The following points highlight the six axiom of preference while building up an ordinal utility theory. The axioms are: 1. Axiom of Completeness 2. Axiom of Reflexiveness 3. Axiom of Transitivity 4. Axiom of Continuity of Preferences 5. The Axiom of Dominance 6. The Axiom of Diminishing Marginal Rate of Substitution (MRS).
1. Axiom of Completeness:
Assume that the consumer can compare any two combinations of the goods—he may prefer one to the other or he may be indifferent between the two. This axiom ensures that the consumer is able to make a choice or express neutrality between any two commodity combinations.
Use the following symbols to indicate preference or indifference:
(a) If a combination A is strictly preferred to another combination B, then it can be written as A > B.
(b) If a combination A is at least as preferred as another combination B, it can be written as A ≥ B. In this case, it can be also said that the consumer weakly prefers A to B.
(c) If the consumer is indifferent or neutral between the combinations A and B, it can be written as A ~ B.
(d) If the consumer weakly prefers A to B and B to A, then it can be concluded that he is indifferent between the two combinations. That is, A ≥ B and B ≥ A => A ~ B.
2. Axiom of Reflexiveness:
It would be assumed that any combination is at least as good as itself, i.e., A(x1, y1) > A(x1, y1).
3. Axiom of Transitivity:
Here it can be assumed that if A, B, and C are any three combinations of the goods X and Y, and if A > B and B > C, then A > C, i.e., if the consumer strictly prefers the combination A to B, and the combination B to C, then he would strictly prefer A to C.
Again, if A ~ B and B ~ C, then A ~ C, i.e., if the consumer is indifferent between the combinations A and B and between B and C, then he would be indifferent between A and C. This axiom ensures some sort of consistency in the behaviour of the consumer without which it is almost impossible to build up a theory of the consumer.
4. Axiom of Continuity of Preferences:
Given some commodity combination A, it can be considered that the set of all combinations at least as well liked as A and the set of all combinations not more liked than A. These two sets are closed.
This means that if it is selected for consideration an infinite sequence of commodity combinations which converged to some limiting combination A* and if each member of the sequence were at least as well liked as A, then the limiting combination would also be at least as well liked as A.
This condition ensures the continuity of consumer’s preferences and rules out “jumps”. It ensures, for example, that if two commodity combinations differ from each other only slightly and if one of these is preferred to some given combination A, then the other will be at least as well liked as A.
This axiom also gives that on the boundary of the two closed sets mentioned above, there would lie the indifferent combinations all of which are as well liked as A. In other words, this axiom ensures the presence of indifference curves.
5. The Axiom of Dominance:
If any combination A has more of one or of both the goods than B, then it is said A dominates B. This axiom states that if A dominates B, then the consumer will prefer A to B. This axiom is also known as the axiom of non-satiation or of monotonicity.
This axiom implies that more the consumer gets of one or of both the goods, the higher would be his level of satisfaction. That is why this axiom is also known as the axiom of “more is better”. Also note that this axiom holds for ‘goods’ only and not for ‘bads’. For ‘bads’ it is likely to get the opposite of dominance, e.g., less of ‘bads’ like air pollution and noise would be preferred to more.
6. The Axiom of Diminishing Marginal Rate of Substitution (MRS):
However, note for the present that the two goods (X and Y) used by the consumer are assumed to be substitutable, but substitution, as it is made, becomes more and more difficult. This gives us that the MRSX,Y diminishes as the consumer has more and more of good X and less and less of good Y.