Economics 590  Fundamentals of Quantitative Economic Analysis I
(8:00-8:50, MWF, BE 313)


Instructor: William H. Hoyt
Professor of Economics
    Office:    335AZ Gatton Business & Economics Bldg.
                  Lexington, KY 40506-0034
    Phone:   (859) 257-2518
    Office Hours: 9:15 - 10:30, WF
    Email: whoyt@uky.edu
    Fax:       (859) 323-1920
 


Syllabus (pdf) Course Description Text and Readings
Grading and Course Assignments Tentative Course Outline

For Current Students Only
Grades and Scores available (by ID)



Current and Future Assignments

Friday, November 5, 2004

Topics:
Constrained Optimization: Second Order Conditions

 Readings:
Simon & Blume, 19.3
Hoyt, Lecture 10.7

 
 

Monday, November 8, 2004

Topics:
Homothetic and Homogeneous Functions

Readings:
Simon & Blume, 20; Hoyt, Lecture 11








Previous Assignment

Monday, November 1, 2004

Topics:
Constrained Optimization: Minimization
Envelope Theorem, LaGrange Multipliers

Readings:
Simon & Blume, 18.5, 19.1 – 19.2

Hoyt, Lecture 10.5-10.6

 Wednesday, November 3, 2004

Topics:
Second Order Conditions

Readings:
Simon & Blume, 19.3

Hoyt, Lecture 10.7

Monday, October 25, 2004

Topics:
Constrained Optimization: Inequality Constraints and Kuhn-Tucker Conditions
Simon & Blume, 18.3 – 18.6

 
Wednesday, October 27, 2004
 Topics: LaGrange Multiplier and the Envelope Theorem
 
Readings: 19.1 – 19.2


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Wednesday, October 20, 2004

Topics:

Review of Exam 1

Examples of Unconstrained Optimization

Constrained Optimization: Equality Constraints

Readings:

Simon & Blume, 18.1 – 18.2

Hoyt, Lecture 10: Constrained Optimization

 

Friday, October 20, 2004

Topics:

Constrained Optimization: Inequality Constraints

Simon & Blume, 18.3 – 18.4

Wednesday, October 6, 2004

Topics:
Shape of Functions

 Readings:
Simon and Blume, 21.1-21.3
Hoyt, Lecture 8.8-8.9

 Friday, October 8, 2004

Topics:
Unconstrained Optimization in RN
Taylor’s Theorem
Second Order Conditions for Unconstrained Optimization

Readings:
Simon & Blume, 17.1-17.5; 30.1-30.3

Hoyt, Lecture 9

Friday, September 24, 2004

Topics:

Higher Order Derivatives
Implicit Function Theorem

Simon & Blume, 15:1-15.4 

Monday, September 27, 2004

 Shapes of Functions

Hoyt, Lecture 8.7-8.9
Simon & Blume, 16;21.1-21.4

Wednesday, September 22, 2004

 Topics:

Gradients

Implicit Function Theorem

Readings:

Hoyt, Lecture 8
Simon & Blume, 14; 15

  Wednesday, September 15, 2004

 Topics:
Matrix Inversion
·       Cramer’s Rule

  Friday, September 17, 2004

Euclidean Space
Limits and Open Sets

 Relevant Readings:     

Simon & Blume, 10.5-10.7; 11; 12.1-12.5





Monday, September 13, 2004

 Topics:
·Determinants     
Inverse Matrices
·       Cramer’s Rule

 Relevant Readings:     

Simon & Blume, 8.1-8.4, 10; Hoyt, Lecture 6; Simon & Blume, 6-7


Friday, September 10, 2004

Topics:
·       Rank & Solutions to Systems of Equations
·       Properties of Determinants
·       Inverse Matrices

 Relevant Readings:      Simon & Blume, 8.1-8.4, 10; Hoyt, Lecture 6; Simon & Blume, 6-7

Friday, September 3, 2004

Topics:
One Variable Case:
          Maxima & Minima
Introduction to Linear Algebra

For Wednesday, September 8

Introduction to Linear Algebra

 
Readings:
Simon & Blume, 3; 6-8.4
Hoyt, Lecture 5: Maxima and Minima (see restricted section)

Hoyt, Lecture 6: Fundamentals of Linear Algebra

Assignment (Due Wednesday, September 8, 2004) (distributed)

Wednesday, September 1, 2004

Topics:
One Variable Case:
Maxima & Minima
Concavity & Convexity
Economic Applications

Introduction to Linear Algebra

For Review:
Rules for Differentiation
          Product Rule
          Quotient Rule
          Chain Rule
          Higher Order Derivatives

For Friday, September 3

Introduction to Linear Algebra

Readings:
Simon & Blume, 3; 6-8.4
Hoyt, Lecture 5: Maxima and Minima (see restricted section)
Hoyt, Lecture 6: Fundamentals of Linear Algebra
 

Assignment (Due Friday, September 3, 2004)
Simon & Blume 2.1, 2.4, 2.5 (p. 15-16); 2.8, 2.9 (p. 21-22);

2.10-2.12 (p. 29); 2.16 (p. 33); 2.20 (p. 34);4.1, 4.5 (p. 75)


Monday, August 30, 2003

Topics:
Course Outline and Introduction
Vocabulary of Functions

Definition of Derivative

For Monday, August 30

Readings:
Simon & Blume, 1.1-1.2; 2.3-2.7; 12.1, 12.4; 4
Hoyt, Lecture 3 (see restricted section)
For review: Hoyt, Lectures 1 & 2 (see restricted section);
Simon & Blume 2.1-2.2; 5

Assignment (Due Friday, September 3, 2004)
Simon & Blume 2.1, 2.4, 2.5 (p. 15-16); 2.8, 2.9 (p. 21-22);

2.10-2.12 (p. 29); 2.16 (p. 33); 2.20 (p. 34);4.1, 4.5 (p. 75)

 For Wednesday, September 1:

Readings:
Simon & Blume, 3
Hoyt, Lecture 4 (restricted section)



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Course Description

From the University Catalog: An introduction to mathematical approaches to economic theory. Emphasis is on linear models, constrained optimization, and techniques used in comparative statics. Prereq: ECO 488G; MA 113; or the consent of the instructor.

While this description has some truth to it, I would add that the purpose of this course, in my view, is not to train you as a mathematical economist. Instead it should provide you with basic tools you need for coursework and research in economic theory and econometrics as well as the applied fields you will encounter later. With this in mind, I shall try to tailor the topics we cover to focus on those techniques and tools that you need to advance in the program and use in your own research.
 
 



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Texts and Readings

The required text for the course is Carl P. Simon and Lawrence Blume, Mathematics for Economists, Norton, 1994. Occasionally, when I believe another text might do a better job of covering a specific topic, I shall make the relevant readings available to you in the file for course readings in BE 324.
 
In addition, “lecture notes” that I try to make available prior to the lecture supplement the text. These are quite extensive and detailed notes on which the class lecture is ge­nerally based. However, these notes should not be used as substitutes for taking notes during class. These notes will be on the course website, http://gatton.uky.edu/Faculty/hoytw/590/590.html, in a section of the website that will require a special access code to access. The code will be given to you in class. Most of these notes will be in a postscript (pdf) format that requires Adobe Acrobat to read. The reader can be obtained free of charge at www.adobe.com.


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Grading and Course Assignments

Your grade for the course is based on my evaluation of your performance on problem sets and three exams. Problem sets will be given on daily basis. Problem sets must not be late to receive full credit with late being defined as any problem set I do not receive at or prior to the beginning of class on the date on which it is due. A problem set that I receive within three days of the date on which it is due can receive at the most half-credit. Any problem set received after that period receives no credit unless the student has an excused absence as defined by the University.

On each problem set a maximum of 50 points is possible. Your total score on problem sets for the course will be based on an average of the scores after discarding your four lowest scores. As the primary purpose of the problem sets is to give you practice, substantial credit will be given for attempting problems even when correct solutions are not obtained. In addition, not all problems on a set will generally be graded. Of course, you will not know in advance which problems will be graded.

While you are encouraged to work together on the problem sets, I encourage you to first work on the problems by yourself and then meet with other students or me to compare answers and perhaps attempt the more challenging problems. I do not want the group to write up the solutions to the problems -- that is the responsibility of the individual. Once you have written up your solutions to the problem set, do not share your answers with anyone else. Remember the purpose of the problem sets is to get you to learn the material; to do this it is necessary for you to make an honest effort to do the work yourself.














Given the nature of the material being tested, if possible, I would like you to allow two and one-half hours to taking the two exams during the semester. This is


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Tentative Course Outline
 

Topic
 

1. Applications of Calculus of One Variable

     Maxima and Minima

     Chain Rule

 

2.  Linear Algebra:  The Basics

     Introduction and Definitions

     Systems of Linear Equations

     Matrix Algebra and Determinants

     Euclidean Spaces

 

3.  Multivariate Calculus    

     Limits and Set Theory

     Functions in RN

     Partial Differentiation and Differentials

     Implicit Functions 

     Comparative Statics

      Concave and Quasiconcave Functions

 

4.  Optimization

     Unconstrained

     Equality Constraints

      Inequality Constraints

      Multiplier and Envelope Theorems

      Second Order Conditions

 

5.   Analysis

      Limits and Compact Sets

      Weierstrass and Mean Value Theorems

      Taylor Series Polynomials

 

6.   Linear Programming

      Examples of Linear Programming

      Convex Sets and Linear Programming

      Duality

 

7.   Differential Equations and Dynamic Programming

      First Order Linear Differential Equations

      Variable Coefficients and Variable Term

      Exact Differential Equations

      Nonlinear Differential Equations

      Higher Order Differential Equations




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