Rubinstein2005-page60

Rubinstein2005-page60 - monotonicity and con-tinuity can be...

This preview shows page 1. Sign up to view the full content.

October 21, 2005 12:18 master Sheet number 58 Page number 42 42 Lecture Four Figure 4.1 % satisfy continuity if for all a , b X ,if a Â b , then there is an ε> 0 such that x Â y for any x and y such that d ( x , a )<ε and d ( y , b )<ε . Existence of a Utility Representation Debreu’s theorem guarantees that any continuous preference rela- tion is represented by some (continuous) utility function. If we assume monotonicity as well, we then have a simple and elegant proof: Claim: Any consumer preference relation satisfying
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: monotonicity and con-tinuity can be represented by a utility function. Proof: Let us Frst show that for every bundle x , there is a bundle on the main diagonal (having equal quantities of all commodi-ties), such that the consumer is indifferent between that bun-dle and the bundle x . (See Fg. 4.1.) The bundle x is at least as good as the bundle 0 = ( 0, . . . , 0 ) . On the other hand, the bundle...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online