compensated demand

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

x_i = h_i(p₁, p₂, U),

i = 1, 2. See also Marshallian demand.