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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.

     

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

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

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