Essay Question number one : “ A number of assumptions are typically made on preferences to give so-called « well behaved indifference curves ». Explain these assumptions and discuss whether or not they appear reasonable”.
Microeconomic theory deals with “choices that individuals and businesses make, the way these choices interact in markets and the influence of governments” . In other words, microecomomics tries to modelise how individual agents behave. Among these agents, consumer theory particularly focuses on actions of the consumer, “an economic agent who makes choices between available combinations of commodities” (consumption bundles) . As we are going to see, consumption models do not always exactly correspond to the reality, but they are nevertheless useful. What are the criteria for the consumer to make choices ? How realistic are these criteria ? I am firstly going to explain what preferences and choices imply in the consumer theory, since these concepts are necessary to define and discuss the assumptions of 'well-behaved indifference curves'.
Between two bundles of goods, any consumer can tell which bundle they prefer. In this case, we say that the chosen bundle is strictly preferred to the other one, and we use the symbol >. There is a distinction between strict and weak preference, but it is not useful to explain it here. When the consumer is equally happy with any of the two bundles, then they are said to be indifferent between the bundles, and the symbol used is ~. These assumptions are based on the idea that all consumers are rational, which means, in this case, that they will always try to maximise any preference relation . Concretely, if a consumer knows to prefer one bundle over some other, they will go for the preferred bundle. Some rules about preferences have been established, to make sure consumer's preferences are 'consistent'. The first is completeness, that states “that any two bundles can be compared” .This is a necessary assumption, that enables us to analyse any group of two bundles with respect to a consumer. The second assumption is reflexivity, i.e. that “any bundle is at least as good as itself” . This hypothesis might seem a bit meaningless, but it is actually necessary for the analysis. It is a way of making sure that bundles can be compared to each other in a logical way. The final assumption of consumer's preferences is transitivity, which is also very useful. Simply put, transitivity establishes a chain between bundles, once again to be able to analyse them logically. If a consumer prefers bundle A to bundle B, and bundle B to bundle C, then they also prefer bundle A to bundle C. If a consumer did not behave like this, it would actually look quite unlogical, so this assumption can be safely made. These three assumptions about preferences are necessary conditions for preferences to be said consistent, according to consumer theory. And if preferences are consistent, we can write down a utility function .
Utility can be simply defined as “the benefit or satisfaction that a person gets from the consumption of a good or service” , or as “how much a product pleases people” . Utility is a function that gives a numerical value to this amount of satisfaction. We can then measure the utility of each consumption bundle relatively to others.We need the notion of utility to be able to represent preferences graphically, by indifference curves. They “plot a set of bundles between which the consumer is indifferent”, or that “gives the consumer the same utility” . Therefore, all the points that are on an indifference curve correspond to bundles that make the consumer equally happy, that give him the same level of utility. Let us have a look at an indifference curve :
If X and Y are two different goods, all the points situated on the black line give the consumer the same level of utility. The coloured area, the 'weakly preferred set', is the area which is better for the consumer, for which utility is higher than on the indifference curve . Indifference curves can have a different shape according to the type of good.
Now that we know what an indifference curve is, let us turn to so called 'well-behaved indifference curves'. What are they ? How useful are they ? The phrase 'well-behaved' suggests that they are not problematic curves, which is useful analyse preferences : “if we want to describe preferences in general, it will be convenient to focus on a few general shapes of indifference curves” . They are mostly conventional, although they obviously have some realistic features as well. There are four assumptions about well-behaved indifference curves, i.e. four hypotheses that define preferences in general.
The first assumption is monotonicity : “It is the condition that more is better” . If the bundle A has more of the two goods than bundle B, then A is preferred to B, and A has a greater utility than B . Graphically, this implies that the indifference curve is downward sloping, because if you decrease the quantity of one of the goods, you have to increase the quantity of the other to keep utility constant . Monotonicity seems to be a rather fair assumption : for most goods, consumers are better off when they get more (until a certain point, as we will see later). But, as Rubinstein emphasizes, “monotonicity is a property that gives commodities the meaning of 'goods'.” , as opposed to bads, “[commodities] that the consumer doesn't like” . If we consider bads, we can find examples where monotonicity does not hold. The most common one is pollution : people do not want more of it. Therefore, monotonicity is useful to describe preferences in general, but there are several situations in real life where monotonicity does not hold.
The assumption of non-satiation is closely linked to monotonicity. Indeed, monotonicity holds only until one point, because for most goods there is a point where more is not better anymore. Be it for food, or pens, or most goods, at some point you do not want them anymore. This point is called the bliss point, or the satiation point . But this gives us particular indifference curves that make the analysis more complex, so well-behaved indifference curves reflect situations before the reach on any such point. Given this condition, it is hard to disprove the assumption of non-satiation. In all situations where monotonicity holds, i.e. when good is better, there is actually some period where there is no satiation.
The third assumption of well behaved indifference curves is based on the idea that consumers generally prefer averages over extremes . Thus, if the two goods are meat and vegetables, and if you are indifferent between the two, you would be happier to have a bit of meat and a bit of vegetables than to have lots of meat and no vegetables (or vice-versa). Graphically, if you can choose between point A (2 units of vegetables ; 8 units of meat), B (8 units of vegetables ; 2 units of meat), or C (5 units of each), you would go for C, because you are indifferent between the two goods, so you would rather have an equal amount of each. This implies convexity : C has to be in the preferred set, and as it is the indifference curves that limits the preferred set, and that we know that the curve is downward sloping, the indifference curve has to be convex.
Here again, although convexity seems to be true for many cases, it is quite easy to find counter examples. For instance, in a period of time (say, one hour), you do not want to have the same quantity of oysters and chocolate. You would rather have lots of oyster, or lots of chocolate, and little of the other good. In this particular case, the indifference curve would be concave, and C would not in the preferred set .
The last assumption of well-behaved indifference curves is continuity, which means that small changes in the quantity of the goods can not induce big changes in utility. Were indifference curves not continuous, it would be quite hard to analyse preferences. Thus, in the next diagram, if the function f is function of x and y, we can see that a small change in x brings about a big change in y (∆y is a lot bigger than ∆x). It is the same with utility. Therefore, the assumption of continuity about preferences seems to be necessary to any consistent analysis.
To sum up, we can say that these four assumptions, monotonicity, non-satiation, convexity and continuity are very useful to analyse preferences in general. They are also quite close to real-life situation in many cases, although it is sometimes possible to find counterexamples. We now understand why consumer theory makes these assumption, and how microeconomics model building works.
Cartright, Edward, EC 500 : Microeconomics (University of Kent, 2007).