EC2104 A+ Cheatsheet
Week 1:
Speaking logically

P is a sufficient condition for Q (if P, then Q)

P is a necessary condition for Q (if Q, then P)

P is a necessary and sufficient condition for Q (P if and only if Q)
and
Models in economic analysis

The structure of a model is described by equations

The aim is to derive a set of logical conclusions that follow from the assumptions

An equation is a mathematical statement setting 2 algebraic expressions equal to one
another
o
Definitional equations: set up an identity between 2 alternative expressions that
have exactly the same meaning:
o
Behavioural equations: specifies the manner in which a variable behaves in response
to changes in other variables
C = 75 + 10Q
Utility = sleep / homework
o
Conditional equations: states a requirement to be satisfied. The standard market
model requires the equilibrium condition, which describes the prerequisite for there
to be an equilibrium in the market
Quantity demanded = quantity supplied
Functions of one variable

If y depends on the value of x, we might be able to say that y is a function of x, or y = f(x)

Here, f is the function. The actual symbol for the function is not important, but f and g are
commonly used for generic functions. f(x) is the value that the function generates when
given input x

x = independent variable, y = dependent variable

Every value of x must generate a unique value of y = f(x) for f to be a valid function. However,
there can be multiple values of x that generate the same y
Formal definition of a function

The domain of function f is the set of values of the argument for which the function is
defined

The range of function f is the set of possible resulting values of f(x)
A note on graphing functions

In economics, we generally use Cartesian coordinates, aka xy or xyz coordinates

In most graphs, the independent variables goes on the xaxis and the dependent variable
goes on the yaxis

In price quantity graphs in economics, the reverse is true. Price, the independent variable, is
always on the yaxis

Demand function: D(p) = 6 – 2p

Inverse demand function:
Common functions:

Polynomial functions
o
Linear functions
o
Quadratic function

Power function

Exponential function

Logarithmic function
Polynomial function


Highest power, n, is called the degree of polynomial

Depending on the degree, n, we have the following subclasses
o
Linear function


Graph is a straight line with slope/gradient a and yintercept b
Market model

Suppose the market demand and supply are given by the following equations
o
Demand: q
D
= 10 – 2p
o
Supply: q
S
= 5 + 3p

Market equilibrium requires demand = supply

10 – 2p = 5 + 3p
p = 3

When p = 3, quantity = 4

Quadratic functions

Quadratic functions are polynomial functions of degree 2


Solution 1: by factoring
o

Solution 2: quadratic formula
o
Power functions


Three classes
o
r > 1: function is increasing and convex
o
0 < r < 1: function is increasing and concave
o
r < 0: function is decreasing and convex
a = 1, r > 1
increasing and convex, global minimum point
a = 1, 0 < r < 1
increasing and concave, there will be a global