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ECO606 : Mathematical Economics I

Course Overview

Course Synopsis

Mathematics is as old as man. Mathematical economics is an interesting approach to economics rather than its branch. It can include problems from microeconomics, macroeconomics, international economics, public finance etc. Mathematics for economics is comprehension of mathematical tools applied to economic situations. These tools include application of algebra on market equilibrium, application of matrices on national income analysis, application of differentiation on marginal utility/cost/product. Mathematical economics use symbols, numerical numbers, equations, identities, trigonometric ratios; calculus etc. that are more convenient to use in deductive reasoning. The use of symbols makes results concise and precise. Mathematical economics give liberty to use more and more variables in one situation. During current time, economics is highly mathematized. Lot of mathematics is now used in latest literature and research journals of economics.

Course Learning Outcomes

At the end of the course, students should be able to:

  • Know about the introduction of mathematical economics, difference between mathematical & non-mathematical economics and difference between mathematical economics versus econometrics.
  • Recognize variables and economic variables, constants and parameters, logic in mathematical economics and relevance of real-numbers in mathematical economics.
  • Know set notation, set operators in economics, laws of set operations and Cartesian coordinates in economics.
  • Understand functions, domains and ranges in a functions, constant functions, linear functions, quadratic functions, cubic functions, rational functions, rectangular hyperbolic functions, non-algebraic exponential functions, non-algebraic logarithmic functions and inverse functions.
  • Differentiate between equations and identities in economics, definitional equations, behavioral equations and conditional equations in economics.
  • Construct a partial equilibrium in linear market model and non-linear market model and general equilibrium.
  • Understand matrices and their types, array and summation forms of matrices, matrices operations, matrix division, commutative, associative, and distributive laws, vector operations, transpose of a matrix, cofactors of a matrix, adjoint of a matrix, determinant of a matrix, inverse of a matrix, Cramer’s rule, input coefficient matrix etc.
  • Know the concept of limit and continuity, rate of change, slope & derivatives.
  • Know about rules of differentiation and to apply those rules on various economics concepts.
  • Comprehend the concept of partial differential and their application on various economics concepts.
  • Comprehend higher order derivatives and their application to economic situations.
  • Learn about Young theorem and its presence in 2nd order conditions of differentiation.
  • Learn the logic of envelope theorem, Roy's identity, Hotelling's lemma and Shephard's lemma in economics.
  • Compare the differentials versus derivatives and their applications.
  • Learn the concept of total differentials and their applications.
  • Comprehend the concept of total derivatives and their applications.
  • Comprehend the concept of implicit differentiation and their applications.
  • Calculate instantaneous rate of growth, continuous vs. discrete growth,
  • Understand discounting and negative growth continuous compounding, applications of instantaneous growth.
  • Learn logarithms, their meaning and types, laws of logarithms etc.
  • Transform CES production function using logarithms, rules of differentiation of exponential and logarithmic functions.
  • Learn about concept of optimization, 1st test and 2nd test in the process of optimization, profit maximization analysis for various economic applications.
  • Know about the rationale for constrained optimization, 2nd order condition: the bordered hessian, utility maximization and consumer demand.
  • Apply optimization on production function, log-transformed CD production function, homogeneity of functions, homothetic functions etc.
  • Recognize CES production function, homogeneity of CES production function, Euler's theorem and their applications etc.

