Show that if in R² are continuous, highly monotonic preferences then indifference curves (i.e. classes of abstraction of relations ~) are graphs of continuous, decreasing functions from the interval [a, b] to [c, d] (the boundaries of the intervals can also be infinite). Give an example illustrating that continuity is essential.

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
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Chapter1: Making Economics Decisions
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Show that if in R2 are continuous, highly monotonic preferences then indifference curves (i.e.
classes of abstraction of relations ~) are graphs of continuous, decreasing functions from the
interval [a, b] to [c, d] (the boundaries of the intervals can also be infinite). Give an example
illustrating that continuity is essential.
Transcribed Image Text:Show that if in R2 are continuous, highly monotonic preferences then indifference curves (i.e. classes of abstraction of relations ~) are graphs of continuous, decreasing functions from the interval [a, b] to [c, d] (the boundaries of the intervals can also be infinite). Give an example illustrating that continuity is essential.
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