Decisions and Consumer Behavior

1. Let \(u(x_{1},x_{2})=x_{1}+x_{2}\) be a utility function. There exists no preference relation which is represented by this utility function. 2. Let \(x_{1}\succ x_{2}\) and \(x_{2}\succ x_{3}\). Then, the assumption of transitivity implies that \(x_{1}\succ x_{3}\). 3. If \(u(x_{1},x_{2})=x_{1}\cdot(x_{2})^{5}\) is a utility representation of a preference ordering, then \(v(x_{1},x_{2})=\frac{1}{5}\ln x_{1}+\ln x_{2}\), too, is a utility representation of the same preference ordering. 4. Preferences that fulfill the principle of monotonicity are always convex.