# Decisions and Consumer Behavior

• Martin Kolmar
• Magnus Hoffmann
Chapter
Part of the Springer Texts in Business and Economics book series (STBE)

## Abstract

1. 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. 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. 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. 4.

Preferences that fulfill the principle of monotonicity are always convex.

Assume an individual has income b > 0 at his disposal, which he can spend on two goods of quantities x 1 and x 2.

1. 1.

A consumer’s preference relation is represented by the utility function $$u(x_{1},x_{2})=x_{1}\cdot x_{2}$$. Let x 1 be marked on the x-axis and x 2 on the y-axis. If so, the price-consumption path for all $$p_{1}> 0,p_{2}> 0$$ is a straight line through the origin with a slope of $$\frac{p_{1}}{p_{2}}$$.

2. 2.

For an individual, two goods are perfect complements. If so, the cross-price elasticity of the Marshallian demand always equals zero.

3. 3.

The individual’s demand will decrease if the price of good 1 decreases, provided that x 1 is an inferior good.

4. 4.

For an individual, two goods are perfect substitutes. In such case, at the optimum, the demand for one good will always be zero.

© Springer International Publishing AG 2018

## Authors and Affiliations

• Martin Kolmar
• 1
• Magnus Hoffmann
• 1
1. 1.School of EconomicsUniversity of St. GallenSt. GallenSwitzerland