Chapter 5: Preferences
5.1: Introduction
In chapters 3 and 4 we considered a particular type of preferences – in which all the indifference
curves are parallel to each other and in which each indifference curve is convex. The first of these
assumptions implies that the individual’s reservation prices are independent of the amount of
money with which the individual starts. The second of these assumptions implies that the individual
has lower and lower reservation prices for additional units of the good as he or she acquires units of
the good – that is, the more he or she has of the good, the less he or she is willing to pay for extra
units. Whether these assumptions are reasonable or not depends upon the individual, the good and
how the individual feels about the good vis-à-vis money – that is, it depends upon the individual’s
preferences with respect to the good. We, as economists, cannot say that a particular kind of
preference is ‘reasonable’ or not – we must simply take the preferences as given.
This chapter recognises that the assumptions made in chapters 3 and 4 may be reasonable for some
people – may accurately describe some people’s preferences – but that they may not be reasonable
for others. This chapter thus considers other possibilities as far as preferences are concerned.
We also take the opportunity to slightly generalise what we are doing. So far we have been working
with one good and money: we have put the quantity of the good on the horizontal axis and the
quantity of money on the vertical axis. We have used p to denote the price of the good. The price of
money is rather obviously 1 (to buy 1 lira costs 1 lira). In this chapter we will work with 2 goods,
good 1 and good 2. We put the quantity of good 1, which we will denote by q1, on the horizontal
axis and the quantity of good 2, which we will denote by q2, on the vertical axis. Later we will use
p1 and p2 to denote the respective prices of the two goods. The material of chapters 3 and 4 is
simply the special case of this when good 2 is money and hence when p2 = 1. So in an obvious
sense this chapter generalises the material of chapters 3 and 4. We assume that both the goods are
genuinely goods in the sense that the individual would always happily accept more of each.
5.2: Perfect Substitutes
It may be the case that the individual considers the two goods as identical – he or she regards any
one unit of one good as exactly the same as any one unit of the other good. In other words the
individual cannot tell any difference between the two goods. For me this is true for any two kinds of
lager – I like lager but I really cannot tell (and really do not care whether there is) any difference
between Lager Number One and Lager Number Two. If these are goods 1 and 2, then my
indifference curves look as follows:
Suppose the quantity units are litres. Consider, for example, the third highest indifference curve in
this figure – joining the points (60, 0) and (0, 60). What do you notice is true along this curve?
Simply that q1 + q2 =60 at every point along it (indeed this is the equation of that line). What does
this mean? That the total quantity (of Lager Number One and Lager Number Two) is equal to 60.
What is not important is how this total is composed – how it is split between Lager Number One
and Lager Number Two. This embodies the notion that I regard the two goods are perfect
substitutes.
Another way of seeing this is to note that everywhere the slope of every indifference curve is equal
to –1. What does this mean? That the reservation price everywhere for one litre of Lager Number 1
is one litre of Lager Number 2 - to take one more litre of Lager Number 1 the individual is
prepared at most to pay one litre of Lager Number 2. Whatever way we look at it, it is clear that the
indifference curves in the figure above are telling us that the individual regards the two goods as
identical – that he or she regards the two goods as perfect one-to-one substitutes – that anywhere
and everywhere he or she would happily substitute one unit of one good with one unit of the other.
It will be useful for future reference to note the equation defining an indifference curve in this case
of perfect 1:1 substitutes. If we look at any curve in the above figure it is apparent that the sum of q1
plus q2 is constant along any one of these curves – along the top one the sum is 80, along the second
to the top the sum is 70, …., along the bottom curve the sum is 20. So an indifference curve is
defined by
q1 + q2 = constant
(5.1)
Note that the higher the constant the higher the level of happiness of the individual – being on the
top indifference curve (with 80 litres of lager) is better than being on the second highest (with 70
litres of lager), …., is better than being on the lowest (with 20 litres of lager). So we can define
perfect 1:1 substitutes as having indifference curves given by equation (5.1). The only problem with
this definition is that it is not unique – note that if q1 + q2 is constant then so is (q1 + q2)2 and so is
(q1 + q2)3 and indeed so is f(q1 + q2) where f(.) is any increasing function. So we have to be careful:
equation (5.1) above defines perfect 1:1 substitutes but is not the only definition. This, as we shall
see later, creates a little difficulty if we want to define a utility function, but it is not an insuperable
problem.
