A demand set is a model of the most-preferred bundle of goods an agent can afford. The set is a function of the preference relation for this agent, the prices of goods, and the agent's endowment.
Assuming the agent cannot have a negative quantity of any good, the demand set can be characterized this way:
Define as the number of goods the agent might receive an allocation of. An allocation to the agent is an element of the space ; that is, the space of nonnegative real vectors of dimension .
Define as a weak preference relation over goods; that is, states that the allocation vector is weakly preferred to .
Let be a vector representing the quantities of the agent's endowment of each possible good, and be a vector of prices for those goods. Let denote the demand set. Then: