In other words, if an individual chooses combination (or bundle) ‘A’ in one situation (given by his budget constraint) in which bundle ‘B’ was also available to him, he will not choose combination ‘B’ in any other situation (given by his new budget constraint) in which combination ‘A’ is also available.
If he chooses combination ‘A’ rather than combination ‘B’ in one particular situation and chooses combination ‘B’ rather than combination ‘A’ in another situation, when ‘A’ and ‘B’ are present in both the situations, then he is not behaving consistently. Symbolically, if A > B, then B > A.
That is, if combination ‘A’ is revealed to be preferred to combination ‘B’ (not expensive than ‘A’) by any individual, then combination ‘B’ cannot be revealed to be preferred to combination ‘A’ by him at any other time, when ‘A’ and ‘B’ are present in both the cases.
The postulate explained above is the exact logical equivalent of Hicks formulation of consistent behaviour in his Revision of Demand Theory. He calls it the ‘two term consistency’, since comparison here is between two situations.
This is explained with the help of Fig. 6.1. In this figure, two combinations (bundles) of two commodities ‘X’ and ‘Y’ (shown on X- axis and Y-axis respectively), Z1 and Z2 are represented on two different budget lines AB and CD respectively.
Three different cases are considered with different relative positions of Z1 and Z2. In Fig. 6.1 (a), consumer chooses bundle Z1 on budget constraint AB, when bundle Z2 is affordable (Z2 lies on budget constraint CD inside the budget constraint AB). When bundle Z2 (lying on budget constraint CD, having different price-income situation) is chosen, bundle Z1 is not affordable.
Hence, the choice of bundle Z, in one situation and bundle Z2 in another situation is consistent. In Fig. 6.1 (b), when the individual chooses bundle Z1, bundle Z2 is not affordable and vice-versa. Thus, the choice of bundle Z1 in one situation and bundle Z2 in another situation is consistent.
In Fig 8.1 (c), the consumer’s behaviour is inconsistent. It implies choice of bundle Z1 on AB, when bundle Z2 is affordable and the choice of bundle Z2 on CD, when bundle Z1 is affordable. The theory like the earlier ones assumes that the consumer is consistent in making choice.
In other words, the amount of each commodity is a single valued function of all prices and income. That is, confronted with the same set of prices and income, the consumer will always choose the same set of commodities.
The assumption of transitivity is an application of the logical theory of ordering. Suppose, in a particular situation, three bundles Z1, Z2 and Z3 of two commodities are available to a consumer. If he prefers bundle Z1 to bundle Z2 and bundle Z2 to bundle Z3, then he must prefer bundle Z1 to bundle Z3. Symbolically, if ‘A’ > ‘B’ and ‘B’ > ‘C’, then ‘A’ > ‘C’. Thus, the ordering has always to be unit directional and never circular.