1.4 Preferences I: Indifference Curves - Class Notes
Contents
Overview
We continue with our model of how individuals choose. Our focus for this class, and next, is what are people’s objectives? How can we operationalize their preferences in a meaningful way? Today we will discuss one tool - indifference curves - and start an explanation of utility and how we can model people as trying to “maximize” it (we will wrap that up in the next class).
Slides
Practice Problems
Answers to the practice problems from the previous class (on budget constraints) have been posted.
Math Survey “Answers”
“Answers” for the math survey have been posted, including some summaries of how your classmates feel.
Math Appendix
Utility Functions and PMTs
Two utility functions u(⋅) and v(⋅) represent the same preferences iff there is a strictly increasing function} f such that v(⋅)=f[u(⋅)]
a=(1,2)b=(2,2)c=(4,3)
The following utility functions express the same preferences:
| u(⋅) | v(⋅) |
|---|---|
| u(a)=1 | v(a)=2 |
| u(b)=2 | v(b)=4 |
| u(c)=3 | v(c)=6 |
v(⋅)=2[u(⋅)]
A positive monotonic transformation (PMT) transforms quantities such that the rank order of the quantities is preserved.
- Examples: v(u)=u+2;v(u)=4u;v(u)=u3;v(u)=ln(u)
Any PMT of a utility function contains the same preferences!