Verfügbarkeit: Introduction to Mathematics for Economics with R.

Introduction to Mathematics for Economics with R.:

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Bibliographische Detailangaben
1. Verfasser:	Porto, Massimiliano (VerfasserIn)
Format:	Elektronisch E-Book
Sprache:	English
Veröffentlicht:	Cham Springer International Publishing AG 2022
Ausgabe:	1st ed
Schlagworte:	Economics-Mathematical models
Online-Zugang:	HWR01
Beschreibung:	Description based on publisher supplied metadata and other sources
Beschreibung:	1 Online-Ressource (866 Seiten)
ISBN:	9783031052026

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505	8		\|a Intro -- Preface -- Contents -- List of Figures -- List of Tables -- 1 Introduction to R -- 1.1 Installing R -- 1.2 Installing RStudio -- 1.3 Introduction to RStudio -- 1.3.1 Launching a New Project -- 1.3.2 Opening an R Script -- 1.4 Packages to Install -- 1.4.1 How to Install a Package -- 1.4.2 How to Load a Package -- 1.5 Good Practice and Notation -- 1.5.1 How to Read the Code -- 1.6 8 Key-Points Regarding R -- 1.6.1 The Assignment Operator -- 1.6.2 The Class of Objects -- 1.6.3 Case Sensitiveness -- 1.6.4 The c() Function -- 1.6.5 Square Bracket Operator [ ] -- 1.6.6 Loop and Vectorization -- 1.6.7 Functions -- 1.6.8 Errors -- 1.6.8.1 Syntax Errors -- 1.6.8.2 class() Type Errors -- 1.6.8.3 Warning Message -- 1.6.8.4 No-Error Message Error -- 1.7 An Example with R -- 1.8 Exercise -- 1.8.1 Exercise 1 -- 1.8.2 Exercise 2 -- Part I Introduction to Mathematics for Static Economics -- 2 Linear Algebra -- 2.1 Set, Group, Ring, Field: Short Overview -- 2.2 Vectors -- 2.2.1 Vector Space -- 2.2.1.1 Properties of Vector Space -- 2.2.1.2 Vector Notation -- 2.2.2 Vector Representation in Two and Three Dimensions -- 2.2.3 Inner Product -- 2.2.4 Outer Product -- 2.2.5 Component Form, Magnitude and Unit Vector -- 2.2.6 Parallel and Orthogonal Vectors -- 2.2.7 Vector Projection -- 2.2.8 Linear Independence -- 2.3 Matrices -- 2.3.1 Matrix Operations -- 2.3.1.1 Addition -- 2.3.1.2 Multiplication -- 2.3.1.3 Transpose -- 2.3.2 Symmetric Matrix -- 2.3.3 Diagonal Matrix and Identity Matrix -- 2.3.3.1 Trace of a Square Matrix -- 2.3.4 Triangular Matrix -- 2.3.5 Idempotent Matrix -- 2.3.6 The Inverse of a Matrix -- 2.3.7 System of Linear Equations -- 2.3.7.1 System of Linear Equations and Matrices -- 2.3.7.2 Gauss Elimination and Gauss-Jordan Elimination -- 2.3.7.3 The Rank of a Matrix -- 2.3.8 Determinant -- 2.3.8.1 The Determinant of a 2 2 Matrix
505	8		\|a 2.3.8.2 Laplace Expansion Method -- 2.3.8.3 The Determinant and the Matrix Inverse -- 2.3.8.4 Cramer's Rule -- 2.3.9 Eigenvalues and Eigenvectors -- 2.3.9.1 Diagonalization and Jordan Canonical Form -- 2.3.10 Partitioned Matrix -- 2.3.11 Kronecker Product -- 2.3.12 Definiteness of Matrices -- 2.3.13 Decomposition -- 2.3.13.1 Spectral Decomposition -- 2.3.13.2 Singular Value Decomposition (SVD) -- 2.3.13.3 Cholesky Decomposition -- 2.3.13.4 QR Decomposition -- 2.4 Applications in Economics -- 2.4.1 Budget Set -- 2.4.2 Applying Cramer's Rule to the IS-LM Model -- 2.4.3 Leontief Input-Output Model -- 2.4.4 Network Analysis -- 2.4.5 Linear Model and the Dummy Variable Trap -- 2.5 Exercises -- 2.5.1 Exercise 1 -- 2.5.2 Exercise 2 -- 2.5.3 Exercise 3 -- 2.5.4 Exercise 4 -- 2.5.5 Exercise 5 -- 2.5.6 Exercise 6 -- 2.5.7 Exercise 7 -- 3 Functions of One Variable -- 3.1 What is a Function? -- 3.1.1 Domain and Range -- 3.1.2 Monotonicity, Boundedness and Extrema -- 3.1.3 Convex and Concave Functions -- 3.1.4 Function Operations -- 3.2 Linear Function -- 3.2.1 Slope of Linear Function -- 3.2.2 Applications in Economics -- 3.2.2.1 The Cost Function -- 3.2.2.2 Break-Even -- 3.2.2.3 Mark-Up and Margin -- 3.2.2.4 Linear Models in Econometrics -- 3.3 Quadratic Function -- 3.3.1 Roots and Vertex -- 3.3.2 The Graph of the Quadratic Function -- 3.3.3 Discriminant -- 3.3.4 Applications in Economics -- 3.3.4.1 The Cost Function -- 3.4 Cubic Function -- 3.4.1 How to Solve Cubic Equations -- 3.4.2 Applications in Economics -- 3.4.2.1 The Cost Function -- 3.5 Polynomials of Degree Greater Than Three -- 3.6 Logarithmic and Exponential Functions -- 3.6.1 What is a Logarithm? -- 3.6.2 Logarithms and Exponents -- 3.6.3 The Natural Logarithm -- 3.6.4 The Natural Logarithmic Function -- 3.6.4.1 How to Solve Logarithmic Equation -- 3.6.5 Applications in Economics
505	8		\|a 3.6.5.1 Logarithms and Growth -- 3.6.5.2 Logarithms and Geometric Mean -- 3.6.5.3 Logarithms and Econometrics -- 3.6.6 Exponential Function -- 3.6.6.1 What is e ? -- 3.6.6.2 How to Solve Exponential Equations -- 3.6.7 Applications in Economics -- 3.6.7.1 Exponential and Investment -- 3.6.7.2 Exponential Growth and Logistic Growth -- 3.7 Radical Function -- 3.7.1 How to Solve Radical Equation -- 3.7.2 Find the Domain of a Radical Function -- 3.7.3 Radicals and Rational Exponents -- 3.7.4 Applications in Economics -- 3.7.4.1 Production Function with a Single Input -- 3.8 Rational Function -- 3.8.1 Intercepts and Asymptotes -- 3.8.2 Applications in Economics -- 3.8.2.1 Indifference Curve -- 3.8.2.2 A ''Work'' Example -- 3.9 Exercises -- 3.9.1 Exercise 1 -- 3.9.2 Exercise 2 -- 3.9.3 Exercise 3 -- 3.9.4 Exercise 4 -- 3.9.5 Exercise 5 -- 4 Differential Calculus -- 4.1 What is the Meaning of Derivatives? -- 4.2 The Limit of a Function -- 4.3 Limits, Derivatives and Slope -- 4.3.1 Newton-Raphson Method -- 4.4 Notation of Derivatives -- 4.5 Differentials -- 4.6 Rules of Differentiation -- 4.6.1 Power Rule -- 4.6.2 Product Rule -- 4.6.3 Quotient Rule -- 4.6.4 Chain Rule -- 4.6.4.1 Implicit Differentiation -- 4.6.5 Radicals Differentiation -- 4.6.6 Logarithmic Differentiation -- 4.6.7 Exponential Differentiation -- 4.6.7.1 Exponential Growth and Logistic Growth -- 4.6.8 Derivatives of Elementary Functions -- 4.7 Derivatives and Inverse Functions -- 4.8 Tangent Line to the Function -- 4.9 Points of Minimum, Maximum and Inflection -- 4.10 Taylor Expansion -- 4.10.1 Nth-Derivative Test -- 4.10.2 Newton-Raphson Method -- 4.11 L'Hôpital Theorem -- 4.12 Derivatives with R -- 4.13 Taylor Expansion with R -- 4.14 Applications in Economics -- 4.14.1 Marginal Cost -- 4.14.1.1 Coefficients of a Cubic Cost Function -- 4.14.2 Marginal Cost and Average Cost
