Utility–possibility frontier

In welfare economics, a utility-possibility frontier (or utility possibilities curve), is a wide-used concept analogous to the better-known production-possibility frontier. The graph shows the maximum amount of one person's utility given each level of utility attained by all others in society. Points on the curve are, by definition, Pareto efficient, while points off the curve are not. However, based on the extent of society’s preferences for an equal distribution of real income, a point off the curve may be preferred. All points on or below the utility-possibility frontier are attainable by society; all points above it are not attainable. The utility-possibility frontier is derived from the contract curve.

The utility-possibility frontier (UPF) is the upper frontier of the utility possibilities set, which is the set of utility levels of agents possible for a given amount of output, and thus the utility levels possible in a given consumer Edgeworth box. The UPF is the contract curve of the Edgeworth box.

In a competitive economy, any allocation over the utility-possibility frontier is a Pareto optimum, as the UPF is a representation of the Pareto contract curve in a different dimension (utilities versus goods). The set of points, which for a given level of utility of person 1, utility of person 2 is maximized (subject to resource availability). Because all points along the UPC represent different real income distributions, all being Pareto efficient, it is difficult to determine which utility combination is preferable to society. Usually, the social welfare function, which incorporates the deservedness of the two individuals and states how society’s well-being relates to that of the two individuals, is required to maximize social welfare. To do so, a point on the UPC would be chosen that also fell on the highest indifference curve for society. It is assumed that the value of social welfare changes as the individual utility of any society members changes, thus shifting the UPC to the right for utility increases or to the left for utility decreases.