Expenditure minimization problem

In microeconomics, the expenditure minimization problem is the dual of the utility maximization problem: "how much money do I need to reach a certain level of happiness?". This question comes in two parts. Given a consumer's utility function, prices, and a utility target,

• how much money would the consumer need? This is answered by the expenditure function.
• what could the consumer buy to meet this utility target while minimizing expenditure? This is answered by the Hicksian demand function.