COMPETENCY AND INDONESIAN QUALIFICATION FRAMEWORK BASED
SYLLABUS
Course Title
: Mathematical Economics
Coordinator
: Prof. Dr. D.S. Priyarsono
Course Code
: EKO 202/3 (2-3)
Semester
: even/4
Prerequisite Course : Introduction to Mathematics (MAT 100), Calculus (MAT 103)
Short Description
: This course is designed to provide knowledge on the concepts, techniques, and problems of
mathematics related to economics and its applications.
Learning Outcome
: After completing this course, students are expected to be able to understand and explain the concept
and technique of mathematics and be able to solve mathematics problems, particularly multivariable
calculus and dynamics that are commonly used in economic analyses.
WEEK
1
EXPECTED LEARNING
OUTCOME
Students can explain
matrix
and
vector,
matrix
operation,
idempotent
matrix,
partitioned
matrix,
kronecker
products,
transpose and inverse
INDICATOR
1) Explain matrix and
vector
2) Explain matrix
operation
3) Explain idempotent
matrix
4) Explain partitioned
matrix
5) Explain kronecker
TOPIC (TEACHING MATERIAL)
LEARNING
METHOD
TIME
ALLOCATI
ON
The
concepts
and
definitions of matrix and
vector, matrix operation,
partitioned
matrix,
kronecker products, the
concept, definition, and use
of matrix transpose and
inverse,
application
examples
Illustratio
n,
discussio
n, and
individual
task
methods,
Tutorial
Lecture:
1x
(50’x2)
Tutorial:
1x
(50’x3)
LEARNIN
G SOURCE
ASSESSMEN
T CRITERIA
SCORE
WEIGH
T (%)
(1), (2)
Written
test,
Students’
activeness
and
individual
task
2.5%
products
6) Explain transpose
and inverse
2
Students can explain
determinant and the
basic characteristic of
determinant, vector and
characteristic
root,
linear combination and
rank, linear equation
system, cramer’s rule,
and
application
in
economic model
1) Explain
determinant and
the basic
characteristics of
determinant,
2) Explain vector and
characteristic root
3) Explain linear
combination and
rank
4) Explain linear
equation system
5) Explain cramer’s
rule
6) Explain application
in economic model
1) Explain linear
differential
equation order 1
and 2
2) Explain linear
difference equation
order 1 and 2
3
Students can explain
linear
differential
equation order 1 and 2
and linear difference
equation order 1 and 2
4
Students can explain the 1) Explain the
characteristics
of
characteristics of
comparative statics, rate
comparative statics
of change and derivative, 2) Explain rate of
derivative and slope of
change and
Explain the concept and
basic characteristics of
determinant, vector and
characteristic root, explain
rank,
linear
equation
system, cramer’s rule as
well as the use in solving
economic problems.
Explain the concept and
function
of
linear
differential equation order
1 and 2 and linear
difference equation order 1
and 2
Explain the concept of
comparative statics and
rate of change as well as
the illustration. Derivative,
derivative and slope of
Illustratio
n,
discussio
n, and
individual
task
methods,
Tutorial
Illustratio
n,
discussio
n, and
individual
task
methods,
Tutorial
Illustratio
n,
discussio
n, and
quiz
Lecture:
1x
(50’x2)
Tutorial:
1x
(50’x3)
Lecture:
1x
(50’x2)
Tutorial:
1x
(50’x3)
Lecture:
1x
(50’x2)
Tutorial:
1x
(1), (2)
Written
test,
Students’
activeness
and
individual
task
2.5%
(1), (2).
