape of PT;
3) Public attention is more apt to focus on the
mainstream issue than on its shadow.
Private Tutoring: An Informal Education
Market
Commodification of Education
• For some, PT is not just a passive entity but is poised
to negatively affect the body it imitates.
• Hartman (2007) uses the phrase “informal market of
education” in contrast to the shadow education
system.
• She conceives of education being turned into a
marketable good or into the object of a commercial
transaction (or, Commodification).
Private Tutoring Characteristics
For whom
Lean on
Low achieving
students, slow
learners
Pass on
Students with busy
parents, lacking
assistance in their
school work
Supplementary
activities
For what
Hidden remedial
activities
With whom
School teachers
School teachers,
small scale
institutions
By whom
Unregulated
Regulated as a
business entity
Ride on
Both low and high
achieving students,
students whose parents
can afford tutorial fee
Structured, remedial
and enrichment
activities
Multinational
institutions, learning
centers, experts in the
field, university
students
Regulated as a
Business or academic
entity
Source: Adapted from Castro and Guzman(2012)
Private Tutoring Trends
Cross National Indicators of Private Tutoring
Location
Year of
study
Bangladesh 2005
Cambodia
1997-1998
Canada
China
1990s
2004
Cyprus
2003
Egypt
Hong Kong
2004
2004 - 2005
India
1997
Rural / Urban area
Primary / Secondary school
28% of rural and 52% of urban primary 31% of primary school students
school students consumed private
consumed private tutoring
tutoring
31% of 77 primary schools surveyed
consumed private tutoring
Tutoring businesses in major cities grew 200 to 500 %
74% of primary 66% of lower
secondary and 54% of upper secondary
students consumed private tutoring
87% of secondary school students
consume private tutoring
64 % in urban and 52% in rural
All levels
36% of primary 28% of lower
secondary,34 48% in upper secondary
school students consumed private
tutoring
70 % of children in urban areas
40% of primary students consume
consume private tutoring
private tutoring
Source: Adapted from Bray 2003 and 2009
Private Tutoring Trends
Cross National Indicators of Private Tutoring
Location
Japan
Year of
study
2007
Kenya
Malta
1997
1997-19998
Republic of
Korea
1997
Romania
1994
Taiwan
1998
Vietnam
2001-2002
Rural / Urban area
Primary / Secondary school
90% children in urban areas
consume private tutoring
65% of junior secondary students consume
private tutoring
69 % of sixth graders consumed private tutoring
50.5 % of primary and secondary school
students consume private tutoring
72.9 % of primary school students, 56% of
middle school and 32 % of high school students
consume private tutoring
58 % of secondary school students consume
private tutoring
32% of secondary school
students consume private
tutoring
81.2% of secondary schools students consume
private tutoring
38% of primary school students paid 29% of
household expenditure to consume private
tutoring
Source: Adapted from Bray 2003 and 2009
Private Tutoring
Game Theoretical Perspective
• Most studies have looked into the public schools
versus the private tutoring environment seeking
policy options for the government.
• Few looked from a game theoretical model
perspective.
• In our paper, we propose to look into the
interaction of private schools, private tutoring,
students, parents, teachers and the government in
a three stage game model.
Private Tutoring
Game Theoretic Setup
Period 1
3-stage
setup
Actors
Stage 1
Higher Authority at
Government funded
Charter School
Stage 2
Stage 3
Objective/ Main Goals
Maximize social return from education
through policies geared through private
tutoring
Decides on four basic policy responses
to private tutoring:
(1) Ignore – most countries;
(2) Prohibit – South Korea;
(3) Regulate – Mauritius, Hong
Kong
(4) Encourage – Singapore, Taiwan
Teachers involved with Maximize expected income through
private tutoring
teaching salary and private tutoring
Parents
Actions
(1) Ignore – do nothing
(2) Prohibit and Regulate
– Low-incentive policies;
(3) Encourage – Highincentive policies
How much time to allocate
for private tutoring
(optimal effort for private
tutoring)
Maximize net benefits of private Amount of money to set
tutoring investments allocated (private aside for private tuition
tuition) for children
Private Tutoring
Game Theoretic Setup
Period 2
Actors
Objective / Main Goals
Higher Authority at
Maximize social return from education policy
Government funded Charter
School
Teachers involved with private Maximize expected income
tutoring
Parents
Children grow up and realize an income through an
earnings function
Or, Children grow up and get access to better colleges
and universities through higher grades
Private Tutoring
Game Theoretic Setup: Parents
 Parent’s lifetime utility function is






