- A utility frontier is a locus of points in a diagram that connects the utility of all allocations of two goods between two people such that the marginal rate of transformation is equal to the marginal rate of substitution. Each such point is a Pareto optimum. Thus, each of the points a, b and c on the downward-sloping curve in the diagram is such an optimum: it is not possible to move from one point to any other without one person losing utility even though the other gains, so such points cannot be ranked using the Pareto criterion. The frontier shows the maximum utility attainable by one individual, given the utility level of the other. Point d is unattainable, given the resources available and the extant technologies that define the maximum outputs that can be produced from them. These background conditions determine the position of the frontier. d cannot be ranked in relation to a or c using the Pareto criterion, nor e in relation to a and c. Point e is not an efficient point since it is possible to move from it to a point on the frontier in such a way that both gain utility (or at any rate none loses). This is shown by the area enclosed by the two arrows from e: any point within this space has more utility for both individuals than point e and some point on the frontier in this space is going to be better for at least one of the individuals than some point below it. To choose between points on the frontier requires a social welfare function that permits the interpersonal comparisons of utility.