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# Calculus-I

Course Code: CAL-111

Title: Calculus-I

Credit Hours: 03

Prerequisite: Mathematics at Secondary Level

## Course Objectives:

To prepare the students with the essential tools of algebra/calculus to apply the concepts and the situations in Economics.

## Preliminaries

·         Demystifying Mathematics and Mathematical Economics

o   Mathematics vs. Non- Mathematical Economics

o   Mathematical Economics versus Econometrics.

·         Ingredients of a Mathematical Model:

o   Variables and Economic Variables

o   Constants

o   Parameters.

·         A Few Aspects of Logic: Proportions, Implications and Necessary and Sufficient Conditions.

·         The Real-Number System.

·         Use of Sets in Economics.

·         Cartesian Coordinates.

## Functions and Equations:

·         Functions and Relations

·         Domain and Range

o   Schultz Demand Function

o   Laffer Curve.

o   Population and Consumption Functions

·         Profit Function of a Monopoly

·         Cubic Cost Functions

·         Rectangular Hyperbolic Functions

·         Population Growth using General Exponential Functions

·         Population Growth using Natural Exponential Functions

## Equations and Identities

·         Definitional Equations

·         Behavioral Equations

·         Conditional Equations

o   Economic examples.

·         Structural and Reduced Form Equations.

·         Partial Linear Market Equilibrium and effects of Tax, shifts in Demand and supply curves.

·         A Nonlinear Model, Numerical Solution of Two Good Case.

·         National Income Equilibrium, extension of Induced and Autonomous Tax, Proportion of Government Expenditure.

## Matrices

·         Matrices and Vectors

·         Matrix Operations.

1.      Commutative Law

2.      Associative Law

3.      Distributive Law

·         Vector Operations of Matrix

·         Transpose of Matrix

·         Cofactors of Matrix

·         Determinant of a Matrix

·         Inverse of a Matrix

·         Minors and Cofactors.

·         Market Model Analysis using Matrix Inversion Method.

·         National Income Analysis using Matrix Inversion Method.

·         Market Model and National Income Determination using Cramer’s Rule.

## Homogeneous Functions

·         Homogeneous Functions, Homogeneity of CES Production Function

·         Cobb-Douglas Production Function and Returns to Scale.

·         Expansion Path using First Order Condition.

·         Homothetic Functions, Homotheticity of Cobb-Douglas Production Function.

## Differentiation

·         The Need and Nature of Comparative Statics

·         Concept of Limit and Continuity

·         Rate of Change

·         Slope & Derivative

·         Differentiation Rules for Single Variable Functions:

1.      Constant Function Rule

2.      Power Function Rule

3.      Sum-Difference Rule of Differentiation

Numerical Analysis of Cost Function

4.      Product Rule of Differentiation

5.      Quotient Rule of Differentiation

Marginal Cost, Marginal Revenue and Marginal Product Analysis.

6.      Chain Rule

Marginal Revenue Product of Labor (MRPL) Analysis.

## Recommended Books:

·                     Budnick, Frank, Applied Mathematics for Business, Economics and Social Sciences. – Latest Edition.

·                     Chiang A.C. Fundamental Methods of Mathematical Economics McGraw Hill –Latest Edition.

·                     Dowling Edward T. Mathematics for Economics Schaum Series, Latest Edition.

·                     Weber E. Jean, Mathematical Analysis, Business and Economic Application (latest edition), Harper and Row Publishers, New York.