Bahan Mata Kuliah Matematika Ekonomi Gratis Terbaru - Kosngosan Situs Anak Kost Mahasiswa Pelajar Course 1
MATHEMATICS FOR
ECONOMICS
“INTRODUCTION”
(Course 1)
SYAIFUL HADI
DJAIMI BAKCE
NOVIA DEWI
JURUSAN AGRIBISNIS
FAKULTAS PERTANIAN
UNIVERSITAS RIAU
CONTENTS
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Function in Economics
Equations in Economics
Macro Economic Models
Change, Rate, Finance and Series
Differentiation in Economics
Maximum and Minimum Values
Further Rules of Differentiation
Partial Differentiation in Economics
Constrained Maxima and Minima
Integration in Economic
1. FUNCTIONS IN ECONOMICS
(2 x)
Penerapan fungsi dalam bidang ekonomi dan
bisnis merupakan salah satu bagian yg penting
dipelajari karena model2 ekonomi yg
berbentuk matematika biasanya dinyatakan
dengan fungsi.
Fungsi dalam matematika menyatakan
hubungan formal di antara dua himpunan data.
Fungsi ialah suatu bentuk hubungan
matematis yg menyatakan hubungan
ketergantungan /fungsional antara satu
variabel dengan variabel lain.
1. FUNCTIONS IN ECONOMICS
(2 x)
Fungsi dapat berbentuk
persamaan: fungsi yg ruas kiri
dan kanannya dihubungkan
dengan tanda kesamaan =.
Fungsi berbentuk ketidaksamaan:
fungsi yg ruas kiri dan kanannya
dihubungkan oleh tanda
ketidaksamaan ≤, ≥.
1. FUNCTIONS IN ECONOMICS
(2 x)
Sebuah fungsi dibentuk oleh : unsur
variabel, koefisien, dan konstanta.
Variabel dan koefisien senantiasa
terdapat dalam setiap bentuk fungsi
tapi tidak demikian halnya dengan
konstanta.
Variabel ialah unsur pembentuk fungsi
yang mencerminkan atau mewakili
faktor tertentu, biasanya
dilambangkan dengan huruf.
1. FUNCTIONS IN ECONOMICS
(2 x)
Berdasarkan kedudukan dan sifatnya
dalam fungsi:
Variabel bebas/independent variable
ialah variabel yg nilainya tidak
tergantung pada variabel lain
Variabel terikat/dependent variable
ialah variabel yg nilainya tergantung
pada variabel lain.
1. FUNCTIONS IN ECONOMICS
(2 x)
Koefisien ialah bilangan atau angka
yg terkait pada dan terletak di depan
suatu variabel dalam suatu fungsi.
Konstanta ialah bilangan atau angka
yg kadang2 turut membentuk
sebuah fungsi tetapi berdiri sendiri
sebagai bilangan dan tidak terkait
pada suatu variabel tertentu.
Jenis2 fungsi
ALJABA
R
RASIONAL
FUNGS
I
IRRASIONAL
TRANSENDEN/NON
ALJABAR
F. EKSPONENSIAL
F. LOGARITMIK
F.
POLINOM
F. LINIER
F.
KUADRAT
F. KUBIK
F. BIKUADRAT
F.
TRIGONOMETRIK
F. HIPERBOLIK
Fungsi polinom: fungsi yg
mengandung banyak suku/polinom
dalam variabel bebasnya
2
n
Y= a0 + a1X + a2X + … + anX
Fungsi linier ialah fungsi polinom yg
pangkat tertinggi dari variabelnya
pangkat satu/fungsi berderajat satu
Fungsi kuadrat ialah fungsi polinom yg pangkat
tertingginya 2
Fungsi pangkat ialah fungsi yg variabel bebasnya
berpangkat sebuah bilangan nyata bukan nol
Fungsi eksponensial ialah fungsi yg variabel
bebasnya merupakan pangkat dari suatu
konstanta bukan nol
Fungsi logaritmik ialah fungsi balik dari fungsi
eksponensial
Fungsi trigonometrik dan hiperbolik ialah fungsi
yg variabel bebasnya bilangan goneometrik
1. FUNCTIONS IN ECONOMICS
(2 x)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
In this chapter you learn to:
Appreciate why economist use mathematics,
Plot points on graphs and handle negative values,
Express relationships using linier and power functions,
substitute values and sketch the functions,
Use the basic rules of algebra and carry out accurate
calculations,
Handle powers and indices,
Interpret functions of several variables,
Apply the approach to economic variables,
Understand the relationship between total and average
revenue,
Obtain and plot various cost function,
Write an expression for profit,
Depict production functions using isoquants and find the
average product of labour.