Of course it could be the case that the individual regards the two goods as perfect substitutes but not
1:1. An example I find in Italy: there they have large bottles of Peroni beer and small bottles. The
large bottles contain 660 ml of beer, the small bottles 330 ml. The beer is the same. For me two
small bottles of beer is exactly the same as one large bottle of beer – I really do not mind which I
have. So, if we take good 1 to be large bottles – with the quantity of good 1 being the number of
large bottles that I have – and we take good 2 to be small bottles – with the quantity of good 2 being
the number of small bottles that I have – then my indifference curves look like the following:
Consider, for example, the third highest indifference curve in this figure – the line going from (45,
0) to (0, 90). At one extreme, the point (45, 0), I have 45 large bottles and no small bottles; at the
other extreme, the point (0, 90), I have 90 small bottles and no large bottles – if I regard 1 large
bottle as the same as 2 small bottles, then these two extremes are identical. Furthermore consider an
intermediate point – the point one-third of the way from (45, 0) to (0, 90) – that is the point (30, 30)
– where I have 30 large bottles and 30 small. This, given that I consider 1 large bottle as always the
same as 2 small bottles, is again exactly equivalent to 45 large bottles (and no small) or 90 small
bottles (and no large).
So if an individual regards the two goods as perfect 1 to 2 substitutes, then his or her indifference
curves look like those in figure 5.5. Moreover we could describe these indifference curves by the
equation:
q1 + q2/2 = constant
(5.2)
Note: the higher the constant the higher the indifference curve. Note also the obvious sense of
equation (5.2): it is simply counting the number of big-bottle-equivalents – counting one big bottle
as one big bottle and one small bottle as half a big bottle. Note too the slope of the indifference
curves – from the figure or from equation (5.2) we can see that the slope of any indifference curve
anywhere is equal to –2. 2 is the rate of substitution: 1 big bottle can everywhere be substituted by 2
small bottles. This (magnitude of the) slope has a name: economists call it the marginal rate of
substitution – it indicates the rate at which good 1 can be substituted by good 21. For perfect
substitutes this marginal rate of substitution is constant everywhere.
We can generalise. We can conceive of goods for which some individual regards the goods as
perfect 1 to a substitutes – that is for which 1 unit of good 1 is everywhere substitutable with a units
of good 2. Clearly for these preferences the indifference curves are everywhere straight lines with
slope –a. The marginal rate of substitution is everywhere a. Moreover, the indifference curves can
be described by:
q1 + q2/a = constant
(5.3)
We note, once again, that this is a description but not a unique description.
1
We should be a little careful – the indifference curves everywhere are downward-sloping – that is, have a negative
slope. The MRS (marginal rate of substitution) is the magnitude of the slope – and therefore is the negative of the slope.
5.3: Perfect Complements
Perfect substitutes are one extreme – the individual regards the goods as perfectly interchangeable.
The other extreme is Perfect Complements. In this type of preference the individual considers that
the goods should be consumed together. One example is Perfect one-with-one Complements for
which the individual regards it as crucial that every one unit of good 1 is consumed with one unit of
good 1, and moreover regards having more of one good without having more of the other as being
pointless. If the individual regards the two goods as having this kind of relationship then his or her
indifference curves look as follows:
Consider, for example, the third indifference curve here. It has an angle at (30, 30) – where the
individual has 30 units of each good. From this angle the indifference curve is horizontal to the right
and vertical above. What does this mean? First, consider the horizontal segment to the right. It says
that the individual is indifferent between the point at the angle (30, 30) and the points to the right,
for example, (40, 30), (50, 30), (60, 30), (70, 30), (80, 30), (90, 30), (100, 30), and, more generally
(q1, 30) for any q1 greater than 30. This simply says that increasing the quantity of good 1 without
increasing the quantity of good 2 does not make the individual any better off – having the extra
units of good 1 without any extra units of good 2 is of no value to the individual. Now consider the
points vertically above the point at the angle – they all lie on the same indifference curve so the
individual is indifferent between the point (30, 30) and the points above: (30, 40), (30, 50), (30, 60),
(30, 70), (30, 80), (30, 90) and (30, 100) and more generally the point (30, q2) for any value of q2
greater than 30. This simply says that increasing the quantity of good 2 without increasing the
quantity of good 1 does not make the individual any better off – having the extra units of good 2
without any extra units of good 1 is of no value to the individual.
The usual example associated with this kind of preferences is left and right shoes: that is good 1 is
left shoes and good 2 is right shoes. Assuming that the individual has 2 feet he or she wants one left
shoe to go with each right shoe (and vice versa). So the preferences are perfect 1 with 1
complements.
