In this article we will discuss about the ordinal utility function of the consumer.
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)
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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.
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Since the utility numbers have no cardinal significance, the two numbers indicating two utility-ranks of two particular combinations of goods may be, say, 2 and 3, or they may even be 2 and 300, the higher number indicating the higher utility rank of the two.
Third, the utility function is defined for a particular time period. The consumer’s optimal expenditure pattern is analysed only with respect to this period. The possibility of transferring consumption expenditure from one period to another has not been considered here.
Remember that the time period should not be so short that the desire for variety cannot be satisfied, neither should it be so long that the consumer’s tastes and the shape of his utility function might change meanwhile. Any intermediate period should be appropriate for the static theory of the consumer behaviour.