Lahore University of Management Sciences

ECON 262 Mathematical Applications in Economics Spring Semester 2014 Instructor Kiran Arooj Room No. 253 Office Hours TBA Email kiran.naseer@lums.edu.pk Telephone - 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 Duration 110 minutes Recitation/Lab (per week) Nbr of Lec(s) Per Week None Duration - Tutorial (per week) Nbr of Lec(s) Per Week None Duration - Course Distribution Core None Elective Elective Open for Student Category All Close for Student Category None COURSE DESCRIPTION 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--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 students 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

Midterm Exam

Yes/No: Yes Combine Separate: Combined Duration: 2 hours Preferred Date: TBA Exam Specifications: Closed books and notes, help sheet not allowed, calculator usage allowed

Final Exam

Yes/No: Yes Combine Separate: Combined Duration: 2 hours Exam Specifications: Closed books and notes, help sheet not allowed, calculator usage allowed

COURSE OVERVIEW

Module Topics Recommended Readings Objectives/ Application

1 One Variable

Calculus

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. An overview of applications to production, cost, revenue, profit, demand functions and elasticity. Log and exponent functions, their properties and logarithmic derivative.

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.

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 Cramers rule and ISLM analysis via Cramers rule.

Carl P. Simon and Lawrence Blume, Mathematics for Economists; W W Norton, 1994. Chapters 8 and 9

Apply linear algebra concepts in economic models.

Lahore University of Management Sciences

3

Multivariate Calculus

Functions of several variables, level curves, isoquants, isoprofit lines, indifference curves, linear functions and matrix representation of the quadratic form. Partial differentiation and its applications including marginal utility, marginal productivity and elasticity, total derivative as a form of linearization, Hessian matrix and Youngs Theorem, implicit functions and nonlinear systems.

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

4 Optimization Techniques

Hessian matrix, definiteness, semi-definiteness, bordered matrices, concave and convex functions. 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. Application to utility and demand, profit and cost and pareto-optimum.

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.

5 Dynamical

Systems

Eigenvalues and Eigenvectors: finding Eigenvalues and Eigenvectors, their properties, difference equations, diagnolization. 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. Systems of Differential Equations: Solving linear systems via Eigenvalues and substitutions, steady states and their stability, phase diagrams.

Carl P. Simon and Lawrence Blume, Mathematics for Economists; W W Norton, 1994. Chapter 23 Alpha C. Chiang and Kevin Wainwright, Fundamental Methods of Mathematical Economics, Fourth Edition. Chapter 15 and 16 Brian S. Ferguson and G.C. Lim, Introduction to Dynamic Economic Models, Manchester University Press, 1998. Chapter 4

Understand the application of differential equations in economics

Lahore University of Management Sciences

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.

Objectives/RecommendedTopicsModuleApplicationReadings