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(11)this implies that the preference order is complete


Academic year: 2021

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x1 = x2

indifference curves are L shaped and form a 90° degree angle at the point of intersection with straight line of desired consumptopn ratio



at D


if indifference curves cross there is a


general convex combination




no convexity no concavity


is a

utility function representing a preference order




---- --- ---


this implies that the preference order is complete. Similar argument applies for transitivity. We can conclude that a preference order can be represented by a utility function only if it is complete and transitive.


Remark: and increasing transformation (also called positive monotonic transformation) preserves ORDER.

This implies that if f(u) is an increasing function, then f(u(x1,x2)) is a utility function representing the same preferences represented by u(x1,x2).



Proof: Because u(x1,x2) ia a utility function representing the given preference order and f(u) is increasing:

V(x1, x2) is another utility function representing the same preferences.


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