Written
test,
Students’
activeness
and
individual
task
2.5%
(1), (2)
Written
test,
Students’
activeness
and
2.5%
curve, the concept of
derivative
limit and continuity and 3) Explain derivative
differentiation function
and slope of curve
4) Explain the concept
of limit
5) Explain continuity
and differentiation
function
1) Explain
differentiation rule
for one-variable
function
2) Explain
differentiation rule
for two or more of
the same variable
function
3) Explain
differentiation rule
with different
variable functions
4) Explain partial
differentiation
5) Explain comparative
and static analysis
application
6) Explain Jacobian
determinant
5
Students can explain
differentiation rule for
one-variable
function,
differentiation rule for
two or more of the same
variable
function,
differentiation rule with
different
variable
functions,
partial
differentiation,
comparative and static
analysis application, and
Jacobian determinant
6
Students can explain 1) Explain differential
differential,
total 2) Explain total
differential, differential
differential
curve. Outline the concept methods,
of limit and requirement Tutorial
for
continuity
and
differentiation in limit
There are several types of
differentiation
rules,
namely the differentiation
rules
for
one-variable
function, two or more of
the same variable function,
different variable function,
and partial differentiation
(50’x3)
Illustratio
n,
discussio
n, and
individual
task
methods,
Tutorial
Lecture:
1x
(50’x2)
Tutorial:
1x
(50’x3)
The lesson on partial Illustratio
derivative allows students n,
to do simple comparative discussio
Lecture:
1x
(50’x2)
individual
task
(1), (2)
Written
test,
Students’
activeness
and
individual
task
2.5%
(1), (2).
Written
test,
Students’
2.5%
7
rules, total derivative, 3) Explain differential
derivative of implicit
rules
function,
and 4) Explain total
comparative statics with
derivative
general function model 5) Explain derivative of
implicit function
6) Explain comparative
statics with general
function model
1) Explain optimum
value and extreme
Students can explain
value
optimum value and
2) Explain first
extreme value, first
derivative test
derivative test, second
3) Explain second and
and more derivative, and
more derivative
second derivative test.
4) Explain second
derivative test
statical problems, but in
the models containing
general function, because
short and explicit solution
cannot be obtained, so total
differentiation is needed.
n, and
individual
task
methods,
Tutorial
Tutorial:
1x
(50’x3)
The most common criteria
in the economy usually
maximize (profit) and
minimize (cost) of a goal.
Optimum value is obtained
by conducting derivative
test on a function.
Illustratio
n,
discussio
n, and
quiz
methods,
Tutorial
Lecture:
1x
(50’x2)
Tutorial:
1x
(50’x3)
Illustratio
n,
discussio
n, and
individual
task
methods,
Tutorial
Lecture:
1x
(50’x2)
Tutorial:
1x
(50’x3)
activeness
and
individual
task
(1), (2).
Written
test,
Students’
activeness
and
individual
task
2.5%
(1), (2)
Written
test,
Students’
activeness
and
individual
task
2.5%
MID-TEST/UTS (40%)
8
Students can explain
exponential
characteristics
and
functions,
natural
exponential
functions
and growth issues, the
concept and functions of
logarithm,
and
derivative of exponential
functions.
1) Explain exponential
characteristics and
functions
2) Explain natural
exponential
functions and
growth issues
3) Explain the concept
of logarithm
4) Explain logarithm
functions
5) Explain derivative of
exponential
functions and
This chapter introduces
new topic, which is the use
of exponential functions.
Exponential functions and
logarithm functions have
close
relationship,
particularly in regard to
growth issues and the
dynamics of the economy
and more specifically in
optimization issues with
time variable
logarithm functions
9
Students can explain
first
derivative
condition,
second
derivative
condition,
square
form,
and
characteristic root.
1) Explain first
derivative condition
2) Explain second
derivative condition
3) Explain square form
4) Explain
characteristic root
1) Explain objective
function with more
than two variables
2) Explain the second
derivative
relationship with
concave and convex.
3) Explain the
application in
economics.
10
Students can explain
objective function with
more than two variables,
the second derivative
relationship
with
concave and convex,
application
in
economics.
11
1)
Students can explain the
method of Lagrange
multipliers,
second
derivative condition, and
2)
bordered hessian.
Explain the method
of Lagrange
multipliers
lagrangian
Explain second
derivative condition
The use of first and second
derivatives
surfaces
because in the previous
chapter optimization is
only with one preference
variable. So, a method is
developed to obtain the
extreme value of an
objective function that
involves two or more
preference
variables.
Therefore, we can handle
problems such as multiproduct companies.
Illustratio
n,
discussio
n, and
individual
task
methods,
Tutorial
Lecture:
1x
(50’x2)
Tutorial:
1x
(50’x3)
Explain objective function
with two variables. The
concept of concave and
convex can be used to
determine the extreme
value of a function. This
characteristic
can
be
obtained through second
derivative test.
