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
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
′
states that the allocation vector
x
is weakly preferred to
x
′
.
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: px <= pe and x >p x' for all affordable bundles x'.
