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 $v_{1}, \dots, v_{m}$ , 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) = max_{j \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.

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 $A ⪰ B$ .
For a utility function: For every set $A$ :

u (A) = max_{x \in 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

↑ Koopmans, T. C.; Beckmann, M. (1957). "Assignment Problems and the Location of Economic Activities" (PDF). Econometrica. 25 (1): 53–76. doi:10.2307/1907742. JSTOR 1907742.

[kb57-1] Koopmans, T. C.; Beckmann, M. (1957). "Assignment Problems and the Location of Economic Activities" (PDF). Econometrica. 25 (1): 53–76. doi:10.2307/1907742. JSTOR 1907742.

Unit demand

Ordinal and cardinal definitions

Connection to other classes of utility functions

See also

References