PS2061 Main Studies
Experiments and studies:
Authors and
date
Kasamatsu
and Hirai,
1999
Aim/Research
Question
How sensory
deprivation affects
brain?
Martinez and
Kesner, 1991
Determining the role
of t
EC5051: Mathematical Methods
Lecture 10
Expected Values, Moments and Functions of
Random Variables
Cheerful seasonal reminders before the end of term
FINAL EXAM:
Assessed. 90% of final grade.
Sect
EC5051: Mathematical Methods
Lecture 7
An Introduction to Difference Equations
Remark on differential equations
Order of a differential equation:
Refers to the highest order of derivatives appearing
EC5051: Mathematical Methods
Lecture 9
Random Variables and Distributions
Assessments and Exams
ONLINE MOODLE TEST TOMORROW 57pm
Assessed and counts 5%
FINAL EXAM
Assessed and counts 90%
Roughly
EC5051: Mathematical Methods
Lecture 6
An Introduction to Differential Equations
Differential equations.
Definition: a differential equation states how a rate of change
in one variable is related to
EC5051: PROBLEM SET 9
1) is a continuous RV with cdf:
() =
1
1 +
Compute () and check its properties. Find (1 < < 2) using both the pdf and the cdf,
and check that you get the same result in both c
Lecture 4
Economic dynamics and Integration
Chapter 14 of the textbook
Introduction
Static models:
the problem is to find the values of endogenous variables that
satisfy the equilibrium conditions.

Problem set 1 Solutions
1. Read paragraph 11.6 Economic examples from the textbook
2. For each of the following functions, determine
a. whether the extreme value theorem implies that the function has
1) is a continuous RV with cdf:
=
1
1 +
Compute and check its properties. Find 1 < < 2 using both the pdf and the
cdf, and check that you get the same result in both cases.
Solution
=

=
1
EC5051:Problem Set 10
1) Find the mean and variance of a binomial (, ), = 4, using the moment generating
function.
2) Find (), where = 2 and [1,1]
a. by the two steps methods
b. by the one step method
EC5051: Mathematical Methods
Lecture 8
An Introduction to Dynamic Optimisation
Some things to note
1) Assessed 1 hour, online Moodle test next week (covers Lecture 4 up to and
including Lecture 7)
2)
EC5051: Problem Set 7
1) At the end of paragraph 17.2: exercise 2
2) At the end of paragraph 17.2: exercise 4
3) At the end of paragraph 17.3: exercise 1
4) At the end of paragraph 17.3: exercise 3
5)
Solution problem set 5
1. Find the general and the definite solution of the following differential equations. Check the
validity of your answers.
a.
b.
c.
(0) = 2
+ 4 = 12;
2 = 0;
(0) = 9
+ 10 = 15;
Problem set 1
1. Read paragraph 11.6 Economic examples from the textbook
2. For each of the following functions, determine
a. whether the extreme value theorem implies that the function has a maximum
Problem set 5
1. Find the general and the definite solution of the following differential equations. Check the
validity of your answers.
a.
b.
c.
d.
+ 4 = 12; (0) = 2
2 = 0; (0) = 9
+ 10 = 15; (0) =
EC5051: Problem set 4 (2016)
Integration
1. Find the indefinite integral of:
a. x + 1
b.
2x 2
c. xex
2. Find the definite integral between 0 and 2 of:
a. 2x 2
b. e0.5x
3. Which of these improper integ
Problem set constrained optimization
1)
a) Write the KT conditions of the following problem:
max
,
. .
100 m 0
4
0
where < 0.5 < 0
b) Write the KT conditions of the modified Lagrangean
c) Check if
Financial Market
Money, which you can use for transactions, pays no interest. In the real world,
there are two types of money:
Currency, coins and bills supplied by the central bank
Deposits account
The ASAD model
The ASAD model  The model of aggregate supply and aggregate demand
describes the movements in output and the price level when account is taken of
equilibrium in the goods market, the
The labour market
The labour force consists of those who are working (employed) or looking for
work (unemployed).
The unemployed rate is equal to the ratio of the number of unemployed to the
number in
The goods market
The gross domestic product (GDP) is the measure of aggregate output in the
national income accounts.
Nominal GDP is the sum of the quantities of final goods produced multiplied by
the
The ISLM Model
The goods market and the IS relation
At equilibrium, Production (Y) = Demand for goods (Z)
Y = Z = CYd + I + G
= C(YT) + I + G
Investment, sales and the interest rate
Investment is in
EC2202 Macroeconomics: Lecture 5
Ija Trapeznikova
Royal Holloway
Autumn Term 2016/2017
I. Trapeznikova (RHUL)
EC2202
Autumn Term 2016/2017
1 / 28
The Labour Market
The Labour Market
Reading
Giavazzi a
Microeconomics  EC2201  2016/2017
Problem Set 1 7: Solutions
Problem Set 1:
Q3 7:
Q8:
Q9:
Q10:
a. 21x2
e. 20x4 3/2 x
b. 24x3
f. (x2 + 1 2x2) / (x2 + 1)2
5/2
c. 9/2 x
d. x
fx(x,y) = 12x3 2xy +
EC1101
MACROECONOMICS
Lecture 10
Long Run Economic Growth:
Solow Growth Model
OUTLINE OF LECTURE 10
Why productivity is the key to longrun growth, and
how productivity is driven by physical capital,