Problem 1
If we observe a consumer choosing \(\left(x_{1}, x_{2}\right)\) when \(\left(y_{1}, y_{2}\right)\) is available one time, are we justified in concluding that \(\left(x_{1}, x_{2}\right) \succ\left(y_{1}, y_{2}\right) ?\)
Problem 2
Consider a group of people A, B, C and the relation "at least as tall as," as in "A is at least as tall as B." Is this relation transitive? Is it complete?
Problem 3
Take the same group of people and consider the relation "strictly taller than." Is this relation transitive? Is it reflexive? Is it complete?
Problem 4
A college football coach says that given any two linemen \(\mathrm{A}\) and \(\mathrm{B}\), he always prefers the one who is bigger and faster. Is this preference relation transitive? Is it complete?
Problem 11
Think of some other goods for which your preferences might be concave.
