ⓘ 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 ..

                                     

ⓘ 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, …, v m {\displaystyle v_{1},\dots,v_{m}}, with v j {\displaystyle v_{j}} representing the subjective value that the agent derives from item j {\displaystyle j}. If the agent receives a set A {\displaystyle A} of items, then his total utility is given by:

u A = max j ∈ A v j {\displaystyle uA=\max _{j\in A}v_{j}}

since he enjoys the most valuable item from A {\displaystyle A} and ignores the rest.

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

                                     

1. Ordinal and cardinal definitions

A unit-demand valuation is formally defined by:

  • For a preference relation: for every set B {\displaystyle B} there is a subset A ⊆ B {\displaystyle A\subseteq B} with cardinality | A | = 1 {\displaystyle |A|=1}, such that A ⪰ B {\displaystyle A\succeq B}.
  • For a utility function: For every set A {\displaystyle A}
u A = max x ∈ A u { x } {\displaystyle uA=\max _{x\in A}u\{x\}}
                                     
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