Course Calendar

Demystifying Mathematics and Mathematical Economics.1Lesson VideoTopic 001
Mathematical versus Nonmathematical Economics1Lesson VideoTopic 002
Mathematical Economics versus Econometrics.1Lesson VideoTopic 003
Ingredients of a Mathematical Model: Variables and Economic Variables.2Lesson VideoTopic 004
Ingredients of a Mathematical Model: Constants and Parameters2Lesson VideoTopic 005
A Few Aspects of Logic: Propositions, Implications and Necessary and Sufficient Conditions.2Lesson VideoTopic 006
The Real-Number System2Lesson VideoTopic 007
Use of Sets in economics: Set Notation.3Lesson VideoTopic 008
Use of Sets in economics: Operations of Sets.3Lesson VideoTopic 009
Use of Sets in economics: Laws of Operations of Sets.3Lesson VideoTopic 010
Cartesian Coordinates3Lesson VideoTopic 011
What are Functions?4Lesson VideoTopic 012
Domain and Range in a Function4Lesson VideoTopic 013
Difference between Function and Relations.4Lesson VideoTopic 014
Economic Example of Schultz Demand Function4Lesson VideoTopic 015
Economic Example of Cost Function of Cleaning Impurities from a Lake4Lesson VideoTopic 016
Economic Example of Function: Laffer Curve4Lesson VideoTopic 017
Types of Functions: Constant Functions.5Lesson VideoTopic 018
Types of Functions: Polynomial Function: Linear Functions.5Lesson VideoTopic 019
Interpreting Linear Economic Functions5Lesson VideoTopic 020
Applications of Linear Functions: Population and Consumption Functions.5Lesson VideoTopic 021
Types of Functions: Polynomial Function: Quadratic Functions.6Lesson VideoTopic 022
Quadratic Cost function and Profit Function of a Monopoly.6Lesson VideoTopic 023
Quadratic Function and Production Possibilities Frontier6Lesson VideoTopic 024
Types of Functions: Polynomial Function: Cubic Functions.6Lesson VideoTopic 025
Cubic Cost functions.6Lesson VideoTopic 026
Rational Functions7Lesson VideoTopic 027
Other Types: Rectangular Hyperbolic Function7Lesson VideoTopic 028
Other Types: Non-algebraic Exponential Functions7Lesson VideoTopic 029
Population Growth using General Exponential Functions7Lesson VideoTopic 030
Other Types: Non-algebraic Natural Exponential Functions7Lesson VideoTopic 031
Population Growth using Natural Exponential Functions7Lesson VideoTopic 032
Other Types: Non-algebraic Logarithmic Functions8Lesson VideoTopic 033
Other Types: Non-algebraic Natural Logarithmic Functions8Lesson VideoTopic 034
Rate of Growth of GNP using Logarithmic Functions8Lesson VideoTopic 035
Inverse Functions8Lesson VideoTopic 036
Functions with Two or More Independent Variables8Lesson VideoTopic 037
Surfaces and Distance in Graphs of two or more independent variables.8Lesson VideoTopic 038
Equations and Identities.9Lesson VideoTopic 039
Types of equations in Economics: Definitional Equations.9Lesson VideoTopic 040
Fiscal Surplus and Fiscal Deficit Using Equations9Lesson VideoTopic 041
Types of equations in Economics: Behavioral Equations9Lesson VideoTopic 042
Types of equations in Economics: Conditional Equation9Lesson VideoTopic 043
Structural and Reduced Form Equations9Lesson VideoTopic 044
Constructing a Partial Linear Market Equilibrium10Lesson VideoTopic 045
Solving using Elimination of Variable Method10Lesson VideoTopic 046
Shifts in Demand in Market Equilibrium10Lesson VideoTopic 047
Shifts in Supply in Market Equilibrium10Lesson VideoTopic 048
Effect of Tax on Producer on Partial Market Equilibrium.10Lesson VideoTopic 049
Effect of Tax on Consumer on Partial Market Equilibrium.10Lesson VideoTopic 050
Partial Market Equilibrium-A Nonlinear Model.11Lesson VideoTopic 051
General Market Equilibrium: General form of Two Good Case.11Lesson VideoTopic 052
General Market Equilibrium: Numerical solution of Two Good Case.11Lesson VideoTopic 053
General Market Equilibrium: n-Good Case.11Lesson VideoTopic 054
National Income Equilibrium11Lesson VideoTopic 055
