In economics, when we want to talk about our preferences we start by assuming that people behave rationally in their choices. Of course, when we use the word “rational” we mean something different than being wise or not being insane. Determining whether a choice is “rational” or not requires some axioms like completeness, transitivity, and continuity.
Completeness: While talking about our choices in economics, we assume that we are sure about our preferences. Completeness is the axiom that allows us to eliminate uncertainty. In daily life you may not be sure whether you prefer one good to another, but to make a comparison in an economical concept you have to be sure about whether you prefer one good to another or you are indifferent between these goods. Hence, you have to explicitly say I am preferring A to B or B to A or I am indifferent between A and B which means either A and B has same attractiveness and gives same utility (happiness or satisfaction) to me.
Transitivity: This axiom of rational choice suggests that if you are preferring good A to B and B to C then it means you prefer A to C when you have A and C. This means preferences do not cycle Exactly same meaning that we used to encounter in mathematics.
Continuity (Reflexivity): This axiom is little bit tricky to understand. Continuity means that we do not have jumps between our preferences which allows us to have “continuous” graphs in our utility functions. By the way utility function is just the mathematical representation of our preferences and it shows how much utility we will gain by choosing one good to another. This axioms states that if we are preferring good A to B then situations close to this also holds we still prefer A to B. In other terms, If I prefer A to B and C lies within a radius of B (really close to B) Let’s say both A and B gives 1 util to me which means when I have 1 A and 1 B I can choose either A or B, it doesn’t matter. For example, let’s say you can buy 8 A or 1 B in same price, in real world this is not gonna happen but for the sake of example, then of course you prefer A to B. What continuity says is that when you have 7 A and 1 B you still prefer A. You don’t suddenly say no I want 1 B because I am stupid. (Remember both A and B gives 1 utility per good)
Given these assumptions people “rank” situations from least desirable to the most. Having said people rank the situations regarding utility, we can understand that utility is ordinal concept which means talking about utility matters when we sort them.
The reason for us to talk about being rational is that in consumer theory, we say for x belongs to R^n any continuous “rational” preference relation can be represented.
There are axioms of consumer preference which are completeness, transitivity, continuity (these three implies that consumer behaves rationally in their preferences), convexity and non-satiation (weak monotonicity). We say preferences are well-behaved if they are rational, monotonic and convex
We already covered three of them. S o all we have to do is now understanding convexity and non-satiation
Convexity: Consumers prefer to mix extreme bundles
Non-satiation: More is better. For example you have two options one is having 2 x and 2 y , bundle (2,2) or having 5 x and 7 y, bundle (5,7). Non-satiation implies that you choose the second option because the more you have the more utility you gain.
More on utility and consumer theory
· Utility is defined as order-preserving (monotonic)transformation
· Ceteris paribus is a term meaning “all else being equal”. This is required if we want to see what will happen when we change one variable while others remain constant. For example we can say if price of A increases, ceteris paribus, what will happen to the good A’s quantity demanded. Here ceteris paribus implies that we hold income and price of y constant.
· Utility means relative desirability
· Usually showed as U(w) when we have only good x, U(a,b) when we have good a and b, U(x,y,z….) and so on
·
Comments