September 2013 Examination
EC400
Probability and Statistics - solutions
Instructions to candidates
Time allowed: 2 hours
This paper contains EIGHT questions. Answer ALL questions.
You are not allowed to use an electronic calculator
c LSE 2013/EC400 Probab

FEB11001X - Microeconomics
TA Session 1
Chapters 1 & 2
01 November 2012
TA 1 (Chapters 1 & 2)
01 November 2012
1 / 17
Introduction
Zara Sharif
email: sharif@ese.eur.nl
O ce: H9-13
O ce hours: Mondays 15.00 - 16.30 (otherwise by appointment)
TA 1 (Chapters

September 2013 Examination
EC400
Probability and Statistics
Instructions to candidates
Time allowed: 2 hours
This paper contains EIGHT questions. Answer ALL questions.
You are not allowed to use an electronic calculator
c LSE 2013/EC400 Probability & Stat

Summary Chapter 12 Monopoly
Defining Monopoly
- A monopoly is a market structure in which a single seller of a product with no close substitutes
serves the entire market
- One practical measure for deciding whether a firm enjoys significant monopoly power

1. Insurance.
The utility function of Peter is given by U = M 2 . M is his yearly income in euros.
With a 31 probability M is equal to 6. With probability 31 , M = 3. Finally, with
probability 13 M = 0.
1. The expected utility of Peter is eqaul to 3.
Supp

1
Solutions to Chapter 3 exercises
1.1
Indierence curves:
U (x; y) = xy = 5 , y = x5
p
p 2
p
p
U (x; y) = x + y = 5 , y = (5
x) = 25 + x 10 x
U (x; y) = x y 1
= 5 , ln x + (1
) ln y = ln 5 , ln y =
ln 5
ln x
ln 5
ln x
, y = exp
1
1
1.2
MRS
U (x; y) = xy !

1
Utility Functions
Consider the following utility function:
U (x; y) = x y ; 0 < ;
< 1:
(1)
Let the prices of goods x and y be respectively px and py :
1. Why can the U (x; y) = 5 indierence curve associated to the above utility
function never touch eith

Chapter 7:
Philosophy Meets Economics?
Tastes, Altruism
and
Nonegoistic Behavior
1
Tastes
Rationality is one of the central concepts of economics in general and microeconomics in particular.
The two most prominent denitions of rationality are:
1. The pres

1
Tennis or Dinner?
Ravin has bought a ticket for the tennis match between Rafael Nadal and Roger Federer.
The ticket costs him 30 euros. Just before leaving for the match, he receives an invitation
to have dinner with one of his friends. Ravin cannot att

Algebra of the Hicksian substitution and income eects
This is NOT exam material (even though it is not di cult.)
1
Problem
Consumer has utility U (x; y) and faces budget constraint
M = px x + py y:
Label with (x ; y ) the initial optimal consumption point

Chapter 2 Summary Supply and Demand
Supply and Demand Curves
- The basic tool for analyzing market outcomes is supply and demand analysis
- A market consists of the buyers and sellers of a good or service
- Markets can have sizes to different extends, as

Exam Version A with answers
Answers are at the end oif the exam. If you had exam version B, use this
version with answers but be careful to refer to the right questions.
1
Demand and Supply
The world demand (Qd ) and supply (Qs ) curves for tea are given

Homework 1
1
Indierence Curves for Quasi-Linear Utility
Functions
1. Draw some indierence curves (for example for utility levels 1, 2 and 3)
for the following two quasi-linear utility functions in the (x; y) space:
p
U1 (x; y) = x + y
p
U2 (x; y) =
x+y
Yo

Erasmus School of Economics
Microeconomis FEB11001X
Midterm 1
November 2010
Calculators, of any type are NOT allowed.All computations that you may be asked to perform yield
positive integers.
1
Theory of the Consumer
The utility function of Carlos if give

