Exercise 1
ECON / MATH C103  Mathematical Economics
Philipp Strack
due Tue Jan 24, 4:59pm
Please raise questions, in the office hours, via email or at bcourses:
office hours: Cristian Ugarte,
email:
Econ. C103, 2003
Daniel McFadden
Problem Set 10. Example Final Exam Questions
(For practice, not to be handed in)
1. There are J firms in an industry. Each can try to convince Congress to give the ind
Consumer Theory: The Mathematical Core
Dan McFadden, C103
Suppose an individual has a utility function U(x) which is a function of nonnegative
commodity vectors x = (x1,x2,.,xN), and seeks to maximiz
Econ C103, 2003
Daniel McFadden
THE THEORY OF FIRSTPRICE, SEALEDBID AUCTIONS
1. Within the class of firstprice, sealedbid auctions, there are a number of
possible variations in environment, inform
Optimization Theory
Lectures 46
Unconstrained Maximization
Problem Maxim afunctionf: 6withinaset A
:
ize
fn.
n
Typically, Ais , or thenonnegativeorthant
n
cfw_x0 x$0
n
Existence of a maximum:
Theor
Robinson Crusoe
Lectures 67
Pounds of Yams per Day
1. Robinson's Production Possibilities
15
12
9
6
3
0
0
4
8
12
16
20
Hours of Leisure per Day
24
2.Robinson's Preference Contours
Pounds/Day of Yams
Econ. C103, 2003
Daniel McFadden
MECHANISM DESIGN, DIRECT SELLING MECHANISMS, EFFICIENT AUCTIONS
The theory of mechanism design provides some general insights into the construction
of resource allocat
Analysis and Linear Algebra
Lectures 13 on the mathematical
tools that will be used in C103
Set Notation
A,B
AcB
A1B
A\B
N.
AfB
. Ac
a0A
aA
sets
union
intersection
the set of objects in A that are no
7. This mechanism is clearly not incentive compatible.
To see this, let us denote by cfw_v1 ,., vN +1 the true valuations of the good for the N+1
consumers, where vn represents the nth highest valuati
C103, Fall 20003, Problem Set 4 (due October 2)
1. Suppose a consumer has a concave utility function U(x), where x = (x1,.,xn) is a vector of n
goods and services, and maximizes utility subject to x $
PROBLEM SET II
1.
This question refers to the notation and equations of Appendix A.1 of
D. McFadden Definite Quadratic Forms Subject to Constraints in M. Fuss and D. McFadden Production
Economics, Vol
C103, Fall 20003, Problem Set 3 (due September 25)
1. In a Robinson Crusoe economy where the goods are leisure (H) and yams (Y), the feasible
resource allocations lie on or below the curve Y = [6(24H
Econ C103, 2003
McFadden
Existence of Walrasian Equilibrium
Theorem (GrandmontMcFadden, 1972)
Define the closed unit simplex U* = cfw_p0m  p $ 0 and [email protected] = 1 and the open unit
simplex U0 = cfw_p0U* 
Economics/Mathematics C103
Introduction to Mathematical Economics
Fall 2014
TTh 89:30
3106 Etcheverry
Professor Chris Shannon
1
Description
C103 is an interdisciplinary topics course in mathematical
Proof by Deduction
Proof by Deduction: A list of statements, the last of which is
the statement to be proven. Each statement in the list is either
an axiom: a fundamental assumption about mathematics
MATH/ECON C103 Problem Set 1 Comments
General Notes
1. PLEASE WRITE LEGIBLY
Please do not write write very small, and please leave adequate
space between your text so that it is easier for your grader
Exercise 2
ECON / MATH C103  Mathematical Economics
Philipp Strack
due Tue Jan 31, 4:59pm
Please raise questions, in the office hours, via email or at bcourses:
office hours: Cristian Ugarte, Fridays
Exercise 4
ECON / MATH C103  Mathematical Economics
Philipp Strack
due Tue Feb 14, 4:59pm
Each subexercise is weighted equally.
Helpful Material:
 Last weeks lecture notes.
Exercise 1: (28 points)
Exercise 3
ECON / MATH C103  Mathematical Economics
Philipp Strack
due Tue Feb 7, 4:59pm
Each subexercise is weighted equally.
Helpful Material:
 Last weeks lecture notes.
Exercise 1: (12 points) C
Single Agent

Material:
 Slides,
 page 6  26 in the book by Tilman Boergers,
 page 110, 1315 in the lecture notes by Juuso Valimaecki
 page 6171 (for multiple agents) in the book by Vijay Kri
ECON/MATH C103
FAQ
Some comments on the questions from this week office hours.
1. How can we interpret the virtual value?
Note that the revenue maximization problem for the principal is equal a the so
Dynamic Mechanism Design
April 18, 2017
1
a simple example  preferences
1. two agents i cfw_1, 2
2. single object x1 + x2 1
3. quasilinear utility
i xi ti
4. independent types i U([0, 1])
2
a simple
Economics/Mathematics 103
Fall 2014
Chris Shannon
Problem Set 4 Due Thursday September 25
1. Consider a marriage market allowing for indierences, in which M = cfw_m1 , m2 , m3 , W =
cfw_w1 , w2 , w3 ,
Economics/Mathematics 103
Fall 2014
Chris Shannon
Problem Set 1 Suggested Solutions
1. Prove that there is no greatest even integer. (Hint: prove this by contradiction)
Solution: Suppose, by way of co
Economics/Mathematics 103
Fall 2014
Chris Shannon
Problem Set 3 Due Thursday September 18
1. Consider the marriage market example from class and problem set 2 #3, with M = cfw_m1 , m2 , m3 ,
W = cfw_w
Economics/Mathematics 103
Fall 2014
Chris Shannon
Problem Set 1 Due Thursday September 4
1. Prove that there is no greatest even integer. (Hint: prove this by contradiction)
2. Prove that if r is a ra
Economics/Mathematics 103
Fall 2014
Chris Shannon
Problem Set 2 Due Thursday September 11
1. Let
be a preference relation on a set X. For each x X, dene
I(x) := cfw_y X : y x
So I(x) is the set of ele
Econ C103, 2003
Daniel McFadden
THE WINNERS CURSE
Consider an auction for a single item whose value to a buyer is not known with certainty,
but must be estimated. Each players bid will be based on his