# 04s - 2011/3/3 Utility Functions 4 A preference relation...

This preview shows pages 1–4. Sign up to view the full content.

2011/3/3 1 4 Utility 2 Utility Functions A preference relation that is complete, reflexive, transitive and continuous can be represented by a continuous utility function. Continuity means that small changes to a consumption bundle cause only small changes to the preference level. 3 Utility Functions A utility function U(x) represents a preference relation if and only if: x’ x” U(x’) > U(x”) x’ x” U(x’) < U(x”) x’ x” U(x’) = U(x”). ~ f p p 4 Utility Functions Utility is an ordinal (i.e. ordering) concept. E.g . if U(x) = 6 and U(y) = 2 then bundle x is strictly preferred to bundle y. But x is not preferred three times as much as is y.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2011/3/3 2 5 Utility Functions & Indiff. Curves Consider the bundles (4,1), (2,3) and (2,2). Suppose (2,3) (4,1) (2,2). Assign to these bundles any numbers that preserve the preference ordering; e.g. U(2,3) = 6 > U(4,1) = U(2,2) = 4. Call these numbers utility levels. p 6 Utility Functions & Indiff. Curves An indifference curve contains equally preferred bundles. Equal preference same utility level. Therefore, all bundles in an indifference curve have the same utility level. 7 Utility Functions & Indiff. Curves So the bundles (4,1) and (2,2) are in the indiff. curve with utility level U   But the bundle (2,3) is in the indiff. curve with utility level U 6. On an indifference curve diagram, this preference information looks as follows: 8 Utility Functions & Indiff. Curves U 6 U 4 (2,3) (2,2) (4,1) x 1 x 2
2011/3/3 3 9 Utility Functions & Indiff. Curves Another way to visualize this same information is to plot the utility level on a vertical axis. 10 U(2,3) = 6 U(2,2) = 4 U(4,1) = 4 Utility Functions & Indiff. Curves x 1 x 2 Utility 11

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 06/12/2011 for the course ECON 101 taught by Professor Dee during the Spring '10 term at Andhra University.

### Page1 / 12

04s - 2011/3/3 Utility Functions 4 A preference relation...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online