505	8		\|a 4.14.3 Profit Maximization -- 4.14.4 Elasticity -- 4.15 Exercise -- 4.15.1 Exercise 1 -- 4.15.2 Exercise 2 -- 4.15.3 Exercise 3 -- 5 Integral Calculus -- 5.1 Indefinite Integrals -- 5.1.1 Anti-derivative Process -- 5.1.1.1 Fundamental Integrals -- 5.1.1.2 Integration by Substitution -- 5.1.1.3 Integration by Parts -- 5.1.1.4 Partial Fractions -- 5.2 Definite Integrals -- 5.2.1 Area Under a Curve -- 5.2.2 Area Between Two Lines -- 5.3 Fundamental Theorem of Calculus -- 5.4 Improper Integrals and Convergence -- 5.4.1 Case 1: Convergence -- 5.4.2 Case 2: Divergence -- 5.5 Integration with R -- 5.6 Applications in Economics -- 5.6.1 Marginal Cost and Cost Function -- 5.6.2 Example: A Problem -- 5.6.3 The Surplus of Consumer and Producer -- 5.7 Exercise -- 6 Multivariable Calculus -- 6.1 Functions of Several Variables -- 6.1.1 Applications in Economics -- 6.1.1.1 Complementary Goods and Substitute Goods -- 6.1.1.2 The Cobb-Douglas Function -- 6.1.1.3 The Constant Elasticity of Substitution (CES) Function -- 6.1.1.4 The Cobb-Douglas Function as a Special Case of the CES Function -- 6.2 Partial and Total Derivatives -- 6.2.1 Partial Derivatives -- 6.2.1.1 Gradient Vector -- 6.2.1.2 Jacobian Matrix -- 6.2.1.3 Hessian Matrix -- 6.2.2 Total Derivatives -- 6.2.3 Derivatives with R -- 6.2.4 Applications in Economics -- 6.2.4.1 Marginal Product of Labour and Capital -- 6.2.4.2 The Law of Diminishing Marginal Productivity -- 6.2.4.3 An Application with the Jacobian -- 6.3 Unconstrained Optimization -- 6.3.1 First Order Condition -- 6.3.2 Second Order Condition -- 6.3.2.1 Concavity and Convexity -- 6.3.3 Optimization with R -- 6.3.4 Applications in Economics -- 6.3.4.1 Multi-product Firm -- 6.3.4.2 Ordinary Least Square -- 6.4 Integration with Multiple Variables -- 6.5 Exercises -- 6.5.1 Exercise 1 -- 6.5.2 Exercise 2 -- 7 Constrained Optimization
505	8		\|a 7.1 Equality Constraints -- 7.1.1 First-Order Condition -- 7.1.2 Multiple Equality Constraints -- 7.1.3 Lagrange Multiplier -- 7.1.3.1 A Mathematical Interpretation -- 7.1.3.2 An Economic Interpretation -- 7.1.4 Second-Order Conditions -- 7.2 Inequality Constraints -- 7.2.1 Kuhn-Tucker Conditions -- 7.3 Constrained Optimization with R -- 7.4 Applications in Economics -- 7.4.1 Utility Maximization Problem -- 7.4.2 Firm's Cost Minimization Problem -- 7.4.3 Transportation Problem -- 7.4.4 CGE Model with R -- 7.4.4.1 Shoven-Whalley Model Without Taxes -- 7.4.4.2 Solving the Model with R -- 7.5 Exercise -- Part II Introduction to Mathematics for Dynamic Economics -- 8 Trigonometry -- 8.1 Right Triangles and Angles -- 8.2 Trigonometric Functions -- 8.3 Sum and Differences of Angles -- 8.4 Derivatives of Trigonometric Functions -- 9 Complex Numbers -- 9.1 Set of Complex Numbers -- 9.2 Complex Numbers: Real Part and Imaginary Part -- 9.3 Arithmetic Operations -- 9.4 Geometric Interpretation and Polar Form -- 9.5 Exponential Form -- 10 Difference Equations -- 10.1 First-Order Linear Difference Equations -- 10.1.1 Solution by Iteration -- 10.1.2 Solution by General Method -- 10.1.3 Time Path and Equilibrium -- 10.2 Second-Order Linear Difference Equations -- 10.2.1 Solution to Second-Order Linear Homogeneous Difference Equation -- 10.2.1.1 Two Distinct Real Roots (Case of D &gt -- 0 ) -- 10.2.1.2 One Real Root (or Repeated Real Roots) (Case of D = 0 ) -- 10.2.1.3 Complex Roots (Case of D &lt -- 0 ) -- 10.2.2 Solution to Second-Order Linear Nonhomogeneous Difference Equation -- 10.2.3 Time Path and Equilibrium -- 10.3 System of Linear Difference Equations -- 10.3.1 Equilibrium -- 10.3.2 Solution with the Powers of a Matrix -- 10.3.3 Eigenvalues Method -- 10.3.3.1 Case 1: Distinct Real Eigenvalues -- 10.3.3.2 Case 2: Repeated Real Eigenvalues
505	8		\|a 10.3.3.3 Case 3: Complex Eigenvalues
650		4	\|a Economics-Mathematical models
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contents	Intro -- Preface -- Contents -- List of Figures -- List of Tables -- 1 Introduction to R -- 1.1 Installing R -- 1.2 Installing RStudio -- 1.3 Introduction to RStudio -- 1.3.1 Launching a New Project -- 1.3.2 Opening an R Script -- 1.4 Packages to Install -- 1.4.1 How to Install a Package -- 1.4.2 How to Load a Package -- 1.5 Good Practice and Notation -- 1.5.1 How to Read the Code -- 1.6 8 Key-Points Regarding R -- 1.6.1 The Assignment Operator -- 1.6.2 The Class of Objects -- 1.6.3 Case Sensitiveness -- 1.6.4 The c() Function -- 1.6.5 Square Bracket Operator [ ] -- 1.6.6 Loop and Vectorization -- 1.6.7 Functions -- 1.6.8 Errors -- 1.6.8.1 Syntax Errors -- 1.6.8.2 class() Type Errors -- 1.6.8.3 Warning Message -- 1.6.8.4 No-Error Message Error -- 1.7 An Example with R -- 1.8 Exercise -- 1.8.1 Exercise 1 -- 1.8.2 Exercise 2 -- Part I Introduction to Mathematics for Static Economics -- 2 Linear Algebra -- 2.1 Set, Group, Ring, Field: Short Overview -- 2.2 Vectors -- 2.2.1 Vector Space -- 2.2.1.1 Properties of Vector Space -- 2.2.1.2 Vector Notation -- 2.2.2 Vector Representation in Two and Three Dimensions -- 2.2.3 Inner Product -- 2.2.4 Outer Product -- 2.2.5 Component Form, Magnitude and Unit Vector -- 2.2.6 Parallel and Orthogonal Vectors -- 2.2.7 Vector Projection -- 2.2.8 Linear Independence -- 2.3 Matrices -- 2.3.1 Matrix Operations -- 2.3.1.1 Addition -- 2.3.1.2 Multiplication -- 2.3.1.3 Transpose -- 2.3.2 Symmetric Matrix -- 2.3.3 Diagonal Matrix and Identity Matrix -- 2.3.3.1 Trace of a Square Matrix -- 2.3.4 Triangular Matrix -- 2.3.5 Idempotent Matrix -- 2.3.6 The Inverse of a Matrix -- 2.3.7 System of Linear Equations -- 2.3.7.1 System of Linear Equations and Matrices -- 2.3.7.2 Gauss Elimination and Gauss-Jordan Elimination -- 2.3.7.3 The Rank of a Matrix -- 2.3.8 Determinant -- 2.3.8.1 The Determinant of a 2 2 Matrix 2.3.8.2 Laplace Expansion Method -- 2.3.8.3 The Determinant and the Matrix Inverse -- 2.3.8.4 Cramer's Rule -- 2.3.9 Eigenvalues and Eigenvectors -- 2.3.9.1 Diagonalization and Jordan Canonical Form -- 2.3.10 Partitioned Matrix -- 2.3.11 Kronecker Product -- 2.3.12 Definiteness of Matrices -- 2.3.13 Decomposition -- 2.3.13.1 Spectral Decomposition -- 2.3.13.2 Singular Value Decomposition (SVD) -- 2.3.13.3 Cholesky Decomposition -- 2.3.13.4 QR Decomposition -- 2.4 Applications in Economics -- 2.4.1 Budget Set -- 2.4.2 Applying Cramer's Rule to the IS-LM Model -- 2.4.3 Leontief Input-Output Model -- 2.4.4 Network Analysis -- 2.4.5 Linear Model and the Dummy Variable Trap -- 2.5 Exercises -- 2.5.1 Exercise 1 -- 2.5.2 Exercise 2 -- 2.5.3 Exercise 3 -- 2.5.4 Exercise 4 -- 2.5.5 Exercise 5 -- 2.5.6 Exercise 6 -- 2.5.7 Exercise 7 -- 3 Functions of One Variable -- 3.1 What is a Function? -- 3.1.1 Domain and Range -- 3.1.2 Monotonicity, Boundedness and Extrema -- 3.1.3 Convex and Concave Functions -- 3.1.4 Function Operations -- 3.2 Linear Function -- 3.2.1 Slope of Linear Function -- 3.2.2 Applications in Economics -- 3.2.2.1 The Cost Function -- 3.2.2.2 Break-Even -- 3.2.2.3 Mark-Up and Margin -- 3.2.2.4 Linear Models in Econometrics -- 3.3 Quadratic Function -- 3.3.1 Roots and Vertex -- 3.3.2 The Graph of the Quadratic Function -- 3.3.3 Discriminant -- 3.3.4 Applications in Economics -- 3.3.4.1 The Cost Function -- 3.4 Cubic Function -- 3.4.1 How to Solve Cubic Equations -- 3.4.2 Applications in Economics -- 3.4.2.1 The Cost Function -- 3.5 Polynomials of Degree Greater Than Three -- 3.6 Logarithmic and Exponential Functions -- 3.6.1 What is a Logarithm? -- 3.6.2 Logarithms and Exponents -- 3.6.3 The Natural Logarithm -- 3.6.4 The Natural Logarithmic Function -- 3.6.4.1 How to Solve Logarithmic Equation -- 3.6.5 Applications in Economics 3.6.5.1 Logarithms and Growth -- 3.6.5.2 Logarithms and Geometric Mean -- 3.6.5.3 Logarithms and Econometrics -- 3.6.6 Exponential Function -- 3.6.6.1 What is e ? -- 3.6.6.2 How to Solve Exponential Equations -- 3.6.7 Applications in Economics -- 3.6.7.1 Exponential and Investment -- 3.6.7.2 Exponential Growth and Logistic Growth -- 3.7 Radical Function -- 3.7.1 How to Solve Radical Equation -- 3.7.2 Find the Domain of a Radical Function -- 3.7.3 Radicals and Rational Exponents -- 3.7.4 Applications in Economics -- 3.7.4.1 Production Function with a Single Input -- 3.8 Rational Function -- 3.8.1 Intercepts and Asymptotes -- 3.8.2 Applications in Economics -- 3.8.2.1 Indifference Curve -- 3.8.2.2 A ''Work'' Example -- 3.9 Exercises -- 3.9.1 Exercise 1 -- 3.9.2 Exercise 2 -- 3.9.3 Exercise 3 -- 3.9.4 Exercise 4 -- 3.9.5 Exercise 5 -- 4 Differential Calculus -- 4.1 What is the Meaning of Derivatives? -- 4.2 The Limit of a Function -- 4.3 Limits, Derivatives and Slope -- 4.3.1 Newton-Raphson Method -- 4.4 Notation of Derivatives -- 4.5 Differentials -- 4.6 Rules of Differentiation -- 4.6.1 Power Rule -- 4.6.2 Product Rule -- 4.6.3 Quotient Rule -- 4.6.4 Chain Rule -- 4.6.4.1 Implicit Differentiation -- 4.6.5 Radicals Differentiation -- 4.6.6 Logarithmic Differentiation -- 4.6.7 Exponential Differentiation -- 4.6.7.1 Exponential Growth and Logistic Growth -- 4.6.8 Derivatives of Elementary Functions -- 4.7 Derivatives and Inverse Functions -- 4.8 Tangent Line to the Function -- 4.9 Points of Minimum, Maximum and Inflection -- 4.10 Taylor Expansion -- 4.10.1 Nth-Derivative Test -- 4.10.2 Newton-Raphson Method -- 4.11 L'Hôpital Theorem -- 4.12 Derivatives with R -- 4.13 Taylor Expansion with R -- 4.14 Applications in Economics -- 4.14.1 Marginal Cost -- 4.14.1.1 Coefficients of a Cubic Cost Function -- 4.14.2 Marginal Cost and Average Cost 4.14.3 Profit Maximization -- 4.14.4 Elasticity -- 4.15 Exercise -- 4.15.1 Exercise 1 -- 4.15.2 Exercise 2 -- 4.15.3 Exercise 3 -- 5 Integral Calculus -- 5.1 Indefinite Integrals -- 5.1.1 Anti-derivative Process -- 5.1.1.1 Fundamental Integrals -- 5.1.1.2 Integration by Substitution -- 5.1.1.3 Integration by Parts -- 5.1.1.4 Partial Fractions -- 5.2 Definite Integrals -- 5.2.1 Area Under a Curve -- 5.2.2 Area Between Two Lines -- 5.3 Fundamental Theorem of Calculus -- 5.4 Improper Integrals and Convergence -- 5.4.1 Case 1: Convergence -- 5.4.2 Case 2: Divergence -- 5.5 Integration with R -- 5.6 Applications in Economics -- 5.6.1 Marginal Cost and Cost Function -- 5.6.2 Example: A Problem -- 5.6.3 The Surplus of Consumer and Producer -- 5.7 Exercise -- 6 Multivariable Calculus -- 6.1 Functions of Several Variables -- 6.1.1 Applications in Economics -- 6.1.1.1 Complementary Goods and Substitute Goods -- 6.1.1.2 The Cobb-Douglas Function -- 6.1.1.3 The Constant Elasticity of Substitution (CES) Function -- 6.1.1.4 The Cobb-Douglas Function as a Special Case of the CES Function -- 6.2 Partial and Total Derivatives -- 6.2.1 Partial Derivatives -- 6.2.1.1 Gradient Vector -- 6.2.1.2 Jacobian Matrix -- 6.2.1.3 Hessian Matrix -- 6.2.2 Total Derivatives -- 6.2.3 Derivatives with R -- 6.2.4 Applications in Economics -- 6.2.4.1 Marginal Product of Labour and Capital -- 6.2.4.2 The Law of Diminishing Marginal Productivity -- 6.2.4.3 An Application with the Jacobian -- 6.3 Unconstrained Optimization -- 6.3.1 First Order Condition -- 6.3.2 Second Order Condition -- 6.3.2.1 Concavity and Convexity -- 6.3.3 Optimization with R -- 6.3.4 Applications in Economics -- 6.3.4.1 Multi-product Firm -- 6.3.4.2 Ordinary Least Square -- 6.4 Integration with Multiple Variables -- 6.5 Exercises -- 6.5.1 Exercise 1 -- 6.5.2 Exercise 2 -- 7 Constrained Optimization 7.1 Equality Constraints -- 7.1.1 First-Order Condition -- 7.1.2 Multiple Equality Constraints -- 7.1.3 Lagrange Multiplier -- 7.1.3.1 A Mathematical Interpretation -- 7.1.3.2 An Economic Interpretation -- 7.1.4 Second-Order Conditions -- 7.2 Inequality Constraints -- 7.2.1 Kuhn-Tucker Conditions -- 7.3 Constrained Optimization with R -- 7.4 Applications in Economics -- 7.4.1 Utility Maximization Problem -- 7.4.2 Firm's Cost Minimization Problem -- 7.4.3 Transportation Problem -- 7.4.4 CGE Model with R -- 7.4.4.1 Shoven-Whalley Model Without Taxes -- 7.4.4.2 Solving the Model with R -- 7.5 Exercise -- Part II Introduction to Mathematics for Dynamic Economics -- 8 Trigonometry -- 8.1 Right Triangles and Angles -- 8.2 Trigonometric Functions -- 8.3 Sum and Differences of Angles -- 8.4 Derivatives of Trigonometric Functions -- 9 Complex Numbers -- 9.1 Set of Complex Numbers -- 9.2 Complex Numbers: Real Part and Imaginary Part -- 9.3 Arithmetic Operations -- 9.4 Geometric Interpretation and Polar Form -- 9.5 Exponential Form -- 10 Difference Equations -- 10.1 First-Order Linear Difference Equations -- 10.1.1 Solution by Iteration -- 10.1.2 Solution by General Method -- 10.1.3 Time Path and Equilibrium -- 10.2 Second-Order Linear Difference Equations -- 10.2.1 Solution to Second-Order Linear Homogeneous Difference Equation -- 10.2.1.1 Two Distinct Real Roots (Case of D &gt -- 0 ) -- 10.2.1.2 One Real Root (or Repeated Real Roots) (Case of D = 0 ) -- 10.2.1.3 Complex Roots (Case of D &lt -- 0 ) -- 10.2.2 Solution to Second-Order Linear Nonhomogeneous Difference Equation -- 10.2.3 Time Path and Equilibrium -- 10.3 System of Linear Difference Equations -- 10.3.1 Equilibrium -- 10.3.2 Solution with the Powers of a Matrix -- 10.3.3 Eigenvalues Method -- 10.3.3.1 Case 1: Distinct Real Eigenvalues -- 10.3.3.2 Case 2: Repeated Real Eigenvalues 10.3.3.3 Case 3: Complex Eigenvalues
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ind1=" " ind2=" "><subfield code="a">1st ed</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cham</subfield><subfield code="b">Springer International Publishing AG</subfield><subfield code="c">2022</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">©2022</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (866 Seiten)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Description based on publisher supplied metadata and other sources</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Intro -- Preface -- Contents -- List of Figures -- List of Tables -- 1 Introduction to R -- 1.1 Installing R -- 1.2 Installing RStudio -- 1.3 Introduction to RStudio -- 1.3.1 Launching a New Project -- 1.3.2 Opening an R Script -- 1.4 Packages to Install -- 1.4.1 How to Install a Package -- 1.4.2 How to Load a Package -- 1.5 Good Practice and Notation -- 1.5.1 How to Read the Code -- 1.6 8 Key-Points Regarding R -- 1.6.1 The Assignment Operator -- 1.6.2 The Class of Objects -- 1.6.3 Case Sensitiveness -- 1.6.4 The c() Function -- 1.6.5 Square Bracket Operator [ ] -- 1.6.6 Loop and Vectorization -- 1.6.7 Functions -- 1.6.8 Errors -- 1.6.8.1 Syntax Errors -- 1.6.8.2 class() Type Errors -- 1.6.8.3 Warning Message -- 1.6.8.4 No-Error Message Error -- 1.7 An Example with R -- 1.8 Exercise -- 1.8.1 Exercise 1 -- 1.8.2 Exercise 2 -- Part I Introduction to Mathematics for Static Economics -- 2 Linear Algebra -- 2.1 Set, Group, Ring, Field: Short Overview -- 2.2 Vectors -- 2.2.1 Vector Space -- 2.2.1.1 Properties of Vector Space -- 2.2.1.2 Vector Notation -- 2.2.2 Vector Representation in Two and Three Dimensions -- 2.2.3 Inner Product -- 2.2.4 Outer Product -- 2.2.5 Component Form, Magnitude and Unit Vector -- 2.2.6 Parallel and Orthogonal Vectors -- 2.2.7 Vector Projection -- 2.2.8 Linear Independence -- 2.3 Matrices -- 2.3.1 Matrix Operations -- 2.3.1.1 Addition -- 2.3.1.2 Multiplication -- 2.3.1.3 Transpose -- 2.3.2 Symmetric Matrix -- 2.3.3 Diagonal Matrix and Identity Matrix -- 2.3.3.1 Trace of a Square Matrix -- 2.3.4 Triangular Matrix -- 2.3.5 Idempotent Matrix -- 2.3.6 The Inverse of a Matrix -- 2.3.7 System of Linear Equations -- 2.3.7.1 System of Linear Equations and Matrices -- 2.3.7.2 Gauss Elimination and Gauss-Jordan Elimination -- 2.3.7.3 The Rank of a Matrix -- 2.3.8 Determinant -- 2.3.8.1 The Determinant of a 2 2 Matrix</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">2.3.8.2 Laplace Expansion Method -- 2.3.8.3 The Determinant and the Matrix Inverse -- 2.3.8.4 Cramer's Rule -- 2.3.9 Eigenvalues and Eigenvectors -- 2.3.9.1 Diagonalization and Jordan Canonical Form -- 2.3.10 Partitioned Matrix -- 2.3.11 Kronecker Product -- 2.3.12 Definiteness of Matrices -- 2.3.13 Decomposition -- 2.3.13.1 Spectral Decomposition -- 2.3.13.2 Singular Value Decomposition (SVD) -- 2.3.13.3 Cholesky Decomposition -- 2.3.13.4 QR Decomposition -- 2.4 Applications in Economics -- 2.4.1 Budget Set -- 2.4.2 Applying Cramer's Rule to the IS-LM Model -- 2.4.3 Leontief Input-Output Model -- 2.4.4 Network Analysis -- 2.4.5 Linear Model and the Dummy Variable Trap -- 2.5 Exercises -- 2.5.1 Exercise 1 -- 2.5.2 Exercise 2 -- 2.5.3 Exercise 3 -- 2.5.4 Exercise 4 -- 2.5.5 Exercise 5 -- 2.5.6 Exercise 6 -- 2.5.7 Exercise 7 -- 3 Functions of One Variable -- 3.1 What is a Function? -- 3.1.1 Domain and Range -- 3.1.2 Monotonicity, Boundedness and Extrema -- 3.1.3 Convex and Concave Functions -- 3.1.4 Function Operations -- 3.2 Linear Function -- 3.2.1 Slope of Linear Function -- 3.2.2 Applications in Economics -- 3.2.2.1 The Cost Function -- 3.2.2.2 Break-Even -- 3.2.2.3 Mark-Up and Margin -- 3.2.2.4 Linear Models in Econometrics -- 3.3 Quadratic Function -- 3.3.1 Roots and Vertex -- 3.3.2 The Graph of the Quadratic Function -- 3.3.3 Discriminant -- 3.3.4 Applications in Economics -- 3.3.4.1 The Cost Function -- 3.4 Cubic Function -- 3.4.1 How to Solve Cubic Equations -- 3.4.2 Applications in Economics -- 3.4.2.1 The Cost Function -- 3.5 Polynomials of Degree Greater Than Three -- 3.6 Logarithmic and Exponential Functions -- 3.6.1 What is a Logarithm? -- 3.6.2 Logarithms and Exponents -- 3.6.3 The Natural Logarithm -- 3.6.4 The Natural Logarithmic Function -- 3.6.4.1 How to Solve Logarithmic Equation -- 3.6.5 Applications in Economics</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">3.6.5.1 Logarithms and Growth -- 3.6.5.2 Logarithms and Geometric Mean -- 3.6.5.3 Logarithms and Econometrics -- 3.6.6 Exponential Function -- 3.6.6.1 What is e ? -- 3.6.6.2 How to Solve Exponential Equations -- 3.6.7 Applications in Economics -- 3.6.7.1 Exponential and Investment -- 3.6.7.2 Exponential Growth and Logistic Growth -- 3.7 Radical Function -- 3.7.1 How to Solve Radical Equation -- 3.7.2 Find the Domain of a Radical Function -- 3.7.3 Radicals and Rational Exponents -- 3.7.4 Applications in Economics -- 3.7.4.1 Production Function with a Single Input -- 3.8 Rational Function -- 3.8.1 Intercepts and Asymptotes -- 3.8.2 