ECN500/FIN580 Fall 2011
Solutions for Problem Set #5
3. Lotteries
3c) To proof this statement rigorously, we need to show it in both directions. If L1 f L2 , then
x1 ~ L1 L2 ~ x 2, so by transitivity, x1 x 2. From x1 x 2 , it follows from monotonicity tha
Econ 2020a / API 111 / HBS 4010
Fall 2006
Solutions: Problem Set #1
MWG 2.D.4:
You should be able to identify the non-convexity of this budget set immediately: if you were to draw a
line connecting the points (24,0) and (a, M), the points on this line wou
Econ 2020a / API-111 / HBS-4010
Fall 2006
Problem Set 3 Solutions
1. EMP with Cobb-Douglas
a)
Solve the Expenditure Minimization Problem (EMP) to derive the Hicksian demand:
p1 x1 + p2 x2
min
a1
1
a
s.t. x x2 2 u
Set up the Lagrangian:
a a
L = p1 x1 + p2
UNIVERSITYOF ILLINOIS AT URBANA-CHAMPAIGN
Department of Finance Department of Economics
Finance 580 / Economics 530: Microeconomic Theory I
Problem Set #7
Due Wednesday, December 7, 2016
*DUE TO THE END OF THE SEMESTER, CHANGES MAY BE MADE TO THE
COVERAGE
U NIVERSITY OF I LLINOIS
ECON530/FIN580
Professor: Nolan Miller
Fall 2016
Review of TA session 4
Sergio Rocha
1. From Walrasian to Hicksian demand and back: Cobb-Douglas case.
Suppose u(x 1 , x 2 ) = x 1 x 21 and usual parameters p 1 , p 2 , w so that
v(p
UNIVERSITYOF ILLINOIS AT URBANA-CHAMPAIGN
Department of Finance Department of Economics
Finance 580 / Economics 500: General Microeconomic Theory
Problem Set #2
Due Wednesday, September 21, 2016.
Please turn in your problem set by 4pm on the date the assi
UNIVERSITYOF ILLINOIS AT URBANA-CHAMPAIGN
Department of Finance Department of Economics
Finance 580 / Economics 530: General Microeconomic Theory
Problem Set #1
Due Friday, September 9, 2016
Please turn in your problem set by 5pm on the date the assignmen
UNIVERSITYOF ILLINOIS AT URBANA-CHAMPAIGN
Department of Finance Department of Economics
Finance 580 / Economics 530: Microeconomic Theory
Problem Set #4
Due: Not Due for Credit
This problem set is not due for credit. However, the material is eligible for
This stimulating and fascinating volume by one of the 20th Centurys greatest philosophers is a It is consequently incorrect to assert that aprioristic insight and pure reasoning do not convey any information about reality and the structure of the universe
Part I, "Systematic Analysis of the Theories of the Business Cycle," includes seven chapters. The method employed presents the theories in a systematic order, beginning with the less complicated and proceeding to the more complicated. In addition, prefere
Although Cohen was unrivaled in contemporary American philosophy for the diversity of the subjects with which he occupied himself, it is from logic that he has drawn the basic principles that enable him to survey so wide a domain with such a unity of view
UNIVERSITYOF ILLINOIS AT URBANA-CHAMPAIGN
Department of Finance Department of Economics
Finance 580 / Economics 530: Microeconomic Theory I
Problem Set #3
Due Friday, October 7, 2016.
Please turn in your problem set by 4pm on the date the assignment is du
UNIVERSITYOF ILLINOIS AT URBANA-CHAMPAIGN
Department of Finance Department of Economics
Finance 580 / Economics 530: Microeconomic Theory I
Problem Set #6
Due Wednesday, November 30, 2016
Please turn in your problem set by 4pm on the date the assignment i
ECN500
HW3 Solutions
1a.
Solve the Expenditure Minimization Problem (EMP) to derive the Hicksian demand:
min
p1x1
a1
1
p2 x2
a2
2
s.t. x x
u
Set up the Lagrangian:
L
p1x1
a
(u
p2 x2
a
x1 1 x2 2 )
FOCs:
1 a
a
1.
L
x1
0
p1
a1x1 1 x2 2
2.