An equation which describes these indifference curves is
min(q1, q2) = constant
(5.4)
We can check – at every point along the third indifference curve in the above figure we have that
the minimum of q1 and q2 is equal to 30. Obviously the higher the constant the higher the
indifference curve. But note, there are obviously other ways to describe the indifference curves –
(5.4) is not the only way.
Preferences can be perfect complement but not necessarily one-with-one. For example, it might be
that the individual considers the two goods as perfect one-with-two complements – that is, for each
one unit of good 1 the individual must have 2 units of good 2 and vice versa. In this case the
indifference map would be
Notice that at the corner points the quantity of good 2 is always the double of the quantity of good
1.
An equation which describes the indifference curves for this kind of preferences is:
min(q1, q2/2) = constant
Obviously we can generalise further – we can have perfect 1 with a complements – 1 unit of good 1
needs to be always combined with a units of good 2 and vice versa. For this kind of preferences the
indifference curves can be specified by:
min(q1, q2/a) = constant
(5.5)
though once again we note that this representation is not unique.
5.4: Concave preferences
The two cases that we have considered so far in this chapter can be considered the two extremes of
the convex preferences case – that is when the indifference curves are convex. The alternative,
which we introduce if only to dismiss as being relatively unrealistic when ordinary goods are being
considered, is the case of concave preferences. Here the indifference curves are concave. You
should be able to work out what such preferences imply. Consider the individual’s reservation
prices – because the indifference curves are concave this implies that the more units of the good that
the individual has the more he or she is willing to pay for additional units. Rather than fall with the
number of units held, the reservation price rises – the individual is willing to pay increasingly more
for extra units. Because this obviously works in both directions it implies that the individual prefers
to consume either one good or the other – rather than the two together. The individual prefers the
extremes (consuming all of one good or the other) to the average (consuming the two together).
An extreme example of this concave preferences case is the following:
The title of the figure shows what is important with these preferences – the maximum of either
good. Note that given a quantity Q of one good, increasing the quantity of the other good from zero
to Q has no effect on the individual. Be careful in interpreting this figure – both goods are still
desirable – it is just that the desirability depends upon the quantity being at least as large as the
quantity of the other good. These preferences can be represented by:
max(q1, q2) = constant
(5.6)
Obviously the higher the value of the constant the better.
5.5: Cobb-Douglas Preferences
The cases that we have considered so far are really all rather special cases, particularly the cases of
perfect substitutes and perfect complements. In reality, most individuals consider most cases to be
somewhere in between these two extremes. We can discover actual preferences in a number of ways
and we can build up pictures of what actual preferences look like. To enable generalisations to be
made (see chapter 16), economists have sought to find functional forms (for indifference curves)
which are reasonably good approximations to actual indifference curves. Two functional forms
which seem to be reasonably good approximations are the Cobb-Douglas preferences and the
Stone-Geary preferences. We shall consider the first of these in this section and the second in the
next; we should note here that the second is a relatively simple generalisation of the first.
Obviously whether Cobb-Douglas (named after its originators) preferences can adequately describe,
or can reasonably approximate, an actual person’s actual preferences, is an empirical question – one
to which we shall turn in chapter 16. For the time being we shall describe these preferences – later
we shall explore the implications.
A Cobb-Douglas indifference curve is given by
q1aq21-a = constant
(5.7)
where a is a given parameter. Clearly this parameter affects the shape of the indifference curves – as
we shall see below. Alternatively (taking the logarithm of equation (5.7)2) a Cobb-Douglas
indifference curve is given by
a ln(q1) + (1-a) ln (q2) = constant
2
Recall the rules for the manipulation of logarithms given in Chapter 1.
(5.8)
Equations (5.7) and (5.8) say the same thing – they can be used interchangeably – since if
something is constant then so is its logarithm.
What does the implied indifference map look like? Well, it obviously depends upon the parameter a
– which determines effectively the relative importance of the two goods in the individual’s
preferences. Let us start with the symmetric case a = 0.5 (note this implies 1-a = 0.5).
