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
be a vector representing the quantities of the agent's endowment of each possible good, and
be a vector of prices for those goods.
denote the demand set.