Quantitative Methods for Economics
Tutorial 7
Katherine Eyal
TUTORIAL 7
20 September 2010
ECO3021S
Part A: Problems
1. You are given the following age and price data for 10 randomly selected Toyota Tazzes
between 1 and 6 years old. Here, age is in years,
Quantum Microeconomics
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Sidney Tyrrell
SPSS: Stats Practically Short
and Simple
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2
SPSS: Stats Practically Short and Simple
2009 Sidney Tyrrell & Ventus Publishing ApS
ISBN 978-87-7681-474-8
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3
Contents
Sta
Leif Mejlbro
Probability Examples c-1
Introduction to Probability
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Probability Examples c-1 Introduction to Probability
2009 Leif Mejlbro & Ventus Publishing ApS
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Tutorial 3: Optimisation
ECO4112F 2011
1. Find and classify the extrema of the cubic cost function C = C (Q) = 2Q3 5Q2 + 2.
2. Find and classify the extreme values of the following functions
(a) y = x2 + 3x2 3x1 x2 + 4x2 x3 + 6x2
1
2
3
(b) y = x1 x3 + x2
Tutorial 2: Comparative Statics
ECO4112F 2011
1
Derivatives and Rules of Dierentiation
For each of the functions below:
(a) Find the dierence quotient.
dy
(b) Find the derivative
.
dx
(c) Find f (4) and f (3).
1. y = 4x2 + 9
2. y = 5x2 4x
3. y = 5x 2
Find
Maths for Economists
Tutorial 0: Revision of Basic Concepts
ECO4112F 2011
In the following paired statements, let p be the rst statement and q the second. Indicate
for each case whether q is necessary or sucient or both necessary and sucient for p (i.e.
w
Quantitative Methods for Economics
Tutorial 5
Katherine Eyal
TUTORIAL 5
23rd-27th August 2010
ECO3021S
PART 1
1. A monopolist sets a price p = q 1/ where p is the price, q is the quantity of the
good being produced, and is the elasticity of demand for the
Quantitative Methods for Economics
Tutorial 4
Katherine Eyal
TUTORIAL 4
16th-20th August 2010
ECO3021S
PART 1
1. The system of equations below describes the market for chocolates, where G is the
price of substitute goods (e.g. jellytots), and N is the pri
Quantitative Methods for Economics
Tutorial 3
Katherine Eyal
TUTORIAL 3
9th-13th August 2010
ECO3021S
PART 1
1. Let the national income model be:
Y
= C +I +G
C = a + b(Y T )
a > 0, 0 < b < 1
T
d > 0, 0 < t < 1
= d + tY
where Y is national income, C is (pl
Quantitative Methods for Economics
Tutorial 2
Katherine Eyal
TUTORIAL 2
2nd-6th August 2010
ECO3021S
PART 1
1. Use Gaussian elimination to solve the system Ax = b, where
234
1
5 6 7 , b = 2
A=
8 9 10
4
2. Use Gaussian elimination to invert the matrices
13
Quantitative Methods for Economics
Tutorial 1
Katherine Eyal
TUTORIAL 1
26th-30th July 2010
ECO3021S
PART 1
1. In the following paired statements, let p be the rst statement and q the second.
Indicate for each case whether p q, p q or p q.
(a) It is a hol
Honours Introductory Maths Course 2011
Integration, Differential and Difference Equations
Reading:
Chiang Chapter 14
Note:
These notes do not fully cover the material in Chiang, but are meant to
supplement your reading in Chiang.
Thus far the optimisation
Section 5: Dynamic Analysis
Eigenvalues and Eigenvectors
ECO4112F 2011
This is an important topic in linear algebra. We will lay the foundation for the discussion of dynamic systems. We will also discuss some properties of symmetric matrices that
are usef
Section 4: Integration
ECO4112F 2011
Reading:
Chiang Chapter 14
Note:
These notes do not fully cover the material in Chiang, but are meant to
supplement your reading in Chiang.
Thus far the optimisation you have covered has been static in nature, that is
Section 3: Optimisation
ECO4112F 2011
Were now going to turn our attention to optimisation problems. Optimisation problems
are central to economics because they allow us to model choice. After all, economics is
all about making choices in order to achieve
Section 2: Comparative Statics
ECO4112F 2011
As weve said before, a key concept in economics is that of equilibrium. A large part
of the mathematical modelling we do in this regard is concerned with comparative statics,
that is, the comparison of dierent
Section 1: Linear Algebra
ECO4112F 2011
Linear (matrix) algebra is a very useful tool in mathematical modelling as it allows us
to deal with (among other things) large systems of equations, with relative ease. As the
name implies however, linear algebra a
Section 0: Revision of Basic Concepts
ECO4112F 2011
We begin by revising some basic mathematical concepts that should be familiar to you
from previous mathematics courses.
1
Ingredients of a Mathematical Model
Variable : Something whose magnitude can cha
Quantitative Methods for Economics
Tutorial 12
Katherine Eyal
TUTORIAL 12
25 October 2010
ECO3021S
Part A: Problems
1. State with brief reason whether the following statements are true, false or uncertain:
(a) In the presence of heteroskedasticity OLS est
Quantitative Methods for Economics
Tutorial 10
Katherine Eyal
TUTORIAL 10
11 October 2010
ECO3021S
Part A: Problems
1. Consider the following regression output:
Q
(se)
(t)
=
300
(60)
(5)
5
(0.5)
(10)
P
where Q is the quantity of cheese demanded in the Wat
Quantitative Methods for Economics
Tutorial 9
Katherine Eyal
TUTORIAL 9
4 October 2010
ECO3021S
Part A: Problems
1. In Problem 2 of Tutorial 7, we estimated the equation
sleep = 3, 638.25 0.148 totwrk 11.13 educ + 2.20 age
(112.28)
(0.017)
(5.88)
(1.45)
2
Quantitative Methods for Economics
Tutorial 8
Katherine Eyal
TUTORIAL 8
27 September 2010
ECO3021S
Part A: Problems
1. The following model is a simplied version of the multiple regression model used by
Biddle and Hamermesh (1990)1 to study the trade-o bet
Quantitative Methods for Economics
Tutorial 6
Katherine Eyal
TUTORIAL 6
13 September 2010
ECO3021S
Part A: Problems
1. (a) In 1857, the German statistician Ernst Engel formulated his famous law: Households with higher incomes spend a smaller fraction of t