Econ 484
First Exam
Answers
All questions count 20 points
1. Joe has a utility function defined on two goods: beer, denoted by x1 and pizza denoted
by x2 , Joes utility function is of the form
1
1
u ( x1 , x2 ) = x12 x22 .
Joes budget constraint is of the
Econ 484
Second Homework assignment
Due in class February 11, 2013
1. Brad consumes goods x1 and y1 and has a utility function of the form
11
u ( x1 , y1 ) = + x12y12 ,
and an initial endowment x = 12 . Angelina consumes goods x2 and y2 and has a utility
Econ 484
Second Homework assignment
Due in class February 13, 2013
1. Brad consumes goods x1 and y1 and has a utility function of the form
1 1
u ( x1 , y1 ) = +x12y12 ,
and an initial endowment x = 12 . Angelina consumes goods x2 and y2 and has a utility
Econ 484
Problem Set 1
Due in Class January 26, 2013
1. An individual consumes goods x1 and x2 . The individual has a utility function of the
form
u ( x1 , x2 ) =
1
1
ln ( x1 ) + ln ( x2 )
2
2
The individuals budget constraints are of the form
I = p1 x1 +
Econ 484 Syllabus
Economics 484
Office Hours
Brito
Dagobert L.
Mon-Wed 3:30-4:30
258 Baker
Hall
Extension 5792
brito@rice.edu
Public goods were at one time a minor topic in economics. Examples were such items as lighthouses and defense.
This is still refl
Econ 484
Spring 2013
Handout 1
Handout 1 based in part on the Appendix to Introduction to Equilibrium Analysis by
Hildenbrand and Kirman. This material is not going to be on the test and the purpose of
this handout is to give you a source for mathematical
Econ 484
2013
Handout 7
Kuhn-Tucker Conditions
Consider the problem
Max f ( x1 , x2 , x3 )
(1)
subject to
(2)
a11 x1 + a12 x2 + a13 x3 ! b1
a21 x1 + a22 x2 + a23 x3 ! b2
with the constraint that x1 ! 0, x2 ! 0 and x3 ! 0 .
The Lagrangian can be written as
Econ 484
Handout 8
1. Envelope Theorem
Consider the problem of maximizing
z = f ( x, y )
(1)
subject to
g ( x, y ) ! 0
(2)
where x is a vector of choice variables and y is a vector of parameters. The Lagrangian is
L = f ( x, y ) + ! g ( x, y )
(3)
The fir
Econ 484
Handout 5
Kuhn-Tucker Conditions
Consider the problem
Max f ( x1 , x2 , x3 )
(1)
subject to
a11 x1 + a12 x2 + a13 x3 ! b1
(2)
a21 x1 + a22 x2 + a23 x3 ! b2
with the constraint that x1 ! 0, x2 ! 0 and x3 ! 0 .
The Lagrangian can be written as
(3)
Econ 484
2013
Handout 6
Kuhn-Tucker Theorem
An intuitive explanation of using the Lagrangian when you are trying to maximize a
function subject to a constraint is that you are trying to find the point of tangency of a
point on an iso-value curve of the ob
Econ 484
2013
Handout 2
Introduction to Lagrangians
Consider the problem of maximizing
f ( x1 , x2 )
(1)
subject to
g ( x1 , x2 ) = 0
(2)
We form a new function called the Lagrangian
L ( x1 , x2 , ! ) = f ( x1 , x2 ) + ! g ( x1 , x2 )
(3)
where ! is the L
Economics 484
Handout 3
Algebra Review
Note on Cramers Rule
If you have a linear system of equations of the form
! a1
#a
# 2
" a3
b1
b2
b3
c1 $ ! z1 $ ! d1 $
c2 & # z2 & = # d2 &
&# & # &
c3 % " z 3 % " d 2 %
then the solution can be found by replacing th
Econ 484
2013
Handout 5
Walrasian Equilibrium in a Pure Exchange Economy
Consider an economy with two individuals and three goods. We will assume that each
individual has a well-behaved utility function of the form ui ( xi1 , xi 2 , xi 3 ) . By well
behav
Econ 484
2013
Handout 4
Competitive Markets and Welfare
1. Introduction
In 1776, Adam Smith's The Wealth of Nations was published. The Wealth of Nations,
probably more that any single work provided an explanation of, and a justification for,
capitalism, t
Econ 484
Homework
Due in class (March 27, 2013 or April 1, 2013)
I. Problems from Feldman & Serrano
pp. 157-158 Problems 1, 2 and 3
pp. 188-189 Problems 1, 2 and 3
II. Assume that there was a tribe of Owls that consumed only beer. They consume the
beer as