Puneet Varma (Editor)

Unit demand

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In economics, a unit demand agent is an agent who wants to buy a single item, which may be of one of different types. A typical example is a buyer who needs a new car. There are many different types of cars, but usually a buyer will choose only one of them, based on the quality and the price.

Contents

If there are m different item-types, then a unit-demand valuation function is typically represented by m values v 1 , … , v m , with v j representing the subjective value that the agent derives from item j . If the agent receives a set A of items, then his total utility is given by:

u ( A ) = max j ∈ A v j

since he enjoys the most valuable item from A and ignores the rest.

Therefore, if the price of item j is p j , then a unit-demand buyer will typically want to buy a single item - the item j for which the net utility v j − p j is maximized.

Ordinal and cardinal definitions

A unit-demand valuation is formally defined by:

  • For a preference relation: for every set B there is a subset A ⊆ B with cardinality | A | = 1 , such that A ⪰ B .
  • For a utility function: For every set A :
    • u ( A ) = max x ∈ A u ( { x } )

    Connection to other classes of utility functions

    A unit-demand function is an extreme case of a submodular set function.

    It is characteristic of items that are pure substitute goods.

    References

    Unit demand Wikipedia
    (Text) CC BY-SA