L
x2
0
p2
a2 x1 1 x
ECN500/FIN580 Fall 2015
Problem Set #2 Solutions
1. Utility Maximization and Expenditure Minimization Problems
1a.
u(tx1,tx 2 ) tx1 1 tx 2 2 t a1 a2 x1 1 x 2 2
The utility function u(x1, x 2 ) is homogenous of degree a1 a2 .
a
a
a
a
1b.
L x1a1 x 2a2 w p1x
ECN500/FIN580 Fall 2011
Some Solutions for Problem Set #7
1. Bayesian Normal Form
6. The Hold-Up Problem
(a) The firm always maximizes revenue by choosing a heat setting such that h*s = 30. If the firm
chooses the local source, then s = .1, and it should
UNIVERSITYOF ILLINOIS AT URBANA-CHAMPAIGN
Department of Finance Department of Economics
Finance 580 / Economics 530: Microeconomic Theory I
Problem Set #3
Due Friday, October 9, 2015.
Please turn in your problem set by 4pm on the date the assignment is du
ECN530/FIN580 Fall 2015
Problem Set #1 Solutions
1. 2.D.4
Consumption
Good
Slope = s(1-t)
A
M
Slope = s
Slope = s
B
24
16
Leisure hours
For a convex set, any point on a line connecting two points, which belong to the set, must also belong to
the set. Poin
ECN500/FIN580 Fall 2011
Some Solutions for Problem Set #6
2. Levels of Affection
Two people play a simultaneous game where each declares a level of commitment to the other
person. Three actions are available to each person, Love, Like, and Tolerate. The g
UNIVERSITYOF ILLINOIS AT URBANA-CHAMPAIGN
Department of Finance Department of Economics
Finance 580 / Economics 530: Microeconomic Theory
Problem Set #4
Due: Friday, October 16, 2015.
Note: this problem set is due at the start of the review session, 11:00
UNIVERSITYOF ILLINOIS AT URBANA-CHAMPAIGN
Department of Finance Department of Economics
Finance 580 / Economics 530: Microeconomic Theory I
Problem Set #5
Due Friday, November 13, 2015
Please turn in your problem set by 4pm on the date the assignment is d
v (p; w) = a ln a + b ln b + (a + b) ln
a) Using Roys Identity,
@v
@p1
a @v
p1 , @w
=
a
( a+b
) pw1 . Similarly, x2 (p; w) =
b
b+a
=
w
a+b
a+b
w ,
a ln p1
so x1 (p; w) =
v (5; 10; w
a ln 5
m)
b ln 10
ln
w
m
w
w
m
w
a
p1
= a+b
w =
w
p2 .
@v
b) @w
= a+b
w .
ECN500/FIN580 Fall 2011
Some Problem Set #4 Solutions
1a. For our graphical solution, we can use the graph given in the problem set. We need to show that as w
changes, x1 stays constant. Note that each dotted line could be a budget line for some given pri
Marx's attack on Proudhon's Systme des Contradictions conomiques ou Philosophie de la Misere was first published in French in 1847. There is a good deal of rather turgid logomachy about "value" but also several interesting details illustrative of the gene
This is Wittgenstein's posthumous book. The original German is given side by side with the English translation by G.E.M. Anscombe, which has undergone many corrections for this edition. Philosophical Investigations, like the Tractatus Logico-Philosophicus
The economic writing of Ludwig von Mises spanned seventy years from 1902 to 1972. His major work, Human Action, is truly the economics bible for all peoples. However, he first rose to eminence
For six decades Mises warned against the fallacious doctrines
It gives a general account of the measures of control taken in Great Britain during the First World War, and though other writers had dealt with the subject previously at the time, and most of the figures given were available elsewhere, Shadwell's judgmen
"Once we venture beyond the rudiments," says Bell, "we may agree that those who cultivate mathematics have more interesting things to say about it than those who merely venerate." No more eloquent substantiation of this assertion could be wished for than
Peters begins by illustrating the thesis that many different sorts of question can be asked about human behavior and that each requires a logically different type of answer. In asking the general question "why did X do that?" at least three sorts of answe
Among the anti-Communist literature written by ex-Communists, Rossi's book (originally published in 1948 as Physiologie du Parti Communiste Franais) is of particular value to the critical student. The author, an Italian socialist who joined the Communist