National Income Equilibrium with Induced and Autonomous Tax11Lesson VideoTopic 056
National Income Equilibrium with Proportion of Government Expenditure11Lesson VideoTopic 057
Matrices and Vectors12Lesson VideoTopic 058
Matrices Operations12Lesson VideoTopic 059
Using Product of Matrices to Calculate Total Cost12Lesson VideoTopic 060
Using Product of Matrices to Calculate Total Revenue and Profit12Lesson VideoTopic 061
Question of Matrix Division.12Lesson VideoTopic 062
Commutative, Associative, and Distributive Laws.13Lesson VideoTopic 063
Vector Operations13Lesson VideoTopic 064
Transpose of a Matrix13Lesson VideoTopic 065
Cofactors of a Matrix13Lesson VideoTopic 066
Adjoint of a Matrix13Lesson VideoTopic 067
Determinant of a Matrix14Lesson VideoTopic 068
Sarrus''s rule for 3x3 order Determinant of a Matrix14Lesson VideoTopic 069
Inverse of a Matrix14Lesson VideoTopic 070
Condition(s) for Non-singularity14Lesson VideoTopic 071
Expression of National Income using Matrix Form14Lesson VideoTopic 072
Minor and Cofactors.14Lesson VideoTopic 073
Market Model Analysis Using Matrix Inversion Method.15Lesson VideoTopic 074
National Income Analysis Using Matrix Inversion Method.15Lesson VideoTopic 075
Equilibrium Prices using Matrix Inversion Method15Lesson VideoTopic 076
Solving Market Model using Cramer''s Rule.16Lesson VideoTopic 077
Equilibrium Prices using Cramer''s Rule16Lesson VideoTopic 078
National Income Determination using Cramer''s Rule.16Lesson VideoTopic 079
Input Coefficient Matrix17Lesson VideoTopic 080
Economic Meaning of Hawkins-Simon Condition17Lesson VideoTopic 081
Input-Output Analysis in case of Open Economy.17Lesson VideoTopic 082
Input-Output Analysis in case of Closed Economy.17Lesson VideoTopic 083
The Need and Nature of Comparative Statics.17Lesson VideoTopic 084
Concept of Limit and continuity.18Lesson VideoTopic 085
Rate of Change, Slope & Derivative.18Lesson VideoTopic 086
Differentiation Rules for Single variable functions: Constant Function Rule and Power Function Rule.19Lesson VideoTopic 087
Sum-Difference Rule of Differentiation.19Lesson VideoTopic 088
Sum-Difference Rule: Numerical Analysis of Cost Function19Lesson VideoTopic 089
Understanding graphs of Function and its derivatives.19Lesson VideoTopic 090
Product Rule of Differentiation.20Lesson VideoTopic 091
Relationship between Average Revenue and Marginal Revenue using Product Rule.20Lesson VideoTopic 092
Quotient Rule of Differentiation.20Lesson VideoTopic 093
Marginal Propensity to Consume via Differentiation with and without Tax20Lesson VideoTopic 094
Relationship Between Marginal-Cost and Average-Cost Functions using Quotient Rule.20Lesson VideoTopic 095
Variable and Fixed Cost components in total cost function.21Lesson VideoTopic 096
Obtaining Marginal Cost function from Average Cost function21Lesson VideoTopic 097
Marginal Cost Analysis21Lesson VideoTopic 098
Marginal Revenue Analysis21Lesson VideoTopic 099
Marginal Product Analysis21Lesson VideoTopic 100
Rules of Differentiation: Functions with different variables: Chain Rule.22Lesson VideoTopic 101
Marginal Revenue Product of Labor (MRPL) Analysis.22Lesson VideoTopic 102
Marginal Analysis of Fishery Production Function22Lesson VideoTopic 103
Inverse Function Rule22Lesson VideoTopic 104
Partial Differentiation: The Concept.23Lesson VideoTopic 105
Marginal Physical Product of Labor and Capital using Partial Derivatives.23Lesson VideoTopic 106
Marginal Utility functions using Partial Derivatives.23Lesson VideoTopic 107
Output Elasticity of Labor and Capital using Partial Derivatives.23Lesson VideoTopic 108
Money Market Analysis using Partial Derivatives.23Lesson VideoTopic 109
Partial Market Model using Partial Differentiation.24Lesson VideoTopic 110
National-Income Model using Partial Differentiation.24Lesson VideoTopic 111
Second and Higher Order Derivatives24Lesson VideoTopic 112
