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Unformatted text preview: Preferences and Budget Constraints (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Listen to Damian Lazarus’ excellent set from Burning Man 2011 (be patient) Lee Burridge’s set from Live at Lightning in a Bottle 2011
As long as Damian Lazarus is assigned a higher utility number than Lee Burridge we will have represented Ajax’s
preferences that he prefers Damian to Lee (and vice versa):
( For Ajax: ) ( ) For example we could assign these utility numbers to Damian and Lee:
( Because ⏟( ) ⏟( ) ) we can say that for Ajax: . Notice )
that just because (
does not mean that Damian Lazarus is “ten
times better than” Lee Burridge, but only that Damian Lazarus is preferred to Lee Burridge. To underscore this point,
suppose we re-assign utility numbers so that now:
11 ECO 204 CHAPTER 2 Modeling Consumer Choice and Behavior: Preferences and Budget Constraints (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Again, because ⏟( ) ⏟( ) we can once again say that for Ajax: . The sizes of the utility numbers have no meaning; rather, only the order of utility numbers tells us how the
consumer ranks bundles.
Now, consider my friend Meredith: she tells us she is indifferent between Damian Lazarus and Lee Burridge. Thus, as
long as Damian Lazarus is assigned the same utility number as Lee Burridge we will have represented Meredith’s
preferences that she is indifferent between Damian and Lee (and vice versa):
( For Meredith: ) ( ) For example, we could say:
( Because ⏟( ) ⏟( ) ) we can say that for Meredith: These examples illustrate two properties a mathematical equation must have to represent (rational) preference
rankings: a utility function assigns a number such that for all bundles in
if and only if ( ) ❶ ( )❷ if and only if ( ) () For the time being, we assume that we know a consumer’s utility function (that she tells us the utility equation). Later in
the course, we will see how it’s possible to deduce (or “recover”) a consumer’s utility function from purchasing data on
quantity purchased and price paid (it’s actually quite simple to do this – be patient). In the meantime, here are some
examples of utility functions defined o...
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