Chapter 5: Preferences

Transcription

1 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 q 1, on the horizontal axis and the quantity of good 2, which we will denote by q 2, on the vertical axis. Later we will use p 1 and p 2 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 p 2 = 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:

2 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 q 1 + q 2 =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 q 1 plus q 2 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 q 1 + q 2 = 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 q 1 + q 2 is constant then so is (q 1 + q 2 ) 2 and so is (q 1 + q 2 ) 3 and indeed so is f(q 1 + q 2 ) 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:

3 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: q 1 + q 2 /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 2 1. 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: q 1 + q 2 /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.

4 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 (q 1, 30) for any q 1 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, q 2 ) for any value of q 2 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(q 1, q 2 ) = constant (5.4) We can check at every point along the third indifference curve in the above figure we have that the minimum of q 1 and q 2 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.

5 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(q 1, q 2 /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: though once again we note that this representation is not unique. min(q 1, q 2 /a) = constant (5.5) 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:

6 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: Obviously the higher the value of the constant the better. max(q 1, q 2 ) = constant (5.6) 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 q 1 a q 2 1-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(q 1 ) + (1-a) ln (q 2 ) = constant (5.8) 2 Recall the rules for the manipulation of logarithms given in Chapter 1.

7 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 q 1 = q 2. Note also how the marginal rate of substitution (the mrs) changes. If q 1 is low but q 2 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 q 1 is high but q 2 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 q 1 and q 2 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)) q q = constant

8 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 q 1 = q 2 the slope has a magnitude less than 1 3. 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 s 1 and s 2 for goods 1 and 2 respectively. Then a Stone-Geary indifference curve is given by (q 1 - s 1 ) a (q 2 -s 2 ) 1-a = constant (5.9) 3 In fact, the slope here is 0.3/0/7, or more generally a/(1-a).

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(q 1 s 1 ) + (1-a) ln (q 2 s 2 ) = 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 s 1 and s 2. You might like to think of these preferences as simply Cobb-Douglas preferences expressed relative to s 1 and s 2 - rather than relative to the usual origin. This will be obvious from the figures below. Note that Cobb-Douglas is a special case of Stone- Geary when the terms s 1 and s 2 are both zero. I give some examples. In all of these I put the subsistence terms s 1 and s 2 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 s 1 and s 2. This should be apparent from the figure. The subsistence levels are the vertical line (at q 1 = 10) and the horizontal line (at q 2 = 20). Note that indifference curves are not defined for values of q 1 below its subsistence level or for value of q 2 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.

10 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) Different people may have different preferences over goods. 2) Some may think of goods as perfect substitutes or perfect complements. 3) Some may have concave preferences. 4) Some may have Cobb-Douglas or Stone-Geary preferences 5) (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. 6) (See the next chapter) If we know their preferences we can predict their demand. 7) (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 (q 1,q 2 ) space which reflects these properties? That is, can we not specify a utility function U(q 1,q 2 ) 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(q 1,q 2 ) = 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(q 1,q 2 ) = f(q 1,q 2 )

11 For example, take perfect 1:1 substitutes. There an indifference curve is defined by q 1 + q 2 = constant (see equation (5.1)) so we simply define the individual s utility function to be U(q 1,q 2 ) = q 1 + q 2 (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(q 1,q 2 ) = 2(q 1 + q 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 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(q 1,q 2 ) = (q 1 + q 2 ) 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 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.

12 perfect 1:1 substitutes: U(q 1,q 2 ) = q 1 + q 2 perfect 1:2 substitutes: U(q 1,q 2 ) = q 1 + q 2 /2 perfect 1:a substitutes: U(q 1,q 2 ) = q 1 + q 2 /a perfect 1 with 1 complements: U(q 1,q 2 ) = min(q 1, q 2 ) perfect 1 with 2 complements: U(q 1,q 2 ) = min(q 1, q 2 /2) perfect 1 with a complements: U(q 1,q 2 ) = min(q 1 + q 2 /a) figure 5.8: U(q 1,q 2 ) = max(q 1, q 2 ) Cobb-Douglas with parameter a: U(q 1,q 2 ) = q 1 a q 2 1-a (or U(q 1,q 2 ) = a ln(q 1 ) + (1-a) ln (q 2 ) ) Stone-Geary with parameter a and subsistence levels of consumption s 1 and s 2 : U(q 1,q 2 ) = (q 1 - s 1 ) a (q 2 -s 2 ) 1-a (or U(q 1,q 2 ) = a ln(q 1 s 1 ) + (1-a) ln (q 2 s 2 ) ) 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

13 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.

14 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.

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