Choices and Preferences of consumer:
Now that we have described what the consumer can do, we will tackle the question of what he/she will do. It is here that we must make some assumptions about behavior, and as I remarked above, we will assume that the consumer always chooses the best alternative from his/hers budget set. Choice theorists (and economists studying microeconomic behavior) start by defining objects of choice. In our case it is consumption bundles which are these objects. A consumption bundle is simply a list of quantities one for each good (a pair in our two-good world). The budget set describes the set of all feasible consumption bundles, and given this set we may contemplate a process in which we ask our consumer to rank all feasible bundles. By this we mean that we ask whether he/she thinks that bundle A is better or worse than bundle B, or if they are equally good. If he/she says that A is better (worse) than B, we say that the consumer has expressed a “preference” for A over B (B over A). If he/she says that A and B are equally good we say that the consumer is “indifferent” between A and B.
It is convenient to use mathematical symbols to express the possible relationships between A and B (it becomes tedious to write e.g. “A is preferred to Bj etc.):
A › B → A is preferred to BA ›∼ B → A is at least as good as BA ∼ B → A indifferent to B.
Note here that the symbol ? shows strict preference, while ›∼ shows weak preference, which means that A could be equally good as B, but it is never the case that B is better than A.
It is very convenient to make some assumptions about preferences, which rules out certain “irrational” choice behavior. For example, it would seem natural to rule out the possibility that the consumer first say that: A › B and then B › A (of course, over time, preferences may change but we assume that preferences are expressed at one point in time). Another set of assumptions about preferences (or axioms of choice) are:
Assumption 1: Complete preferences. The consumer is able to compare all possible bundles, and rank them.
Assumption 2: Transitivity. In a comparison between three bundles (A, B and C), assume that the consumer says that A is at least as good as B, and that B is at least as good as C, it then follows that A is at least as good as C, or,
A ›∼ B & B ›∼ C → A ›∼ C
These axioms imply that preferences are rational. The meaning of rationality in this context is that preferences, and choice behavior, are consistent. If transitivity did not hold, for example, it would imply that we could have that A ›∼ B & B›∼ C & C ›∼ A. In this case all bundles are at least as good compared to any other bundle, and it would be impossible to pick out any “best” bundle, which is what we want to do. Hence, the assumption of rational preferences is indispensable to any theory of choice.
Assumption 3: “More is better” (Greed assumption). This is not a crucial assumptions to make, the basic theory works well without it (assumptions 1 and 2 are indispensible). However, it will simplify our analysis because no goods will ever be left unused (and we have to decide what to do with them). It means that consumers always will use their entire budget to spend on goods.
Assumption 4 & 5: Continuity and strict convexity. These are “technical” (or rather mathematical) assumptions, but they are necessary to rule out some “weird” or unusual behavior. As assumption 3, they are not necessary, but convenient.
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