ECON 255 - Introduction to Mathematical Economics
FALL TERM 2013
Instructor: Jan Zabojnik
Queens University
HOMEWORK ASSIGNMENT #7
Due by 11:25am on Wednesday, November 20. The assignment box is on th
ECON 255 - Introduction to Mathematical Economics
WINTER TERM 2016
Instructor: Jan Zabojnik
Queens University
HOMEWORK ASSIGNMENT #2
Due by 11:25am on Wednesday, January 20. The assignment box is on t
Plan for today
Finish on-the-job training
Signaling theory of education
Job search and unemployment
Specific training as a shared investment
w
VMP
VMPH
Employers benefits
Employees benefits
w*H
WL = V
Plan for today
Estimating marginal returns to education
Ability
bias
Self-selection bias
On-the-job training
Signaling theory of education
The optimal number of years in school
MRR
0
Years of
school
Plan for today
Theory of compensating wage differentials
Market
for risky jobs
Optimal level of job safety
The hedonic wage function
Effects of safety regulations
Value of statistical life
The market
Solution to a System of Linear Equations
Ex 1: Find the solution to
2 x1 3 x2 7
x1 4 x2 6
Plan for Today
Cramers rule
Examples
Rate of change of a function
Limits
Cramers Rule
Let Aj be the matrix obt
Matrices 2
An element is indicated by its row and column position
Let aik (xik , etc.) denote an element in the i-th row and
k-th column
Then we can write, for example
How does matrix algebra help us?
Plan for today
Theory of human capital
Education as an investment decision
Estimating marginal returns to education
Human Capital
Human Capital: Introduction
Recall: Workers differ in
tastes and pref
Midterm
Mean = 72.3
Median = 76
Highest score = 100
(6)
Many 90
(33)
But also many < 50
Mean with Fs excluded = 78.4
Re-grading
Explain reason in e-mail (to me)
The whole test will be re-graded
Mark c
Plan for today
Debate on 2 theories of education
Search theory
Job tenure and turnover
Job search and
unemployment
Why is there
unemployment?
Unemployment: Canada vs. U.S.
Unemployment: Canada vs. U.S
Exercise 2.4
Question 1
a)
S 1 x S 2=cfw_ ( 3, a ) ; ( 3, b ) ; ( 6,a ) ; ( 6, b ) ; ( 9, a ) ; ( 9, c )
b)
S 2 x S 3= cfw_( a ,m ) ; ( a , n ) ; ( b , m) ; ( b , n )
c)
S 3 x S 1= cfw_( m , 3 ) ; (
ECON 255 - Introduction to Mathematical Economics
FALL TERM 2015
Instructor: Jan Zabojnik
Queens University
HOMEWORK ASSIGNMENT #3
Due by 12:55pm on Thursday, October 8. The assignment box is on the 2
ECON 255 - Introduction to Mathematical Economics
FALL TERM 2015
Instructor: Jan Zabojnik
Queens University
HOMEWORK ASSIGNMENT #1
Due by 12:55pm on Thursday, September 24. The assignment box is on th
ECON 255 - Introduction to Mathematical Economics
FALL TERM 2015
Instructor: Jan Zabojnik
Queens University
HOMEWORK ASSIGNMENT #2
Due by 12:55pm on Thursday, October 1st. The assignment box is on the
ECON 255 - Introduction to Mathematical Economics
FALL TERM 2015
Instructor: Jan Zabojnik
Queens University
HOMEWORK ASSIGNMENT #5
Due by 12:55pm on Thursday, November 12. The assignment box is on the
FRED Graph Observations
Federal Reserve Economic Data
Link: https:/research.stlouisfed.org/fred2
Help: https:/research.stlouisfed.org/fred2/help-faq
Economic Research Division
Federal Reserve Bank of
Midterm
Wednesday, Oct 25, regular class time
Location:
Last names A to K:
Last names L to Z:
Dunning 14
MacDonald 1
Midterm
Everything that has been covered in class (including
today)
No books, note
Office hours today
Todays office hours: 2:30 3:20pm
Assignment 2, Q6
Show that B = I A(AA)-1A is idempotent.
Note:
A(AA)-1A I
Plan for Today
Properties of determinants
Finding A-1
Solving a matrix equ
ECON 255 - Introduction to Mathematical Economics
WINTER TERM 2016
Instructor: Jan Zabojnik
Queens University
HOMEWORK ASSIGNMENT #3
Due by 11:25am on Wednesday, January 27. The assignment box is on t
Last time
A quick review of basic concepts:
Sets
The
Real Number System
Ordered
Tuples, Product Sets
Functions
Plan for Today
Quick review of functions
Systems of equations
Matrices
Vectors as spe
Plan for Today
Rules of differentiation example
Total derivative
Implicit function and its derivative
Rules of Differentials
Suppose f and g are two functions
Rule I
dk = 0 (k is a constant)
Rule II
d
Plan for Today
Partial derivative
Higher order partial derivatives
Hessian of a function
Total derivative
Linear approximation of a function
Partial derivatives
Partial Differentiation
Def: The partia
Tutorial
Midterm tutorial with TA
Monday, 4:00 - 5:20
Dunning Hall 213 (conference room)
Plan
Rules of differentiation
Examples
Composite functions
Chain rule
Higher order derivatives
Chapter 7: RULES
Plan for Today
Implicit function given by a single equation
examples
Implicit functions defined by a system of
equations
Example
F(x,y) = x2 + y2 4 = 0
y
x
The Implicit Function Theorem
Theorem: Cons
Plan for Today
Rate of change of a function and the derivative
Limits
Properties of derivatives
Continuity of a function
Continuity and differentiability
Graphical Representation
y
0
x
Rate of Change
Class reps for Econ 255
Need 2 class representatives to
organize the USAT evaluations
make the occasional class announcement
about events in the department
Plan for Today
Special matrices
Rules of mat
Plan for Today
Continuity of a function
Continuity and differentiability
Rules of differentiation
Examples
Continuity
of a function
Continuity
f is continuous at t if
(i) t is in the domain of f
(ii)
Solution of Linear-Equation System
Ax = d
Theorem: Suppose A is n n and nonsingular.
Then the unique solution is
x* = A-1d
Solution of Linear-Equation System 2
All we need is
1) a method to figure out
Example
Ex:
Y C I 0 G0
C C (Y , T0 )
=>
Y C (Y , T0 ) I 0 G0
Y * Y * ( I 0 , G0 , T0 )
C is a general function => no explicit solution
But: In the neighborhood of Y*, the following identical
equality
Plan for Today
Implicit functions defined by a system of
equations example
Higher order approximations
Taylor approximation
A Two Equations Case
Suppose 2 equations (n = 2 and m = 1):
F ( y1, y2 , x)
Class reps for Econ 255
Need 1 more class representative to
organize the USAT evaluations
make the occasional class announcement
about events in the department
Plan for Today
Inverse of a matrix and i
Plan for today
Midterm
Estimating marginal returns to education
Ability
bias
Self-selection bias
On-the-job training
Midterm
Mean
= 68.1
Median
= 71.5
Without Fs
= 75.2
Max
= 98.5
Re-grading
Only if
Econ 255 Introduction to
Mathematical Economics
Econ 255 Introduction to
Mathematical Economics
Instructor:
TAs:
Jan Zabojnik
Boer (Polly) Chen
Baiyou Chen
Plan for Today
Prerequisites, grading, and o