Abstract
This chapter describes the regular utility functions and utility for the lexicographic order. Utility is a powerful tool of economic analysis. It is found that although some of economic theory can be stated without reference to utility, utility is still required in other places. It is observed that even where the utility function can be discarded, it is not always easy to do so. The study of utility, while not the sine qua non it was thought to be, plays an important role in foundations of preferences, the theory of demand, and the analysis of intertemporal consumer choice. Among usual properties of real-valued functions, only regular functions can be depended on to take a maximum upon the closed compact sets that are assumed in economic analysis. Any utility function that failed to have this property would be unsatisfactory for such analysis. On the other hand, it can easily be demonstrated that the upper contour sets of regular utility functions are closed. The closedness of the upper contour sets is necessary and sufficient for an acceptable utility function.
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