2. EQUATION IN ECONOMICS
(2 x)
In this chapter you learn to:
1. Understand how equations are used in economics,
2. Rewrite and solve equation,
3. Substitute expressions,
4. Solve simple linier demand and supply equations to find market
equilibrium,
5. Carry out cost – volume – profit analysis,
6. Identify the slope and intercept of line,
7. Plot the budget constraint to obtain the budget line,
8. Appreciate there is a constant rate of substitution as you move
along a line,
9. Solve quadratic equations,
10.Find the profit maximizing output and also the supply function for a
perfectly competitive firm,
11.Solve simultaneous equations,
12.Discover equilibrium values for related markets,
13. Model growth using exponential function,
3. MACROECONOMICS MODELS
(1 X)
In this chapter you learn to:
1.
Appreciate the role of macroeconomic modelling,
2.
Understand the notation for macroeconomic models,
3.
Write down a condition for macroeconomic equilibrium,
substitute and then solve to find equilibrium income,
4.
Use keysinesian cross models to analysis the good market,
5.
Apply IS – LM analysis , which includes the money market.
LM stands for ‘investment equals savings’ and LM stands for
‘liquidity preference equals money supply’.
4. CHANGES, RATE, FINANCE AND
SERIES
(2 X)
In this chapter you learn to:
1.
Measure interest and growth rates as percentages or decimals,
2.
Calculate percentage changes and percentage point changes,
3.
Calculate the future value of a principal earning simple or compound
interest and use different frequencies of compounding,
4.
Find the annual percentage rate of interest as standardized measure,
5.
Compute the real of interest,
6.
7.
Understand why logarithmic graph are useful for representing variables that
are grow over time, and calculate the average growth rate over a period,
Calculate depreciation using the straight line and reducing balance
methods,
8.
Use net present value and internal rate of return for investment appraisal,
9.
Recognize a series and find the sum of geometric progression,
10.
Carry out loan and annuity calculation involving regular payment,
11.
Find how the price of bills and the bonds changes with the rate of interest.
5.
DIFFERENTIATION IN
ECONOMICS
(2 X)
In this chapter you learn to:
1.
2.
3.
4.
5.
6.
7.
8.
9.
Understand that differentiation lets us identify marginal
relationships in economics,
Measure the rate of change along a line or curve,
Find dy/dx for power function and practice the basic rules of
differentiation,
Apply differentiation notation to economics examples,
Obtain a marginal revenue function as the derivative of the total
revenue function,
Differentiate a short run productions function to find the marginal
product of labour,
Understand the relationship between total cost and marginal cost,
Measure point elasticity of demand and supply,
Find the investment multiplier in simple macroeconomic model.
6. MAXIMUM & MINIMUM VALUES
(1 X)
In this chapter you learn to:
1.
2.
3.
4.
5.
6.
7.
8.
Appreciate that economic objectives involve optimization,
Identify maximum and minimum turning point by
differentiating and then finding the second derivative,
Find the maximum revenue,
Show which output maximizes profit and whether it changes if
taxation is imposed,
Identify minimum turning point on cost curve,
Find the level of employment at which the average product of
labour is maximized,
Choose the per unit tax which maximizes tax revenues,
Identify the economic order quantity which minimizes total
inventory cost.
7. FURTHER RULES OF
DIFFERENTIATION
(1 X)
In this chapter you learn to:
1.
Appreciate when further rule of differentiation are needed,
2.
Differentiation composite functions using the chain rule,
3.
Use the product rule of differentiation,
4.
Apply the quotient rule
5.
(the derivative of the first term times the second minus
derivative of the second term times the first, all divided by the square of the second
term),
Show the relationship between marginal revenue, elasticity and
maximum total revenue,
6.
Analysis optimal production and cost relationship,
7.
Differentiate natural logarithmic and exponential function,
8.
Use logarithmic and exponential relationships in economic analysis.
8. PARTIAL DIFFERENTIATION IN
ECONOMICS
(2 X)
In this chapter you learn to:
1.
