A demand set is a model of the most-preferred bundle of goods an

agent Agent may refer to: Espionage, investigation, and law *, spies or intelligence officers * Law of agency, laws involving a person authorized to act on behalf of another ** Agent of record, a person with a contractual agreement with an insuranc ...

can afford. The set is a function of the

preference relation The term preference relation is used to refer to orderings that describe human preferences for one thing over an other. * In mathematics, preferences may be modeled as a weak ordering or a semiorder, two different types of binary relation. One speci ...

for this agent, the prices of goods, and the agent's

endowment Endowment most often refers to: *A term for human penis size It may also refer to: Finance *Financial endowment, pertaining to funds or property donated to institutions or individuals (e.g., college endowment) *Endowment mortgage, a mortgage to b ...

. 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 Allocation may refer to: Computing * Block allocation map * C++ allocators * Delayed allocation * File allocation table * IP address allocation * Memory allocation * No-write allocation (cache) * Register allocation Economics * Asset alloca ...

of. An allocation to the agent is an element of the space

\mathbb_+^L

; that is, the space of nonnegative real vectors of dimension

L

. Define

\succeq_p

as a weak preference relation over goods; that is,

x \succeq_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(\succeq_p,p,e)

denote the demand set. Then:

D(\succeq_p,p,e) :=  \{x: p_x \leq p_e ~~~and~~~ p_{x'}\leq p_e \implies x'\preceq_p x   \}

External links

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

See also

External links