Matematika Ekonomi 1 – Bank Soal

Deskripsi

Produk : Question Bank

Daftar Topik:

Introduction

• The nature of mathematical economics
• Functions: definition, types, domain-range, generalization, and diagram
• Model ingredients: determining constants, coefficients, and exogenuous / endogenuous variables

Introduction: Equilibrium Analysis

• The meaning of equilibrium: market mechanism (shifting-movement along the curve)

Equilibrium Analysis

• Partial market equilibrium – linear and non-linear model
• General market equilibrium: two-commodity market model
• Equilibrium in national income analysis
• Government’s market intervention

Linear Model and Matrix Algebra (1)

• How to arrange a matrix system: various economic models
• Matrices and vectors
• Matrix and vector operations
• Identity matrices and null matrices
• Transposes and inverses
• Vector concept to non-singularity test

Linear Model and Matrix Algebra (2)

• Non-singular matrix: conditions and tests
• Concept of determinants
• Finding determinant using Laplace expansion: concept of minor and cofactor
• Finding the inverse matrix
• From matrix inversion to Cramer’s rule

Linear Model and Matrix Algebra (3)

• Applications of matrix inversion and Cramer’s rule in economic models: market, national income, IS-LM, or 1-O models

Comparative Statics and Derivative

• The nature of comparative statics and derivative
• Rate of change
• Limit rules and roles
• Derivative and slope of curve
• Inequality and absolute value concept
• Continuity and differentiability

Rules of Differentiation

• Basic rules of differentiation
• Chain rule
• Inverse function and monotonicity

Partial Differentiation

• Applications to comparative statics analysis: market and national income model
• Other economic applications: marginal concepts, money creation analysis
• Jacobian determinants

Concepts of differential and elasticity

• Total differentials
• Total derivatives
• Derivatives of implicit functions
• Introducing the use of total derivatives in general economic model

Introduction: optimization problem

• Optimum vs extremum values
• Interpretation of first and second derivatives
• Optimization without constraint: single variable case, using first and higher derivative tests
• Necessary vs sufficient condition
• Nth derivative test

Exponential and Logarithmic Function (1)

• The nature of exponential function
• Natural exponential function and the problem of growth
• Logarithm and logarithmic function
• Derivatives of exponential and logarithm functions
• Finding growth rate, interest compounding (discrete and continuous case), discount and present value, and point elasticity

Exponential and Logarithmic Function (2)

• Optimal timing: first and second derivative test

Optimization without constraint: two or more than two variable cases

• Finding relative extremum
• First and second order condition
• Determinant test and characteristic roots 

Economic applications of optimization without constraint: 2 or >2 variable cases

• Two-product firm case: competitive and monopolistic
• Third-degree price discrimination
• Elasticity in price discrimination
• Input decision of a firm

Optimization with Equality Constraints (1)

• Effects of a constraint
• Finding stationary values using Lagrange
• Second-order conditions: Bordered Hessian and Bordered Determinant
• Economic applications: utility maximization and consumer demand

Optimization with Equality Constraints (2)

• Economic applications: homogeneity and return to scale, least-cost combination of inputs

Dynamic Analysis and Integral (1)

• Indefinite integral
• Definite integral
• Improper integral
• Economic applications: from marginal to total function, finding time path of capital and capital formation

Dynamic Analysis and Integral (2)

• Economic applications: finding net present value (NPV) from different, cash streaming cases