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.
Lexicographic preferences can still exist with general equilibrium. For example,
- Different people have different bundles of lexicographic preferences such that different individuals value items in different orders.
- Some, but not all people have lexicographic preferences.
- Lexicographic preferences extend only to a certain quantity of the good.
Lexicographic preferences are the classical example of rational preferences that are not representable by a utility function, if amounts can be any non-negative real value. If there were such a function U then, e.g. for 2 goods, the intervals would have a non-zero width and be disjoint for all x, which is not possible for an uncountable set of x-values. If there are a finite number of goods and amounts can only be rational numbers, utility functions do exist.
The relation is not continuous because for a decreasing convergent sequence we have, while the limit (0,0) is smaller than (0,1).
Read more about this topic: Lexicographic Preferences
Famous quotes containing the word implications:
“Philosophical questions are not by their nature insoluble. They are, indeed, radically different from scientific questions, because they concern the implications and other interrelations of ideas, not the order of physical events; their answers are interpretations instead of factual reports, and their function is to increase not our knowledge of nature, but our understanding of what we know.”
—Susanne K. Langer (1895–1985)
“The power to guess the unseen from the seen, to trace the implications of things, to judge the whole piece by the pattern, the condition of feeling life in general so completely that you are well on your way to knowing any particular corner of it—this cluster of gifts may almost be said to constitute experience.”
—Henry James (1843–1916)
“When it had long since outgrown his purely medical implications and become a world movement which penetrated into every field of science and every domain of the intellect: literature, the history of art, religion and prehistory; mythology, folklore, pedagogy, and what not.”
—Thomas Mann (1875–1955)