Note the symmetry about the line q1 = q2. Note also how the marginal rate of substitution (the mrs)
changes. If q1 is low but q2 is high (the top left of the figure) the mrs is very high – the individual is
willing to give up a lot of good 2 in order to get a little more of good 1. Conversely, if q1 is high but
q2 is low (the bottom right of the figure) the mrs is very low – the individual is not willing to give
up much of good 2 in order to get more of good 1. However note that when q1 and q2 are
approximately equal then the mrs is close to unity – the individual in this region is willing to give
up one unit of good 2 to get one more of good 1 (and vice versa). Note crucially that the
indifference curves are not parallel in any direction – so that reservation prices are not independent
of the quantity of good 2 – Cobb-Douglas preferences are not quasi-linear. Nor is the mrs constant
as in the case of perfect substitutes. Nor are the indifference curves in the shape of an L as in the
case of perfect complements. The case of Cobb-Douglas preferences is somewhere between the two
extremes of perfect substitutes and perfect complements.
Now consider a non-symmetrical case – here with a = 0.3
Note that if a = 0.3 it follows that (1-a) = 0.7 so that the indifference curves are given by (from
(5.7))
q10.3q20.7 = constant
You might like to think of this as putting more weight on the quantity of good 2 consumed. Now
look at the indifference map. We note a number of things – first it is not symmetric. Second at any
point in the space the indifference curves are flatter (the magnitude of the slope is smaller) than in
the case of symmetrical Cobb-Douglas considered above. For example, it is clear that along the line
q1 = q2 the slope has a magnitude less than 13. So when the individual has the same amount of both
goods he is willing to give up less than one unit (in fact 0.3/0.7 of a unit) of good 2 to have an extra
unit of good 1. This embodies the idea that this individual puts relatively more weight on good 2
than on good 1.
A contrary case – when more weight is put on good 1 – is when a = 0.7. Here the indifference map
is as below
Note that this is just the reverse of the a = 0.3 case.
Now it may be the case that an individual’s preferences are such that they can be reasonably well
approximated by a Cobb-Douglas preference function for some appropriate value of the parameter
a. However it may equally well be the case that for no value of a does the Cobb-Douglas
preferences represent actual preferences. In such a case we need to seek a more general
specification of preferences. There are many that economists use – but most of these are really too
sophisticated to be included in this course. However I do include one more – which is a rather
simple extension of the Cobb-Douglas preferences that we have already considered. This
generalisation is known as Stone-Geary preferences (once again named after its originators) which
we discuss in the next section.
5.6: Stone-Geary Preferences
Stone-Geary preferences are a simple extension of the Cobb-Douglas preferences. The extension is
simple: the individual has to consume subsistence levels of the two goods before allocating the
residual income between the two goods. Denote the subsistence levels by s1 and s2 for goods 1 and
2 respectively. Then a Stone-Geary indifference curve is given by
(q1 - s1) a(q2 -s2)1-a = constant
3
In fact, the slope here is –0.3/0/7, or more generally a/(1-a).
(5.9)
where a is a given parameter. Clearly this parameter affects the shape of the indifference curves – as
we shall see below. Alternatively (taking the logarithm of equation (5.9)4) a Stone-Geary
indifference curve is given by
a ln(q1 – s1) + (1-a) ln (q2 – s2) = constant
(5.10)
Note the difference between (5.7) and (5.9) and the difference between (5.8) and (5.10) – the
inclusion of the subsistence terms s1 and s2. You might like to think of these preferences as simply
Cobb-Douglas preferences expressed relative to s1 and s2 - rather than relative to the usual origin.
This will be obvious from the figures below. Note that Cobb-Douglas is a special case of StoneGeary when the terms s1 and s2 are both zero.
I give some examples. In all of these I put the subsistence terms s1 and s2 equal to 10 and 20
respectively. In the first example, the parameter a = 0.5, so it is a sort of symmetric case – but note
only with respect to the subsistence levels s1 and s2. This should be apparent from the figure.
The subsistence levels are the vertical line (at q1= 10) and the horizontal line (at q2 = 20). Note that
indifference curves are not defined for values of q1 below its subsistence level or for value of q2
below its subsistence level. Note also the symmetry of the indifference map relative to the
subsistence levels, but not relative to the normal axes.
A non-symmetric example with the same subsistence levels is given by a = 0.3. This has the
following indifference map:
Note the similarities with and the differences from the Cobb-Douglas case with the same parameter
(figure (5.10) above).
4
Recall the rules for the manipulation of logarithms given in Chapter 1.
