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Unformatted text preview: d average. We illustrate through examples with bundles consisting of
followed by
goods.
Consider bundles of a single good. For example, suppose
combination of and will be: and
( Similarly, a 80:20 combination of and ) units of a good. Then a 50:50 () will be:
( ) () 38
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. In general for ( a ) combination of and will be:
( ) (
( Now suppose
and will be: ( )
) ( ( ) ) ) ) combination of bundles
) combination of good 2. ( ) ( ( ) ) ( ( ( ( ) ) ( ) units of goods 1 ( ) ( ) ) will be:
(( )
( ( ) ( ( ) ) and ) ) and )(
( ( ) ( ( ) and ) units of goods 1 and 2. Then a 50:50 combination of ) combination of bundles
( ( ( ( (
That is, a (
good 1 and ( ( ) and )
a ) ( ) (
In general for ( ) ) ( Now consider bundles of two goods. For example, suppose
and 2. Then a 50:50 combination of and will be: ) ) ( ) ) ) ) is a bundle of a ( ) combination of A C B We can now give a formal definition of convex preferences, or a taste for variety. Suppose a consumer is indifferent
between two bundles and , i.e.
. Then a consumer has a taste for variety if every convex combination
(“mixture”) of
is preferred to either or . For
consumption sets, convex preferences means that for all
()
( ) ( ( ) ( ) )
39 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. Intuitively, with convex preferences, regardless of how bundles and are combined, the bundle always lies on a
higher indifference curve than and . This implies that a consumer with convex preferences always has nice smooth
curved indifference curves (ones that don’t look like the coast line) – see examples below: Example: A Consumer with Convex Preferences
A C B Example: A Consumer with NonConvex Preferences
A C B 40
ECO 204 CHAPTER 2 Modeling Consumer Choice and Behavior: Prefer...
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 Fall '09
 AJAZHUSSAIN
 Economics, Microeconomics

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