ECON 331
Written Assignment 1
due in class Sept. 23
1. In ordinary arithmetic a b c a b c a. Use a Venn diagram to show
however that
A B C A B C A
2. Let X x 1 , x 2 : 0 x 2 x 2 1 where U 2 . X is not
ECON 331
Homework #5
due in class March 30th
Late homework will not be considered.
Show detailed calculations and/or provide detailed explanations to get full credit.
Partial credit may be given.
1. A
Homework note (for Nov 18).
(i) Since ux , uy , uz > 0 on the domain of u, u is strictly increasing. If (x, y, z) is
a bundle, and px x + py y + pz z < I , then, the bundle (x + px , y + py , z + pz )
Linda is 31 years old, single, outspoken, and very bright.
As a student, she was deeply concerned with issues of
discrimination and social justice, and also participated in
anti-nuclear demonstrations
Gaussian Elimination
how can we solve systems of equations?
e.g. multimarket supply and demand with complements and
substitutes
Gaussian elimination: an approach to solving linear systems of
equations
Claim:
If a and b are vectors in R2 , then |a b| a b .
Proof:
Since |a b|, a b 0, it is equivalent to show that a 2 b 2 |a b|2 .
If a = 0 or b = 0, then both sides of the expression are equal to zero
Vectors
vectors are a convenient way of denoting a multidimensional
quantities
e.g. consumption bundle
dened a vector as a matrix with either only one row or only
one column
can instead think of a vec
Mathematical Thinking
mathematical models force us to think logically based clearly
I
but: need to apply mathematical reasoning correctly!
Example
Problem
Find solutions to the equation x + 2 =
p
4
x.
Matrix Multiplication
matrix multiplication provides a useful way of using vectors
and matrices to represent systems of equations
next we'll dene matrix multiplication and show how it can be
applied
S
ECON 331
ANSWERS - Homework #4
1. (a) f2 (Y T, r) and h (r) are presumably both negative because when the interest
rate increases, both consumption and investment are likely to decrease.
(b) Dierentia
ECON 331
ANSWERS - Homework #5
1.(a) The net prot function writes:
(x, y) = px + qy C(x, y) = ax 2x3 + by 1/2 cx dy e
The optimization problem writes:
max (x, y)
x0,y0
- First we look for stationary i
ECON 331 - Homework #5
due in class December 5th
Late homework will not be considered.
Show detailed calculations and/or provide detailed explanations to get full credit.
Partial credit may be given.
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