Sometimes we find that preferences can be better approximated with a Stone-Geary function;
sometimes not. If not, we have to search further. For reasons that will be discussed in chapter 16
economists prefer to approximate preferences (and indeed anything) with a function that contains
just a few parameters rather than describe preferences precisely. To this end, economists have found
a number of functional forms which are good approximations of many of the preferences that exist
in society. We can not go into detail – as some of these forms are mathematically rather
complicated. In a sense this does not matter – what I want to convince you of is the following:
1)
2)
3)
4)
5)
6)
7)
Different people may have different preferences over goods.
Some may think of goods as perfect substitutes or perfect complements.
Some may have concave preferences.
Some may have Cobb-Douglas or Stone-Geary preferences
(As we shall see formally later but which should be obvious now) If people have
different preferences then they will in general have different demand and supply
functions for goods.
(See the next chapter) If we know their preferences we can predict their demand.
(See later and using point 6) If we can observe their demand we can infer their
preferences and hence predict their future demand.
In the next two chapters we will find the demands for the preferences we have examined in this
chapter. Because of the technical difficulty (and the fact that this book cannot contain everything) I
do not find the demands for other kinds of preferences. In a sense this does not matter as you can
look up the results in a more advanced text. But, more importantly, it should not matter – as this
book is designed to teach you methods rather than details. If you follow the points 1 to 7 above, you
are well on the way to becoming an economist.
5.7: Representing Preferences with Utility Functions
You might be asking whether there is some mathematical way to describe preferences. We have
used a graphical method involving indifference curves. We note the properties. First, along a
particular indifference curve we know that the individual is indifferent – he or she is equally happy
at all points along it. Second, if we compare the happiness of the individual at any point on one
indifference curve with his or her happiness at any point on a lower indifference curve, then we can
say that the individual prefers to be at – is happier at – the first of these two points.
Can we not specify a ‘happiness’ or ‘utility’ function – defined over (q1,q2) space – which reflects
these properties? That is, can we not specify a ‘utility’ function U(q1,q2) such that this remains
constant along an indifference curve and increases as we move to higher and higher indifference
curves?
Well clearly we can. Suppose for example that a particular preference is such that an indifference
curve is defined by
f(q1,q2) = constant
where the value of the constant rises as we move from a lower to a higher indifference curve. Then
we simply define our utility function as
U(q1,q2) = f(q1,q2)
For example, take perfect 1:1 substitutes. There an indifference curve is defined by q1 + q2 =
constant (see equation (5.1)) so we simply define the individual’s utility function to be
U(q1,q2) = q1 + q2
(5.11)
This has all the right properties. The implied utility is constant along a particular indifference curve
and rises as we move up the indifference curves. Referring to figure (5.4) we see that utility is equal
to 20 at all points on the first indifference curve, equal to 40 at all points on the second indifference
curve, …., equal to 180 at all points on the last indifference curve.
That works fine. But then so does any increasing transformation. Consider, instead of (5.11), the
following:
U(q1,q2) = 2(q1 + q2)
This also has all the right properties. The implied utility is constant along a particular indifference
curve and rises as we move up the indifference curves. Referring to figure (5.4) we see that utility is
equal to 40 at all points on the first indifference curve, equal to 80 at all points on the second
indifference curve, …., equal to 360 at all points on the last indifference curve.
So that works to. So does
U(q1,q2) = (q1 + q2)2
This also has all the right properties. The implied utility is constant along a particular indifference
curve and rises as we move up the indifference curves. Referring to figure (5.4) we see that utility is
equal to 400 at all points on the first indifference curve, equal to 1600 at all points on the second
indifference curve, …., equal to 32400 at all points on the last indifference curve.
It follows that whereas equation (5.11) correctly describes the individual’s preferences, it is not
unique. Any increasing transformation also describes the preferences. But is this a problem – or a
strength? If we look at the different representations above we see that the different representations
simply attach different numbers to each indifference curve. So, if we take the bottom indifference
curve in figure (5.4) we see that the first representation attaches the number 20 to this, the second
representation the number 40 and the third representation the number 400. This seems to be telling
us that any old number can be attached to the indifference curve – the actual number is unimportant.
Recall what this number is meant to tell us – the happiness or the utility of the individual at a point.
So we are being told that we cannot attach a meaningful number. Should that surprise us?
Clearly not. It would be amazing if we could say that Julie has a happiness measurement of 10
today and that David has a happiness measurement of 20 and is therefore happier than Julie – but
our analysis is telling us that this is not possible. Which is not surprising – but is still somewhat of
a relief.
So our conclusion is as follows: we can represent preferences through utility functions, but these
representations are not unique (and therefore no meaning can be attributed to the utility numbers
that emerge).