Economic Applications of Second Derivative: Profit Maximization Condition.24Lesson VideoTopic 113
Numerical Example of Profit Maximization Condition using Second Derivative24Lesson VideoTopic 114
Young''s Theorem25Lesson VideoTopic 115
Demand for Money Function Analysis using Partial Derivatives.25Lesson VideoTopic 116
Income Elasticity of Demand using Partial Derivatives25Lesson VideoTopic 117
Cross Price Elasticity of Demand using Partial Derivatives25Lesson VideoTopic 118
Partial Derivatives Application on Herring Production Function25Lesson VideoTopic 119
Partial Derivatives Application on Three Input Production Function25Lesson VideoTopic 120
Envelope Theorem26Lesson VideoTopic 121
Roy''s Identity26Lesson VideoTopic 122
Hotelling''s Lemma26Lesson VideoTopic 123
Shephard Lemma26Lesson VideoTopic 124
Differentials versus Derivatives27Lesson VideoTopic 125
Point Elasticity using Differentials.27Lesson VideoTopic 126
Elasticity of Rectangular Hyperbolic Demand Curve.27Lesson VideoTopic 127
Income and Price Elasticity of Demand using Differentials.27Lesson VideoTopic 128
Income Elasticity of Consumption using Differentials.27Lesson VideoTopic 129
Income and Price Elasticity of Import Function using Differentials.27Lesson VideoTopic 130
Output Elasticity of Cost27Lesson VideoTopic 131
Concept of Total Differentials.28Lesson VideoTopic 132
Savings Function and Total Differentials.28Lesson VideoTopic 133
General Utility Function and Total Differentials.28Lesson VideoTopic 134
Specific Utility Function and Total Differentials.28Lesson VideoTopic 135
Price and Rain Elasticity of Supply using Total Differentials.28Lesson VideoTopic 136
Local Price Elasticity of Foreign Demand of Exports using Total Differentials.28Lesson VideoTopic 137
Concept of Total Derivatives29Lesson VideoTopic 138
Complementarity between Coffee and Sugar Using total Derivative29Lesson VideoTopic 139
General Production Function with time-dependent Labor and Capital.29Lesson VideoTopic 140
Specific Production Function with time-dependent Labor and Capital.29Lesson VideoTopic 141
Concept of Implicit Differentiation.30Lesson VideoTopic 142
Production Function Analysis using Implicit Differentiation.30Lesson VideoTopic 143
Marginal Rate of Technical Substitution using Implicit Differentiation30Lesson VideoTopic 144
Marginal Utilities and Marginal Rate of Substitution using Implicit Differentiation.30Lesson VideoTopic 145
Nerlove-Ringstad Production Function using Implicit Differentiation.30Lesson VideoTopic 146
Marginal Products of Three Input Logarithmic Production Function30Lesson VideoTopic 147
Exponential Functions and Growth31Lesson VideoTopic 148
Instantaneous Rate of Growth31Lesson VideoTopic 149
Numerical Examples of Instantaneous Rate of Growth31Lesson VideoTopic 150
Continuous vs Discrete Growth31Lesson VideoTopic 151
Discounting and Negative Growth31Lesson VideoTopic 152
Applications of Continuous Compounding31Lesson VideoTopic 153
Logarithms: Meaning and Types32Lesson VideoTopic 154
Laws of Logarithms32Lesson VideoTopic 155
Laws of Logarithms for Transformation of CES Production Function32Lesson VideoTopic 156
Rules of Differentiation of Exponential and Logarithmic Functions.33Lesson VideoTopic 157
Optimal Timing: A Problem of Wine Storage33Lesson VideoTopic 158
Optimal Timing: A Problem of Timber Cutting33Lesson VideoTopic 159
Optimal Timing: Land Purchase for Speculation33Lesson VideoTopic 160
Optimal Timing: Art Collection33Lesson VideoTopic 161
Optimal Timing: Diamond Purchase33Lesson VideoTopic 162
Finding the Rate of Growth using Exponential and Logarithmic Functions.34Lesson VideoTopic 163
Growth of Exports of a Country34Lesson VideoTopic 164
Finding the Point Elasticity34Lesson VideoTopic 165
Rates of Growth of Population, Consumption, and Per Capita Consumption34Lesson VideoTopic 166
Rate of Growth of Per Capita Employment34Lesson VideoTopic 167
