Utility - Indifference Curves

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Indifference curves
Indifference curves represent a
summary of the consumer’s taste
and preferences for various
products.
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There is no accounting for the taste of the consumer.
Consumers like what they like(various things influence
what they like - advertising, customs...). Consumers
derive utility or happiness by consuming goods and
services. In economics we summarize the likes or tastes
of the consumer by using indifference curves.
An indifference curve shows different combinations of
goods that give the same level of utility to the consumer.
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Diagram used in analysis
good y
The amount
of good y a
consumer
may have is
measured
vertically
good x
The amount of good x is measured on the horizontal
axis.
This type of diagram is used extensively when
considering the behavior of consumers.
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Indifference curves - definition

y
As mentioned earlier, an indifference curve
shows various combinations of goods that
yield some specific level of utility or
satisfaction for the individual.
A
B
x
This is one type (and the
one we consider most,
initially) of
indifference curve. We
assume the
individual is equally happy
at point A or B or any other
point on the indifference
curve.
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Indifference curves - feature 1

We assume more goods are preferred to less
and thus indifference curves slope downward
to the right.
y
2
1
3
4
Say the individual is at
the point in the middle
of the graph. Keep this
in mind as we explore
the following screens.
x
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Indifference curves - feature 1
If the individual is at the point in the
diagram, then all those points in area 1 and
on the boundary are more preferred because
those points have either more of both items or
more of one and the same amount of the
other item compared to the point chosen.
 Points in area 3 and the boundary are less
preferred to the point in the diagram because
the point chosen has more of both items.

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Indifference curves - feature 1
An individual may think that points in areas
2 and 4 are preferable, less preferred or
equally desirable to the point indicated.
 Since areas 2 and 4 are the only ones that
could have a point of indifference to the one
chosen, the indifference curves must have
negative slope.

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slope
In economics we often use graphs and with graphs you can
look at the concept called slope. Often in economics the idea
of slope will have an economic interpretation. Let’s review
the idea of slope.
Slope = rise/run.
With a curve that slopes downward from left to right the slope
is a negative number.
With a curve that slopes upward from left to right the slope is
a positive number.
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Indifference curves - feature 2
y
Say the consumer is at
point A. If the
consumer gives up one
unit of x, m units of y
must be given back to
hold the consumer at a
constant level of utility.
B
m
A
x
1
You could say the
consumer is willing to
trade 1 unit of x to get m
units of y.
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Indifference curves - feature 2
The shape of the indifference curve on the
previous screen is said to be convex.
 Part of the reason for this is that it is assumed
that the amount of good y one receives in
return for one unit of x depends on how
much of each the individual starts out with.

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Indifference curves - feature 2
y
A
B
You can tell that point A has
less x than at B. As the
individual takes even one less
unit of x from either point A or
B, some y must be given in
return.
But more is given in return if
point A is the initial point.
x
The point is the less you have of something(like x at
point A compared to point B), the more of other things
you must be given in return to compensate for the loss of
the one unit, assuming the same level of utility is
obtained.
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Indifference curves - feature 2


The marginal rate of substitution(MRS) is the amount
of y given in return for the one unit of x, while
maintaining the same level of utility.
We can think of the MRS as a fraction:


MRS=absolute value of
(change in y)/(change in x) .
In this sense, the MRS is the absolute value of the
slope of the curve at various points. Note the slope
changes from point to point. In absolute value the
fraction gets smaller the farther down the curve one
moves. This is another way of saying the curve gets
flatter.
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feature 2
In general, it is assumed that consumers value additional units
of a good less and less the more they have of the good. (Or
you could say when consumers give up good x they require
more and more of good y the less of good x they start with.)
The indifference curve gets flatter.
This notion is summarized with the phrase – diminishing
marginal rates of substitution.
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y
Indifference curves - feature 3
x
Indifference Map
Every point in the graph
has one, and only one,
indifference curve running
through it.
Curves farther out from
the origin have more
utility.
So, the consumer can
compare every bundle and
make a determination of
preference or indifference.
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y
Indifference curves - feature 4
A
Indifference curves for an
individual do not cross. Say they
did, like in this diagram. Then
individual would be
indifferent to A and B,
indifferent to A and C,
and thus by logic should be
indifferent to B and C.
C
B
x
But C has more of both goods compared to B and thus C
is preferred to B. So the curves can not cross for an
individual. Transitivity of preferences holds.
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Indifference curves - feature 5
Different people can have different general
shapes of indifference curves. Some are
relatively steep and some are relatively flat.
 On the next slide I will put two peoples’
indifference curves and they will cross.
Before we said one individual’s curves could
not cross.

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Indifference curves - feature 5
y
Mr. A
Mr. B
x
Note how Mr. A has a steeper curve than Mr. B. From the
point where the curves cross if both give up a unit of
x, note how Mr. A has to be given more y to
make up for the loss of x than Mr. B. Mr. A is said to have
a relatively strong preference for x because he needs much
more y in return for the one unit of x given up.
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A math example of a utility function might be
U = sqrt(XY) – this means utility is a function of the square root of
the product of the amount of x and the amount of y a person would
get.
To get an indifference curve pick a value of U. Let’s say U = 4.
Then some points on the indifference curve would be
X
Y
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1
1
16
4
4
8
2
2
8
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Y
indifference curve when U = sqrt(xy) = 4
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16
14
12
10
8
6
4
2
0
1, 16
2, 8
4, 4
8, 2
0
5
10
16, 1
15
20
X
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