Demand set

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

Define ${⪰}_p$ as a weak preference relation over goods; that is, $x{⪰}_p{x}^{\prime }$ states that the allocation vector $x$ is weakly preferred to $x^{\prime }$.

Let $e$ be a vector representing the quantities of the agent's endowment of each possible good, and $p$ be a vector of prices for those goods. Let $D({⪰}_p,p,e)$ denote the demand set. Then:

$D({⪰}_p,p,e):=\{x:p_x\le p_{e}and{p}_{x^{\prime }}\le p_e⟹x^{\prime }{⪯}_{p}x\}$.

See also

• Demand
• Economics

External links

• http://economics.about.com/library/glossary/bldef-demand-set.htm?terms=Demand+Set Template:Webarchive