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) a
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 Ta
Quantum Microeconomics
with Calculus
Version 4.02
January 2009
Available with and without calculus at
http:/www.smallparty.org/yoram/quantum
Email contact: yoram@smallparty.org
This work is licensed u
Sidney Tyrrell
SPSS: Stats Practically Short
and Simple
Download free ebooks at bookboon.com
2
SPSS: Stats Practically Short and Simple
2009 Sidney Tyrrell & Ventus Publishing ApS
ISBN 978-87-7681-47
Leif Mejlbro
Probability Examples c-1
Introduction to Probability
Download free ebooks at bookboon.com
2
Probability Examples c-1 Introduction to Probability
2009 Leif Mejlbro & Ventus Publishing ApS
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 = x
Tutorial 1: Linear Algebra
ECO4112F 2011
1. Suppose
3
p+2
x = 2q , y = 5
6
3r
If x = 2y, nd p, q, r.
2. Which of the following sets of vectors are linearly dependent?
1
0
1
,
,
0
1
1
1
1
0
1 , 0 , 1
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
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
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
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,
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
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
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
suppl
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 disc
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 optimisati
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, ec
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 c
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 relat
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 Mathemati
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 uncer
Quantitative Methods for Economics
Tutorial 11
Katherine Eyal
TUTORIAL 11
18 October 2010
ECO3021S
Part A: Problems
1. An equation explaining chief executive ocer salary is (standard errors in parenth
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
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 b
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: House