![]() A third common utility function is quadratic, which has the form u(x, y) = 2 a x - (b - y) 2. This function has the form u(x, y) = (a x r + b y r) 1/r. Another common form for utility is the Constant Elasticity of Substitution (CES) utility function. One of the most common is the Cobb-Douglas utility function, which has the form u(x, y) = x a y 1 - a. There are several classes of utility functions that are frequently used to generate demand functions. ![]() Once demand is represented by a function, it can be used to develop a model of exchange, and it can be combined with the supply functions of firms to model trade in a market. In this section, we assume that the consumer has preferences that are represented by a utility function, and we then carry out this derivation of demand. If preferences are represented by a utility function, then demand can be derived from maximization of utility for various prices and income. But when economists evaluate markets, they would like to have a representation of demand. Faced with choice alternatives, it is reasonable to expect that a consumer will be able to rank the alternatives. Preferences are a natural psychological concept. Much of the preceeding material in the consumer theory section is focused on the relationship between a consumer's preferences and a utility function that represents these preferences.
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