EEP 101/Econ 125 Spring 2002 GSIs: Alix, McKim, Schoengold
Problem Set #1: due on Thursday, February 14 at lecture.
Late assignments will not be accepted. Numerical Questions (1) Suppose that an industry has an inverse demand curve given by P = 90
EEP 101/ECON 125
Problem Set #5 Suggested Solutions
1) The Impacts of Climate Change
Crop Profits Before and After Climate Change
south
north
a) I drew the new profit curves everywhere to the right of the old profit curves. This represents t
Department of Environmental Economics and Policy University of California, Berkeley Midterm
Economics EEP101/ECON125, Spring 2003 Professor Zilberman
Instructions: Please remember to write your name and Student ID# on your bluebook. Answer all ques
Econ 101A Solution to Midterm 1
Th 3 October.
Problem 1. Labor supply with social comparison. (48 points) In this exercise, we consider a
labor supply model with Cobb-Douglas preferences. The non-standard feature in this problem is that the
preferences fo
EEP 101/Econ 125 Spring 2002 GSIs: Alix, McKim, Schoengold Solutions to Problem Set #1 Numerical Questions: For the numerical questions, there are graphs at the end of the solution key that show how to calculate the answers using graphical methods. T
Section 8
Econ 101A, Spring 2014
GSIs: Ivan Balbuzanov, Anne Karing1
Below we specify separately the setup for the utility maximization and expenditure minimization problems, and highlight a few things.
Utility Maximization
Expenditure Minimization
s.t. p
Section 11
Econ 101A, Spring 2014
GSIs: Ivan Balbuzanov, Anne Karing1
Expected Value and Expected Utility
The expected value of any lottery is the sum of all possible outcomes times their respective probabilities:
E(X) =
xi P rcfw_xi
where
P rcfw_xi = 1
Section 12
Econ 101A, Spring 2014
GSIs: Ivan Balbuzanov, Anne Karing1
Example: Selling a Book
Lets calculate the expected utility from selling the book to your friend and to posting a yer when
preferences over lotteries are determined by the utility, lett
Econ 101A Midterm 1
Th 3 October.
You have approximately 1 hour and 20 minutes to answer the questions in the midterm. I will collect
the exams at 12.30 sharp. Show your work!
Problem 1. Labor supply with social comparison. (48 points) In this exercise, w
Section 13
Econ 101A, Spring 2014
GSIs: Ivan Balbuzanov, Anne Karing1
Midterm 2 Problem: 2004 #1
Mary is worried about car accidents next year. She has $10,000 in wealth, including the value of her car.
With probability 2/3 she will have an accident and s
Section 15
Econ 101A, Spring 2014
GSIs: Ivan Balbuzanov, Anne Karing1
Two-Step Cost Minimization
Prot maximization.
[Note: this is just another way to think about the two-step cost minimization we saw in lecture.]
Firms decision:
max R(y; p) C(y; w, r)
Section 15
Econ 101A, Spring 2014
GSIs: Ivan Balbuzanov, Anne Karing1
Cost Curves
If there are no xed costs, then:
The AC and M C curves begin at the same point.
If M C is always increasing, then AC always lies below it.
If M C is always decreasing, th
Section 14
Econ 101A, Spring 2014
GSIs: Ivan Balbuzanov, Anne Karing1
Time inconsistency example
Example: Time inconsistency
Amy inherits M dollars when born. She will live for 3 periods (t = 0; 1; and 2) and must allocate M
over her lifetime so as to con
Section 7
Econ 101A, Spring 2014
GSIs: Ivan Balbuzanov, Anne Karing1
Example:
max
(x1 ,x2 )R2
+
x2 (x1 + 4)
p1 x1 + p2 x2 M
s.t
To show that we can set p1 x1 + p2 x2 = M :
cfw_x2 (x1 + 4) = x2 0 on R2 .
+
x1
cfw_x2 (x1 + 4) = x + 4 > 0 on R2 .
+
x2
Thus,
Section 10
Econ 101A, Spring 2014
GSIs: Ivan Balbuzanov, Anne Karing1
Labor Supply
As in lecture, we derive the budget constraint. The total endowment will be M + wh, or initial endowment
plus wages earned from working hours h. Utility will be over consum
Section 2
Econ 101A, Spring 2014
GSIs: Ivan Balbuzanov, Anne Karing1
Optimization
Finding optimums, i.e. maximums and minimums, of scalar functions.
One may want to minimize a scalar function. Minimizing a function gives the same solution as maximizing
Section 4
Econ 101A, Spring 2014
GSIs: Ivan Balbuzanov, Anne Karing1
Constrained Optimization (continued)
Example: Studying during nals week
1. Write the maximization problem in Lagrangian form:
2
2
L = GP A = 3 C hL + 3 hE (hL + hE 12)
2. Write down th
Section 1
Econ 101A, Spring 2014
GSIs: Ivan Balbuzanov, Anne Karing1
Math Review
Let i = 1, 2, . . . , m denote the rows of a matrix (or the elements of a column vector) and j = 1, 2, . . . , n the
columns. (The exception is that in the Hessian both i and
Section 3
Econ 101A, Spring 2014
GSIs: Ivan Balbuzanov, Anne Karing1
Multivariate Denition
First, assume we have a function f : Rn Rn , and f (x; p) = [0, ., 0]T . We now have a set of equations
(whereas above we have only one f equation). The two conditi
Tim drives a Toyota and expects to nd himself in an accident within the next year with probability p. The cost of an accident will run him L. Tims utility over wealth is u(w) = ln(w).
Assume Tim starts with wealth w0 . Also, Tim can choose how much (if an
Section 5
Econ 101A, Spring 2014
GSIs: Ivan Balbuzanov, Anne Karing1
Preferences
Economists often call upon utility functions to help describe behavior. In particular, they model agents as
utility maximizers. However, none of us actually take a set of fea
Section 8
Econ 101A, Spring 2014
GSIs: Ivan Balbuzanov, Anne Karing1
Below we specify separately the setup for the utility maximization and expenditure minimization problems, and highlight a few things.
Utility Maximization
Expenditure Minimization
s.t. p
Section 6
Econ 101A, Spring 2014
GSIs: Ivan Balbuzanov, Anne Karing1
Indierence Curves (IC)
(a) Can ICs ever intersect each other? If not, why not?
No: otherwise the fact that U is a function would be violated. Functions are single valued by denition
(in
Section 16
Econ 101A, Spring 2014
GSIs: Ivan Balbuzanov, Anne Karing1
Aggregation and Market Equilibrium
So far, we have learned to solve a rms supply function of a good (quantity
produced as a function of price) and a consumers demand function for a good
Section 20
Econ 101A, Spring 2014
GSIs: Ivan Balbuzanov, Anne Karing
1
Game Theory
Notation
A game consists of a set of players (1, 2, ., I), a strategy set for each player, and a full specication
of payos to each player for each possible combination of s
Depressions:
Theory and Evidence
Blanchard:Chapters14,22,28
Krugman:Chapters1and 4 ( ti
K
Ch t
1 d 4(optional)
l)
ChristinaRomer:article@bspace (optional)
A depression is an extended period of economic
stagnation/decline that substantially exceeds in
t
ti
Depressions:
Theory and Evidence
Blanchard:Chapters14,22,28
Krugman:Chapters1and 4 ( ti
K
Ch t
1 d 4(optional)
l)
ChristinaRomer:article@bspace (optional)
A depression is an extended period of economic
stagnation/decline that substantially exceeds in
t
ti
Policy Options and the
Business Cycle
Read
Greenspan: Chapters 5, 7, 10, and 11 (optional)
Blanchard: Chapters 24-26
Marvin Goodfriends article (optional)
Business Cycle Analysis
1. Assessing the validity of the model by comparing the response
g
y
y
p
g
p