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A Text on Mathematical Economics
Pawas Prabhakar & Alka Budhiraja;
Paper Back Book ;  Pages : 302
1995 Edition; ISBN - 81-7188-101-7
Price : Rs. 295.00 ; US $ 30.00
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About The Book :

Mathematics has been an indispensible tool in economic analysis. Generally, most of the students are found to have, what is called, mathematics phobia. For them studying mathematical methods is somewhat unpleasant and taxing experience. Such an attitude, the authors feel (from their experience of teaching honors student), arises out of the students' inability to derive maximum benefit from a book due to complex presentation of its text. Even in cases, where presentation is simple, the lack of many solved examples minimizes the students' efficiency to grasp the concepts. An ideal way out of this would be to explain various concepts with the help of solved examples. In specially designing this textbook, the authors have made a sincere effort to incorporate the above methodology by presenting a variety of problems, after explaining every concept. These problems elucidate the concepts and their applications. Throughout the book, emphasis is given on applications rather than pure mathematical tools needed in economic analysis. Every concept in the book has been dealt with very patiently. The mathematics presented is easily accessible. However, this has not been done at the expense of rigour. The book contains more than 300 problems with solutions to give the reader sufficient practice and confidence. The book has been divided into five parts. Part - I contains the notion of sets, sequences, functions and analytical geometry with applications. Part- II is concerned with differential calculus with one independent variable. Limits and continuity, meaning of derivatives and applications of derivatives are discussed here. Part - III deals with logarithmic functions. Part - IV extends differentiation to multivariate functions. In this connection partial derivatives, differentials and optimization unconstrained as well as constrained are explained. Matrices and their application to linear models is discussed in Part - V. This volume is intended to serve as a useful reference book for honours course in economics and masters course in mathematical economics in the Indian Universities.

 

CONTENTS IN DETAIL :

Part - I

 
1. Sets and Set Theory
• Concept of a Set 
• Relationship between Sets 
• Set Operations 
• Ordered Pairs and Cartesian Product 
• Relations and Functions 
• Boundary Points and Closed and Open Sets 
• Convex Sets
2. Functions
• Continuous and Discontinuous Functions 
• Implicit and Explicit Functions 
• Single Valued and Multi-Valued Functions 
• Monotonic Functions 
• Type and Functions. 
3. Analytical Geometry 
• Straight Line 
• Parabola 
• Rectangular Hyperbola 
• Circle 
• Economic Functions and Curve Classes 
a. Demand functions and curves
b. Total Revenue functions and curves
c. Transformation functions and curves
d. Indifference Curves  
4. Arithmetic Progression and Geometric Progression 
• The Arithmetic Progression "A.P" 
• The Geometric Progression "G.P" 
• Compound Interest and Geometric Progression    
 
Part - II
 
5. Limits and Continuity
• Notion of a Sequence 
• Limit of a Sequence 
• Right Hand Limit of a Function 
• Left Hand Limit of a Function 
• Limit of a Function 
• Continuous Functions 
• Properties of Limits of Functions
6. An Introduction to Derivatives
• Derivative : Measure of Rate of Change 
• Derivative : Slope of a Curve 
• Derivative and Approximation 
• Continuity and Differentiability 
• Higher Order Derivatives 
• Derivatives in Economic Theory
7. Rules of Differentiation
• The Derivative of a Power Function 
• The Derivative of Constant times a Function 
• The Derivative of Sum (or Difference) of Function 
• The Derivative of Product of Functions 
• The Derivative of Quotient of Functions 
• The Derivative of Composite Function 
• The Derivative of an Inverse Function 
• Evaluation of Nth Order Derivative : Leibniz's Theorem
8. Application of Derivatives
• Sign of First Derivative : Increasing and Decreasing Functions 
• Sign of Second Derivative : Convex and concave Functions 
• Stationary Values : Maxima and Minima 
• Points of Inflexion 
• Nth Derivative Method 
• Monopoly Problem 
• Duopoly Problem    
 

Part - III

 
9. Exponential and Logarithmic Functions
• Form of an Exponential Function 
• Meaning of 'e' 
• Economic Applications of Exponential Functions 
Continuous Interest Compounding
Rate of Growth, Discounting and Negative Growth 
• Meaning of Logarithm 
• Rules of Logarithms 
• Logarithmic Functions 
• Application of Logarithmic Functions 
A problem of wine storage 
A problem of timber cutting
 
Part - IV
 
10. Functions of Several Variables
• Partial Derivatives 
• Second and Higher Order Partial Derivatives 
• Total Differential 
• Some Rule Concerning Differentials 
• Homogeneous Functions 
• Linearly Homogeneous Function
11. Optimization with Several Variables
• Unconstrained Optimization 
Necessary Condition for Maximum Value and Saddle Point, 
Sufficient Condition : Hessian Matrix, 
Generalization to n-variable Case, 
Economic Applications. 
• Constrained Optimization 
Necessary Condition, 
Sufficient Conditions : Bordered Hessian, 
Interpretation of Langrange Multiplier (lamda)    
 
Part - V
 
12. Matrices
• Definitions of Matrices and vectors 
• Matrix Operations 
• The Transpose and Inverse 
• Solution of Linear Equation System
13. Matrix Applications to Economic Models
• Market Model 
• National Income Model 
• National Income Model with Money 
• Leontief Input-Output Model 
 

ABOUT THE author :

Pawas Prabhakar :

Pawas Prabhakar is on the Faculty of Economics, Shri Ram College of Commerce, University of Delhi. He completed his post-graduation in Economics from Delhi School of Economics, specializing in Game Theory and Industrial Economics. He has also been a guest lecturer at the Institute of Economic Growth, Delhi on quantitative techniques in Economics.

 
Alka Budhiraja :

 

Alka Budhiraja is a Senior lecturer in the Department of Economics, Miranda House, University of Delhi. She is a post-graduate in Economics from Delhi School of Economics with specialization in Econometrics. She has a teaching experience of fourteen years of which ten years have been exclusively devoted to mathematical Economics at the under-graduate level.

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