Advanced Microeconomic Theory I
9:00am - 12:00noon, December 8, 2005
There are five questions in this exam.
You must answer ALL que
Economics 811: Assignment 3
November 7, 2010.
Due: November 12, 2010.
Question 1. Suppose that there are three individuals, A, B and C. The capacity to generate payoffs,
either independently or in coalitions is given by the following table:
Economics 813: Assignment 1
September 24, 2010.
Due: October 1, 2010.
Question 1. Suppose there are three possible prizes: 0, 1 million and 5 million. The prize vector is
then (0, 1, 5). Represent a lottery by a triple p : (p1 , p2 , p3 ), where p1 is the
November 26, 2010
Question 1. Players 1 and 2 must decide whether or not to carry an umbrella when leaving home. They
know that there is a 50 50 chance of rain. Each players payoff is -5 if he doesnt carry an umbrella and
Economics 811: Assignment 1
September 25, 2012.
Due: October 2, 2012.
i. In the weighted utility model, for i = 1, 2, 3, let u(xi ) = i and w(xi ) = 2i. Plot some indifference
curves and find the point of intersection of the indifference curve
Economics 811: Assignment 2
October 12, 2010.
Question 1. Show that good i is a normal good if and only if
Question 2. Let x = (x1 , x2 , x3 , . . . , xn1 ) be a vector of n 1 goods, and let z be a single good. Suppose
that the utility functi
-1. (15 points)
f) do ~ I(\. I b'1 -! E +1 i=J:2.DI'~
Consider the following normal-form game:
. ~ d Fdo~'~cd"~
(a) (10 points) Find all pure and mixed strategy Nash equilibria (if any).
(b) (5 points) Find the pure-strategy