Understand that partial derivative show the separate effects of
different variables,
2.
Find partial derivatives using appropriate notation,
3.
Find own-price, cross price and income elasticity of demand,
4.
Use the small increment formula,
5.
Find macroeconomic multipliers,
6.
Use differentials and implicit differentiation,
7.
Find the slope of and indifference curve,
8.
Measure returns to scale and factors shares for homogenious
production function,
9.
Identify second elasticity for logarithmic demand function,
10.
Find second order partial derivatives,
11.
Optimize multivariate function,
12.
Find what prices are charged by a monopolist using price dicrimination.
9. CONSTRAINED MAXIMA & MINIMA
(1 X)
In this chapter you learn to:
1.
2.
3.
Appreciate how constrained optimization problems
arise in economics,
Solve constrained maximization and minimization
problem using substitution method,
Use the more general lagrange multiplier methods.
10. INTEGRATION IN ECONOMICS
(1 X)
In this chapter you learn to:
1.
Understand that integration is the inverse procedure to
differentiation,
2.
Recognize the notation and apply the rules of
integration,
3.
Find total function from marginal function,
4.
Use definite integration to find the area under a curve,
5.
Evaluate the sizes of areas on economics diagrams,
giving measures of total revenue, total variable cost,
consumer surplus and producer surplus.
LITERATURE
Alpha C Chiang and Kevin Wainwright. 2005.
“Fundamental Methods of Mathematical Economics” –
4th. McGraw-Hill International Edition.
Jean Soper,
1999. Mathematics for Economics
and Business – An Interactive Introduction. Blackwell
Publishers.
Michael Harrison and Patrick Waldrom. 1998.
Mathematical Economy and Finance. www.4shared. Com
Herman J Bierens, ‘Introduction to the Mathematical and
Statistical Foundations of Econometrics. Pennsylvania
State University USA. www.4shared. Com.
ETC
Komponen Penilaian
Tugas : 15%
Quis : 10%
Ujian Tengah Semester
Ujian Akhir Semester : 35%
GRADE
(A – B – C – D – E – F)
Nilai
Point
Range
A
4
81
B
3
66 – 80
C
2
56 – 65
D
1
41 – 55
E
0
40
: 35%
ECONOMICS
“INTRODUCTION”
(Course 1)
SYAIFUL HADI
DJAIMI BAKCE
NOVIA DEWI
JURUSAN AGRIBISNIS
FAKULTAS PERTANIAN
UNIVERSITAS RIAU
CONTENTS
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Function in Economics
Equations in Economics
Macro Economic Models
Change, Rate, Finance and Series
Differentiation in Economics
Maximum and Minimum Values
Further Rules of Differentiation
Partial Differentiation in Economics
Constrained Maxima and Minima
Integration in Economic
1. FUNCTIONS IN ECONOMICS
(2 x)
Penerapan fungsi dalam bidang ekonomi dan
bisnis merupakan salah satu bagian yg penting
dipelajari karena model2 ekonomi yg
berbentuk matematika biasanya dinyatakan
dengan fungsi.
Fungsi dalam matematika menyatakan
hubungan formal di antara dua himpunan data.
Fungsi ialah suatu bentuk hubungan
matematis yg menyatakan hubungan
ketergantungan /fungsional antara satu
variabel dengan variabel lain.
1. FUNCTIONS IN ECONOMICS
(2 x)
Fungsi dapat berbentuk
persamaan: fungsi yg ruas kiri
dan kanannya dihubungkan
dengan tanda kesamaan =.
Fungsi berbentuk ketidaksamaan:
fungsi yg ruas kiri dan kanannya
dihubungkan oleh tanda
ketidaksamaan ≤, ≥.
1. FUNCTIONS IN ECONOMICS
(2 x)
Sebuah fungsi dibentuk oleh : unsur
variabel, koefisien, dan konstanta.
Variabel dan koefisien senantiasa
terdapat dalam setiap bentuk fungsi
tapi tidak demikian halnya dengan
konstanta.
Variabel ialah unsur pembentuk fungsi
yang mencerminkan atau mewakili
faktor tertentu, biasanya
dilambangkan dengan huruf.
