Unformatted text preview: Monotonic Transformation of the Cobb-Douglas Utility Model ⏟ ⏟ __________________________________________________________________________________________________
[Optional] Proof that a Positive Monotonic Transformation Doesn’t Impact
Consider an arbitrary utility function:
( ) )
) Now, a PMT is a mathematical operation which “bumps up” a utility function. Put another way, a PMT is an increasing
( )). As such, the postfunction of the utility function (an increasing function is one such that if
then ( )
PMT utility function and it’s
is: (( )) ((
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8. Convex (“Taste for Variety”) Preferences10
We have assumed that all consumers have rational preferences: indeed, this is the only assumption required for
modeling consumer behavior. We have already discussed “Monotone Preferences” (when a consumer with rational
10 Please read this even though we haven’t yet discussed this in lectures.
37 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. preferences perceives all commodities in the consumption set to be “good” goods). Now we discuss “Convex
Preferences”: when a consumer (with rational preferences) has a “taste for variety”.
Consumers often have a taste for variety. For example, suppose that restaurants only serve either steaks or sushi. A
consumer with a taste for variety will sometimes go out for steaks and other times for sushi. Put another way, such a
consumer prefers a mixture of steaks and sushi to either steaks or sushi alone.
We can generalize the notion of a taste for variety to bundles of two or more goods. For example, consider two bundles
and such that
B Intuitively, if the consumer has a taste for variety, then she prefers a mixture of bundles and to either or alone.
To depict a bundle that is a mixture of bundles
we need know convex combinations, a fancy expression for a
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