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Unformatted text preview: reserves the order of utility rankings and therefore represents
the same preference rankings as the original prePMT utility function.
For example, consider a consumer who loves hand bags and where for this person, “more is better”. For convenience,
{
}A
let’s consider all bundles in the consumption set consisting of one good, “handbags”, and where
{
} is:
utility function which represents this handbag loving consumer’s preferences over Notice that for example that (for convenience we compute utilities for integer amounts):
() (
⏟ ) ()
⏟ ()
⏟ ()
⏟ ()
⏟ These utility rankings reveal that: Remembering that the size of the utility number means nothing whatsoever and that the only thing which matters is the
order of utility numbers, suppose we “bump” up the utility function
by adding any positive number (say 4) to the
right hand side (RHS) (notice that we add the number to the RSH not the LHS – this doesn’t matter as we see after the
graph): 7 Cardinal numbers are physical measures like temperature, weight, height, speed, etc. As such, a temperature of 100 degrees
Celsius is twice as hot as the temperature of 50 degrees Celsius.
17
ECO 204 CHAPTER 2 Modeling Consumer Choice and Behavior: Preferences and Budget Constraints (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. According to the new utility function:
() (
⏟ ) ()
⏟ ()
⏟ ()
⏟ ()
⏟ Despite the fact that we have scaled up the utility function by 4, the new utility function also implies that: In fact, any mathematical operation (PMT) which “bumps up” a utility function yields another utility function
representing the same preferences. This is because a PMT bumping up a utility function preserves the “preference
rankings”. Notice that the PMT is applied to the RHS, not the LHS, of a utility function – after all, if you were to do it to
the LHS you’d get back the original utility function. Doing the PMT simply raises the utility graph or utility surface as the
following examples show.
Examples of positive monotonic transformations of utility functions: ❶ Add a positive number to the RHS of utility function
Example: ❷ Multiply RHS of utility function by a positive number
Example: ( ) 18
ECO 204 CHAP...
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This note was uploaded on 03/20/2014 for the course ECON 204 taught by Professor Ajazhussain during the Fall '09 term at University of Toronto Toronto.
 Fall '09
 AJAZHUSSAIN
 Economics, Microeconomics

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