1. FUNCTIONS IN ECONOMICS
(2 x)
Berdasarkan kedudukan dan sifatnya
dalam fungsi:
Variabel bebas/independent variable
ialah variabel yg nilainya tidak
tergantung pada variabel lain
Variabel terikat/dependent variable
ialah variabel yg nilainya tergantung
pada variabel lain.
1. FUNCTIONS IN ECONOMICS
(2 x)
Koefisien ialah bilangan atau angka
yg terkait pada dan terletak di depan
suatu variabel dalam suatu fungsi.
Konstanta ialah bilangan atau angka
yg kadang2 turut membentuk
sebuah fungsi tetapi berdiri sendiri
sebagai bilangan dan tidak terkait
pada suatu variabel tertentu.
Jenis2 fungsi
ALJABA
R
RASIONAL
FUNGS
I
IRRASIONAL
TRANSENDEN/NON
ALJABAR
F. EKSPONENSIAL
F. LOGARITMIK
F.
POLINOM
F. LINIER
F.
KUADRAT
F. KUBIK
F. BIKUADRAT
F.
TRIGONOMETRIK
F. HIPERBOLIK
Fungsi polinom: fungsi yg
mengandung banyak suku/polinom
dalam variabel bebasnya
2
n
Y= a0 + a1X + a2X + … + anX
Fungsi linier ialah fungsi polinom yg
pangkat tertinggi dari variabelnya
pangkat satu/fungsi berderajat satu
Fungsi kuadrat ialah fungsi polinom yg pangkat
tertingginya 2
Fungsi pangkat ialah fungsi yg variabel bebasnya
berpangkat sebuah bilangan nyata bukan nol
Fungsi eksponensial ialah fungsi yg variabel
bebasnya merupakan pangkat dari suatu
konstanta bukan nol
Fungsi logaritmik ialah fungsi balik dari fungsi
eksponensial
Fungsi trigonometrik dan hiperbolik ialah fungsi
yg variabel bebasnya bilangan goneometrik
1. FUNCTIONS IN ECONOMICS
(2 x)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
In this chapter you learn to:
Appreciate why economist use mathematics,
Plot points on graphs and handle negative values,
Express relationships using linier and power functions,
substitute values and sketch the functions,
Use the basic rules of algebra and carry out accurate
calculations,
Handle powers and indices,
Interpret functions of several variables,
Apply the approach to economic variables,
Understand the relationship between total and average
revenue,
Obtain and plot various cost function,
Write an expression for profit,
Depict production functions using isoquants and find the
average product of labour.
2. EQUATION IN ECONOMICS
(2 x)
In this chapter you learn to:
1. Understand how equations are used in economics,
2. Rewrite and solve equation,
3. Substitute expressions,
4. Solve simple linier demand and supply equations to find market
equilibrium,
5. Carry out cost – volume – profit analysis,
6. Identify the slope and intercept of line,
7. Plot the budget constraint to obtain the budget line,
8. Appreciate there is a constant rate of substitution as you move
along a line,
9. Solve quadratic equations,
10.Find the profit maximizing output and also the supply function for a
perfectly competitive firm,
11.Solve simultaneous equations,
12.Discover equilibrium values for related markets,
13. Model growth using exponential function,
3. MACROECONOMICS MODELS
(1 X)
In this chapter you learn to:
1.
Appreciate the role of macroeconomic modelling,
2.
Understand the notation for macroeconomic models,
3.
Write down a condition for macroeconomic equilibrium,
substitute and then solve to find equilibrium income,
4.
Use keysinesian cross models to analysis the good market,
5.
Apply IS – LM analysis , which includes the money market.
LM stands for ‘investment equals savings’ and LM stands for
‘liquidity preference equals money supply’.
4. CHANGES, RATE, FINANCE AND
SERIES
(2 X)
In this chapter you learn to:
1.
Measure interest and growth rates as percentages or decimals,
2.
Calculate percentage changes and percentage point changes,
3.
Calculate the future value of a principal earning simple or compound
interest and use different frequencies of compounding,
4.
Find the annual percentage rate of interest as standardized measure,
5.
Compute the real of interest,
6.
7.
Understand why logarithmic graph are useful for representing variables that
are grow over time, and calculate the average growth rate over a period,
Calculate depreciation using the straight line and reducing balance
methods,
8.
Use net present value and internal rate of return for investment appraisal,
9.
Recognize a series and find the sum of geometric progression,
10.
