01 Flashcards
What is the purpose of an economic model
To generate insights
What are 4 advantages of maths in economics
Precise - provides clarity
Certainty - can be verified to remove doubt
Generation of insights - more successful than other method
Removes abstraction
What doe a budget set contain
All affordable alternatives
What does a utility function do
Assigns a numerical value to each alternative
Why does a consumer make choices
To maximise utility from a given set
What is a set
A collection of 0 or more distinct objects
What are natural numbers
How are they denoted
(0),1,2,3,4,…
IN (notation N)
What is an integer
How are they denoted
What types of integers are there
Any whole number which does not contain a decimal
Notation Z
Positive, negative or non-negative (0)
What are rational numbers
How are they denoted
What does this mean
Any number that can be written as a fraction using only integers
Notation Q
It is any decimal with a repeating pattern
What is a real number
How are they denoted
Any number that can be represented on a number line
IR (Notation R)
What are irrational numbers
Give 3 examples
Numbers that are real but are not rational
Pi, e, root 2
What are elements
Objects that belong to a set
What is the empty set
The set with no elements
What notation is used to show that something is part of a set
Epsilon (Looks similar to E)
How to show something is not part of a set
Epsilon with a cross though it
How to denote a set
USING CAPITAL LETTERS
How to denote elements of a set
by using lowercase letters
What are the two ways of specifying sets
Listing all of the elements and enclosing them in curly brackets
Writing down the property/s that the elements of this set must satisfy
When are two sets equal
When they contain exactly the same elements
What does the existence of set equality imply
That there is exactly one empty set which contains no elements
When can one set A be a subset of another set B
When all the elements of A are also elements of B
What if two sets are subsets of each other
They are equal sets
What is the subset symbol
Capital U rotated 90 deg clockwise
What does AUB mean
A union B (A or B) is the set that belongs to A, B, or both
What does AnB mean
A intersect B (A and B) is the set that belongs to both A and B
What does A\B mean
A minus B is the set of elements that belong to A but not to B
What is a useful way to visualise set operations
Venn Diagrams
If X and Y are sets, what is the Cartesian product XxY
The set of pairs (x,y) such that x (epsilon)X and y(epsilon)Y
Cartesian product of (1,2)x(3,4)
(1,2)x(3,4)=((1,3),(1,4),(2,3),(2,4))
IR x IR = ?
The set of all real numbers on a plane
IR^2
Every pong on the plane corresponds to a set which is a pair of real numbers
