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 = U(x1, x2). The compensated demand functions for the two goods are obtained as the solution to
min p1x1 + p2x2 subject to U(x1, x2) ≥ U
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.