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 $v\_1,\backslash dots,v\_m$, 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:

:$u(A)=\backslash max\_\{j\backslash in\; A\}v\_j$

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.