U  C1  C    C2  C 




Where, C1  Period 1 Consumption; C2  Period 2 Consumption
and,  = discount factor
Private Tutoring
Game Theoretic Setup: Parents
• For Charter School going children:
_
C1  pqPT  Y  T  C  y, Assume, y  0
Here, qPT  Amount of private tuition; p  Private tuition fees (price)
T  Tax paid; Y  Parental current income
• For Private School going children:
_
C1  pqPT  m  Y  T  C  y, Assume, y  0
Here, qPT  Amount of private tuition; p  Private tuition fees (price)
m  Private School fees; T  Tax paid; Y  Parental current income
Private Tutoring
Game Theoretic Setup: Parents
 Parent’s period 2 goal of having their child placed at
University / College with Scholarships or ensuring higher
intergenerational income mobility with their child earning
more than their income
E2
Y (E)  b  E 
for E  b
2
b2
=
for E  b
2
Here, b  Highest level of education ( E ) a child should could receive
Education Function, E  s  e  qPT
Here, e  Teacher's dutifulness  e  1
s  School infrastructure (capturing "quality" of school education)
qPT  Private tuition
Private Tutoring
Game Theoretic Setup: Parents
• Parent’s utility maximization problem is

MaxU  C1   C2  1     C
qPT
Subject to,
C1  y  px  m [Period 1 consumption]
E2
C2  Y ( E )  b  E 
2
[Period 2 consumption]
Private Tutoring
Game Theoretic Setup: Parents
• Parent’s utility maximization problem is

MaxU  C1   C2  1     C
qPT
Subject to,
C1  y  px  m
[Period 1 consumption]
E2
C2  Y ( E )  b  E 
2
[Period 2 consumption]
U
FOC:
   b  se    qPT  p  0 if se  b
qPT
Otherwise, if se  b, parents do not demand private tutorials
Private Tutoring
Game Theoretic Setup: Parents
• Parent’s inverse market demand for private
tutorial, utilizing QPT  N  qPT
p     b  se    
Q PT
N
QPT
   b  s   s  1  e     
N
If s  b, tutorial demand will not go away even if e  1
If s  b, teacher shirking  e  1 will create tutorial demand
If C1  0 and pqPT  y, the inverse demand function is not valid
Private Tutoring
Game Theoretic Setup: Higher Authority
Goal: Improve the overall level of school education
Policy options:
 Do Nothing (Policy 1) and Encourage (Policy 4): No
penalty imposed on the teacher for shirking responsibilities
to create private tutoring demand
 Prohibit (Policy 2) and Regulate (Policy 3): Impose
penalty on the teacher for shirking school responsibilities to
create private tutoring demand
Private Tutoring
Game Theoretic Setup: Higher Authority
Penalty Structure:
R    w 1 e 
Here,
w : Teacher's school salary;
e : Teacher's dutifulness
(1  e) : Proportion that the teacher might shirk if total sets of school duties are normalized to 1
: the degree of penalty
Private Tutoring
Game Theoretic Setup: Teacher
Teacher Profit Function:
  w  p  QPT  R
= w  p  QPT    w(1  e)
Assume,
QPT  A(1 e)
[By shirking (1  e), the teacher saves her time or capacity to work
which then be utlized to supply upto A(1  e) amount of private tuition]
and, w0  Teacher's reservation income
Private Tutoring
Game Theoretic Setup: Teacher
Total Supply of Tutoring:
Q  QPT  QPTf
[Here, QPTf is the total supply of the competitive fringe tutors]
MC  c  QPTf
p  c.QPTf
Supply curve for each fringe tutor:
f
QPT
p  c
with n numbers of competitive fringe tutors
n
Private Tutoring
Game Theoretic Setup: Teacher
Assume,
A b
N
This implies that teacher cannot impart highest desirable education b
A
For simplicity, a  b, where, a   amount of education for each student
N
Private Tutoring
Game Theoretic Setup: Teacher
Residual Fringe Demand:
QPT 
QPT

