Welcome everyone. Welcome to part three,
the last part of chapter two: preferences
in this part we are going to
talk about the well-behaved preference
assumptions so in economics it is
important to to to make some assumptions
in order to create some models for our
consumer choice and here in this part we
will talk about certain assumptions
which we call them well-behaved
preferences if they satisfy these
assumptions so the first one is the
monotonicity the easiest way to define
the monotonicity
is saying "more is better" so imagine that
you have two options both of them are
free you are not going to pay anything
the first option is offering you one
apple and the second option is offering
you five apples which one will you
choose? the one which is more because you will have more apples so the more is
better principle says a preference is
monotonic if X is weakly prefer to Y for
any x and y which satisfied x 1 is
larger than or equal to y1 and x2 is
larger than or equal to y2 or we can say
the preference is strictly monotonic if
we have strict preferences and just
greater than equation and no equality so
the monotonicity implies the negative
slope of the indifference curve so if
the preferences satisfy the monotonicity
then the indifference curves have a
negative slope and it is violated when
there is a situation or when there is a
bad instead of both of these are good. so
let's have a look what we say here in
this example we pick two points x and y
and x1 is larger than y1 and x2 is
larger than y2 so that means the
consumer if the consumer prefers X to Y
either strictly or weakly here in this
example it is strictly preferred for
sure because it is on a higher
indifference curve then we can say that
the monotonicity is satisfied so if my
indifference curves are moving in that
direction the higher is giving a better
satisfaction level than for this example
we have the monotonicity which is
satisfied so for a preference which
satisfy the monotonicity we will always
have better bundles once we move in that
direction and we will have worse bundles
if we move in that direction
so an indifference curve which is like
that so if indifference curve one
indifference curve two if the
preferences are satisfying the
monotonicity indifference curve one is
giving less satisfaction than
indifference curve 2. so let's have a look
to the examples of bads so here let's
assume that x2 is bad and x1 is good so
we are having better conditions if we
move from X to Y so which means the
indifference curve Y is better than
indifference curve X so here in this
example when I check let's say here I
have 10 X 1 10 of good 1 and 5 and 10
let's say in X bundle I have 10 and 10
so in total I have 20 units and in y
bundle I have 10 and 5 so 15 units but
because x2 is bad I have less which is
preferred to the more so in this example
we say that the monotonicity is violated.
if a consumer is prefers more to less
than we know that the monotonicity is
satisfied otherwise it is violated
another assumption is the convexity so
the convexity is saying the moderates
are better than extremes so imagine that
you have different options one is eating
just icecream all day and the second
one is eating beef all day but the the
better one is the moderate so not only
eating ice cream or only beef but eating
both are screamin and beef is better
than the extreme cases. so we can say
that the the Preferences is
convex for any X 1 and X 2 bundles if X
1 and X 2 are indifferent so that means
they are on the same indifference curve
same indifference curve then multiplying
these bundles by a by a constant number
between 0 and 1 T, T X 1 plus (1 minus T)
y1 and T X 2 plus (1 minus T) y2 if that
new bundle is weakly or strictly
preferred to our original bundle then we
satisfy the convexity that means the set
of bundles weakly preferred to x1 and x2
is a convex set so let's have a look to
this example I have two bundles they're
on the same indifference curve x and y
x1 and y1 and x2 and y2 and I choose T
which is between 0 & 1 so let's say I
choose T equal to 0.5 so I'm going to
check T multiply X 1 plus (1 minus T) y1
so I'm taking the
average of these x1 and x2 this or x1
and y1 so it is 0.5 X 1 plus 0.5 y1 and
same for good to 0.5 X 1 plus 0.5 Y 1
and that combination lies on a
indifference curve which is higher than
my original indifference curve 0 right?
