Problem Set 7
1. A rich man is facing the risk of being ruined. He is an expected utility
maximizer. His initial wealth is $10 million. He has the option to fully
insure himself against the risk of ruin. It is known that when the risk
of ruin is 1/3, he i
Problem Set 2 Answer Key
Fall 2011
1. The income elasticity of demand is given by
"xi =
@gi (x; p)
x
:
@x
gi (x; p)
(a) Show that if two goods have the same income elasticities then
@gi (x; p)
@gj (x; p)
=
:
@pj
@pi
In order to answer this question use (1
ECON 500
Practice Midterm Exam 2
Answer Key
1. The income elasticity of demand is given by
"xi =
@gi (x; p)
x
:
@x
gi (x; p)
(a) (10 points) Show that if two goods have the same income elasticities
then
@gj (x; p)
@gi (x; p)
=
:
@pj
@pi
In order to answer
Problem Set 3
Answer Key
1. Using the area representation of EV, CV, and change in Consumer Surplus,
analyze the relationship between these three measures for an inferior good
when its price increases.
(x;p
If we deal with an inferior good then @[email protected] ) <
Problem Set 5
Answer Key
1. A rich man is facing the risk of being ruined. He is an expected utility
maximizer. His initial wealth is $10 million. He has the option to fully
insure himself against the risk of ruin. It is known that when the risk
of ruin i
Practice Midterm Exam
1. (10 points) Suppose a person preferences can be represented by
s
the following utility function
q
1= 2
u (q1 ; q2 ) = q1 + q2 :
Can you write down another utility function that represents the
same preferences as the utility functi
ECON 500
Fall 2012
Practice Midterm
1. The income elasticity of demand is given by
"xi =
x
@gi (x; p)
:
@x
gi (x; p)
(a) (10 points) Show that if two goods have the same income elasticities
then
@gi (x; p)
@gj (x; p)
=
:
@pj
@pi
(b) (10 points) Show that,
ECON 500
Fall 2013
Midterm Exam
1. (30 points) Suppose a person Cobb-Douglas utility function is given by
s
1
u (q1 ; q2 ) = q1 q2
wihere 0 <
< 1:
(a) (10 points) Is the utility function homothetic? Proof your answer.
(b) (10 points) Find the Marshallian
Practice Midterm Exam
Answer Key
1. (10 points) Suppose a person preferences can be represented by
s
the following utility function
q
1= 2
u (q1 ; q2 ) = q1 + q2 :
Can you write down another utility function that represents the
same preferences as the uti
Answer Key to Midterm 2
1.) a) In order to nd the cost function of the rm, there are two
ways to do it. The most intuitive way is to set up the cost minimization
problem and solve for the cost function.
We do this by
min wL + rK +
y
L;K;
LK
FOCs are neces
ECON 500
Fall 2013
Answer Key to Midterm Exam
1. (30 points)Suppose a person0 s Cobb-Douglas utility function is given by
1
u (q1 ; q2 ) = q1 q2
where 0 <
< 1:
(a) (10 points) Is the utility function homothetic?
