Unit demand


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, with representing the subjective value that the agent derives from item. If the agent receives a set of items, then his total utility is given by:
since he enjoys the most valuable item from and ignores the rest.
Therefore, if the price of item is, then a unit-demand buyer will typically want to buy a single item – the item for which the net utility is maximized.

Ordinal and cardinal definitions

A unit-demand valuation is formally defined by:
A unit-demand function is an extreme case of a submodular set function.
It is characteristic of items that are pure substitute goods.