Illustratio
n,
discussio
n, and
individual
task
methods,
Tutorial
Lecture:
1x
(50’x2)
Tutorial:
1x
(50’x3)
This chapter discusses the
limitation of constraint (for
example production quota)
where
there
is
a
relationship
between
variables.
The
new
Illustratio
n,
discussio
n, and
quiz
methods,
Lecture:
1x
(50’x2)
Tutorial:
1x
(50’x3)
(1), (2)
Written
test,
Students’
activeness
and
individual
task
2.5%
(1), (2)
Written
test,
Students’
activeness
and
individual
task
2.5%
(1), (2).
Written
test,
Students’
activeness
and
individual
2.5%
3) Explain bordered
hessian
12
13
Students can explain
quasy
concave
and
quasy convex, maximum
satisfaction
and
consumer’s demand, and
comparative
statics
analysis.
Students can explain
integral basic rules,
definite
integral,
indefinite
integral,
economic application of
integral, and Domar’s
growth model
1) Explain quasy
concave and quasy
convex
2) Explain maximum
satisfaction and
consumer’s demand
3) Explain comparative
statics analysis
1) Explain integral
basic rules
2) Explain definite
integral and
indefinite integral
3) Explain the
economic
application of
integral
4) Explain Domar’s
growth model
optimum level that fulfils
production
quota
requirement is constrained
optimization. The solution
is through the method of
Lagrange
multipliers,
second derivative, and
bordered hessian.
The understanding on
quasy concave and quasy
convex
of
objective
function eliminates the
need to check second order
requirement. After that,
examples of problems are
given about maximum
satisfaction and consumer’s
demand in simple cases
(two-good case) until more
complex cases.
Integral calculus is known
as primitive function (basic
function) or anti derivative.
In the lecture, integral
basic rules are introduced
and then it continues to
integral operation rules.
Definite integral is the
integral that has specific
numeric value (has top and
bottom limits), whereas
indefinite integral is the
contrary.
Tutorial
task
Illustratio
n,
discussio
n, and
individual
task
methods,
Tutorial
Lecture:
1x
(50’x2)
Tutorial:
1x
(50’x3)
Illustratio
n,
discussio
n, and
individual
task
methods,
Tutorial
Lecture:
1x
(50’x2)
Tutorial:
1x
(50’x3)
(1), (2)
Written
test,
Students’
activeness
and
individual
task
2.5%
(1), (2)
Written
test,
Students’
activeness
and
individual
task
2.5%
14
Students can explain non
linear
programming,
Kuhn-Tucker condition,
Kuhn-Tucker condition
interpretation,
constraint qualification,
concave programming,
and
quasy
concave
programming
1) Explain non linear
programming,
2) Explain KuhnTucker condition
3) Explain KuhnTucker condition
interpretation
4) Explain constraint
qualification,
5) Explain concave
programming
6) Explain quasy
concave
programming
This chapter discusses two
main topics. The first is non
linear programming, which
is
the
extension
of
controlled
optimization
technique marked with the
involvement of inequality
constraint
into
the
problems. The second is
the review of classic
controlled optimization to
discuss several new topics
Illustratio
n,
discussio
n, and
quiz
methods,
Tutorial
FINAL TEST/UAS (40%)
ASSIGNMENT/QUIZ (20%)
Reading Sources:
(1) Chiang. 2005. Fundamental methods of Mathematical Economics. McGraw-Hill.
(2) Sydsaeter, K. & P.J. Hammond, 2005. Mathematics for Economic Analysis. Prentice Hall.
Lecturer Team:
-
Prof. Dr. D.S Priyarsono (K)
-
Dr. Toni Bahtiar
-
Dr. Sri Mulatsih
-
Dr. Yusman Syaukat
Lecture:
1x
(50’x2)
Tutorial:
1x
(50’x3)
(1), (2)
Written
test,
Students’
activeness
and
individual
task
2.5%
-
Ir. Farida Hanum, M.S
-
Ir. Doni Citra Lesmana, M.Sc
-
Novindra, S.P, M.Si
-
Andromeda, M.Si
-
Dicky Firmansyah, M.Si
-
Indra, M.Si
-
Izzudin, M.Si
-
Perdana, S.E
ASSESSMENT FORMAT
: Exam and Assignment
Mid-test (UTS)
: 40 %
Final test (UAS)
: 40 %
Assignment/Quiz
: 20 %