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 x_i = h_i(p₁, p₂, U), i = 1, 2. See also Marshallian demand.