Applications in Economics -- 3.8.2.1 Indifference Curve -- 3.8.2.2 A ''Work'' Example -- 3.9 Exercises -- 3.9.1 Exercise 1 -- 3.9.2 Exercise 2 -- 3.9.3 Exercise 3 -- 3.9.4 Exercise 4 -- 3.9.5 Exercise 5 -- 4 Differential Calculus -- 4.1 What is the Meaning of Derivatives? -- 4.2 The Limit of a Function -- 4.3 Limits, Derivatives and Slope -- 4.3.1 Newton-Raphson Method -- 4.4 Notation of Derivatives -- 4.5 Differentials -- 4.6 Rules of Differentiation -- 4.6.1 Power Rule -- 4.6.2 Product Rule -- 4.6.3 Quotient Rule -- 4.6.4 Chain Rule -- 4.6.4.1 Implicit Differentiation -- 4.6.5 Radicals Differentiation -- 4.6.6 Logarithmic Differentiation -- 4.6.7 Exponential Differentiation -- 4.6.7.1 Exponential Growth and Logistic Growth -- 4.6.8 Derivatives of Elementary Functions -- 4.7 Derivatives and Inverse Functions -- 4.8 Tangent Line to the Function -- 4.9 Points of Minimum, Maximum and Inflection -- 4.10 Taylor Expansion -- 4.10.1 Nth-Derivative Test -- 4.10.2 Newton-Raphson Method -- 4.11 L'Hôpital Theorem -- 4.12 Derivatives with R -- 4.13 Taylor Expansion with R -- 4.14 Applications in Economics -- 4.14.1 Marginal Cost -- 4.14.1.1 Coefficients of a Cubic Cost Function -- 4.14.2 Marginal Cost and Average Cost</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">4.14.3 Profit Maximization -- 4.14.4 Elasticity -- 4.15 Exercise -- 4.15.1 Exercise 1 -- 4.15.2 Exercise 2 -- 4.15.3 Exercise 3 -- 5 Integral Calculus -- 5.1 Indefinite Integrals -- 5.1.1 Anti-derivative Process -- 5.1.1.1 Fundamental Integrals -- 5.1.1.2 Integration by Substitution -- 5.1.1.3 Integration by Parts -- 5.1.1.4 Partial Fractions -- 5.2 Definite Integrals -- 5.2.1 Area Under a Curve -- 5.2.2 Area Between Two Lines -- 5.3 Fundamental Theorem of Calculus -- 5.4 Improper Integrals and Convergence -- 5.4.1 Case 1: Convergence -- 5.4.2 Case 2: Divergence -- 5.5 Integration with R -- 5.6 Applications in Economics -- 5.6.1 Marginal Cost and Cost Function -- 5.6.2 Example: A Problem -- 5.6.3 The Surplus of Consumer and Producer -- 5.7 Exercise -- 6 Multivariable Calculus -- 6.1 Functions of Several Variables -- 6.1.1 Applications in Economics -- 6.1.1.1 Complementary Goods and Substitute Goods -- 6.1.1.2 The Cobb-Douglas Function -- 6.1.1.3 The Constant Elasticity of Substitution (CES) Function -- 6.1.1.4 The Cobb-Douglas Function as a Special Case of the CES Function -- 6.2 Partial and Total Derivatives -- 6.2.1 Partial Derivatives -- 6.2.1.1 Gradient Vector -- 6.2.1.2 Jacobian Matrix -- 6.2.1.3 Hessian Matrix -- 6.2.2 Total Derivatives -- 6.2.3 Derivatives with R -- 6.2.4 Applications in Economics -- 6.2.4.1 Marginal Product of Labour and Capital -- 6.2.4.2 The Law of Diminishing Marginal Productivity -- 6.2.4.3 An Application with the Jacobian -- 6.3 Unconstrained Optimization -- 6.3.1 First Order Condition -- 6.3.2 Second Order Condition -- 6.3.2.1 Concavity and Convexity -- 6.3.3 Optimization with R -- 6.3.4 Applications in Economics -- 6.3.4.1 Multi-product Firm -- 6.3.4.2 Ordinary Least Square -- 6.4 Integration with Multiple Variables -- 6.5 Exercises -- 6.5.1 Exercise 1 -- 6.5.2 Exercise 2 -- 7 Constrained Optimization</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">7.1 Equality Constraints -- 7.1.1 First-Order Condition -- 7.1.2 Multiple Equality Constraints -- 7.1.3 Lagrange Multiplier -- 7.1.3.1 A Mathematical Interpretation -- 7.1.3.2 An Economic Interpretation -- 7.1.4 Second-Order Conditions -- 7.2 Inequality Constraints -- 7.2.1 Kuhn-Tucker Conditions -- 7.3 Constrained Optimization with R -- 7.4 Applications in Economics -- 7.4.1 Utility Maximization Problem -- 7.4.2 Firm's Cost Minimization Problem -- 7.4.3 Transportation Problem -- 7.4.4 CGE Model with R -- 7.4.4.1 Shoven-Whalley Model Without Taxes -- 7.4.4.2 Solving the Model with R -- 7.5 Exercise -- Part II Introduction to Mathematics for Dynamic Economics -- 8 Trigonometry -- 8.1 Right Triangles and Angles -- 8.2 Trigonometric Functions -- 8.3 Sum and Differences of Angles -- 8.4 Derivatives of Trigonometric Functions -- 9 Complex Numbers -- 9.1 Set of Complex Numbers -- 9.2 Complex Numbers: Real Part and Imaginary Part -- 9.3 Arithmetic Operations -- 9.4 Geometric Interpretation and Polar Form -- 9.5 Exponential Form -- 10 Difference Equations -- 10.1 First-Order Linear Difference Equations -- 10.1.1 Solution by Iteration -- 10.1.2 Solution by General Method -- 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spelling	Porto, Massimiliano Verfasser aut Introduction to Mathematics for Economics with R. 1st ed Cham Springer International Publishing AG 2022 ©2022 1 Online-Ressource (866 Seiten) txt rdacontent c rdamedia cr rdacarrier Description based on publisher supplied metadata and other sources Intro -- Preface -- Contents -- List of Figures -- List of Tables -- 1 Introduction to R -- 1.1 Installing R -- 1.2 Installing RStudio -- 1.3 Introduction to RStudio -- 1.3.1 Launching a New Project -- 1.3.2 Opening an R Script -- 1.4 Packages to Install -- 1.4.1 How to Install a Package -- 1.4.2 How to Load a Package -- 1.5 Good Practice and Notation -- 1.5.1 How to Read the Code -- 1.6 8 Key-Points Regarding R -- 1.6.1 The Assignment Operator -- 1.6.2 The Class of Objects -- 1.6.3 Case Sensitiveness -- 1.6.4 The c() Function -- 1.6.5 Square Bracket Operator [ ] -- 1.6.6 Loop and Vectorization -- 1.6.7 Functions -- 1.6.8 Errors -- 1.6.8.1 Syntax Errors -- 1.6.8.2 class() Type Errors -- 1.6.8.3 Warning Message -- 1.6.8.4 No-Error Message Error -- 1.7 An Example with R -- 1.8 Exercise -- 1.8.1 Exercise 1 -- 1.8.2 Exercise 2 -- Part I Introduction to Mathematics for Static Economics -- 2 Linear Algebra -- 2.1 Set, Group, Ring, Field: Short Overview -- 2.2 Vectors -- 2.2.1 Vector Space -- 2.2.1.1 Properties of Vector Space -- 2.2.1.2 Vector Notation -- 2.2.2 Vector Representation in Two and Three Dimensions -- 2.2.3 Inner Product -- 2.2.4 Outer Product -- 2.2.5 Component Form, Magnitude and Unit Vector -- 2.2.6 Parallel and Orthogonal Vectors -- 2.2.7 Vector Projection -- 2.2.8 Linear Independence -- 2.3 Matrices -- 2.3.1 Matrix Operations -- 2.3.1.1 Addition -- 2.3.1.2 Multiplication -- 2.3.1.3 Transpose -- 2.3.2 Symmetric Matrix -- 2.3.3 Diagonal Matrix and Identity Matrix -- 2.3.3.1 Trace of a Square Matrix -- 2.3.4 Triangular Matrix -- 2.3.5 Idempotent Matrix -- 2.3.6 The Inverse of a Matrix -- 2.3.7 System of Linear Equations -- 2.3.7.1 System of Linear Equations and Matrices -- 2.3.7.2 Gauss Elimination and Gauss-Jordan Elimination -- 2.3.7.3 The Rank of a Matrix -- 2.3.8 Determinant -- 2.3.8.1 The Determinant of a 2 2 Matrix 2.3.8.2 Laplace Expansion Method -- 2.3.8.3 The Determinant and the Matrix Inverse -- 2.3.8.4 Cramer's Rule -- 2.3.9 Eigenvalues and Eigenvectors -- 2.3.9.1 Diagonalization and Jordan Canonical Form -- 2.3.10 Partitioned Matrix -- 2.3.11 Kronecker Product -- 2.3.12 Definiteness of Matrices -- 2.3.13 Decomposition -- 2.3.13.1 Spectral Decomposition -- 2.3.13.2 Singular Value Decomposition (SVD) -- 2.3.13.3 Cholesky Decomposition -- 2.3.13.4 QR Decomposition -- 2.4 Applications in Economics -- 2.4.1 Budget Set -- 2.4.2 Applying Cramer's Rule to the IS-LM Model -- 2.4.3 Leontief Input-Output Model -- 2.4.4 Network Analysis -- 2.4.5 Linear Model and the Dummy Variable Trap -- 2.5 Exercises -- 2.5.1 Exercise 1 -- 2.5.2 Exercise 2 -- 2.5.3 Exercise 3 -- 2.5.4 Exercise 4 -- 2.5.5 Exercise 5 -- 2.5.6 Exercise 6 -- 2.5.7 Exercise 7 -- 3 Functions of One Variable -- 3.1 What is a Function? -- 3.1.1 Domain and Range -- 3.1.2 Monotonicity, Boundedness and Extrema -- 3.1.3 Convex and Concave Functions -- 3.1.4 Function Operations -- 3.2 Linear Function -- 3.2.1 Slope of Linear Function -- 3.2.2 Applications in Economics -- 3.2.2.1 The Cost Function -- 3.2.2.2 Break-Even -- 3.2.2.3 Mark-Up and Margin -- 3.2.2.4 Linear Models in Econometrics -- 3.3 Quadratic Function -- 3.3.1 Roots and Vertex -- 3.3.2 The Graph of the Quadratic Function -- 3.3.3 Discriminant -- 3.3.4 Applications in Economics -- 3.3.4.1 The Cost Function -- 3.4 Cubic Function -- 3.4.1 How to Solve Cubic Equations -- 3.4.2 Applications in Economics -- 3.4.2.1 The Cost Function -- 3.5 Polynomials of Degree Greater Than Three -- 3.6 Logarithmic and Exponential Functions -- 3.6.1 What is a Logarithm? -- 3.6.2 Logarithms and Exponents -- 3.6.3 The Natural Logarithm -- 3.6.4 The Natural Logarithmic Function -- 3.6.4.1 How to Solve Logarithmic Equation -- 3.6.5 Applications in Economics 3.6.5.1 Logarithms and Growth -- 3.6.5.2 Logarithms and Geometric Mean -- 3.6.5.3 Logarithms and Econometrics -- 3.6.6 Exponential Function -- 3.6.6.1 What is e ? -- 3.6.6.2 How to Solve Exponential Equations -- 3.6.7 Applications in Economics -- 3.6.7.1 Exponential and Investment -- 3.6.7.2 Exponential Growth and Logistic Growth -- 3.7 Radical Function -- 3.7.1 How to Solve Radical Equation -- 3.7.2 Find the Domain of a Radical Function -- 3.7.3 Radicals and Rational Exponents -- 3.7.4 Applications in Economics -- 3.7.4.1 Production Function with a Single Input -- 3.8 Rational Function -- 3.8.1 Intercepts and Asymptotes -- 3.8.2 Applications in Economics -- 3.8.2.1 Indifference Curve -- 3.8.2.2 A ''Work'' Example -- 3.9 Exercises -- 3.9.1 Exercise 1 -- 3.9.2 Exercise 2 -- 3.9.3 Exercise 3 -- 3.9.4 Exercise 4 -- 3.9.5 Exercise 5 -- 4 Differential Calculus -- 4.1 What is the Meaning of Derivatives? -- 4.2 The Limit of a Function -- 4.3 Limits, Derivatives and Slope -- 4.3.1 Newton-Raphson Method -- 4.4 Notation of Derivatives -- 4.5 Differentials -- 4.6 Rules of Differentiation -- 4.6.1 Power Rule -- 4.6.2 Product Rule -- 4.6.3 Quotient Rule -- 4.6.4 Chain Rule -- 4.6.4.1 Implicit Differentiation -- 4.6.5 Radicals Differentiation -- 4.6.6 Logarithmic Differentiation -- 4.6.7 Exponential Differentiation -- 4.6.7.1 Exponential Growth and Logistic Growth -- 4.6.8 Derivatives of Elementary Functions -- 4.7 Derivatives and Inverse Functions -- 4.8 Tangent Line to the Function -- 4.9 Points of Minimum, Maximum and Inflection -- 4.10 Taylor Expansion -- 4.10.1 Nth-Derivative Test -- 4.10.2 Newton-Raphson Method -- 4.11 L'Hôpital Theorem -- 4.12 Derivatives with R -- 4.13 Taylor Expansion with R -- 4.14 Applications in Economics -- 4.14.1 Marginal Cost -- 4.14.1.1 Coefficients of a Cubic Cost Function -- 4.14.2 Marginal Cost and Average Cost 4.14.3 Profit Maximization -- 4.14.4 Elasticity -- 4.15 Exercise -- 4.15.1 Exercise 1 -- 4.15.2 Exercise 2 -- 4.15.3 Exercise 3 -- 5 Integral Calculus -- 5.1 Indefinite Integrals -- 5.1.1 Anti-derivative Process -- 5.1.1.1 Fundamental Integrals -- 5.1.1.2 Integration by Substitution -- 5.1.1.3 Integration by Parts -- 5.1.1.4 Partial Fractions -- 5.2 Definite Integrals -- 5.2.1 Area Under a Curve -- 5.2.2 Area Between Two Lines -- 5.3 Fundamental Theorem of Calculus -- 5.4 Improper Integrals and Convergence -- 5.4.1 Case 1: Convergence -- 5.4.2 Case 2: Divergence -- 5.5 Integration with R -- 5.6 Applications in Economics -- 5.6.1 Marginal Cost and Cost Function -- 5.6.2 Example: A Problem -- 5.6.3 The Surplus of Consumer and Producer -- 5.7 Exercise -- 6 Multivariable Calculus -- 6.1 Functions of Several Variables -- 6.1.1 Applications in Economics -- 6.1.1.1 Complementary Goods and Substitute Goods -- 6.1.1.2 The Cobb-Douglas Function -- 6.1.1.3 The Constant Elasticity of Substitution (CES) Function -- 6.1.1.4 The Cobb-Douglas Function as a Special Case of the CES Function -- 6.2 Partial and Total Derivatives -- 6.2.1 Partial Derivatives -- 6.2.1.1 Gradient Vector -- 6.2.1.2 Jacobian Matrix -- 6.2.1.3 Hessian Matrix -- 6.2.2 Total Derivatives -- 6.2.3 Derivatives with R -- 6.2.4 Applications in Economics -- 6.2.4.1 Marginal Product of Labour and Capital -- 6.2.4.2 The Law of Diminishing Marginal Productivity -- 6.2.4.3 An Application with the Jacobian -- 6.3 Unconstrained Optimization -- 6.3.1 First Order Condition -- 6.3.2 Second Order Condition -- 6.3.2.1 Concavity and Convexity -- 6.3.3 Optimization with R -- 6.3.4 Applications in Economics -- 6.3.4.1 Multi-product Firm -- 6.3.4.2 Ordinary Least Square -- 6.4 Integration with Multiple Variables -- 6.5 Exercises -- 6.5.1 Exercise 1 -- 6.5.2 Exercise 2 -- 7 Constrained Optimization 7.1 Equality Constraints -- 7.1.1 First-Order Condition -- 7.1.2 Multiple Equality Constraints -- 7.1.3 Lagrange Multiplier -- 7.1.3.1 A Mathematical Interpretation -- 7.1.3.2 An Economic Interpretation -- 7.1.4 Second-Order Conditions -- 7.2 Inequality Constraints -- 7.2.1 Kuhn-Tucker Conditions -- 7.3 Constrained Optimization with R -- 7.4 Applications in Economics -- 7.4.1 Utility Maximization Problem -- 7.4.2 Firm's Cost Minimization Problem -- 7.4.3 Transportation Problem -- 7.4.4 CGE Model with R -- 7.4.4.1 Shoven-Whalley Model Without Taxes -- 7.4.4.2 Solving the Model with R -- 7.5 Exercise -- Part II Introduction to Mathematics for Dynamic Economics -- 8 Trigonometry -- 8.1 Right Triangles and Angles -- 8.2 Trigonometric Functions -- 8.3 Sum and Differences of Angles -- 8.4 Derivatives of Trigonometric Functions -- 9 Complex Numbers -- 9.1 Set of Complex Numbers -- 9.2 Complex Numbers: Real Part and Imaginary Part -- 9.3 Arithmetic Operations -- 9.4 Geometric Interpretation and Polar Form -- 9.5 Exponential Form -- 10 Difference Equations -- 10.1 First-Order Linear Difference Equations -- 10.1.1 Solution by Iteration -- 10.1.2 Solution by General Method -- 10.1.3 Time Path and Equilibrium -- 10.2 Second-Order Linear Difference Equations -- 10.2.1 Solution to Second-Order Linear Homogeneous Difference Equation -- 10.2.1.1 Two Distinct Real Roots (Case of D &gt -- 0 ) -- 10.2.1.2 One Real Root (or Repeated Real Roots) (Case of D = 0 ) -- 10.2.1.3 Complex Roots (Case of D &lt -- 0 ) -- 10.2.2 Solution to Second-Order Linear Nonhomogeneous Difference Equation -- 10.2.3 Time Path and Equilibrium -- 10.3 System of Linear Difference Equations -- 10.3.1 Equilibrium -- 10.3.2 Solution with the Powers of a Matrix -- 10.3.3 Eigenvalues Method -- 10.3.3.1 Case 1: Distinct Real Eigenvalues -- 10.3.3.2 Case 2: Repeated Real Eigenvalues 10.3.3.3 Case 3: Complex Eigenvalues Economics-Mathematical models Erscheint auch als Druck-Ausgabe Porto, Massimiliano Introduction to Mathematics for Economics with R Cham : Springer International Publishing AG,c2022 9783031052019
spellingShingle	Porto, Massimiliano Introduction to Mathematics for Economics with R. Intro -- Preface -- Contents -- List of Figures -- List of Tables -- 1 Introduction to R -- 1.1 Installing R -- 1.2 Installing RStudio -- 1.3 Introduction to RStudio -- 1.3.1 Launching a New Project -- 1.3.2 Opening an R Script -- 1.4 Packages to Install -- 1.4.1 How to Install a Package -- 1.4.2 How to Load a Package -- 1.5 Good Practice and Notation -- 1.5.1 How to Read the Code -- 1.6 8 Key-Points Regarding R -- 1.6.1 The Assignment Operator -- 1.6.2 The Class of Objects -- 1.6.3 Case Sensitiveness -- 1.6.4 The c() Function -- 1.6.5 Square Bracket Operator [ ] -- 1.6.6 Loop and Vectorization -- 1.6.7 Functions -- 1.6.8 Errors -- 1.6.8.1 Syntax Errors -- 1.6.8.2 class() Type Errors -- 1.6.8.3 Warning Message -- 1.6.8.4 No-Error Message Error -- 1.7 An Example with R -- 1.8 Exercise -- 1.8.1 Exercise 1 -- 1.8.2 Exercise 2 -- Part I Introduction to Mathematics for Static Economics -- 2 Linear Algebra -- 2.1 Set, Group, Ring, Field: Short Overview -- 2.2 Vectors -- 2.2.1 Vector Space -- 2.2.1.1 Properties of Vector Space -- 2.2.1.2 Vector Notation -- 2.2.2 Vector Representation in Two and Three Dimensions -- 2.2.3 Inner Product -- 2.2.4 Outer Product -- 2.2.5 Component Form, Magnitude and Unit Vector -- 2.2.6 Parallel and Orthogonal Vectors -- 2.2.7 Vector Projection -- 2.2.8 Linear Independence -- 2.3 Matrices -- 2.3.1 Matrix Operations -- 2.3.1.1 Addition -- 2.3.1.2 Multiplication -- 2.3.1.3 Transpose -- 2.3.2 Symmetric Matrix -- 2.3.3 Diagonal Matrix and Identity Matrix -- 2.3.3.1 Trace of a Square Matrix -- 2.3.4 Triangular Matrix -- 2.3.5 Idempotent Matrix -- 2.3.6 The Inverse of a Matrix -- 2.3.7 System of Linear Equations -- 2.3.7.1 System of Linear Equations and Matrices -- 2.3.7.2 Gauss Elimination and Gauss-Jordan Elimination -- 2.3.7.3 The Rank of a Matrix -- 2.3.8 Determinant -- 2.3.8.1 The Determinant of a 2 2 Matrix 2.3.8.2 Laplace Expansion Method -- 2.3.8.3 The Determinant and the Matrix Inverse -- 2.3.8.4 Cramer's Rule -- 2.3.9 Eigenvalues and Eigenvectors -- 2.3.9.1 Diagonalization and Jordan Canonical Form -- 2.3.10 Partitioned Matrix -- 2.3.11 Kronecker Product -- 2.3.12 Definiteness of Matrices -- 2.3.13 Decomposition -- 2.3.13.1 Spectral Decomposition -- 2.3.13.2 Singular Value Decomposition (SVD) -- 2.3.13.3 Cholesky Decomposition -- 2.3.13.4 QR Decomposition -- 2.4 Applications in Economics -- 2.4.1 Budget Set -- 2.4.2 Applying Cramer's Rule to the IS-LM Model -- 2.4.3 Leontief Input-Output Model -- 2.4.4 Network Analysis -- 2.4.5 Linear Model and the Dummy Variable Trap -- 2.5 Exercises -- 2.5.1 Exercise 1 -- 2.5.2 Exercise 2 -- 2.5.3 Exercise 3 -- 2.5.4 Exercise 4 -- 2.5.5 Exercise 5 -- 2.5.6 Exercise 6 -- 2.5.7 Exercise 7 -- 3 Functions of One Variable -- 3.1 What is a Function? -- 3.1.1 Domain and Range -- 3.1.2 Monotonicity, Boundedness and Extrema -- 3.1.3 Convex and Concave Functions -- 3.1.4 Function Operations -- 3.2 Linear Function -- 3.2.1 Slope of Linear Function -- 3.2.2 Applications in Economics -- 3.2.2.1 The Cost Function -- 3.2.2.2 Break-Even -- 3.2.2.3 Mark-Up and Margin -- 3.2.2.4 Linear Models in Econometrics -- 3.3 Quadratic Function -- 3.3.1 Roots and Vertex -- 3.3.2 The Graph of the Quadratic Function -- 3.3.3 Discriminant -- 3.3.4 Applications in Economics -- 3.3.4.1 The Cost Function -- 3.4 Cubic Function -- 3.4.1 How to Solve Cubic Equations -- 3.4.2 Applications in Economics -- 3.4.2.1 The Cost Function -- 3.5 Polynomials of Degree Greater Than Three -- 3.6 Logarithmic and Exponential Functions -- 3.6.1 What is a Logarithm? -- 3.6.2 Logarithms and Exponents -- 3.6.3 The Natural Logarithm -- 3.6.4 The Natural Logarithmic Function -- 3.6.4.1 How to Solve Logarithmic Equation -- 3.6.5 Applications in Economics 3.6.5.1 Logarithms and Growth -- 3.6.5.2 Logarithms and Geometric Mean -- 3.6.5.3 Logarithms and Econometrics -- 3.6.6 Exponential Function -- 3.6.6.1 What is e ? -- 3.6.6.2 How to Solve Exponential Equations -- 3.6.7 Applications in Economics -- 3.6.7.1 Exponential and Investment -- 3.6.7.2 Exponential Growth