Interview Question: Utilitarian Expressions

Sample Question #75 (economics – utility function)

Let U(x) be an investor’s utility function over some x. For example, x could be wealth level or total returns from her asset holdings.

Write the mathematical expression that describes an investor who prefers more of x to less.

Write the mathematical expression that describes an investor who is risk-averse with regard to x.

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One Response to Interview Question: Utilitarian Expressions

  1. Brett says:

    ANSWER
     
    Preferring more of x to less means the utility function must be increasing in x. So U'(x) > 0, where the prime symbol indicates first derivative.
     
    Risk aversion means the investor, when facing uncertainty over changes in x, gets more disutility from losing some amount of x than utility from getting that same amount. In other words, the utility of getting extra x is decreasing in x. Mathematically, this is just U"(x) < 0.

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