Professor Gronberg
Econ 607
Fall 2013
Problem Set 10
You should work through all nine of the problems below. You will turn in your answer to
problem one only. You may work on these problems collaboratively, but you will each
write up and turn in your own
Econ 607
Fall 2012
Problem Set 1
1. Reconsider the model of a profit-maximizing firm that we looked at in Lecture 1.
Let
R(x) = total revenue function (depending on output x)
C(x) = total cost function
tx = total tax revenue collected, where the per-unit
Econ 607
Professor Gronberg
Fall 2012
Problem Set 7
1. The government is considering building an office block outside a householders back window.
Two economists propose different approaches to evaluating the householders loss of daylight.
Economist A says
Econ 607
Professor Gronberg
Fall 2012
Problem Set 6
1. Do Problem 5.9 in Nicholson and Snyder.
2. Do Problem 16.2 in Nicholson and Snyder.
3. Do Problem 16.10 in Nicholson and Snyder.
4. An economist estimates the following demand function for beef:
ln(x)
Econ 607
Fall 2012
Problem Set 7 Answer Key
1.
As question assumes that eectively he starts with no daylight and u equals,
say, ui . He is then asked how much he will pay for daylight. If the variable x equals 1 when he has daylight and 0 when he does not
Econ 607
Fall 2012
Problem Set 6 Answer Key
1.
(a)
esx ,I
( px x ) I
x I
I
= ex,I 1.
=
px x =
I
Ix
I
(b)
( p x x ) px
x px
I
= ex,px + 1.
px x =
px I
px x
esx ,px =
(c)
expx ,px
( px x ) 1
1
x
I
=
px ) = ex,px + 1.
= (x +
px x
px
x
(d)
esx ,py
( p x x
Econ 607
Fall 2012
Problem Set 8 Answer Key
1.
(a)
= = It is a perfect complement case.
Since she buys 25 units of y and 100 units of m, then u0 = mincfw_m, 4y =
100.
From the indirect utility function we can derive the expenditure function:
E (pm , py
Econ 607
Professor Gronberg
Fall 2012
Problem Set 9
1. Do Problem 7.3 in Nicholson and Snyder.
2. Do Problem 7.6 in Nicholson and Snyder. The point here is to compare the
relative responsiveness of the expected utility of the illegal parking gamble to a
p
Professor Gronberg
Econ 607
Fall 2012
Problem Set 5
1. Do Problem 5.7 in Nicholson and Snyder.
2. Do Problem 5.12 in Nicholson and Snyder.
3. Do Problem 16.3 in Nicholson and Snyder.
4. Suppose that an individuals utility function for consumption, c, and
Econ 607
Fall 2012
Problem Set 6 Answer Key (Correction)
2.
(a) Using the Lagrange method to solve this problem:
L = c w (24 h) + (U c h1 )
L
= w (1 )c h = 0 (1)
c
L
= 1 c1 h1 = 0 (2)
h
L
= U c h1 = 0 (3)
Combining (1) and (2), we can get:
h
wh
1
=
c=
w
(
Econ 607
Fall 2012
Problem Set 1 Answer Key
1.
Assume the behavioral objective of the rm is to maximize its gross sales
(gross revenues), we can write that:
max R(x)
(1)
x
Then, the rst-order (necessary) condition for a maximum is:
R (x) = 0
(2)
And the s
Econ 607
Professor Gronberg
Midterm Exam
Fall 2011
Do all four problems. Each problem is worth 25 points. Be sure to show all your work.
Partial credit will be given.
You have until 9:30 to finish.
Your Name
_
1. Consider a simple two-period intertemporal
Econ 607
Professor Gronberg
Midterm Exam Answer Key
Fall 2011
1. Consider a simple two-period intertemporal choice problem with intertemporal utility
function:
R
R
U (c , c ) = c / R + (1/(1+) c /R
0
1
0
= ln
1
+
1
1+
ln
if 0 R 1
if R= 0.
and intertempora
Professor Gronberg
Econ 607
Fall 2012
Problem Set 2
1. Do Problem 3.10 in Nicholson and Snyder (same problem in both the 10th and 11th ed.).
2. Do Problem 3.12 in Nicholson and Snyder (same problem in both the 10th and 11th ed.).
3. Suppose the consumer h
Econ 607
Fall 2012
Problem Set 4 Answer Key
1.
Assume y is consumption of other goods and l is leisure. Leahs budget constraint under these two cases can be written as
First case:
y=
3360 20l if l 128,
4640 30l if 0 l 128
Second case:
y = 3696 22l 0 l 168
Professor Gronberg
Econ 607
Fall 2012
Problem Set 3
1. Do Problem 4.12 in Nicholson and Snyder.
2. Do Problem 4.14 in Nicholson and Snyder.
3. In lecture, we considered two different CES utility functions:
The first function is
and the second function is
Econ 607
Fall 2012
Problem Set 5 Answer Key
1.
(a) Since ham(h) and cheese(c) are pure complements, the demand for ham
I
is h = pc +ph and the demand for cheese is c =
Thus,
eh,ph =
I
.
p c +p h
I
ph
h ph
ph
=
=
I
2
ph h
( pc + ph ) p c + p
pc + ph
h
Simi
Professor Gronberg
Econ 607
Fall 2012
Problem Set 4
1. Leah currently has a job where she can work as many hours as she chooses. She is paid
$20/hr for the first 40 hours she works per week and $30/hr for each hour over 40 (per week).
Leah currently choos
Professor Gronberg
Econ 607
Fall 2012
Problem Set 8
1. Assume that a representative consumers indirect utility function is given as
V = I / (pm + 0.25py).
This is an indirect utility function associated with a direct utility function of the CES type in
Ni
Econ 607
Fall 2012
The corrected answer key to problem 1 in Problem Set 10
1.
Note: the original answers to parts (c) and (d) were for a risk neutral individual rather than for the risk averse individual in parts (a) and (b)
(c)
For the risk averse indivi
I la W0 ‘1 iAﬂA II: A) I . 'A
x
"u!" ‘ds =0 MW "2!
' 1? Ak.1;LAAn :rL' raalv A L;L ‘ 53"e-‘ 655:“
I”
.A 11.1
, .1 ‘
141' N: ' +ord9v mud/Km i W. -'
u'
ii 'QL/é ="/& + A: A =0
iii = a '0! :O
I: W‘l‘ﬁ bid/7
mm' o A. ' a! =" "v a“: =
.’.,.1n, ' A y t I' #1