Carry out loan and annuity calculation involving regular payment,
11.
Find how the price of bills and the bonds changes with the rate of interest.
5.
DIFFERENTIATION IN
ECONOMICS
(2 X)
In this chapter you learn to:
1.
2.
3.
4.
5.
6.
7.
8.
9.
Understand that differentiation lets us identify marginal
relationships in economics,
Measure the rate of change along a line or curve,
Find dy/dx for power function and practice the basic rules of
differentiation,
Apply differentiation notation to economics examples,
Obtain a marginal revenue function as the derivative of the total
revenue function,
Differentiate a short run productions function to find the marginal
product of labour,
Understand the relationship between total cost and marginal cost,
Measure point elasticity of demand and supply,
Find the investment multiplier in simple macroeconomic model.
6. MAXIMUM & MINIMUM VALUES
(1 X)
In this chapter you learn to:
1.
2.
3.
4.
5.
6.
7.
8.
Appreciate that economic objectives involve optimization,
Identify maximum and minimum turning point by
differentiating and then finding the second derivative,
Find the maximum revenue,
Show which output maximizes profit and whether it changes if
taxation is imposed,
Identify minimum turning point on cost curve,
Find the level of employment at which the average product of
labour is maximized,
Choose the per unit tax which maximizes tax revenues,
Identify the economic order quantity which minimizes total
inventory cost.
7. FURTHER RULES OF
DIFFERENTIATION
(1 X)
In this chapter you learn to:
1.
Appreciate when further rule of differentiation are needed,
2.
Differentiation composite functions using the chain rule,
3.
Use the product rule of differentiation,
4.
Apply the quotient rule
5.
(the derivative of the first term times the second minus
derivative of the second term times the first, all divided by the square of the second
term),
Show the relationship between marginal revenue, elasticity and
maximum total revenue,
6.
Analysis optimal production and cost relationship,
7.
Differentiate natural logarithmic and exponential function,
8.
Use logarithmic and exponential relationships in economic analysis.
8. PARTIAL DIFFERENTIATION IN
ECONOMICS
(2 X)
In this chapter you learn to:
1.
Understand that partial derivative show the separate effects of
different variables,
2.
Find partial derivatives using appropriate notation,
3.
Find own-price, cross price and income elasticity of demand,
4.
Use the small increment formula,
5.
Find macroeconomic multipliers,
6.
Use differentials and implicit differentiation,
7.
Find the slope of and indifference curve,
8.
Measure returns to scale and factors shares for homogenious
production function,
9.
Identify second elasticity for logarithmic demand function,
10.
Find second order partial derivatives,
11.
Optimize multivariate function,
12.
Find what prices are charged by a monopolist using price dicrimination.
9. CONSTRAINED MAXIMA & MINIMA
(1 X)
In this chapter you learn to:
1.
2.
3.
Appreciate how constrained optimization problems
arise in economics,
Solve constrained maximization and minimization
problem using substitution method,
Use the more general lagrange multiplier methods.
10. INTEGRATION IN ECONOMICS
(1 X)
In this chapter you learn to:
1.
Understand that integration is the inverse procedure to
differentiation,
2.
Recognize the notation and apply the rules of
integration,
3.
Find total function from marginal function,
4.
Use definite integration to find the area under a curve,
5.
Evaluate the sizes of areas on economics diagrams,
giving measures of total revenue, total variable cost,
consumer surplus and producer surplus.
LITERATURE
Alpha C Chiang and Kevin Wainwright. 2005.
“Fundamental Methods of Mathematical Economics” –
4th. McGraw-Hill International Edition.
Jean Soper,
1999. Mathematics for Economics
and Business – An Interactive Introduction. Blackwell
Publishers.
Michael Harrison and Patrick Waldrom. 1998.
Mathematical Economy and Finance. www.4shared. Com
Herman J Bierens, ‘Introduction to the Mathematical and
Statistical Foundations of Econometrics. Pennsylvania
State University USA. www.4shared. Com.
ETC
Komponen Penilaian
Tugas : 15%
Quis : 10%
Ujian Tengah Semester
Ujian Akhir Semester : 35%
GRADE
(A – B – C – D – E – F)
Nilai
Point
Range
A
4
81
B
3
66 – 80
C
2
56 – 65
D
1
41 – 55
E
0
40
: 35%