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 a closed or an open
1
2
set and neither is it a convex
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 interior points by solving the FOC:
1 (x, y) = 0
2 (x, y
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 ) also
satises he budget constraint whenever (0, I ]. Si
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.
Linda is 31 years old, single, outspoken, and very br
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 with many unknowns
System of Equations: Example
x1 + x
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 and
the expression holds.
Now suppose a = 0.
Dene c = (
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 vector in n-dimensional Euclidean space
Rn
then, the row/c
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.
Example
Problem
Find solutions to the equation x + 2 =
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
Systems of equations in matrix form
Example: consider th
Leontie Model (example)
consider an economy that produces three things:
food (good 1)
raw materials (good 2)
manufactured goods (good 3)
suppose that workers supply labour inelastically, but are paid in
food and manufactured goods
production of each good
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.
Exercise 1:
Jack is a farmer who plans to fence o a rec
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Printout
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2. Matrices I Page 1
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2. M
Mathematical Thinking
mathematical models force us to think logically
I but: need to apply mathematical reasoning correctly!
Example
Problem
Find solutions to the equation
x +2=
4
x.
Example
Problem
Find solutions to the equation
x +2=
4
Solution.
x +2 =