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.