econ 245
solution to problem set 2
Max
January 29, 2012
Exercise 1
Simon and Blume: Problems 15.1 and 15.2 on page 342.
15.1
Solution: a)
Let F (x, y ) := x2 xy 3 + y 5 17. Note that F (5, 2) = 0 and
Lecture 21:
Optimization and
Curvature II
Cecilia Fieler
Economics 245
Lecture 21: Optimization and Curvature II
Cecilia Fieler
April 12, 2012
Concave and
quasi-concave
programs
Readings
Lecture 21:
O
Lecture 18:
Production
Economy
Cecilia Fieler
An economy with
production
Economics 245
Lecture 18: An economy with production
Cecilia Fieler
April 3, 2012
Second Welfare
Theorem
First welfare
theorem
Lecture 19:
Existence and
Denite Matrices
Cecilia Fieler
Existence
Economics 245
Lecture 19: Existence and Denite Matrices
Cecilia Fieler
April 5, 2012
Denite Matrices
Readings
Lecture 19:
Existence a
Lecture 16: The
Envelope Theorem
Cecilia Fieler
Value function
Envelope Theorem
Economics 245
Lecture 16: The Envelope Theorem
Cecilia Fieler
March 22, 2012
Why envelope?
Short run and long
run
Readin
Lecture 15: Value
Functions
Cecilia Fieler
Value function
Envelope Theorem
Economics 245
Lecture 15: Value Functions
Cecilia Fieler
March 13, 2012
Shephards lemma
Readings
Lecture 15: Value
Functions
Lecture 13: The
Second
Fundamental
Welfare Theorem
Cecilia Fieler
Economics 245
Lecture 13: The Second Fundamental
Welfare Theorem
Welfare optimum
benchmark
Competitive
equilibrium
Non-uniqueness of
(
Lecture 11:
Shadow Prices,
Exchange
Economies, and
Social Planners
Cecilia Fieler
Economics 245
Lecture 11: Shadow Prices, Exchange
Economies, and Social Planners
Cecilia Fieler
February 21, 2012
Inte
Lecture 14: The
First Fundamental
Welfare Theorem
Cecilia Fieler
Economics 245
Lecture 14: The First Fundamental Welfare
Theorem
Cecilia Fieler
March 1, 2012
Competitive
equilibrium
First Welfare
Theo
Lecture 17:
Optimization and
Curvature III
Cecilia Fieler
Economics 245
Lecture 22: Optimization and Curvature III
Cecilia Fieler
April 19, 2012
Separating
Hyperplane
Theorem
An economy with
productio
ECON 245
ps1 solution
Max
January 23, 2012
Exercise 1
f : R R is dierentiable, and let A = [a, b] be a closed interval
< a < b < . State the necessary rst-order conditions (i.e., ones
involving just
Economics 245
Spring 2012
Cecilia Fieler
University of Pennsylvania
Problem Set 2
Due Tuesday, January 31
Simon and Blume: Problems 15.1 and 15.2 on page 342.
1. Demand for a good is given by a functi
Economics 245
Spring 2012
Cecilia Fieler
University of Pennsylvania
Problem Set 1
Due Jan. 24
1. Suppose f : R R is dierentiable, and let A = [a, b] be a closed interval with
< a < b < . State the ne
Find the competitive equilibrium in an economy with two consumers, 1 and 2 and two
goods x and y . The endowment of consumers is (x1 , y1 , x2 , y2 ). Utility is ui = ax + yi
i
for i = 1, 2.
Solution
Economics 245
Spring 2012
Cecilia Fieler
University of Pennsylvania
Mock Midterm 1
80 points total. Closed book and notes. 1.25 hours max.
1. (30 pts) When a gas station sells a gallon of gas, it rece
Economics 245
Spring 2012
Cecilia Fieler
University of Pennsylvania
Mock Midterm 2 - solutions
100 points total. Closed book and notes. 1.15 hours max.
1. (30 pts) Consider this problem:
(P)
max xy su
Economics 245
Spring 2012
Cecilia Fieler
University of Pennsylvania
Midterm 2
100 points total. Closed book and notes. 1.15 hours max.
1. (30 pts) Consider this problem:
(P)
max xy such that
x,y 0
x +
Economics 245
Spring 2012
Ana Cecilia Fieler
University of Pennsylvania
Solutions to Midterm 2
Thursday, March 29
110 points total. Closed book and notes. 1 1 hours max.
3
1. (20 pts) Consider this pr
Economics 245
Spring 2012
Cecilia Fieler
University of Pennsylvania
Midterm 1 Solutions
80 points total. Closed book and notes. 1.25 hours max.
1. (30 pts) There is a market in a good with one supplie
Economics 245
Spring 2012
Cecilia Fieler
University of Pennsylvania
Midterm 2
Thursday, March 29
110 points total. Closed book and notes. 1.15 hours max.
1. (20 pts) Consider this problem:
(P)
max x +
Lecture 5:
Constraint
Qualication and
the Lagrangian
Approach
Cecilia Fieler
Economics 245
Lecture 5: Constraint Qualication and the
Lagrangian Approach
Substitution
method using the
IFT
Constraint
qu
Economics 245
Spring 2012
Cecilia Fieler
University of Pennsylvania
Problem Set 7
Due Tuesday, April 17
1. Consider the denition of a competitive equilibrium with production from the lecture
notes 17:
Econ245-2012
ps7_sol
April 6, 2012
max
Exercise 1
The sum of the rms revenues is gG p g g . The sum of the consumers
incomes is cC I c . Consumers budget constraints say that I c = gG p g x c .
g
But
ECON245
problem set 6 sol
max
March 13, 2012
The problems below are about a private ownership exchange economy in which each
consumer
c
has a given endowment vector,
endowment of good
g
is
Xg :=
xc ,
Economics 245
Spring 2012
Cecilia Fieler
University of Pennsylvania
Problem Set 6
Due Tuesday, March 20
The problems below are about a private ownership exchange economy in which each
consumer c has a