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Unformatted text preview: ption, which we’ll see later in ECO 204, is to deduce the consumer’s utility function
from data on her purchases (items, quantities, prices). Yet another option is to pick a utility model from a set of wellknown utility models which matches some observed characteristics of the consumer’s preferences and/or behavior.
“Indifference curves” and their slope often assist us with finding a utility model that matches a particular consumer’s
preferences and/or behavior. Indifference curves are analogous to topographical contour lines in geographical maps. For
example, take a look at this contour plot of a mountain (notice the peak at 5,117’): 22
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. By definition, all points on a contour line are at the same altitude on the 3-D topographical mountain. For example, the
two red dots are both at an altitude of 4,400’. In reality, there are an infinite number of contour lines corresponding to
the infinite number of “altitudes”. By definition, contour lines can’t cross because then the intersection point would
simultaneously be at two different altitudes!
By the same token, one can draw “utility-contour” lines on “utility surface plots” where by definition all points on a
utility-contour line are at the same altitude on the 3-D utility mountain which means the consumer must be indifferent
to all bundles on a particular utility-contour (iso-utility) line. Here are some examples of 3-D utility surface plots with
some utility-contour lines depicted: 23
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. ) plane (see graphs below).
We can project the “utility-contour” lines from 3-D utility surface plots onto the 2-D (
By definition, all bundles on these 2-D utility-contours have the same utility number which means the consumer must be
indifferent to all bundles on a particular utility-contour line – hence the term “indifference curves”.
For example, consider the linear utility function which, for , goods has the form8: The graphs below show the 3-D linear utility surface plot and 2-D indifference curves map for the case: : In Wolfram Alpha type plot u=2q1...
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