Lahore University of Management Sciences
ECON 262 – Mathematical Applications in Economics Spring Semester 2011‐2012 Instructor Kiran Arooj Room No. 290 Office Hours TBA Email [email protected] Telephone 042‐35608120 Secretary/TA TBA TA Office Hours TBA Course URL (if any) ‐ Course Basics Credit Hours 4 Lecture(s) Nbr of Lec(s) Per Week 2 Recitation/Lab (per week) Nbr of Lec(s) Per Week None Tutorial (per week) Nbr of Lec(s) Per Week None Course Distribution Core None Elective Elective Open for Student Category All Close for Student Category None COURSE DESCRIPTION Duration Duration Duration 110 minutes ‐ ‐ While an economic model is a theoretical framework and need not necessarily be mathematical, a non-mathematical approach has
severe limitations when analyzing any even moderately complex economic situation. Thus there is a need to study mathematical
methods vis-à-vis their applications in economics.
This course provides instruction in basic tools of mathematical economics and their applications to economic analysis. Techniques
discussed include elementary algebra, linear algebra, single and multivariable calculus, optimization, equilibrium analysis,
comparative static analysis and dynamic optimization. Depth of treatment of each topic will vary according to our needs.
COURSE PREREQUISITE(S) Calculus I 
Principles of Microeconomics 
COURSE OBJECTIVES 
Boost the student’s ability to understand economic reasoning using basic mathematical tools and to understand the
link between mathematics and economics.
Lahore University of Management Sciences
Learning Outcomes Have a complete grasp over mathematical concepts used in economics. 
Ability to use mathematical concepts for problem solving in economic models. 
Grading Breakup and Policy Quiz(s): 30% (4 quizzes) Midterm Examination: 30% Final Examination: 40% Examination Detail Yes/No: Yes Combine Separate: Combined Midterm Duration: 2 hours Exam Preferred Date: TBA Exam Specifications: Closed books and notes, help sheet not allowed, calculator usage allowed Yes/No: Yes Combine Separate: Combined Final Exam Duration: 2 hours Exam Specifications: Closed books and notes, help sheet not allowed, calculator usage allowed COURSE OVERVIEW Recommended Module Topics Readings Types of functions, composition of
functions, inverse functions, slope of linear
and nonlinear functions, differentiability
and continuity, higher order derivatives,
convexity and concavity, critical points.
1 One Variable Calculus Objectives/ Application Carl P. Simon and Lawrence
Blume, Mathematics for
Economists; W W Norton, 1994.
Chapters 2, 3, 4 and 5 Understand the application of
differentiation, logs and
exponents in economics.
Carl P. Simon and Lawrence
Blume, Mathematics for
Economists; W W Norton, 1994.
Chapters 8 and 9
Apply linear algebra concepts in
economic models.
An overview of applications to production,
cost, revenue, profit, demand functions and
elasticity.
Log and exponent functions, their
properties and logarithmic derivative.
2 Linear Algebra Elementary matrix operations, laws of
matrix algebra, elementary row operations,
rank of a matrix, linear independence,
special kinds of matrices, algebra of square
matrices, determinants, inverse of a matrix,
solving linear systems using Cramer’s rule
and ISLM analysis via Cramer’s rule.
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3 Multivariate Calculus Functions of several variables, level
curves, isoquants, isoprofit lines,
indifference curves, linear functions and
matrix representation of the quadratic
form.
Carl P. Simon and Lawrence
Blume, Mathematics for
Economists; W W Norton, 1994.
Chapters 13, 14 and 15
Grasp the techniques of
multivariate calculus and learn to
apply them in economic problems
Partial differentiation and its applications
including marginal utility, marginal
productivity and elasticity, total derivative
as a form of linearization, Hessian matrix
and Young’s Theorem, implicit functions
and nonlinear systems.
Hessian matrix, definiteness, semidefiniteness, bordered matrices, concave
and quasi-concave functions.
4 Optimization Techniques Carl P. Simon and Lawrence
Blume, Mathematics for
Economists; W W Norton, 1994.
Chapters 16, 17, 18, 19, 20, 21
and 22
Use optimization techniques to
solve maximization and
minimization problems in
economics.
Eigenvalues and Eigenvectors: finding
Eigenvalues and Eigenvectors, their
properties, difference equations,
diagnolization.
Carl P. Simon and Lawrence
Blume, Mathematics for
Economists; W W Norton, 1994.
Chapter 23
Understand the application of
differential equations in
economics
Ordinary Differential Equations: solving
linear first order and second order
differential equations, homogenous and
non-homogenous equations, phase
diagrams and stability conditions and
application to the Solow growth model.
Alpha C. Chiang and Kevin
Wainwright, Fundamental
Methods of Mathematical
Economics, Fourth Edition.
Chapter 15 and 16
Unconstrained optimization: sufficient and
necessary conditions, global maxima and
minima, application to profit
maximization, discriminating monopolist
and least squares.
Constrained optimization: Types of
constraints, Lagrange multiplier, solving
models with several equality constraints,
solving models with inequality constraints,
Kuhn Tucker conditions.
Application to utility and demand, profit
and cost and pareto-optimum.
5 Dynamical Systems Systems of Differential Equations: Solving
linear systems via Eigenvalues and
substitutions, steady states and their
stability, phase diagrams.
Brian S. Ferguson and G.C. Lim,
Introduction to Dynamic
Economic Models, Manchester
University Press, 1998.
Chapter 4
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Textbook(s)/Supplementary Readings Principle Text:
Carl P. Simon and Lawrence Blume, Mathematics for Economists; W W Norton, 1994.
Supplementary Text:
Alpha C. Chiang and Kevin Wainwright, Fundamental Methods of Mathematical Economics, Fourth Edition.
Brian S. Ferguson and G.C. Lim, Introduction to Dynamic Economic Models, Manchester University Press, 1998.