Yes, it is. For homotheticity, we must nd t
ECON 500
Fall 2010
Answer Key Midterm 2
1. Suppose that a consumer has rational, continuous, nonsatiated and strictly
convex preferences over two goods, x1 and x2 :
(a) (5 points) Find the own substitution eect for good 1 if the Marshallian demand for goo
Answer Key
Problem Set 7
1. A rich man is facing the risk of being ruined. He is an expected utility
maximizer. His initial wealth is $10 million. He has the option to fully
insure himself against the risk of ruin. It is known that when the risk
of ruin i
Problem Set 5
1. A rich man is facing the risk of being ruined. He is an expected utility
maximizer. His initial wealth is $10 million. He has the option to fully
insure himself against the risk of ruin. It is known that when the risk
of ruin is 1/3, he i
only has cobb-douglas on midterm
need to find cost function
max p.y =c(w,r,y)
Problem Set 5
Answer Key
I Given is a CES production function f (z ) : <2 ! <+ with f (z1 ; z2 ) =
+
1
(z1 + z2 ) :
1. Find the MRTS. For which values of
The MRTS is given by
ar
Practice Final Exam
E. Gugl
Econ500
December 2, 2012
1. (20 points)Consider the consumer choice problem in the two commodity
model with xed income x: Suppose the government imposes a price of
good 1 in the amount of t; so that the new price of good 1 is e
Problem Set 1
I. Short Problems
1. Check whether the following three functions represent the same underlying preferences
check if slope are the same
1=2
1=2
u (q1 ; q2 ) = q1 + q2
u (q1 ; q2 ) = q1 + q2
u (q1 ; q2 ) = ln q1 + ln q2
increasing
any 2 are gi
Practice Final Exam
Answer Key
E. Gugl
Econ500
December 2, 2012
1. (20 points)Consider the consumer choice problem in the two commodity
model with xed income x: Suppose the government imposes a price of
good 1 in the amount of t; so that the new price of
Practice Final Exam
E. Gugl
Econ500
December 9, 2013
1. (20 points)Consider the consumer choice problem in the two commodity
model with xed income x: Suppose the government imposes a price of
good 1 in the amount of t; so that the new price of good 1 is e
Problem Set 2
Fall 2011
1. The income elasticity of demand is given by
"xi =
@gi (x; p)
x
:
@x
gi (x; p)
(a) Show that if two goods have the same income elasticities then
@gi (x; p)
@gj (x; p)
=
:
@pj
@pi
(b) Show that, for the two-good case, the income e
Problem Set 1 Answer Key
I. Short Problems
1. Check whether the following three functions represent the same underlying preferences
u (q1 ; q2 )
u (q1 ; q2 )
u (q1 ; q2 )
1=2
1=2
= q1 + q2
= q1 + q2
= ln q1 + ln q2
All three represent dierent underlying p
Problem Set 3
1. Using the area representation of EV, CV, and change in Consumer Surplus,
analyze the relationship between these three measures for an inferior good
when its price increases.
2. A consumer preferences lead to the cost function
s
p
c (u; p)
ECON500
Problem Set 4
1. Suppose one person considers goods 1 and 2 as perfect substitutes i.e.
u1 (x1 ; y1 ) = x1 + y1 ; while the other person considers them as perfect
complements, i.e. u2 (x2 ; y2 ) = min fx2 ; y2 g. Initial endowments are
(x1 ; y 1 )
Problem Set 5
I Given is a CES production function f (z ) : <2 ! <+ with f (z1 ; z2 ) =
+
1
(z1 + z2 ) :
1. Find the MRTS. For which values of
are the isoquants convex?
2. Does the production set exhibit constant returns to scale? Does this
imply that the
ECON500
Problem Set 4
Answer Key
1. Suppose one person considers goods 1 and 2 as perfect substitutes i.e. u1 =
x1 + y1 ; while the other person considers them as perfect complements,
i.e. u2 = min fx2 ; y2 g. Initial endowments are
(x1 ; y 1 )
(x2 ; y 2
Problem Set 6
1. In a one-producer, two consumer economy, the consumption good (good
2) is produced with labor only according to
p
f (z ) = z:
The consumers have preferences over leisure (denoted by x1 and x2 ; respectively) and over the consumption good
Problem Set 6
Answer Key
1. In a one-producer, two consumer economy, the consumption good (good
2) is produced with labor only according to
p
f (z ) = z:
The consumers have preferences over leisure (denoted by x1 and x2 ; respectively) and over the consum
Practice Final Exam
E. Gugl
Econ500
December 6, 2013
1. (20 points)Consider the consumer choice problem in the two commodity
model with xed income x: Suppose the government imposes a price of
good 1 in the amount of t; so that the new price of good 1 is e