Utility functions represent ordinal preferences and do not have natural units, unlike production functions. As a result, a monotonic transformation of a utility function represents the same preferences. Unlike with a Cobb-Douglas production function, where the sum of the exponents determines the degree of economies of scale, the sum can be normalized to one for a utility function because normalization is a monotonic transformation of the original utility function. Thus, let us define formula_8 and formula_9, so formula_10, and write the utility function as: