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 the
neurotransmitter
acetylcholine on
memory.
Robert Hea
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.
Section A: Multiple Choice (approx. 1/3 of exam)
Please gi
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 in the
equation.
First order differential equations ha
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 1/3 multiple choice, 2/3 long answer questions
First
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 other variables.
A differential equation contains one
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 cases.
8 0 1
0 otherwise.
Check that (, ) satisfies the
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.
 Market equilibrium, supply = demand
 Profit maximizati
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 a maximum and a minimum
and
b. if the extreme value the
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 +
is positive for all possible values of
We che
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
3) Find () where = 4 + 3 and () = 7 7 if 0 < < , 0 oth
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) An updated lecture schedule:
Lecture 1: Unconstrained
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) At the end of paragraph 17.4: exercise 3
6) At the end
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;
(0) = 0
d. 2 + 4 = 6;
(0) = 1.5
Solution
a.
Particular
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 and a
minimum and
b. if the extreme value theorem does
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) = 0
2 + 4 = 6; (0) = 1.5
2. Solve the following first ord
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 integrals exists?
2
a.
0 2
b.
0 2
4. Use the substitution
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 these conditions are both necessary and sufficient
2)
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 accounts, the bank deposits on which you can write cheques.
s
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 financial markets and the labour market.
The aggregate
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 labour force.
The participation rate is equal to t
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
their current price. It increases over time because:
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 fact far from constant, and depends primarily on two f
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 and Blanchard Chapter 8
Mankiw Chapter 6
Objectives:
Pro
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,
human capital, and technological progress
The factors
EC2202 Macroeconomics: Lecture 8
Ija Trapeznikova
Royal Holloway
Autumn Term 2016/2017
I. Trapeznikova (RHUL)
EC2202
Autumn Term 2016/2017
1 / 31
Inflation, Unemployment and Output
Inflation, Unemployment and Output
Reading
Giavazzi and Blanchard Chapter