Lexicographic preferences

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Lexicographic preferences (lexicographical order based on the order of amount of each good) describe comparative preferences where an economic agent infinitely prefers one good (X) to another (Y). Thus if offered several bundles of goods, the agent will choose the bundle that offers the most X, no matter how much Y there is. Only when there is a tie of Xs between bundles will the agent start comparing Ys.

For example, if for a given bundle (X;Y;Z) an agent orders her preferences according to the rule X>Y>Z, then the bundles {(5;3;3), (5;1;6), (3,5,3)} would be ordered, from most to least preferred:

  1. 5;3;3
  2. 5;1;6
  3. 3;5;3
  • Even though the first option contains fewer total goods than the second option, it is preferred because it has more Y.
  • Even though the third option has the same total goods as the first option, the first option is still preferred.
  • Even though the third option has far more Y than the second option, the second option is still preferred because it has slightly more X.

[edit] Implications

If all agents have the same lexicographic preferences, then general equilibrium cannot exist because agents won't sell to each other (as long as price of the less preferred is more than zero). But if the price of the less wanted is zero, then all agents want an infinite amount of the good. Equilibrium cannot be attained.

LP can still exist with GE. For example,

  • Different people have different bundles of lexicographic preferences.
  • Some people have lexicographic preferences, not all.
  • Lexicographic preferences extend only to a certain quantity of the good.

LP preferences are the classical example of rational preferences that are not representable by a utility functionhttp://en.wikipedia.org../../../../articles/u/t/i/Utility.html#Utility_functions.

The relation is not continuous because for a decreasing convergent sequence x_n \rightarrow 0 we have (xn,0) > (0,1), while the limit (0,0) is smaller than (0,1).