p    b  s   s 1  e     
 

N 
N

f
QPT
= H  
N
f
Total Tutorial supply of the fringe:
nN
cN   N
increasing in n but decreasing in QPT (via H )
QPTf  H 
Here, QPTf
Private Tutoring
Game Theoretic Setup: Teacher
Teacher’s Maximization Problem:
  w  p  QPT    w(1  e)
2
QPT
 w   v   (b  s)  s(1  e)   QPT   v
   w(1  e)
N
Here, v captures the impact of fringe tutorial supply
Subject to,
QPT  A(1  e)
Private Tutoring
Game Theoretic Setup: Teacher
First Order Condition,

  vA  b  s   2  a  s 1  e    w  0
(1  e)
w
 b  s   2(a  s)(1  e)   {
144444444442 44444444443 MC of shirking
MR (marginal return) to shirking
Private Tutoring
Game Theoretic Setup: Teacher
Second Order Condition,

2
 1  e 
2
 2 vA  a  s   0 iff, a  s
 If a > s, the teacher’s incentive to work varies smoothly, as the
marginal returns from shirking declines gradually from a value
greater than the marginal cost of shirking.
 This also suggests that school infrastructure (professional
development for teachers) affects the teacher’s incentive in a
significant way.
Private Tutoring
Game Theoretic Setup: Teacher
Optimal shirking for the Teacher,
1  e   0,
*
if w  wH
(b  s )   w
(1  e ) 
 1, if wL  w  wH
2(a  s)
*
(1  e* )  1,
if w  wL
Private Tutoring
Game Theoretic Setup: Teacher
Assuming partial shirking, we derive the teacher’s optimal dutifulness and the
resultant school education,
e* 
 w  ( s  b  2a )
2(a  s)
Dutifulness (e) increases with salary, but with professional development, s, the
result is ambiguous
se  s 
*
 w   s  b  2a 
2(a  s)
Education received at school is increasing with salary but the impact of
professional development on teacher is ambiguous
Private Tutoring
Game Theoretic Setup: Teacher
Total Education for a Student,
E  se  Q
*
*
*
PT
f*
PT
Q

N
f*
PT
Q
 se  a (1  e ) 
N
(b  s )   w 

 s 
  v  b(1  v)
2


*
*
Private Tutoring
Game Theoretic Setup: Teacher
Teacher’s expected income,

*
b  s   w

  vA 
4(a  s)
2
w
 The teacher’s expected income is decreasing in school
infrastructure as private tuition demand goes down and
increasing in teacher’s salary
Private Tutoring
Game Theoretic Setup: Higher Authority
Max H ( s, w)
subject to,
w  rS  B
(budget constraint)
 (S , w)  w0 (Teacher's participation constraint)
Private Tutoring
Game Theoretic Setup: Higher Authority
w
B0
E0
E1
w0
E*
w*
 0  w0
S*
a B0
r
b
S
Major Findings…
Teacher’s Perspectives:
 Teacher’s dutifulness increases with salary but with professional
development, the result is ambiguous
 Education received at school is increasing with teacher salary
but with professional development, the result is ambiguous
 The teacher’s expected income is decreasing in school
infrastructure (via fall in private tuition demand) and increasing
in teacher’s salary
Major Findings…
Higher Authority’s Perspectives:
• If the higher authority cares only about the total education of the
students and therefore is unmindful of its sources, he would not
mind lowering the wage, even if it reduces teacher’s dutifulness;
• Such policy would encourage more private tutoring from the
teachers.
Parent’s Perspectives:
 Given the circumstances, the parents are expected to prefer this
outcome as overall education and parent’s utility will be higher
with this policy choice. Explains why there is lack
Future Directions…
 Check how the results vary with “no penalty”
Do Nothing (Policy 1) and Encourage (Policy 4):
No penalty imposed on the teacher for shirking responsibilities
to create private tutoring demand
 Also, verify other possible policy options for the higher
authority with governmental and community support to get the
most out of teacher professional development and private
tutoring mix.
Thank you