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Micro I. Lesson 3. Preferences Lesson 2 was concerned with what consumers can do. This lesson is concerned with what consumers would like to do. 3.1 Consumer preferences We have two goods: x and y. A bundle of goods is a set with given quantities of both goods. We will represent a bundle as (x,y). Preferences: A representation of how the consumer ranks all possible bundles. - If a bundle (x,y) is strictly preferred to another bundle (x’, y’), then x, y x, y A consumer faced with both bundles will always choose the strictly preferred one. - If a bundle (x,y) is equally preferred to another bundle (x’, y’), then x, y x, y A consumer faced with two equally preferred bundles will be equally satisfied with one or the other. We say, he is indifferent between the two bundles.
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- If a consumer prefers or is indifferent between two bundles, we say that he weakly prefers one to other x, y x, y Assumptions To ensure that preferences are “consistent”, we assume that preference relations are: - Complete: Any two bundles can be compared. This is equivalent to saying that all bundles in the goods space can be compared. - Reflexive: Any bundle is at least as good as itself (a technical condition with no economic relevance). - Transitive: If bundle A is at least as good as B, and B is at least as good as C, then A is at least as good as C.
3.2 Indifference curves The above three assumptions are sufficient to formally describe preferences, but first it is convenient to introduce another concept (the indifference curve), which will be very useful for the graphical representation of preferences. Indifference curve that passes through (x,y): The set of bundles which are indifferent to (x,y).
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- If in addition to the three assumptions above, we consider one more assumption we can obtain the result that indifference curves are negatively sloped. This additional assumption is that for economics goods, more is preferred to less.
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Equally preferred bundles to (x,y) must necessarily be in the north west and south east quadrants. Therefore, the indifference curve must be downward sloping.
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- Finally we add a fifth assumption that is related to what we observe as consumer behaviour. Namely, we assume that indifference curves are convex to the origin. That is, they have the following shape y
(x,y)
x
Another way of denoting that the indifference curve is convex is to say that the weakly preferred set to (x,y) (the shaded area) is itself convex. A set is convex if any linear combination of two points of this set (any point on the straight line in the figure), lies within the set.
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Economic meaning and implications of the above assumptions The economic meaning of convexity is that consumers prefer bundles that combine (mix) goods to bundles that specialize in only one good. If two bundles are equally preferred, the average of these two bundles (or any linear combination of them) must be preferred to any of the two bundles. Example x: kgs. of meat; y: kgs. of vegetables Suppose A(10,6) B(2,50). Find arithmetic average of these two bundles: C(6,28). It must be that C(6,28)>A(10,6) and C(6,28)>B(2,50). You can see that this is so in the following figure: Veg.
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Meat
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An implication of the above assumptions (in particular, of transitivity) is that indifference curves cannot cross. A situation like the one depicted in the following figure is impossible: it leads to a contradiction; it is not consistent.
A C i.c. I
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i.c. II
If we begin with indifference curve I, we have: A C and C>B; therefore A>B. But this is wrong according to i.c. II. If we begin with indifference curve II, we have: A B and B