Workbook for Principles of Microeconomics pp 75-89 | Cite as

# Decisions and Consumer Behavior

## Abstract

- 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.

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

- 3.
The individual’s demand will decrease if the price of good 1 decreases, provided that

*x*_{1}is an inferior good. - 4.
For an individual, two goods are perfect substitutes. In such case, at the optimum, the demand for one good will always be zero.