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EF 2452 Mathematics for Economics and Finance
Tutorial 1
1. Announcement:
(a) Attendence of tutorial will also be counted towards 10% participation part of the
overall raw score. Being late for 15 m
Tutorial 3
1. Example 6.4 Textbook P63
A firm has cost function C(q) = 1500 + 15q 3q 2 + q 3 . Show that its marginal cost is always
positive.
2. Exercise 6.6 Textbook P66
Suppose that the demand func
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LINEAR EQUATIONS II
Arbitrage portfolios and state prices
Suppose there are assets and states, then the
returns matrix is defined as each of its
entry being the return from investing in one unit
of a
INTRODUCTION TO
CALCULUS
Finding Derivatives
Rate of change of a function
We are interested in: how does the dependent
variable change responding to a change in the
independent variable?
Idea: Take a
MATHEMATICAL TERMS
AND NOTATIONS
Sets, functions and equations
brief introduction: why math?
Math vs. language
Concision and precision.
Example: John is always willing to exchange apples for bananas o
VECTORS AND MATRICES
Preferences and convexity
Vectors
An n-vector is a list of numbers. It can be
written either as a row-vector,
1 , 2 , , ,
Or a column-vector,
1
2
. .
.
.
Vectors
E.g. (1, 2) is a
PARTIAL DERIVATIVES
Functions of several variables
A function of one variable: =
+1
.
2 +1
A function of two variables:
, = 2 2 + 3 2 ;
, =
;
+ 1
2 +
, =
;
, = 0.5 0.5 .
Use the notation : 2 f
THE DERIVATIVE IN
ECONOMICS
Some examples
Global maximum/minimum
Global refers to the constraint set of our
optimization problem. A global maximum is
necessarily a local maximum, but a local maximum
m
MATHEMATICAL TERMS
AND NOTATIONS
A Model of Market, Sequences and Examples
A model of the market
The market of a single good, say Coke.
Care about price and quantity of Coke: (, ).
From producers poin
OPTIMIZATION IN TWO
VARIABLES
Profit maximization again
Suppose Apple produces two goods, iPhones and
iPads. Let be the unit of iPhones and be the unit
of iPads that Apple produces.
Assume the cost of
MATRIX ALGEBRA
What is a matrix
A matrix is an array of numbers
1
11
21 2
.
Lets call this matrix . is an matrix, or it has
size and sometimes we denote it as . This
means has rows and columns. An e
LINEAR EQUATIONS
Linear equations in matrix form
A system of linear equations in unknowns
1 , 2 , , is a set of equations of the form
11 1 + 12 2 + + 1 = 1
21 1 + 22 2 + + 2 = 2
1 1 + 2 2 + + = .
The
INTRODUCTION TO
OPTIMIZATION
A first look
Some special functions: power
If is a natural number: 0.
= for times.
+ = .
0
= 1.
=
(
1
)
1
.
=
Since = 0 = 1.
+()
=
1
.
= . Call th root of .
1
= ( )