ORDINAL THEORY:
INDIFFERENCE CURVE APPROACH In indifference curve approach consumer is assumed to be rational, so that consumer's objective is to maximise her utility by choosing a commodity bundle among all other available commodity bundles (under budget constraint) where total utility ('U') depends on quantity consumption given her taste and preferences. Therefore, in a two-commodity world (say x1 and x2) utility function is given by U = U (x1,x2) and it depends on taste and preferences of the consumer, which is specified by axioms given below:
Axiom of reflexiveness: Consumer's choice is reflexive. Implication: Weak preference relation is denoted by 'R'. Suppose there are two goods x1 and x2 and suppose x1 is weakly preferred to x2 i.e., x1Rx2 which implies that either x1 is strictly preferred over x2 (it is denoted by x1Px2) or x1 is indifference to x2 (it is denoted by x1Ix2), where 'P' and 'I' implies strict preference relation and indifference respectively. The set constituted by all commodity bundles or vector is known as commodity set (X). Any one commodity bundle is denoted by 'x' is weakly preferred (i.e., either strictly preferred or indifferent) over any other commodity bundle (i.e., in respect to 'x'). Therefore, we have xRx. Clearly, any one commodity bundle may be indifferent to another commodity bundle i.e., there is a possibility of indifference or same level of utility between the commodity bundles. None of the commodity bundles are not preferred i.e., consumer can choose any commodity bundle. So choice set of this consumer is specified by the commodity set 'X'.