THE EARNED INCOME TAX CREDIT ABROAD:
IMPLICATIONS OF THE BRITISH WORKING FAMILIES TAX CREDIT
FOR PAY-AS-YOU-EARN ADMINISTRATION
Janet Holtzblatt
Ofce of Tax Analysis US. Department of the Treasury
Jerey B. Liebman
John F. Kennedy School of Government, Har
Social Security Unfair to the Poor?
By Jeffrey Liebman
Sunday, July 29, 2001; Page B07
The interim report of President Bush's Social Security Commission argues that the current system is
unfair to low-income beneficiaries, particularly minorities, whose s
Article #1
Article #3
Article #5
Small Grants
Article #2
Article #4
Article #6
Visiting Scholars
The EITC compliance problem
Jeffrey B. Liebman*
ince the 1960s, economists have advocated the use of the tax system as a means of
transferring income
Lecture 13
LINEAR PROGRAMMING AND LINEAR
INEQUALITIES
Linear Inequalities:
A linear equation in two variables x and y is written in the
form
Ax + By = C
Where A, B and C are real numbers. Also A & B both are
not zero. If we replace the Equal Sign by an in
MTH507 Lecture 12
FUNCTIONS & GRAPHS
LINEAR EQUATIONS:
A linear equation is of the form Ax +B y=C where A and B are both non-zero.
The graph of an equation is the set of all points (x, y) whose coordinates satisfy
the equation. The points at which the gra
MTH507
LECTURE 8
Theorem: Laplaces Expansion of a determinant
Expression by Cofactors
Let A be a square matrix of order n. Then the determinant of A is given by
det ( A ) = A =
n
a c
j =1
ij ij
= ai1ci1 + ai 2 ci 2 + . + ain cin
Or
det ( A ) = A =
n
a c
i
MTH507
LECTURE 4
Inverse of a Matrix
Consider the real number equation
Solve the equation for x
ax = b
ax = b
( a a ) x = a 1b
1
a 1
1x = a 1 b
x = a 1 b
is called the multiplicative inverse of a.
An Inverse of a Matrix
An n n matrix A is invertible(or no
MTH507
LECTURE 9
Evaluation of a Determinant using Elementary Operations
4
2 3
1
1.
A=
and
B
=
2 3
4
1
Matrix B was obtained from A by interchanging the rows of A
2 3
A=
= 11
4
1
and
4
1
B =
= 11
2 3
Interchanging rows changed the sign of its
MTH507
LECTURE 10
Cramers Rule
Uses determinants to solve a system of n linear equations in n variables. It is only applied to
systems of linear equations that have unique solutions.
Consider the solution of a general system involving two linear equations
MTH507
LECTURE 1
Matrices
1.
A matrix can be denoted by an uppercase letter such as A, B, C,
2.
3.
A matrix can be denoted by a representative element enclosed in brackets, such as
aij , bij , cij ,.
A matrix can be denoted by a rectangular array of numb
MTH507
LECTURE 2
Properties of matrix operation
If A, B and C are m n matrices and c and d are scalars then these properties are true
1.
A+B=B+A
Commutative property of addition
2.
A + (B + C) = (A + B) + C
Associative property of addition
3.
(cd) A = c(d
MTH507
LECTURE 7
Determinant of a Matrix
2 x 2 Matrices
The determinant of the matrix
a
A = 11
a21
a12
a22
is given by det (A) = |A| = a11 a22 - a21 a12
Example
1.
2 1
A=
then
4 2
A =
2 1
= 2 ( 2 ) 4 (1) = 0
4 2
2.
0 3
B=
2 4 then
B=
0 3
=
0 ( 4 ) 2
MTH507
LECTURE 5
Properties of Inverses
If A is an invertible matrix, k is a positive integer, and c is a scalar, than A1 , Ak , cA and AT
are invertible and
(A ) = A
2. ( A )
=
A=
. A . A ( A )
1 1
1.
k 1
1
1
1
1 k
k factors
3. =
( cA)
1
4.
(A )
T
1
1 1
MTH507
LECTURE 6
Elementary Matrices
An n n matrix is called an elementary matrix if it can be obtained from the identity matrix
I n by a single row operation.
The identity matrix I n is elementary by this definition because it can be obtained from itself
MTH507
LECTURE 11
Linear Equations
The equation of a line in two- dimensional space is of the form.
a1 x + a2 y =
b
a1 , a2 and b are constants
This is a linear equation in two variables x and y
The equation of a plane in three- dimensional space is
a1 x
MTH507
LECTURE 3
Identity Matrix
Consider a special type of square matrix that has 1s on the main diagonal and 0s elsewhere
1 0 0 0
0 1 0 0
I n = 0 0 1 0
0 0 0 1
is called the identity matrix of order n
If
n=1
1 x 1 identity matrix
I1 = [1]
1 0
I2
MTH 507: T-3, 2014
Probability
Experiment:
Any activity that yields a result or an outcome is called an experiment.
There are two types of experiment we observe in our natural phenomenon.
1. Deterministic Experiment.
2. Non-deterministic Experiment (or Ra
TOPIC 4: STATISTICS
MEASURES OF CENTRAL TENDENCY:
MEAN: The arithmetic mean or mean of a set of real numbers
x , x ,., x
1
2
n
_
denoted by
X
and is defined as
x x . x
n
_
X
1
2
n
Where n is the number of items being averaged.
Example 1: Find the mean fo
LINEAR PROGRAMMNING AND
LINEAR INEQUALITIES
WORD PROBLEMS
Tiggers Diet
Tigger the Tiger needs a strict diet. In a day, he needs at least
30 grams of protein and at least 16 grams of fat. Each ounce
of Cat Food A supplies 2 grams of protein and 4 grams of
Topic: MATRICES
Here we are going to learn the following three methods for solving a system of linear equations in two
variables:
Substitution Method
Elimination Method
Matrix Method
SUBSTITUTION METHOD:
Example -1: Solve the following system of linear eq
Differentiation
RulesforDerivatives
d (xn )
n x n 1
dx
1.
d (c )
0; wherecisaconstant
dx
2.
d [ c f ( x )]
d [ f ( x )]
c
dx
dx
3.
d
d
d
[ f ( x ) g ( x )] [ f ( x )] [ g ( x )] (SumandDifferenceRule)
dx
dx
dx
4.
Findthefirstorderderivativeofeachfunct
MTH507 MATHEMATICS FOR SOCIAL SCIENCES
Assignment 1 Trimester 3, 2016
Total Marks: 20
1.
Due: 6th October (2pm)
Weighting: 10 %
Given below are the demand and supply equations for a particular brand of 1 GB USB flash drive.
S 4 p 26
and
D 3 p 51
where p
Integration
RulesforIndefiniteIntegration:
1.
adx ax C
x n 1
C ; n (1)
2. x dx
n 1
n
3.
4.
[ f ( x) g ( x)]dx f ( x)dx g ( x)dx
c f ( x)dx c f ( x)dx
Evaluateeachofthefollowingindefiniteintegrals:
1.
2.
3.
4.
5.
3dx
xdx
x dx
x( x 2)dx
(
MTH507 MATHEMATICS FOR SOCIAL SCIENCES
Assignment 2 Trimester 3, 2016
Total Marks: 20
1.
Given the following data:
4
5
2
3
0
1
3
6
2
4
3
2
5
6
1
2
0
7
3
5
4
1
2
6
3
2
a)
b)
c)
d)
2.
Due: 16th November (2pm)
Weighting: 10 %
Collate the data in a frequency