The Topography of Preferences
A consumer's preferences for two goods can be visualized as a three-dimensional 'utility surface.' Explain how the concept of a topographical map, which uses contour lines to represent a three-dimensional landscape on a two-dimensional surface, helps us understand the properties of an indifference map.
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Imagine a consumer's level of satisfaction from consuming various quantities of two goods is represented by a three-dimensional landscape, where the 'elevation' at any point corresponds to the level of satisfaction. If you were to draw a single, continuous contour line on this landscape, connecting all points that have the exact same elevation, what would this line represent in economic terms?
A consumer's preferences for two goods can be visualized as a three-dimensional 'utility surface,' similar to a mountain. The two-dimensional representation of these preferences is an 'indifference map,' which is like a topographical map of that mountain. Match each feature of the 3D utility surface (the mountain) with its corresponding feature on the 2D indifference map (the topographical map).
A consumer's preferences for two goods are represented by an indifference map, which can be thought of as a two-dimensional contour map of their three-dimensional utility surface. If a particular region of this map shows several indifference curves spaced very closely together, what does this imply about the corresponding region of the three-dimensional utility surface?
The Topography of Preferences
When a consumer moves from one point to another along the same indifference curve, this is analogous to walking directly up the steepest part of their three-dimensional utility 'hill'.
Interpreting Preference Landscapes
Evaluating the Topographical Analogy for Consumer Preferences
A consumer's satisfaction from consuming two goods can be visualized as a three-dimensional 'hill' of utility. If this hill has a single, distinct peak representing the absolute maximum possible satisfaction, how would this peak be represented on a corresponding two-dimensional contour map of the consumer's preferences?
A consumer's preferences for two goods are visualized as a two-dimensional contour map derived from a three-dimensional 'satisfaction surface'. If this map consists of a series of parallel, straight lines, what is the most likely shape of the underlying three-dimensional surface?
Comparing Satisfaction Landscapes
The Topography of Preferences