Unit demand explained

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.

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\in} 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\subseteq B with cardinality |A| =1 , such that A \succeq B .

• For a utility function: For every set

A :^[1] u(A) =max _{x\in} 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.

See also

• Utility functions on indivisible goods
• Matching (graph theory)

Notes and References

1. 10.2307/1907742. 1907742. Assignment Problems and the Location of Economic Activities. Econometrica. 25. 1. 53–76. 1957. Koopmans . T. C. . Beckmann . M. .