 
 
The foundation for economics is
rationality. In order to choose
you must have a set of preferences over
the options you're presented with.
These preferences must fulfil a set of
criteria in order to fulfil
the necessary requirements being classed
as 'rational'.
The first axiom is completeness. That is,
whether one is indifferent to, or prefers,
one set of options over another,
they must always be able to make that
choice.
For all A and B, elements of set X, we have that
either
A is at least as preferred as B,
or B is at least as preferred as A,
or both at the same time.
Transitivity is the second axiom by
which consumers are able to
order their preferences in a logical way.
For all A, B and C,
elements of set X, we have that if
A is at least is preferred as B,
while B is at least as preferred as C,
consequently A should be at least as preferred as C.
The axiom of reflexiveness has a purely
formal purpose.
This axiom simply implies that A is at
least as preferred as itself.
Continuity simply means that there are
no 'jumps' in people's preferences.
In mathematical
terms,
if we prefer point A along a preference
curve to point B,
points very close to A will also be
preferred to B.
This allows indifference curves to be
differentiated.
This axiom provides to the utility
function its continuous condition.
These four
axioms
are the basic set of premises that
Economics requires of individuals
in order to be rational economic agents.
It also enables us to represent preferences graphically
However, a later set of axioms were
studied and added by Samuelson as 'preferable'.
Because people are
inherently insatiable
and we always one more what we like we
derive the premise
have monotonicity week monotonicity
implies that if a contains more than be
or at least the same quantity of goods
aids at least is preferred as be on the
other hand
strong monotonicity implies and if 18b
contain the same amount
but a contains more at least one good
then
a strictly preferred to be this axiom
is responsible for the increasing
function characteristic
at the utility function further
developing
artist for variety we inherently prefer
baskets of goods
or traces which contain a wider range
for all
AB and C elements upset next we have
that if A's at least is preferred as be
and B is at least as prefer to see
there is one combination of both A&B
that is at least
s preferred St the utility function is
represented
as a quasi concave function as a result
of this
utility is the satisfaction we get from
using owning
or doing something is what allows us to
choose between options
this can be plotted on a chart the
x-axis
or horizontal axis shows the amount of
income am available to the consumer
while the y-axis or vertical axis sure
the amount of utility you
derived from consuming goods
utility functions follow the same color
product
the same axioms as preferences because
there simply numerical representations
of them
as a result up the monotonicity axiom
the utility functions increasing
to more than we have a good the higher
our utility will be
between a different points we have a
continuous function
showing that there are no jumps between
preferences fulfilling the continually
axiom as a result of diminishing returns
the utility function has a quasi concave
shape
representing that marginal utility
decreases
and the number of goods consumed in
terms of income spent
increases this is explained s
an extra unit have a good has a greater
value when the individual
has a low amount of that good then when
they have many a bit
indifference curves airlines in a
coordinate system
for which each of its points express a
particular combination
a number of goods or bundles of goods
that the consumers indifferent to
consume
the consumer will therefore have no
preference between two bundles locate in
the same indifference curve
since they all provide the same to
grieve utility in this graph
the x-axis or horizontal axis represents
the amount of good x1
which corresponds to Apple's and on the
y-axis
or vertical axis the amount a good XQ
which corresponds to bananas
let's see again all the axioms we've
just added
using the chart reflexive NIS
completeness
continuity transitivity
convexity monotonicity when we try
indifference curves showing different
degrees of utility
we call it indifference map which is
helpful to determine how utility
increases
when consumption increases utility
functions may be represented with
indifference curves
various shapes depending on each
function
