Diminishing Marginal Utility
Consumers derive utility from consumption of goods. In symbols, we can write U = f(X) where U is utility and X is the amount of a particular good being consumed. Marginal utility is the change in utility from consuming another unit of the good: MUX = D U/D X = f ’(X). Marginal utility is assumed to be positive, and the law of diminishing marginal utility implies that f ’(X) is declining in X. These two assumptions can be written symbolically as: f ’(X) > 0, f ’’(X) < 0.
More generally, utility depends on consumption of all goods and services: U = f(X1, X2, X3, -). In this more general specification, diminishing marginal utility is implied by assuming that the utility function satisfies ¶ f/¶ Xi > 0 and ¶ 2f/¶ Xi2 < 0 for each good.