Demand for a good expressed as a function of prices and utility. Compensated demand functions are obtained by the minimization of expenditure subject to the achievement of a given level of utility. Assume there are two goods consumed in quantities x1 and x2 with prices p1 and p2. Represent the preferences of the consumer by the utility function U(x1, x2). The compensated demand functions for the two goods are obtained as the solution to
where U is the utility level that must be achieved. The structure of the minimization shows that the compensated demand functions can be written in the form xi = hi(p1, p2, U), i = 1, 2. See also Marshallian demand.