1
Utility Functions
Consider the following utility function:
U (x; y) = x y ; 0 < ;
< 1:
(1)
Let the prices of goods x and y be respectively px and py :
1. Why can the U (x; y) = 5 indierence curve associated to the above utility
function never touch eith

Microeconomics
FEB11001X
Benot S Y Crutzen
General Information
O ce hours:
H08-11, upon request, via email: crutzen@ese.eur.nl
Required reading:
Frank, Robert H, Microeconomics and Behavior, 8th edition, McGrawHill
YOU SHOULD HAVE THE BOOK BY NOW!
Additio

Midterm test 2
Answers:
TENNIS:
(A) Federer
w
eN
eF
+v
eF + eN
eF + eN
1 2
e , maximize w.r.t. eF
2 F
(B) rst order condition:
w
(eF + eN ) eF
eN
+v
2
(eF + eN )
(eF + eN )2
eN
(w v)
(eF + eN )2
eF = 0
eF = 0
Symmetry between the two playersproblem implie

Answers Exam Micro 13 July 2010 IBEB
(version 1)
1. wrong: expected utility is equal to
1
3
36 +
1
3
9 = 15
2. wrong: Peter is willing to pay something for an insurance that gives him
a utility of 42 = 16 > 15;his expected utility without insurance;
3. wr

Microeconomics FEB11001X
MIDTERM 2
7 December 2010
Name and Surname: Student number GROUP number
Calculators and dictionaries are NOT allowed.
1
Of Land, Capital and men (5 points)
Consider a rm that uses optimally its three inputs: land, capital and labo

FEB11001X
Microeconomics IBEB
Toets 1
17 November 2008
There are 3 questions.
All questions yield 10 points.
Answer all questions.
Do not forget to JUSTIFY all your answers.
Do not forget to put your name on your test!
Total time at your disposal is 45 mi

Chapter 16:
Externalities, the Coase Theorem
and
Government Intervention (13, 16,
17)
Part 1:
Externalities and the Coase Theorem
1
1.1
Externalities
What is an externality?
In economics, an externality is a cost or benet that impacts a partys objective
f

Chapter 14-15:
Labor and Capital
My coverage of chapters 14 and 15 is not as extensive as that of the other
chapters we covered so far.
(But remember that statistical discrimination, which we dealt with when we
looked at the agents choice problem under un

More on the CDF, with a focus on the CDF of the
Uniform Distribution
IBEB Micro 2012
EUR
14 November 2012
IBEB Micro 2012 (EUR)
CDF of Uniform
14 November 2012
1/7
The CDF
Then cumulative distribution function of a random variable (r.v.) X tells
us how li

Microeconomics, FEB 11001X
Midterm 2
14 december 2010
1
Tennis
Federer en Nadal play in one of their many nals. The winner gets a prize worth w and the
runnerup a prize worth v < w (with w > v > 0). Let ei denote player is eort to win. The
chance that pla

Microeconomics FEB11001X
MIDTERM 2
7 December 2010
Name and Sirname: Student number GROUP number
Calculators and dictionaries are NOT allowed.
1
Of Land, Capital and men (5 points)
Consider a rm that uses optimally its three inputs: land, capital and labo

Erasmus School of Economics
Microeconomics FEB11001X
MIDTERM 1
16 November 2010
Calculators and dictionaries are NOT allowed.
1
Pizza!
Johns utility function is given by the following Cobb-Douglas:
U (y; q) = y q
where q is pizza consumption, y is the com

1
A Public Good Problem
A government needs to provide a public good that is necessary for society to
function (this good could be order and justice, for example).
The government must nance the provision of the public good via taxes. Its
budget constraint

Erasmus University Rotterdam
Erasmus School of Economics
Bachelor 1 IBEB
Microeconomics IBEB
FEB11001X
15 July 2009
This exam contains 19 problems for a total of 40 questions or
statements. Please make sure immediately that your exam copy
has indeed 19 pr