Revealed preference.
Pasha Andreyanov
October 7, 2015
1
Revealed preference
Let D be a collection of prices and choices ppi , xi q, but such that prices are strictly positive.
revealed preferred: xi xj iff pi xi pi xj
strictly revealed preferred: xi xj
Econ 201A: Problem Set II
Due on October 16, 2015
1. Properties of Various Utility Functions
Examine carefully if the following utility functions on R2+ are (a) (strictly)
concave/quasi-concave, (b) homogeneous of degree 1, and (c) (strictly) increasing.
HW 2 Solutions.
Pasha
October 16, 2015
Youve got thirteen and you take away seven, and that leaves five.
well, six, actually, but the idea is the important thing.
New Math.
1
Properties of Various Utility Functions
Before we start, note that all whatever-
Econ 201A: Problem Set I
Due on October 9, 2015
1. Weak Preference and Strict Preference.
(a) Let
be a strict preference relation that is derived from a complete
and transitive preference on X RL
y , fx y and y xg.
+ by x
Prove that
is asymmetric (x
y )y
Econ 201A: Suggested Answer for Midterm Exam
1. (30 pts.) Is each statement below true or false? If you think that it is true,
prove it. If you this that it is false, provide a counterexample.
(a) Take any preference on X that is complete and transitive a
Econ 201A: Suggested Answer for the Final Exam
1. True or False? (24 pts.).
Is each of the following statements true or false? If you think it is, prove it. If
you dont, nd a counterexample.
(a) Let
be a preference on a nite set X; which is antisymmetric
Expected Utility.
Pasha Andreyanov
October 22, 2015
I will face my fear. I will permit it to pass over me and through me. And
when it has gone past I will turn the inner eye to see its path. Where the fear
has gone there will be nothing. Only I will remai
Econ 201A: Midterm Exam
November 12, 2014
This is a closed-book exam. You have 75min. Good luck!
1. (30 pts.) Is each statement below true or false? If you think that it is, prove
it. If you dont, find a counterexample.
(a) Let be a preference over the se
Choice, preference and utility.
Pasha Andreyanov
October 8, 2015
In the beginning, it is always dark.
The Neverending Story.
1
Choice, preference and utility
Imagine a guy that goes every evening to Whole Foods to get a bottle of beer. Every day he comes
Utility for money.
Pasha Andreyanov
October 31, 2015
1
Intro
Here were going to compare utilities by taking expectation with respect to different lotteries.
2
Ordering of lotteries
Consider a pair p, q where
X - is the space of outcomes
is the space of
Debreu theorem.
Pasha Andreyanov
October 6, 2015
You can help me. Whatever comes out of these gates, weve got a better
chance of survival if we work together. Do you understand? If we stay
together we survive.
Gladiator.
1
Debreu theorem
On the midterm/ex
Utility maximization.
Pasha Andreyanov
October 14, 2015
1
Utility maximization
Fix the domain D to be Rn` from the very beginning. Were only going to work with positive amounts of
consumption goods. You can not unconsume your breakfast, you know.
n`1
Defi
Expenditure minimization.
Pasha Andreyanov
October 14, 2015
1
Expenditure minimization
Let our domain be D Rn` again. Fix a function u : D R.
Definition 1. Denote U LS : R D the upper-level-set correspondence
U LSpvq tx P D : upxq vu
Again, our favorite q
Econ 201A: Suggested Answer for Midterm Exam
1. (32 pts.) Choice Function
Let X be the space of all possible alternatives and A be a collection of subsets
of X: There are two decision makers 1 and 2 with choice function C1 and C2
respectively, where Ci ;
Maximum theorem.
Pasha Andreyanov
October 6, 2015
I checked it very thoroughly, said the computer, and that quite definitely is
the answer. I think the problem, to be quite honest with you, is that youve
never actually known what the question is. So once
HW 1 Solutions.
Credits to Akina Ikudo for fancy solutions
October 16, 2015
1
Weak preference and strict preference
Definition 1. A preference relation on X is a binary relation, that is
Complete:
px yq y x
Transitive: x y, y z x z
1.1
part a
Let be a s