Risk Aversion
HW#4:
Provide the missing proofs.
Due Monday, November 6
Let the set of lotteries L be the set of probability distributions on Z R (for
which expectation is well-dened) with a typical element F . If not mentioned
otherwise, X is a random var
HW#1
Due Monday, Sept 12, class time
1
Part 1. Excess Demand and Equilibrium
Problem 1 Show that in an exchange economy with L goods and I consumers, such that all consumers have strictly convex, continuous and locally
non-satiated (not necessarily monoto
Advanced Microeconomics Homework 1 Answer Key
Problem 1
(Answer key)
Discussion: Locally non-satiation and strongly monotone.
Monotone preferences imply that all the commodities are good and that more of even
one commodity strictly increases utility. Loca
Solutions to some review questions
December 14, 2006
1
Contract Theory
Problem 1 Consider the monopolistic screening problem with a continuum
of types from chapter 2 of BD. Solve for the full information allocation rule
(for a monopolist who can perfectly
Adverse selection
(based on BD(2005)
November 30, 2006
1
1.1
Full information
Monopolist Problem
Seller: T cq
Buyers have quasi-linear preferences i v (qi ) + mi
U (q, T, i ) = i v (q) T
Two types of buyers cfw_h, l , fraction of h-type buyers
1.1.1
No pr
HW on Contract Theory
due November 28
Problem 1 Section 2.3 of the textbook. Consider the one-buyer one-seller
problem with a continuum of possible (payo-relevant) types, from , .
Suppose that monotonicity and local incentive constraint hold. Show that
HW#1
Due Monday, Sept 18, class time
1
Edgeworth Box Economy
Problem 1 15.B.1
Problem 2 15.B.2. Pick some values for the endowments and let = =
1/2. Depict the two oer curves in the Edgeworth Box.
Problem 3 15.B.9.
Problem 4 Consider the Edgeworth Box eco
HW#1
Suggested solutions
1
Edgeworth Box Economy
Problem 1 Consider the Edgeworth Box economy with two consumers: A, B
and strictly positive endowments = ( 1A , 2A , 1B , 2B ) > 0. Let the
preferences (of A and B correspondingly) be represented by the uti
HW#2
Due Wednesday Oct 4, class time
1
Part 1. First welfare theorem: A group
project
Problem 1 Refer to the link on our webpage (right below) for an incompelte "easy" proof of the First Welfare Theorem for the two individuals, two
outputs, two inputs eco
HW#2
Suggested Solutions
1
Part 1. First welfare theorem: A group
project
Problem 1 Refer to the link on our webpage (right below) for an incomplete "easy" proof of the First Welfare Theorem for the two individuals, two
outputs, two inputs economy. Impose
Proposition 1 If SCF f : LN A is stratefy-proof and f LN = A, then f
is Pareto ecient and monotonic.
0
Proof. 1. Monotonicity. Suppose that f (L) = a. Take i. Consider Li :
0
aLi b aLi b b
want to show that f (L0 , Li ) = a. Suppose to the contrary that
EUT, an easy version.
October 11, 2006
Let L be the set of (simple) lotteries over the set of consequences (outcomes) C = cfw_x1 , ., xN .
L = (p1 , ., pN ) N1 .
Let a degenerate lottery with associated probability 1 on outcome xi be
denoted by Lxi .
Con