For the record there follows a list of possible utility representations for the preferences we have
considered in this chapter.
perfect 1:1 substitutes: U(q1,q2) = q1 + q2
perfect 1:2 substitutes: U(q1,q2) = q1 + q2/2
perfect 1:a substitutes: U(q1,q2) = q1 + q2/a
perfect 1 with 1 complements: U(q1,q2) = min(q1, q2)
perfect 1 with 2 complements: U(q1,q2) = min(q1, q2/2)
perfect 1 with a complements: U(q1,q2) = min(q1 + q2/a)
figure 5.8: U(q1,q2) = max(q1, q2)
Cobb-Douglas with parameter a: U(q1,q2) = q1aq21-a
(or U(q1,q2) = a ln(q1) + (1-a) ln (q2) )
Stone-Geary with parameter a and subsistence levels of consumption s1 and s2:
U(q1,q2) = (q1 - s1) a(q2 -s2)1-a
(or U(q1,q2) = a ln(q1 – s1) + (1-a) ln (q2 – s2) )
5.8: Summary
In a sense this chapter has been a preparatory chapter for future reference. We have not really done
any kind of analysis – we have simply defined things for future use. However in addition to the
various definitions you should have got the following out of the chapter.
The shape of indifference curves depends upon the preferences of the individual.
There are two broad classes, convex and concave.
Indifference curves are convex if the individual likes to consume the two goods together. They are
concave if the individual prefers to consume them separately.
Two special cases include perfect substitutes and perfect complements.
Indifference curves are linear if the individual regards the two goods as perfect substitutes. They
are L-shaped if the individual regards the two goods as perfect complements.
We studied two more general cases:
Two important special cases of convex preferences are Cobb-Douglas and Stone-Geary.
And we discovered (perhaps not to our surprise) that
Preferences can be represented by utility functions but these utility functions are not unique.
5.9: What if the individual can become satiated?
In this chapter we have assumed throughout that both of the goods we have been studying are
always considered by the individual to be goods rather than bads – that the individual always will
prefer more of each. You may well have been wondering what happens if one or both of the goods
is a bad, or becomes a bad at some stage. Suppose, for example, that the individual could have ‘too
much’ of one or both goods – that is, becomes sated with a good, and thereafter the good becomes a
bad. How does this affect our graphical representation of preferences? As we will see, much
depends on whether the individual has indeed to consume the goods, even when he or she considers
them as bads. (For example, as we shall see in chapter 32, I was forced in Bari to ‘consume’ the
loud music provided by my neighbours.) We shall first assume here that the individual is indeed
forced to consume the bads – then we discuss how our analysis changes if that is not the case.
We consider here just one possibility – where the individual likes both goods up to a consumption
level of 50, but if he or she has to consume more than 50 units of a good, then that good becomes a
bad. Then his or her indifference curves become like those in the figure that follows.
We can divide the figure up into 4 quadrants. In the south-west quadrant the indifference curves
have the usual downward-sloping convex shape; the individual still considers both goods as goods since the consumption level of each good is less than 50. In the south-east, however, the curves are
upward-sloping. This is a consequence of the fact that, in this quadrant, he or she has too much of
good 1 – the individual is sated with good 1. The upward-sloping shape of the indifference curves
indicates the fact that the individual would be happy to give up some units of good 2 (which he or
she still considers as a good) in return for consuming less of good 1 (which he or she now considers
a bad); or, alternatively, he or she would only consume more of the bad if he or she were
compensated by consuming more of the good. The same is true mutatis mutandis in the north-west
quadrant. In the north-east quadrant, the indifference curves once again resume their downwardsloping form – because in this quadrant both of the goods are bads: if the individual has less of one
bad, then to keep him or her indifferent, he or she has to have more of the other. Interestingly the
shape is now concave – you might like to think why.
The point labelled ‘B’ in the figure could be considered the individual’s bliss point – up to this
point he or she gets happier and happier, after it he or she gets more and more unhappy.
If the individual is not forced to consume the goods when they become bads, then the indifference
curves in the south-east quadrant become horizontal and in the north-west quadrant they become
vertical. Where do you think the ‘indifference curves’ are in the north-east quadrant?5
5
This is an unfair question: if the individual can refrain from consuming more than he or she wants, then all the points
in the north-east quadrant are indifferent to the bliss point.
The final thing you might think about, particularly when you are reading the next two chapters, is
how the existence of bads may affect the individual’s behaviour when deciding how to allocate his
or her income.