MU10= TU10, TU9
In general, we can write
MUn =TUn – Tun-1
Where MUn is marginal utility of nth unit.
TUn is total utility of ‘n’ units.
TUn-1 is total utility of (n-1) units.
If information regarding total utilities of successive units is not given, the marginal utility can be defined as a ratio of extra utility to extra units of the commodity consumed.
In terms of symbols, we have, MU = ? (TU)/?Q
Thus, the marginal utility can also be defined as increase in total utility (?TU), when the quantity of the commodity is increased by a small amount (?Q). When change in quantity of the commodity is 1, the above formula reduces to
MU = ?TU
Or, MUn =TUn – Tun-1
Initially, marginal utility of a commodity is positive due to a feeling of an urge for the commodity. However, as the process of consumption is continued, a point of saturation is reached. Consequently, marginal utility becomes zero.
Thereafter, marginal utility will become negative. This is explained in details in the next sub- section on the law of diminishing marginal utility. If consumer’s taste is represented by means of a utility function of the form
U = f (Q1, Q2, Q3………… Qn)
then marginal utility derived from consuming, say, commodity ‘1’ is given by the first partial derivative of ‘U’ with respect to Q(, that is, d U/<9 Q15 and so on. Here, Marshall made an important assumption of independence of utility, that is, utility derived from consuming one commodity is independent of utility derived from consuming other commodities.
Further, every commodity is assumed to be perfectly divisible and so it is possible to vary the consumption in small amount as possible. This makes utility function continuous and twice differentiable.