and Logistic Growth -- 3.7 Radical Function -- 3.7.1 How to Solve Radical Equation -- 3.7.2 Find the Domain of a Radical Function -- 3.7.3 Radicals and Rational Exponents -- 3.7.4 Applications in Economics -- 3.7.4.1 Production Function with a Single Input -- 3.8 Rational Function -- 3.8.1 Intercepts and Asymptotes -- 3.8.2 Applications in Economics -- 3.8.2.1 Indifference Curve -- 3.8.2.2 A ''Work'' Example -- 3.9 Exercises -- 3.9.1 Exercise 1 -- 3.9.2 Exercise 2 -- 3.9.3 Exercise 3 -- 3.9.4 Exercise 4 -- 3.9.5 Exercise 5 -- 4 Differential Calculus -- 4.1 What is the Meaning of Derivatives? -- 4.2 The Limit of a Function -- 4.3 Limits, Derivatives and Slope -- 4.3.1 Newton-Raphson Method -- 4.4 Notation of Derivatives -- 4.5 Differentials -- 4.6 Rules of Differentiation -- 4.6.1 Power Rule -- 4.6.2 Product Rule -- 4.6.3 Quotient Rule -- 4.6.4 Chain Rule -- 4.6.4.1 Implicit Differentiation -- 4.6.5 Radicals Differentiation -- 4.6.6 Logarithmic Differentiation -- 4.6.7 Exponential Differentiation -- 4.6.7.1 Exponential Growth and Logistic Growth -- 4.6.8 Derivatives of Elementary Functions -- 4.7 Derivatives and Inverse Functions -- 4.8 Tangent Line to the Function -- 4.9 Points of Minimum, Maximum and Inflection -- 4.10 Taylor Expansion -- 4.10.1 Nth-Derivative Test -- 4.10.2 Newton-Raphson Method -- 4.11 L'Hôpital Theorem -- 4.12 Derivatives with R -- 4.13 Taylor Expansion with R -- 4.14 Applications in Economics -- 4.14.1 Marginal Cost -- 4.14.1.1 Coefficients of a Cubic Cost Function -- 4.14.2 Marginal Cost and Average Cost 4.14.3 Profit Maximization -- 4.14.4 Elasticity -- 4.15 Exercise -- 4.15.1 Exercise 1 -- 4.15.2 Exercise 2 -- 4.15.3 Exercise 3 -- 5 Integral Calculus -- 5.1 Indefinite Integrals -- 5.1.1 Anti-derivative Process -- 5.1.1.1 Fundamental Integrals -- 5.1.1.2 Integration by Substitution -- 5.1.1.3 Integration by Parts -- 5.1.1.4 Partial Fractions -- 5.2 Definite Integrals -- 5.2.1 Area Under a Curve -- 5.2.2 Area Between Two Lines -- 5.3 Fundamental Theorem of Calculus -- 5.4 Improper Integrals and Convergence -- 5.4.1 Case 1: Convergence -- 5.4.2 Case 2: Divergence -- 5.5 Integration with R -- 5.6 Applications in Economics -- 5.6.1 Marginal Cost and Cost Function -- 5.6.2 Example: A Problem -- 5.6.3 The Surplus of Consumer and Producer -- 5.7 Exercise -- 6 Multivariable Calculus -- 6.1 Functions of Several Variables -- 6.1.1 Applications in Economics -- 6.1.1.1 Complementary Goods and Substitute Goods -- 6.1.1.2 The Cobb-Douglas Function -- 6.1.1.3 The Constant Elasticity of Substitution (CES) Function -- 6.1.1.4 The Cobb-Douglas Function as a Special Case of the CES Function -- 6.2 Partial and Total Derivatives -- 6.2.1 Partial Derivatives -- 6.2.1.1 Gradient Vector -- 6.2.1.2 Jacobian Matrix -- 6.2.1.3 Hessian Matrix -- 6.2.2 Total Derivatives -- 6.2.3 Derivatives with R -- 6.2.4 Applications in Economics -- 6.2.4.1 Marginal Product of Labour and Capital -- 6.2.4.2 The Law of Diminishing Marginal Productivity -- 6.2.4.3 An Application with the Jacobian -- 6.3 Unconstrained Optimization -- 6.3.1 First Order Condition -- 6.3.2 Second Order Condition -- 6.3.2.1 Concavity and Convexity -- 6.3.3 Optimization with R -- 6.3.4 Applications in Economics -- 6.3.4.1 Multi-product Firm -- 6.3.4.2 Ordinary Least Square -- 6.4 Integration with Multiple Variables -- 6.5 Exercises -- 6.5.1 Exercise 1 -- 6.5.2 Exercise 2 -- 7 Constrained Optimization 7.1 Equality Constraints -- 7.1.1 First-Order Condition -- 7.1.2 Multiple Equality Constraints -- 7.1.3 Lagrange Multiplier -- 7.1.3.1 A Mathematical Interpretation -- 7.1.3.2 An Economic Interpretation -- 7.1.4 Second-Order Conditions -- 7.2 Inequality Constraints -- 7.2.1 Kuhn-Tucker Conditions -- 7.3 Constrained Optimization with R -- 7.4 Applications in Economics -- 7.4.1 Utility Maximization Problem -- 7.4.2 Firm's Cost Minimization Problem -- 7.4.3 Transportation Problem -- 7.4.4 CGE Model with R -- 7.4.4.1 Shoven-Whalley Model Without Taxes -- 7.4.4.2 Solving the Model with R -- 7.5 Exercise -- Part II Introduction to Mathematics for Dynamic Economics -- 8 Trigonometry -- 8.1 Right Triangles and Angles -- 8.2 Trigonometric Functions -- 8.3 Sum and Differences of Angles -- 8.4 Derivatives of Trigonometric Functions -- 9 Complex Numbers -- 9.1 Set of Complex Numbers -- 9.2 Complex Numbers: Real Part and Imaginary Part -- 9.3 Arithmetic Operations -- 9.4 Geometric Interpretation and Polar Form -- 9.5 Exponential Form -- 10 Difference Equations -- 10.1 First-Order Linear Difference Equations -- 10.1.1 Solution by Iteration -- 10.1.2 Solution by General Method -- 10.1.3 Time Path and Equilibrium -- 10.2 Second-Order Linear Difference Equations -- 10.2.1 Solution to Second-Order Linear Homogeneous Difference Equation -- 10.2.1.1 Two Distinct Real Roots (Case of D &gt -- 0 ) -- 10.2.1.2 One Real Root (or Repeated Real Roots) (Case of D = 0 ) -- 10.2.1.3 Complex Roots (Case of D &lt -- 0 ) -- 10.2.2 Solution to Second-Order Linear Nonhomogeneous Difference Equation -- 10.2.3 Time Path and Equilibrium -- 10.3 System of Linear Difference Equations -- 10.3.1 Equilibrium -- 10.3.2 Solution with the Powers of a Matrix -- 10.3.3 Eigenvalues Method -- 10.3.3.1 Case 1: Distinct Real Eigenvalues -- 10.3.3.2 Case 2: Repeated Real Eigenvalues 10.3.3.3 Case 3: Complex Eigenvalues Economics-Mathematical models
title	Introduction to Mathematics for Economics with R.
title_auth	Introduction to Mathematics for Economics with R.
title_exact_search	Introduction to Mathematics for Economics with R.
title_exact_search_txtP	Introduction to Mathematics for Economics with R.
title_full	Introduction to Mathematics for Economics with R.
title_fullStr	Introduction to Mathematics for Economics with R.
title_full_unstemmed	Introduction to Mathematics for Economics with R.
title_short	Introduction to Mathematics for Economics with R.
title_sort	introduction to mathematics for economics with r
topic	Economics-Mathematical models
topic_facet	Economics-Mathematical models
work_keys_str_mv	AT portomassimiliano introductiontomathematicsforeconomicswithr

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