Rate of Growth of Export Earnings of a Country34Lesson VideoTopic 168
Rate of Growth of Sales34Lesson VideoTopic 169
Rate of Growth of Profit34Lesson VideoTopic 170
Concept of Optimization35Lesson VideoTopic 171
Calculus Approach to Optimization: 1st Order Test.35Lesson VideoTopic 172
Average Cost Analysis35Lesson VideoTopic 173
Calculus Approach to Optimization: 2nd Order Test35Lesson VideoTopic 174
Matrix Approach to Optimization: 2nd Order Test - Hessian35Lesson VideoTopic 175
Profit Maximization Analysis36Lesson VideoTopic 176
Numerical Example of Profit Maximization36Lesson VideoTopic 177
Profit Maximization of Technically Related Goods36Lesson VideoTopic 178
Profit Maximization of Monopolistic Firm producing Related Goods36Lesson VideoTopic 179
Profit Maximization of Firm producing Substitute Goods36Lesson VideoTopic 180
Marginal and Average Revenue Analysis37Lesson VideoTopic 181
Short Run Production Function Analysis37Lesson VideoTopic 182
Total Cost, Total Revenue and Profit Maximization37Lesson VideoTopic 183
Quadratic Profit Function Analysis38Lesson VideoTopic 184
Optimization of Exponential Revenue Function38Lesson VideoTopic 185
Optimization of More than one Choice variable.38Lesson VideoTopic 186
Economic Application on Multi-product Firm38Lesson VideoTopic 187
Economic Application on Multi-plant Firm38Lesson VideoTopic 188
Price Discrimination by Monopoly39Lesson VideoTopic 189
Price Discrimination by Monopsony39Lesson VideoTopic 190
Input Decision of a Firm39Lesson VideoTopic 191
Profit Maximization of two-product firm.39Lesson VideoTopic 192
Comparative-Static Aspects of Optimization40Lesson VideoTopic 193
Rationale for Constrained Optimization.40Lesson VideoTopic 194
Finding Stationary Values using Substitution/Elimination Method.40Lesson VideoTopic 195
Finding Stationary Values using Method of Lagrange Multiplier.40Lesson VideoTopic 196
Interpretation of the Lagrange Multiplier.40Lesson VideoTopic 197
Second Order Condition: The Bordered Hessian40Lesson VideoTopic 198
Two Period Model of Utility.41Lesson VideoTopic 199
Convexity and Concavity using Second Order Derivative.41Lesson VideoTopic 200
Utility Maximization and Consumer Demand: First Order Condition41Lesson VideoTopic 201
Utility Maximization and Consumer Demand: Second Order Condition41Lesson VideoTopic 202
Numerical Example of Utility Maximization41Lesson VideoTopic 203
Law of Equi-marginal Utility using Lagrangian Multiplier41Lesson VideoTopic 204
Economic Application of Production Function Maximization42Lesson VideoTopic 205
Economic Application on Logarithmically Transformed Production Function42Lesson VideoTopic 206
Homogeneous Functions42Lesson VideoTopic 207
Homogeneous Production Function, Average Products and Capital-Labor ratio.42Lesson VideoTopic 208
Homogeneous Production Function, Marginal Products and Capital-Labor ratio.42Lesson VideoTopic 209
Homogeneous Production Function and Euler''s Theorem42Lesson VideoTopic 210
Cobb-Douglas Production Function and Returns to Scale.43Lesson VideoTopic 211
Homogeneity and Returns to Scale of Three input Production Function.43Lesson VideoTopic 212
Least-Cost Combination in Cobb-Douglas Production Function.43Lesson VideoTopic 213
Expansion Path using First Order Condition.43Lesson VideoTopic 214
Homothetic Functions43Lesson VideoTopic 215
Homotheticity of Cobb-Douglas Production Function.43Lesson VideoTopic 216
Introducing CES Production Function44Lesson VideoTopic 217
Homogeneity of CES Production Function44Lesson VideoTopic 218
Marginal Products of CES Production Function44Lesson VideoTopic 219
Share of Labor and Capital in CES Production Function45Lesson VideoTopic 220
CES Production Function and Euler''s Theorem45Lesson VideoTopic 221
Numerical CES Production Function Calculation45Lesson VideoTopic 222
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