The foundation for Economics is rationality. Rationality implies that people will act in ways that best suit their particular set of circumstances, including, but not limited to, the choices they face. In order to choose, you must necessarily have a set of preferences over the options you are presented with. Although utility theory was born in the 18th century, this approach, which simply implied consumers being able to rank preferences (and not assign a numerical ‘utility factor’ to each choice) really took off at the beginning of the 20th century because it offered an empirical, logical structure to microeconomics. Frisch was a pioneer in this in the early 1920s, but the definite birth of consumer behaviour as an economic science is probably attributable to Samuelson in the 1940s.
These preferences must fulfil a set of criteria in order to fulfil the necessary requirement of being classed as ‘rational’ (in a purely economic sense of the word).
- The first axiom is completeness. That is, whether one is indifferent to, or prefers, one set of options over another, they must always be able to make that choice. That is, a consumer can always rank a set of possibilities as either better, worse, equal or at least as good/bad as another.
or 
or both at the same time
- Transitivity. This simply means that consumers are able to order their preferences in a logical way- that is, if you prefer A to B and B to C, you must prefer A to C. It is useful to express this in binary logical form, with a set of symbols that represent:
- A is preferred to B,
… - …or B offers less utility than A,
- …or A and B are indifferent,
- …or A is at least as good as B,
- …and therefore, to be transitive, if and
, then 
.
- A is preferred to B,
- Continuity: in order for preference theory to be useful mathematically, we need to assume continuity. Continuity simply means that there are no ‘jumps’ in people’s preferences. In mathematical terms, if we prefer point A along a preference curve to point B, points very close to A will also be preferred to B. This allows indifference curves to be differentiated.
- Sometimes, and for purely formal purposes, a fourth axiom, reflexiveness, is mentioned:
Which simply implies that A is at least as good as itself.
This is the basic set of premises, or axioms that Economics requires of individuals in order to be rational economic agents. It also enable us to represent preferences graphically. However, a later set of axioms was studied and added by Samuelson as ‘preferable’, because their functions will also behave ‘preferably’, i.e., will be easier and more useful to work with:
- Because people are inherently insatiable, and we always want more of what we like, we derive the premise of monotonicity: weak monotonicity implies that if A contains more than B, A is at least as good as B. On the other hand, strong monotonicity implies that if A and B contain the same amount, but A contains more of at least one good, then A is strictly preferred to B.
- Convexity: Further developing our taste for variety, we inherently prefer baskets of goods, or choices, which contain a wider range. This can be represented with an indifference curve, which shows the rate at which we are willing to substitute units of A for B.
As tends to happen with any axiom, there are plenty of examples of people violating them. A good example is when deciding what shade of blue to paint your living room. If presented with two shades, where one is very slightly lighter than the other, you will probably be indifferent to either if you cannot tell the difference. However, when presented with a thousand shades, each progressively lighter, and asked to choose between the original shade (midnight blue) and the last shade (azure), you will probably find you have a definite preference. This, of course, violates the premise of transitivity.
Video – Utility function: