# Demand set

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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 ${\displaystyle L}$ as the number of goods the agent might receive an allocation of. An allocation to the agent is an element of the space ${\displaystyle R+l}$; that is, the space of nonnegative real vectors of dimension ${\displaystyle L}$.

Define ${\displaystyle >p}$ as a weak preference relation over goods; that is, ${\displaystyle x>px'}$ states that the allocation vector ${\displaystyle x}$ is weakly preferred to ${\displaystyle x'}$.

Let ${\displaystyle e}$ be a vector representing the quantities of the agent's endowment of each possible good, and ${\displaystyle p}$ be a vector of prices for those goods. Let ${\displaystyle D(>p,p,e)}$ denote the demand set. Then: D(>p,p,e) = {x: px <= pe and x >p x' for all affordable bundles x'.