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Erfle, Stephen. Bracketing Utility. International Journal of Economics, Commerce and Management 2, no. 1 (2014): 1-9.

Preferences are the primitive notion in consumer theory. Preferences exist. By contrast, utility is an artificial construct used by economists to represent the underlying primitive notion of preferences. Utility functions are a convenient numerical construct that represents preferences. Utility functions are computationally efficient because they reduce the complexity of solving the consumer’s constrained optimization problem. If we have a utility function then the underlying preference map is readily determined by mapping level sets of the utility function. A more interesting question is whether we can always find a utility function that represents a given a set of preferences? If preferences are monotonic and can be represented by indifference curves then it is easy to show it can be represented by a utility function using the 45o line. Even without indifference map of preferences, for example, if one only knew discrete indifferent bundles, then one can use monotonicity and convexity to bracket utility using a strategy similar to that used in creating a utility function using the 45o line. In the process, students gain a deeper understanding of monotonicity and convexity. This article focuses attention on monotonicity and convexity and provides a methodology for linking utility to preferences in the event that you do not have a geometric representation of the preference map via indifference curves.