Consider a simple case where the consumer purchases only two goods, Q1 and Q2.

His ordinal utility function is:

U = f(q1, q2)                            (6.1)

where U is the ordinal utility number, and q1 and q2 are the quantities consumed of the two goods. Assume that U is a single-valued function of q1 and q2, and f (q1, q2) is continuous, and it has continuous first-order and second-order partial derivatives. Remember also that U has to be a regular strictly quasi-concave function of qi and q2.

Since,it shall be assumed that the consumer will desire to have more of both the goods, the partial derivatives of U (w.r.t.) q1 and q2 will be positive unless otherwise men­tioned as in some unusual cases. But remember some more points about the utility function.

First, the consumer’s utility function is not unique. Any function which is a positive monotonic transformation of his utility function may also be taken as a utility function of the consumer, for it would represent the same preference-indifference pattern.

Second, as noted, U in stands for the ordinal utility number for a particular combination of the goods. This number has no cardinal significance. It has only ordinal significance. It indicates the utility-rank of the said combination to the consumer.