so that's Z point point Z is
strictly preferred to X and Z is
strictly preferred to Y because it is on
a higher indifference curve so that
means my preferences are strictly
strictly convex or what I can say if I
combine linear if I draw a linear
line between Y and X if the combination
of these two bundles x and y lies on
any point on that blue line it will
always satisfy the convexity and when I
check the perfect substitute examples so
here I have two bundles on the same
indifference curve and the average
bundle Z is not making the consumer
worse off may it is not also making
better but the the convexity says the
consumer should not be worse off so here
in this case we have satisfied
the convexity so basically in convexity
we we should definitely check whether
the average bundle
makes the consumer not worse off
okay as long as the consumer  is not
worse off by the average bundle we
satisfy the convexity on the other side
if that average bundle makes the
consumer better off then the preferences
are not only convex but also strictly
convex so let's have a look to some
other examples: non convex preferences so here I I combined the two points X and Y
with a line and there is a
point which gives me a lower benefit
level because that set lies on a lower
indifference curve so here that's why I
call it is non convex. of course there
are some points for instance here or
here  which are making
the consumer better off but at least
there is one point which makes the
consumer worse off that means my
convexity is violated or when I check
this indifference curve I choose and I
choose an averaged bundles at which which
makes the consumer definitely worse off
so shortly I can say in Part B and in
Part C  Z point the averaged bundle
makes the consumer worse off or at least
I have at least one point at least one
bundle which one averaged bundle which
makes the consumer worse off means that
my preferences are not convex so if I
combine all these knowledge and well
behaved preferences preference must
satisfy both the monotonicity and the
convexity as long as
i satisfy both the monotonicity and the
convexity at the same time i can say the
preference of the consumer is
well-behaved so the best examples or the
the easiest examples for the
well-behaved preferences are perfect
complements perfect substitutes or the
original smooth convex preferences so
that is the original smooth convex
preferences or perfect substitute or
perfect complements they are all
satisfying both the monotonicity and the
convexity they're all well behaved. ok so
the last thing about chapter 2 is the
marginal rate of substitution so the
marginal rate of substitution is
checking what happens to the whether the
consumer is better off or worse off when
there is a exchange between the between
the goods so let's assume that I have X
1 and X 2 bundle and I decrease good 1
and increase X 2 to make the consumer
still stay  on the same indifference curve so
as long as I that I have that
indifferent sign that means my X 1 and X
2 and X 1 minus Delta X 1 X 2 plus Delta
X 2 they are all on the same on the same
indifference curve so the consumer can
decrease some amount of good 1 in order
to increase good 2 or the vice versa and
we check the exchange rate between two
goods to make the consumer indifferent
to the original bundle that exchange
rate is called the marginal rate of
substitution so why we call it marginal
but not just the exchange rate because
we looked an exchange rate but the
change must be so small so we we
increase or we decrease
one of the goods so little and check
what happens to the other good okay so
my MRS at a point is the is that
different than the slope of indifference
curve at that point so let's have a look
to the graph for instance I have such
indifference curve and I have one point
point X I am going to decrease x1 just a
little so small and check what happens
to x2 because I have less x1 to keep the
consumer on consumer on the same
indifference curve I have to increase x2
just a little as well so I'm looking to
the exchange rate between good 2 and
good 1 when the change of good one is
so close to zero so for the perfect
substitute because I have the constant
slope of the indifference curves I have
the constant marginal rate of
substitution
so it is perfect substitutes so that
means for every point I have equal
marginal rate of substitution but if I
have smoothly convex preferences like
that one I will not have a constant
slope on different points of the
indifference curve and my slope will
change for sure so what I can say the
MRS marginal rate of substitution is
definitely a negative number typically
because I have to increase one good if I
want to increase one good if I have to
decrease the other one and the monotonic
preferences imply that the indifference
curve must have a negative slope so as
long as I satisfy the monotonic preferences
my indifference curves has negative
slopes
and since the MRS is the numerical
measure of the slope of an indifference
curve then it will be naturally be a
negative number
so shortly I can say for all well
behaved preferences the marginal rate of
substitution must be negative that means
to have more x2 I have to give up some
of x1 or vice-versa
okay and the last thing is about the
marginal rate of substitution as I said
before it for the perfect substitute the
slope of my indifference curve is
constant but it will not be constant if
I have the strictly convex indifference
curves so the strictly convex
indifference curves which has a general
shape of like that the MRS or the slope
of the indifference curve will decrease
in absolute value it should be negative
definitely so I need to think about the
absolute values as long as I increase X
1 so that means if my MRS is decreasing
in absolute value when I increase X 1 my
indifference curve exhibit a diminishing
marginal rate of substitution this means
that if I I would like to have more and
more x1 the amount of good 2 I have to
I'm willing to give up will 
decrease right so let's have a look to
the graph so I'm I'm trying to pass from
point A to point B I increase good one
by one unit and I am ready to
give up four units of x2 so passing from
A to B I have one additional x1 but
I decrease the amount of x2 by 4
and if I keep increasing X 1 from 2 to 3
I will pass to Point C because I have to
stay on the same indifference curve here
I have one
additional X1 but this time the amount of X
to I'm going to I'm willing to give up
will be just 1 unit 1 X 2 and if I
keep increasing X 1 from 3 to 4 the
amount of X 2 to get 1 X 1 I have to
give up half of X 2 okay so the more I
have the X 1 the less I'm willing to
give up of X 2 so to increase X 1 by 1
unit I will be willing to give up less
and less X2 when X 2 increases so in
absolute value the slope of my
indifference curve is decreasing if I
keep increasing X 1 that means I have a
diminishing marginal rate of
substitution that happens for the
strictly convex indifference curves and
for the perfect substitutes as I said
before we have a constant marginal rate
of substitution. Thanks for listening we
will meet in chapter 3 next week. Thank
you.
