What this implies is that the consumer has the ability to rank alternative choices of goods.
The phenomenon of ignorance is denied to this consumer which may seem a very strong assumption. In particular, it suggests experience with all possible consumption alternatives. However, this may be a reasonable description of reality for choices which the consumer actually has to make.
For example while it is unreasonable to believe that a consumer is really able to compare between eating at Jollibee for lunch or at Manila Hotel chances are that he is able to decide between situations he is likely to face. Intuitively we say that the consumer knows his/her mind.
As to Monotonicity. Simply means that more is better. Any bundle which has more of one or more commodities and no less of any other is liked better by the consumer. One can easily think of an example-after consuming 2 kilos of lanzones the third one may well make you sick but for the relevant range of goods this may not be an appropriate assumption.
This makes intuitive sense. If I hate Econometrics as much as Macroeconomics as Macroeconomics and Macroeconomics as much as Calculus then I must hate Econometrics as much as Calculus. An exception to transitive behavior is for the case of addiction goods. Initially I may hate cigarettes so less is preferred to more but after a point I get addicted so more is preferred to less. This violates transitivity.
Convexity This is another assumption on behavior which can be interpreted to mean that mixtures are preferred to extreme. In words if the consumer is indiﬀerent to 2 goods X and Y convexity of preferences imply that any linear combination of X and Y would be at least as good (if not better) as X or Y . A linear combination of goods X and Y is any commodity of the form kX + (1 − k)Y , where 0 < k < 1. The idea is that if X and Y are bundles of goods (apples, bananas, carrots etc.), then a linear combination takes percentages from each of the bundles (which add up to a hundred percent) of goods.
Illustration: Let X= 2 apples and 3 bananas and Y be 4 apples and 1 banana. If a consumer is indiﬀerent between X and Y it must be the kX + (1 − k)Y is at least as good as X and Y . Note 0 < k < 1. For example k could be 0.5. What this means is that consumers have diminishing marginal rate of substitution. This assumption ensures that the choices consumers make display diversity. That is consistent with our empirical observation that the consumer chooses to consume a wide variety of goods.
If preferences were not convex theory would predict monomaniac behavior (consuming only one good) – that seems at odds with what we see around us. (What is missing in this preference representation is intensity of preferences-we are not able to say how much more a consumer likes two apples over one. In other words preferences are ordinal -only the ranking is known.)
Indiﬀerence curves are downward sloping, smooth and bowed out (convex). This follows from the structure we imposed on preferences. Since more of each good is preferred it must be that in a 2 good world more of a good world, say eggs and chicken it must be that we must be given more of eggs to be compensated for less of chicken. Continuity of preferences imply continuity of indiﬀerence curves and similarly for convexity.
2. Higher indiﬀerence curves are preferred to lower indiﬀerence curves. (Why?)
3. Indiﬀerence curves cannot intersect-what does this follow from? Transitivity of preferences is enough but by using monotonicity a simpler proof is obtained.
4. Through every point on the 2-dimensional plane (representing bundles of apples and bananas, say) one can draw an indiﬀerence curve. In other words, every point lies on some indiﬀerence curve. This is because every point can be compared to something. It may the case that an indiﬀerence curve is a point